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Education is on the brink of a new era based on these changes. Online delivery of educational instructions provides the opportunity to bring colleges and universities new energy, students, and revenues. Many leading educational institutions are working to establish an online teaching and learning presence. Several systems with different capabilities and approaches have been developed to deliver online education in an academic setting (Mallard; WebCT; CouseInfo; eCollege; TopClass; Virtual University). In particular, Michigan State University (MSU) has pioneered some of these systems to provide an infrastructure for online instruction (Multi-Media Physics; CAPA; LectureOnline; PhysNet; Kortmeyer and Bauer, 1999; Kashy et al., 1997, LON-CAPA). My research is being performed on a part of the latest online educational system developed at MSU, the Learning Online Network with Computer-Assisted Personalized Approach (LON-CAPA). In LON-CAPA, we are involved with two kinds of large data sets: 1) educational resources such as web pages, demonstrations, simulations, and individualized problems designed for use on homework assignments, quizzes, and examinations; and 2) information about users who create, modify, assess, or use these resources. In other words, we have two ever-growing pools of data. As the resource pool grows, the information from users who have multiple transactions with these resources also increases. The LON-CAPA system logs any access to these resources as well as the sequence and frequency of access in relation to the successful completion of any assignment. We study the possible data mining methods for extracting useful knowledge from the large database of students who are using online educational resources and their recorded paths through the web. In this study, we aim to answer the following two research questions:Can we find classes of students? Do groups of students exist who use these online resources in a similar way? If so, can we identify a prediction for any individual student, such as which group they belong to? Can we use this information to help a student use the resources better, based on the usage of the resource by other students in their groups?Can we classify the problems that have been used by students? If so, can we show how the different types of problems impact students achievements? Can we help instructors to develop the homework more effectively and efficiently?We hope to find similar patterns of use in the data gathered from LON-CAPA, and eventually be able to make predictions as to the most-beneficial course of studies for each student based on a limited number of variables for each individual student. Based on the current state of the learner in a learning sequence, the system could then make suggestions to the learner as to how to proceed. This survey is organized as follows: Chapter 2 provides information about current online education systems and a background on intelligent tutoring systems. The second part of this chapter presents a system overview of LON-CAPA in detail to show the amplitude of growing homework and student data in LON-CAPA and the inadequacy of current statistical measures for classifying the students efficiently. Chapter 3 introduces the basic concepts of data mining clustering methods and describes the important algorithms and methods for data classification. Chapter 4 explains how to use fuzzy clustering for classifying students to improve the quality of learning objects. Chapter 5 will present a conclusion of the survey and indicate future work. Chapter 2BackgroundIn this chapter we review briefly intelligent tutoring systems and discuss online education systems, especially the LON-CAPA online education system. In this survey, we are not going to develop a complicated intelligent tutoring system; instead we apply the main ideas of intelligent tutoring systems in an online education system using possible data mining methods. Intelligent Tutoring Systems (ITS)Intelligent tutoring systems are computer-based instructional systems that attempt to determine information about a students learning status, and use that information to dynamically adapt the instruction to fit the students needs. (UrbanLurain, 1996; Petrushin, 1995; Benyon and Murray, 1993; Winkkels, 1992; Farr and Psotka, 1992; Venezky and Osin, 1991; Larkin and Cabay, 1991; Goodyear, 1990; Frasson and Gauthier, 1988, Wenger, 1987; Yazdani, 1987) ITSs are often known as knowledge-based tutors, because they have separate knowledge bases for different domain knowledge. The knowledge bases specify what to teach and different instructional strategies specify how to teach. (Murray, 1996) One of the fundamental assumptions in ITS design is from an important experiment in the theory of learning, which states that individualized instruction is far superior to class-room style learning. Both the content and style of instruction can be continuously adapted to best meet the needs of a student. (Bloom, 1984) Educational psychologists report that students learn best by doing, learn through their mistakes, and learn by constructing knowledge in a very individualized way. (Kafaei and Resnik, 1996; Ginsburg and Opper, 1979; Bruner 1966) For many years, researchers have argued that individualized learning offers the most effective and efficient learning for most students (Juel, 1996; Woolf, 1987, Bloom 1956). Intelligent tutoring systems epitomize this principle of individualized instruction. Recent studies have found that intelligent tutoring systems can be highly effective learning aides. (Shute and Regine, 1990) Shute evaluated several intelligent tutoring systems to judge how they live up to the main promises of intelligent tutoring systems to provide more effective and efficient learning in relation to traditional instructional techniques. Results of such studies show that tutoring systems do accelerate learning with no degradation of the final outcome. Learning Enhancement in the ITS In one study, Bloom (1984) stated that conventional teaching methods provide the least effective method of learning. As instruction becomes more focused and individualized, learning is enhanced. He compared students scores on achievement tests using three forms of instruction: conventional teaching, mastery teaching, and individualized tutoring. Mastery teaching is an instructional technique whereby a teacher supplements a lecture with diagnostic tests to determine where students are having problems, and adjusts the instruction accordingly. The result of this comparison is shown in figure 2. Students receiving conventional teaching scored in the 50th percentile, students receiving mastery teaching scored in the 84th percentile, while students receiving individualized tutoring scored in the 98th percentile.  EMBED Word.Picture.8 Figure 2.1: Distributions for different learning conditions (Adapted from Bloom, 1984)Bloom replicated these results four times with three different age groups for two different domains, and thus, provided concrete evidence that tutoring is one of the most effective educational delivery methods available.Since ITSs attempt to provide more effective learning through individualized instruction, many computer-assisted instruction techniques exist that can present instruction and interact with students in a tutor-like fashion, individually or in small groups. The incorporation of artificial intelligence techniques and expert systems technology to computer-assisted instruction systems gave rise to intelligent tutoring systems, i.e., systems that model the learners understanding of a topic and adapt the instruction accordingly. A few examples of systematically controlled evaluations of ITSs reported in the literature are shown in the following table: ITSLiteratureObjectiveprogressLISP tutor(Anderson, 1990)Instructing LISP programming33-66% less timeSmithtown(Shute and Glaser, 1990)Teaches scientific inquiry skills1/2 time, same knowledgeSherlock(Lesgold et al.,1990)For avionics troubleshooting1/5 time, same knowledgePascal ITS(Shute, 1991)Teaches Pascal programming1/3 time, same knowledgeStat Lady(Shute et al., 1993)Instructing statistical proceduresMore performanceGeometry Tutor(Anderson et al., 1985)Teaching Geometry theoremsBetter solvingTable 2.1: Different Specific ITSs and their affects on learning rateShute and Poksta (1996) examined the results of these evaluations, which show that these tutors do accelerate learning with no degradation in outcome performance. The tutors should be evaluated with respect to the promises of ITSs. In all cases, individuals using the ITSs learne faster, and perform at least as well as those learning from traditional teaching environments. The results show that these tutors could not only reduce the variance of outcome scores, but also make learning less dependent on aptitudes, thereby providing every student with a fair chance at learning.Basic Architecture of an ITSThere is no standard architecture for an ITS. Nevertheless, four components emerge from the literature as part of an ITS (Wasson, 1997; Costa, 1992; Polson and Richardson, 1988; Yazdani, 1987; Wenger, 1987; Sleeman and Brown, 1982). These are the student model, the pedagogical module, the expert model, and the communication module or interface. These four components and their interactions are illustrated in figure 2.2. The student model stores information of each individual learner. For example, such a model tracks how well a student is performing on the material being taught or records misconceptions. Since the purpose of the student model is to provide data for the pedagogical module of the system, all of the information gathered should be usable by the tutor. The pedagogical module provides a model of the teaching process. For example, information about when to review, when to present a new topic, and which topic to present is controlled by this module. As mentioned earlier, the student model is used as input to this component, so the pedagogical decisions reflect the differing needs of each student. The expert model contains the domain knowledge, the information being taught to the learner. However, it is more than just a representation of the data; it is a model of how someone skilled in a particular domain represents the knowledge. By using an expert model, the tutor can compare the learner's solution to the expert's solution, pinpointing the places where the learner has difficulties. This component contains information the tutor is teaching, and is the most important since without it, there would be nothing to teach the student. Generally, this aspect of ITS requires significant knowledge engineering to represent a domain so that other parts of the tutor can access it. The communication module controls interactions with a student, including the dialogue and the screen layouts. For example, it determines how the material should be presented to the student in the most effective way. This component the least researched of the group.These four components, the student model, the pedagogical module, the expert model, and the communication module interact to provide the individualized educational experience promised by ITS technology. Current research trends focus on making tutoring systems truly intelligent. The evolution of ITSs demands more controlled research in four areas of intelligence: the domain expert, student model, tutor, and interface.The domain knowledge must be understood by the computer well enough for the expert model to draw inferences or solve problems in the domain.The system must be able to deduce a students approximation of that knowledge.The tutor must be intelligent to the point where it can reduce differences between the expert and student performance.The interface must possess intelligence in order to determine the most effective way to present information to the student.For ITSs to have a great impact on education, these and other issues must be resolved. To take advantage of newer, more effective instructional techniques, ITSs of the future will have to allow for increased student initiative and between-student collaboration (Shute and Psotka, 1996). ITSs must also assess learning as it transfers to authentic tasks, not standardized tests, and establish connections across fields, so topics are not learned in isolation. A more fruitful approach for ITS development may be to develop specific cognitive tools, for a given domain or applicable across domains. Such a transition would allow future ITSs to be everywhere, as embedded assistants, to explain, critique, provide online support, coach, and perform other ITS activities.Learning and Cognition Issues for ITS Development and UseThere are some findings in the areas of cognition and the learning process that impact the development and use of intelligent tutoring systems. Many recent findings are paving the way towards improving our understanding of learners and learning (Bransford, Brown et al., 2000). Learners have preconceptions about how the world works. If their initial understanding is not referenced or activated during the learning process, they may fail to understand any new concepts or information.One key finding regarding competitance in a domain is the need to have a more than deep knowledge base of information related to that domain. They must also be able to understand that knowledge within the context of a conceptual framework. They must also be able to organize that knowledge in a manner that facilitates its use. A key finding in the learning and transfer literature is that organizing information into a conceptual framework allows for greater transfer of knowledge. By developing a conceptual framework, students are able to apply their knowledge in new situations and to learn related information more quickly. For example, a student who has learned problem solving for one topic in the context of a conceptual framework will use that ability to guide the acquisition of new information for different topic within the same framework.A relationship exists between the learning and transfer of knowledge to new situations. Transferring is usually a function of the relationships between what is learned and what is tested. For students to transfer knowledge successfully across domains, they must conceive of their knowledge base as growing continuously, instead of discrete steps.Recent research by Singley and Anderson indicates that the transfer of knowledge between tasks is a function of the degree to which the tasks share cognitive elements (Singley and Anderson, 1989) In their study, Singley and Anderson taught students several text editors, one after the other. They found that students learned subsequent text editors more rapidly and that the number of procedural elements shared by the two text editors predicted the amount of transfer. Their results showed that there was large transfer across editors that were very different in surface structures but had common abstract structures. Singley and Anderson were able to generate similar results for the transfer of mathematical competence across multiple domains.Emerging computer-based technologies hold great promise as a means of supporting and promoting learning. There are several ways that such technology can be used to help meet the challenges of developing effective learning environments (El-Sheikh, 2001):Bringing real-world problems to the learning environment.Providing scaffolding support to students during the learning process. Scaffolding allows students to participate in complex cognitive experiences, such as model-based learning, that is more difficult without technical support.Increasing opportunities for learners to receive feedback and guidance from software tutors and learning environments.Building local and global communities of teachers, administrators, students, and other interested learners.Expanding opportunities for teachers learning.Learning environments need to be developed and implemented with a full understanding of the principles of learning and developmental psychology. In addition, these new learning environments need to be assessed carefully, including how their use can facilitate learning, and the cognitive, social, and learning consequences of using these new tools. Online Education systemsSeveral Online Education systems such as Blackboard (CouseInfo), WebCT, Virtual University (VU), and some other similar systems have been developed to focus on course management issues. The objectives of these systems are to present courses and instructional programs through the web and other technologically enhanced media. These new technologies make it possible to offer instruction without the time and place limitations of traditional university programs. However, these systems tend to use existing materials and present them as a static package via the Internet. There is another approach that is pursued in LON-CAPA to construct more-or-less new courses using the new network technology. In this model of content creation, college faculty, K-12 teachers, and students interested in collaboration can access a database of hypermedia software modules that can be linked and combined (Kortemeyer and Bauer, 1999). The LON-CAPA is the primary focus of this chapter. LON-CAPA, System OverviewLON-CAPA is a distributed instructional management system, which provides students with personalized problem sets, quizzes, and exams. Personalized (or individualized) homework means that each student sees a slightly different computer-generated problem. LON-CAPA provides students and instructors with immediate feedback on conceptual understanding and correctness of solutions. It also provides faculty the ability to augment their courses with individualized, relevant exercises. It also allows faculty to develop and share modular online resources. LON-CAPA aims to put this functionality on a homogeneously distributed platform for creating, sharing, and delivering course content with emphasis on cross-institutional collaboration and intellectual property rights management. LON-CAPA TopologyLON-CAPA is physically built as a geographically distributed network of constantly connected servers. Figure 2 shows an overview of this network. Every user in LON-CAPA is a member of one domain. Domains could be defined by departmental or institutional boundaries like MSU, FSU, OHIOU, or the name of a publishing company, students, authors and other users. These domains can be used to limit the flow of personal user information across the network, set access privileges and enforce royalty schemes. Thus, the student and course data are distributed amongst several repositories. Internally, all resources are identified primarily by their URL. Every user in the system has one library server, which is their home server. It stores the authoritative copy of all of their records.LON-CAPA currently runs on Redhat-Linux Intel-compatible hardware. The current MSU production setup consists of five access servers and two library servers. Three of the access servers are set up on a round-robin IP scheme as frontline machines, and are accessed by the students for user session. The current implementation of LON-CAPA uses mod_perl inside of the Apache web server software.Data Distribution in LON-CAPALearning objects in LON-CAPA could be simple paragraphs of text, movies, applets, and CAPA-style individualized homework problems. Online educational projects at MSU have produced extensive libraries of resources across disciplines. By combining these resources, LON-CAPA will produce a national distributed digital library with mechanisms to store and retrieve these objects. Participants in LON-CAPA can publish their own learning objects in the common pool. LON-CAPA will allow groups of organizations (departments, universities, schools, commercial businesses) to link their online instructional resources in a common marketplace, thus creating an online economy for instructional resources (lon-capa.org).LON-CAPA would enable faculty to combine and sequence these objects at several levels. For example, an instructor from Community College A in Texas could compose a page by combining a text paragraph from University B in Detroit with a movie from College C in California and an online homework problem from Publisher D in New York. Another instructor from High School E in Canada might take that page from Community College A and combine it with other pages into a module, unit or section. Those in turn can be combined into whole course packs. Participants in LON-CAPA can publish their own learning objects in the common pool.Resource Variation in LON-CAPALON-CAPA provides three types of resources for organizing a course. LON-CAPA refers to these resources as Content Pages, Problems, and Maps. Maps may be either of two types: Sequences or Pages. You will use these LON-CAPA resources to build the outline, or structure, for the presentation of your course to your students. A Content Page displays course content. It is essentially a conventional HTML page.These resources use the extension .html.A Problem resource represents problems for the students to solve, with answers stored in the system. These resources are stored in files that must use the extension .problem.A Page is a type of Map which is used to join other resources together into one HTML page. For example, a page of problems will appear as a problem set. These resources are stored in files that must use the extension .page.A Sequence is a type of Map, which is used to link other resources together. Sequences are stored in files that must use the extension .sequence. Sequences can contain other sequences and pages.Authors create these resources and publish them in library servers. Then, instructors use these resources in online courses. The LON-CAPA system logs any access to these resources as well as the sequence and frequency of access in relation to the successful completion of any assignment. All these accesses logged.LON-CAPA Strategy for Data StorageAll data are stored as URLs distributed over a wide area network. Internally, the student data is stored in a directory:/home/httpd/lonUsers/domain/1st.char/2nd.char/3rd.char/username/For example /home/httpd/lonUsers/msu/m/i/n/minaeibi/Figure 2.3 shows a list of a student data; files ending with .db are GDBM files (Berkeley database). Files with a course-ID as name, for example msu_12679c3ed543a25msul1.db, store performance data for that student in the course.ls -alF /home/httpd/lonUsers/msu/m/i/n/minaeibi-rw-r--r-- 1 www users 13006 May 15 12:21 activity.log-rw-r----- 1 www users 12413 Oct 26 2000 coursedescriptions.db-rw-r--r-- 1 www users 11361 Oct 26 2000 coursedescriptions.hist-rw-r----- 1 www users 13576 Apr 19 17:45 critical.db-rw-r--r-- 1 www users 1302 Apr 19 17:45 critical.hist-rw-r----- 1 www users 13512 Apr 19 17:45 email_status.db-rw-r--r-- 1 www users 1496 Apr 19 17:45 email_status.hist-rw-r--r-- 1 www users 12373 Apr 19 17:45 environment.db-rw-r--r-- 1 www users 169 Apr 19 17:45 environment.hist-rw-r----- 1 www users 12315 Oct 25 2000 junk.db-rw-r--r-- 1 www users 1590 Nov 4 1999 junk.hist-rw-r----- 1 www users 23626 Apr 19 17:45 msu_12679c3ed543a25msul1.db-rw-r--r-- 1 www users 3363 Apr 19 17:45 msu_12679c3ed543a25msul1.hist-rw-r----- 1 www users 18497 Dec 21 11:25 msu_1827338c7d339b4msul1.db-rw-r--r-- 1 www users 3801 Dec 21 11:25 msu_1827338c7d339b4msul1.hist-rw-r----- 1 www users 12470 Apr 19 17:45 nohist_annotations.db-rw-r----- 1 www users 765954 Apr 19 17:45 nohist_email.db-rw-r--r-- 1 www users 710631 Apr 19 17:45 nohist_email.hist-rw-r--r-- 1 www users 13 Apr 19 17:45 passwd-rw-r--r-- 1 www users 12802 May 3 13:08 roles.db-rw-r--r-- 1 www users 1316 Apr 12 16:05 roles.histFigure 2.4: Directory listing of users home directoryCourses are assigned to users, not vice versa. Internally, courses are handled like users without login privileges. The username is a unique ID, for example msu_12679c3ed543a25msul1 every course in every semester has a unique ID, there is no semester transition. The userdata of the course includes the full name of the course, a pointer to its top-level resource map (course map), and any associated deadlines, spreadsheets, etc., as well as a course enrollment list. The latter is somewhat redundant, since in principle, this list could be produced by going through the roles of all users, and looking for the valid role for a student in that course.ls -alF /home/httpd/lonUsers/msu/1/2/6/12679c3ed543a25msul1/-rw-r----- 1 www users 17155 Apr 25 16:20 classlist.db-rw-r--r-- 1 www users 60912 Apr 25 16:20 classlist.hist-rw-r----- 1 www users 12354 Jan 4 16:40 environment.db-rw-r--r-- 1 www users 82 Jan 4 16:40 environment.hist-rw-r----- 1 www users 103030 May 15 14:47 nohist_calculatedsheets.db-rw-r----- 1 www users 13050 May 9 21:04 nohist_expirationdates.db-rw-r--r-- 1 www users 6 Jan 4 16:40 passwd-rw-r----- 1 www users 17457 May 9 21:04 resourcedata.db-rw-r--r-- 1 www users 8888 May 9 21:04 resourcedata.histFigure 2.5: Directory listing of courses home directoryAn example of course data is shown in figure 2.5. classlist is this list of students in the course, environment includes the courses full name, etc, and resourcedata are deadlines, etc. The parameters for homework problems are stored in these files.To identify a specific instance of a resource, LON-CAPA uses symbols or symbs. These identifiers are built from the URL of the map, the resource number of the resource in the map, and the URL of the resource itself. The latter is somewhat redundant, but might help if maps change. An example is msu/korte/parts/part1.sequence___19___msu/korte/tests/part12.problemThe respective map entry is <resource id="19" src="/res/msu/korte/tests/part12.problem" title="Problem 2"> </resource>Symbs are used by the random number generator, as well as to store and restore data specific to a certain instance of a problem. More details of the stored data and the their exact structures will be explained in chapter 4, when we will describe the data acquisition of system.Resource Evaluation in LON-CAPAOne of the most challenging aspects of the system is to provide resource users with information concerning the quality and effectiveness of the various materials in the resource pool in terms of their effects on student understanding of concepts and their knowledge of procedures. These materials will include web pages, demonstrations, simulations, and individualized problems designed for use on homework assignments, quizzes, and examinations. The system generates a range of statistics that can be useful in evaluating the degree to which individual problems are effective in promoting formative learning for students. Each exam problem contains attached metadata that catalog its degree of difficulty and discrimination for students at different phases in their education (i.e., introductory college courses, advanced college courses, and so on). To evaluate resource pool materials, a standardized format will be required so that materials from different sources can be compared. This will help resource users in selecting the most effective materials available. LON-CAPA has provided questionnaires, which are completed by faculty and students who use the educational materials to assess the quality and efficacy of resources. In addition to providing the questionnaires and using the statistical reports, we investigate methods to find criteria for classifying students and grouping problems. We plan to include information, such as time spent on a particular resource, resources visited (other web pages), due date for each homework, and the difficulty of problems (observed statistically). Thus, we should gather floods of data on individual usage patterns. Especially as students go through multiple steps to solve problems, and choose between multiple representations of the same educational objects like video lecture demonstrations, a derivation, a worked example, case-studies, and so forth. As the resource pool grows, multiple content representations will be available to students. There has been an increasing demand for automated methods for evaluating resources. One such method is data mining, which is focus of this survey. So, in this survey we are to use some automated methods using data mining to evaluate the resources in LON-CAPA, whether we would be able to have a good perspective of system description to figure out the association rules and dependency model of the system objects.Chapter 3Literature ReviewPresently, the amount of data stored in databases increases at an amazing speed. This gives rise to the expressive need for new techniques and tools to aid humans in automatically and intelligently analyze huge data sets to get useful information. This growing need gives birth to a new research field called Knowledge Discovery in Databases (KDD) or Data Mining, which has attracted more attention from researchers in many different fields including database, statistics, pattern recognition, machine learning, and data visualization. In this chapter well indicate the definition of KDD and Data Mining describing its tasks, methods, and applications. Our motivation in this study is gaining the best technique for extracting useful information from large amounts of data in an online educational system, in general, and from the LON-CAPA system, in particular. We aim to obtain an optimal predictive model for students who take part in such systems.What is Data Mining?Data Mining or KDD is the process of analyzing data from different perspectives and summarizing it into useful information. It has been defined as "the nontrivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data" (Frawley et al., 1992; Fayyad et al., 1996). It uses machine learning, statistical, and visualization techniques to discover and present knowledge in a form that is easily comprehensible. The word Knowledge in KDD refers to patterns, which are extracted from the processed data. A pattern is an expression describing facts in a subset of the data. Thus, the difference between KDD and data mining is that KDD refers to the overall process of discovery knowledge from data while data mining refers to application of algorithms for extracting patterns from data without the additional steps of the KDD process (Fayyad et al., 1996). However, since Data Mining is the crucial and important part of the KDD process, most researchers usually use both terms indistinguishably.Figure 3.1 presents the iterative nature of the KDD process. Here we outline some of its basic steps as are mentioned in (Brachman & Anad, 1996):Providing an understanding of the application domain, the goals of the system and its users, and the relevant prior background and prior knowledge. This step in not specified in this figure.Selecting a data set, or focusing on a subset of variables or data samples, on which discovery is to be performed.Preprocessing and data cleaning, removing the noise, collecting the necessary information for modeling, selecting methods for handling missing data fields, accounting for time sequence information and changes.Data reduction and projection, finding appropriate features to represent data, using dimensionality reduction or transformation methods to reduce the number of variables to find invariant representations for data.Choosing data mining task depending on the goal of KDD: clustering, classification, regression, and so forth.Selecting methods and algorithms to be used for searching for the patterns in the data.Mining the knowledge: searching for patterns of interest.Evaluating or interpreting the mined patterns, possible return to any of previous steps.Using this knowledge for promoting the performance of the system and resolving the potential conflicts with previously believed or extracted knowledge.Data Mining TasksGenerally, the objective of data mining in practice is prediction and description. Prediction is to predict unknown or future values of the attributes of interest using other attributes in the databases while description is to find patterns to describe the data in a manner understandable and interpretable to humans. Predicting sale amounts of new product based on advertising expenditure, or predicting wind velocities as a function of temperature, humidity, air pressure, etc., are examples of predictive tasks in data mining. The relative importance of description and prediction could vary in different applications. These two goals can be fulfilled by the following data mining tasks: classification, regression, clustering, summarization, discrimination, dependency modeling, prediction, and change and deviation detection. Predictive tasksClassification is to segregate items into several predefined classes. Given a collection of training samples, is to find a model for class attribute as a function of the values of other attributes.Regression is to predict a value of a given continuous valued variable based on the values of other variables, assuming a linear or nonlinear model of dependency. This is studied in statistics and neural network fields. Deviation Detection is to discover the most significant changes in data from previously measured or normative values. Descriptive tasksClustering is to identify a set of categories or clusters to describe the data. (Jain & Dubes, 1988)Summarization is to find a concise description for a subset of data. Tabulating the mean and standard deviations for all fields is a simple example of summarization. There are more sophisticated techniques for summarization and are usually applied to automated report generation and interactive data analysis (Fayyad et al., 1996).Dependency modeling is to find a model, which describes significant dependencies between variables. For example, probabilistic dependency networks use conditional independence to specify the structural level of the model and probabilities or correlation to specify the strengths (quantitative level) of dependencies (Heckerman, 1996).Discrimination is to discover the features or properties that distinguish one set of data (called target classes) from other sets of data (called contrasting classes).There are some tasks in data mining that has both descriptive and predictive aspects In other Mixed tasksThere are some tasks in data mining that has both descriptive and predictive aspects. Using these tasks, we can move from basic descriptive tasks toward higher predictive tasks. Here, we indicate two of them:Association Rule Discovery: Given a set of records each of which contain some number of items from a given collection; Produce dependency rules which will predict occurrence of an item based on occurrences of other items.Sequential Pattern Discovery: Given a set of objects, with each object associated with its own timeline of events, find rules that predict strong sequential dependencies among different events. Rules are formed by first discovering patterns. Event occurrences in the patterns are governed by timing constraints. Data Mining Approaches/MethodsThere are different methodological approaches to data mining including machine learning, statistics, database-oriented, knowledge representation and visualization, neural network and so forth. Machine learning approaches include learning from examples, conceptual clustering, decision tree induction, and so forth. Mathematical and statistical approaches include Bayesian inference, and rough set theory, while database-oriented approaches include attribute-oriented induction, a priori, and so forth.This survey focuses on methods and algorithms in the context of data mining according to the descriptive and predictive tasks. First, we describe clustering methods in data mining. Then we study the classification methods developed in the related research and extend them for predictive purposes.ClusteringData clustering is a sub-field of data mining that is dedicated to techniques for finding similar groups in a large database. Data clustering is a tool for exploring data and finding a valid and appropriate structure of objects for grouping and classifying the data (Jain & Dubes, 1988). A cluster indicates a number of similar objects, such that the members inside a cluster are as similar as possible (homogeneity), but the data belong to different clusters that are as dissimilar as possible (heterogeneity) (Hoppner et al., 2000). The property of homogeneity is similar to the cohesion attribute between objects of a class in software engineering. Heterogeneity is similar to the coupling attribute between the objects of different classes in software engineering. Unlike data classification, data clustering does not require the category labels or predefined group information. Thus, clustering has been studied in the field of machine learning as a type of unsupervised learning, because it relies on the learning from observation instead of the learning from examples. We use data clustering methods in LON-CAPA, because we have a large amount of data without any category labels for the students and learning objects. Two general categories of clustering methods are partitioning method, and hierarchical method:Partitioning MethodsA partitioning algorithm assuming a set of n objects in d-dimensional space and an input parameter k organizes the objects into k clusters such that the total deviation of each object from its cluster center is minimized. The deviation of an object in a cluster depends on the similarity function, which depends on the criterion employed to distinguish objects of different clusters. Clusters can be of arbitrary shapes and sizes in multidimensional space. Every particular clustering criterion enforces a specified discipline on the data. Many criteria are introduced in related literatures. Here, we study some of the most popular partitioning methods: such as the square error approach, mixture density model, density or mode estimation, graph connectivity, and near neighbor relationship.The most common approach in these methods is to optimize the criterion function using an iterative, hill climbing technique. Starting from an initial partition, objects are moved from one cluster to another in an effort to improve the value of the criterion function (Jain & Dubes, 1988). Each algorithm has different way for representing its clusters. k-mean AlgorithmThe k-means algorithm (McQueen, 1967), uses the mean value of the objects in a cluster as the cluster center. The mean value of a cluster is computed according to this function:EMBED Equation.3= EMBED Equation.3where ni is number of patterns in cluster Ci, (among exactly k clusters: C1, C2, , Ck) and x is the point in space representing the given object. The total squared-error is computed in this way:E = EMBED Equation.3The steps of the iterative algorithm for partitional clustering are as follows: 1. Choose an initial partition with k < n clusters (EMBED Equation.3, EMBED Equation.3, , EMBED Equation.3 are cluster centers and n is the number of patterns).2. RepeatGenerate a new partition by assigning a pattern to its nearest cluster center EMBED Equation.3.Recompute new cluster centersEMBED Equation.3.Loop Until no change in EMBED Equation.3.6. ReturnEMBED Equation.3, EMBED Equation.3, , EMBED Equation.3 as the mean values of C1, C2, , Ck.The idea behind this iterative process is to start from an initial partition assigning the patterns to clusters and to find a partition containing k clusters that minimizes E for fixed k. In step 3 of this algorithm, k-means assigns each object to its nearest center forming a set of clusters. In step 4, all the centers these new clusters are recomputed with function E by taking the mean value of all objects in every cluster. This iteration is repeated until the criterion function E no longer changes. The k-means algorithm is an efficient algorithm with the time complexity of O(ndkt), where n is the total number of objects, d is the number of features, k is the number of clusters, and t is the number of iterations such that t<k<n. The weaknesses of this algorithm include a requirement to specify the parameter k, inability to find arbitrarily shaped clusters, and it is very sensitive to noise and outlier data. Some of the noise data can influence the mean value. Because of this, Jain & Dubes, (1988) have added an step before step 6: Adjust the number of clusters by merging and splitting the existing clusters or by removing small, or outlier clusters. Graph ConnectivityA graph can represent the relationship between patterns. Every vertex represent show a pattern and every edge would represent the relation between two patterns. The edge weights are distances between two adjacent vertices. The criterion function here is that the pairs of patterns, which belong to the same cluster, should be closer than the pairs belong to different clusters. Several graph structures, such as minimum spanning trees (MST) (Zahn, 1971), relative neighborhood graphs (Toussaint, 1980), and Gabriel Graphs (Urquhart, 1982), have been applied to present a set of patterns in a graph in order to detect the clusters. Here we only indicate the first algorithm. The basic idea of Zahns algorithm consist of the following steps:Construct the MST for the set of given n patterns. Determine the inconsistent edges in MST.Delete the inconsistent edges from MST. The remaining components are our clusters.This algorithm can be applied recursively on the resulting components to determine the new clusters. The crucial point of this algorithm is the definition of inconsistency. Zahn presents several criteria for inconsistency. An edge is inconsistent if its weight is so much larger than average of nearby edge weights. Other definitions of inconsistency are the standard deviation by which an edge weight differs from the average of nearby edge weights, and the ratio of the edge weight differs from average of nearby edge weights can be considered. More details about the comparison amongst MST-based algorithms and other structures of graph theory could be found in Jain & Dubes, (1988). Nearest Neighbor MethodIn this method every pattern is put in the same cluster as its nearest neighbor. Lu and Fu, (1978) have presented a simple clustering algorithm, which is based on the nearest neighbor method. This algorithm partitions a set of {x1, x2, , xn} patterns into a set of k clusters {C1, C2, , Ck}. The user should specify a threshold r, which determines the nearest neighbor distance. Let i = 1 and k = 1. Assign pattern x1 to cluster C1. Mark pattern x1.i = i + 1. Find the nearest neighbor of xi among the patterns already assigned to its nearest neighbor. Let dj denote the distance between pattern xi and its nearest neighbor in cluster j.If dj EMBED Equation.3r, then assign xi to Cj; otherwise k = k + 1 and assign xi to a new cluster Ck. Mark pattern xi .If all the patterns have been marked, stop; else go to step 2.The number of cluster k, which are generated, is a function of the parameter r. As the value of r is increased the number of clusters k is decreased. Mixture DensityIn this approach we assume that the patterns are drawn from the k known number of populations. The chance that a pattern comes from EMBED Equation.3 or the prior probabilities P(EMBED Equation.3) for each population are known where EMBED Equation.3 is ith population or cluster, and i=1, 2, , k. The populations do not label the patterns. The probability density function for population EMBED Equation.3 is p(x|EMBED Equation.3,EMBED Equation.3), where EMBED Equation.3 is a vector of unknown parameters for EMBED Equation.3. The mixture density can be written as:p(x |EMBED Equation.3) = EMBED Equation.3Where EMBED Equation.3 = (EMBED Equation.3,EMBED Equation.3, , EMBED Equation.3). The conditional densities p(x|EMBED Equation.3,EMBED Equation.3) are called the component densities, and the prior probabilities P(EMBED Equation.3) are called mixing parameters. We know that EMBED Equation.3Our goal is to use the patterns to estimate the parameter vector EMBED Equation.3 so that the mixture can be decomposed into its component clusters (Duda et al., 2001; Jain & Dubes, 1988). This approach is model based, but the model is Gaussian. The parameter vectorEMBED Equation.3is usually estimated by the maximum likelihood or Bayesian approach. Maximum Likelihood EstimationThis approach is also called density estimation or mode seeking. Clusters are considered in the regions of pattern space in which the patterns are found dense. The regions that include less numbers of patterns separate the clusters. One of the simplest ways to determine the modes in the data is to construct a histogram by portioning the pattern space into k number of non-overlapping regions. Regions with relatively high frequency counts are the modes or cluster centers (Jain & Dubes, 1988). The advantage of density estimation method is that it does not require knowing the number of clusters and their prior probabilities. The disadvantages of this approach are that the process of the looking for the peaks and valleys in the histogram is difficult in more than a few dimensions and requires the user to identify the valleys in histograms for splitting interactively. Fuzzy k-means clustering In all partitioning algorithms, i.e. in the previous k-means algorithm, each data point is allowed to be in exactly one cluster. We put away this condition in the fuzzy clustering algorithm and assume that each pattern has some fuzzy membership in a cluster. That is, each object is permitted to belong to more than one cluster with a grade of membership. Fuzzy clustering has three main advantages: 1) it maps numeric values into more abstract measures (fuzzification); 2) student features may overlap multiple abstract measures, and there may be a need to find a way to cluster under such circumstances; and 3) most real-world classes are fuzzy rather than crisp (usual). Therefore, it is natural to consider the fuzzy set theory as a useful tool to deal with the classification problem (Dumitrescu et al., 2000). Some of the fuzzy algorithms are modifications of the algorithms of the square error type such as k-means algorithm. The definition of the membership function is the most challenging point in a fuzzy algorithm. Baker, (1978) has presented a membership function based on similarity decomposition. The similarity or affinity function can be based on the different concept such as Euclidean distance, neighborhood, or probability. Baker and Jain (1981) define a membership function based on the mean vectors of clusters:EMBED Equation.3(x) = EMBED Equation.3Where EMBED Equation.3is the Euclidean distance, between pattern vector x and the mean vector EMBED Equation.3 of cluster Ck .The parameterEMBED Equation.3 indicates the neighborhood size and cluster membership. This fuzzy partitional clustering has the same steps of squared error algorithm.Hierarchical MethodsHierarchical methods decompose the given set of data items forming a tree, which is called dendrogram. A dendrogram splits the dataset recursively into smaller subsets. A dendrogram can be formed in two ways: Bottom-up approach, which is called agglomerative approach, starts with each object forming a distinct group. It successively merges the groups according to some measures like the distance between the centers of the groups and this is done until all of the groups are merged into one, the top most level of hierarchy. Top-down approach, which is called divisive approach, starts with all the objects in the same cluster. In every successive iteration, a cluster is split into smaller according to some measures clusters until eventually each object is in one cluster, or until a termination condition is met.Hierarchical methods are popular in biological, social and behavioral systems, which need to construct taxonomies. Dendrogram are impractical when the number of patterns exceeds a few hundred patterns (Jain & Dubes, 1988). Partitional techniques are more appropriate in the case of large data sets.Classification and Predictive ModelingClassification is to find a model that segregates data into predefined classes. This classification is based on the features present in the data. The result is a description of the present data and a better understanding of each class in database. Thus, it provides a model for describing future data (Duda et al., 2001; McLachlan, 1992; Weiss and Kulikowski, 1991; Hand, 1987). Prediction helps people to make a decision. Predictive modeling for knowledge discovery in databases is to predict unknown or future values of some attributes of interest based on the values of other attributes in a database (Masand and Shapiro, 1996). Different methodologies have been used for classification and developing predictive modeling including Bayesian inference (Kontkanen et al., 1996), neural net approaches (Lange, 1996), decision tree-based methods (Quinlan, 1986) and genetic algorithms-based approaches (Punch et al., 1995).Bayesian Classifier One of the major statistical methods in data mining is the Bayesian inference. The naive Bayesian classifier provides a simple and effective approach to classifier learning. It assumes that all class-conditional probability densities are completely specified and this assumption is often violated in the real world (Jain et al., 1999; Duda et al., 2001; Wu et al., 1991). The Bayes classifier shown in figure 3.2, could be explained as follows: A set of patterns aj, j = 1,,n, is given, every pattern is sensed by a sensing device which is capable of capturing the features. Each pattern is considered in terms of a measurement vector xi. A pattern aj belongs to a classification set EMBED Equation.3, which includes all the possible classes that can be assigned to pattern aj. For simplicity all feature measurement are considered identical and each pattern belongs only to one of the m possible classes EMBED Equation.3, i = 1,,m.To classify a pattern into one of the m classes, a feature space is constructed according to the measurement vector x, which is considered as a measurement of true values damaged by random noisy data. The class-conditional probability density functions estimated from a training data set represent the uncertainty in discovered knowledge.EMBED Equation.3, i = 1,,m.Bayes decision theory states that the a-posteriori probability that an event may be calculated according to the following equation: EMBED Equation.3 , i = 1,,m.Eventually, the decision criteria can be applied for classification. To gain the optimal solution, the maximum likelihood classification or the Bayesian minimum error decision rule is applied. It is obtained by minimizing the misclassification and errors in classification. Thus, a pattern classified into class EMBED Equation.3 with the highest posteriori probability or likelihood:EMBED Equation.3The quadratic discriminant function using the Bayesian approach is the most common method in supervised parametric classifiers. The feature vectors in our datasets are assumed to be Gaussian distributed, and the parameters of the Gaussians are estimated using maximum likelihood estimation. The discriminant function decision rule and the a-posteriori probabilities for each classification are calculated for each sample test x using the following equation (Duda et al., 2001):EMBED Equation.3where is the mean value and EMBED Equation.3 is the covariance matrix of the training set. To obtain the optimal solution, the maximum likelihood classification or the Bayesian minimum error decision rule is applied. The sample is then assigned to the type that produces the highest a-posteriori probability. It is obtained by minimizing the misclassification and errors in classification. Decision tree-based methodThe Decision tree-based methods are the most popular methods in data mining context. The decision tree classifier uses hierarchical or layered approach to classification. Each vertex in the tree represents a single test or decision. The outgoing edges of a vertex correspond to all possible outcomes of the test at that vertex. These outcomes partition the set of data into several subsets, which are identified by every leaf in the tree accordingly. A leaf of the tree specifies the expected value of the categorical attribute for the records described by the path from the root to that leaf. Learned trees can also be represented as sets of if-then-else rules. (Mitchell, 1997)An instance is classified by starting at the root node of the tree. At each level of the tree the attributes of instances are matched to a number of mutually exclusive nodes. The leaf nodes assign classes to the instances. The classification of an instance therefore involves a sequence of tests, with each successive test narrowing the interpretation. The sequence of tests for the classifier is determined during a training period. Given some new data, the ideal solution would test all possible sequences of actions on the attributes of the new data in order to find the sequence resulting in the minimum number of misclassifications. Tree-based classifiers have an important role in pattern recognition research because they are useful with non-metric data in particular. (Duda et al., 2001) Decision tree methods are robust to errors, both errors in classifying the training examples and errors in the attribute values that describe these examples. Decision tree can be used when the data contain missing attribute values. (Mitchell, 1997) Most of algorithms that have been developed for decision trees are based on a core algorithm that uses a top-down, recursive, greedy search on the space of all possible decision trees. This approach is implemented by ID3 algorithm (Quinlan, 1986) and its successor C4.5 (Quinlan, 1993). C4.5 is an extension of ID3 that accounts for unavailable values, continuous attribute value ranges, pruning of decision trees, rule derivation, and so on. We used C5.0, CART, and Quest software for tree-based classification, whose results will be explained in the next chapter. What is the best feature for splitting?The first question that arises in all tree-based algorithms is which properties tested in each node, are binary-valued or multi-valued? The second question that arises in all tree-based algorithms is that, which property should be tested at a node? In other words, which attribute is the best classifier? We would like to select the attribute is the most informative of the attributes not yet considered in the path from the root. This establishes what is a "Good" decision tree. Entropy is used to measure a nodes information. Claude Shannon (1984) introduced this notion in Information Theory. Based on entropy, a statistical property called information gain measures how well a given attribute separate the training examples in relation to their target classes. Entropy impurityEntropy characterizes impurity of an arbitrary collection of examples S at a specific node N. Sometimes (Duda et al., 2001) the impurity of a node N is denoted by i(N). Entropy(S) = EMBED Equation.3where EMBED Equation.3 is the fraction of examples at node N that go to category EMBED Equation.3. So, if all the patterns are from the same category the impurity is 0, otherwise it is positive; if all categories are equally distributed at node N then the impurity has its greatest value 1. Now we come up with the key question at a sub-tree down to node N, what value of feature should we select for the test at node N when property query T is used? Duda et al. (2001) suggested a heuristic to select a query that decreases the impurity as much as possible.EMBED Equation.3where EMBED Equation.3 and EMBED Equation.3 are the left and right descendent nodes, and the EMBED Equation.3 and EMBED Equation.3 are their impurities respectively, and EMBED Equation.3 is fraction of patterns at node N that will go to EMBED Equation.3 when the property query T is used. The goal of the heuristic is to maximize the EMBED Equation.3, thus minimizing the impurities corresponds to an information gain, which is provided by the query.Gini impurityOne of the CART activities is to rank and order each splitting rule on the basis of a quality-of-split criterion. The default criterion used in CART is the Gini impurity; essentially a measure of how well the splitting rule separates the classes contained in the parent node (Duda et al., 2001). EMBED Equation.3As shown in the above equation, it is strongly peaked when probabilities are equal. So what is Gini trying to do? Gini attempts to separate classes by focusing on one class at a time. It will always favor working on the largest or, if you use costs or weights, the most "important" class in a node. While this approach might seem short sighted, Ginis performance is frequently so good that you should experiment and see how well it does. Gini is the default rule in CART precisely because it is often the best splitting rule. Twoing impurity An alternative criterion also available in CART is Twoing impurity. The philosophy of Twoing is far different than that of Gini. Rather than initially pulling out a single class, Twoing first segments the classes into two groups, attempting to find groups that together add up to 50 percent of the data. Twoing then searches for a split to separate the two subgroups (Duda et al., 2001). This is an ideal split. It is unlikely that any real-world database would allow you to cleanly separate four important classes into two subgroups in this way. However, splits that approach this ideal might be possible, and these are the splits that Twoing seeks to find.Avoid overfittingIf we continue to grow the tree until each leaf node corresponds to the lowest impurity then the data is typically overfit. In some cases every node corresponds to a single training input. In such cases we cannot expect an appropriate generalization in noisy problems having high Bayes error (Duda et al. 2001; Russell and Norvig, 1997). On the other hand if we stop splitting early, then a high performance tree classifier will not be met. There are several approaches to avoid overfitting in the training phase of tree-based classification:Cross-ValidationCross-validation is a technique to eliminate the occurrence of overfitting. The main idea of cross-validation is to estimate how well the current hypothesis will predict unseen data (Duda et al. 2001; Russell and Norvig, 1997). This is done by dividing randomly the data into two subsets, training and test. Usually, the test subset is a fraction of all of the data, i.e. 10%. The hypothesis induced from the training phase is tested on the rest of data to get the prediction performance. This should be repeated on different subsets of data, and then the result averaged. Cross-validation could be used in order to select a tree with good prediction performance.Setting a thresholdAnother method is to consider a small threshold value in minimizing the impurity. We stop splitting when the impurity at a node reduces by less than the considered threshold. The benefit of this method over the cross-validation is that the tree is trained using all the training data. Another benefit of this method is that leaf node can lie in different levels of the tree.PruningThe principal alternative of stop splitting is pruning (Duda et al., 2001). One approach, called reduced-error pruning (Quinlan, 1987), is to set every nodes in the decision tree to be candidate for pruning. Pruning a decision node consist of removing the subtree rooted at that node, making it a leaf node, and assigning it the most common classification of the training examples affiliated with that node. Nodes removed only if the resulting pruned tree performs no worse than the original over the validation set. (Mitchell, 1997)In C4.5, Quinlan (1993) applied a successful technique for finding high accuracy hypothesis during the pruning process, which is called rule post pruning. It involves the following steps:Induce the decision tree from the training set, growing the tree until the training data is fully fitted as well as possible, allowing overfitting to occur.Convert the learned tree into an equivalent set of rules by creating one rule correspond to a path from root to a leaf node.Prune each rule by deleting any preconditions that lead to promoting the estimated accuracy.Sort the pruned rules by their estimated accuracy, and set them in a sequence for classifying the instances.Why we prefer short hypothesis? Create small decision trees so that records can be identified after only a few questions. According to Occam's Razor, Prefer the simplest hypothesis that fits the data (Duda et al., 2001). Neural Network ApproachA neuron is a special biological cell with information processing ability (Jain et al., 1996). The classification approach based on Artificial Neural Network (ANN), which is called connectionist model, generates a lower classification error than the decision tree approach in several cases, but it needs longer training time (Quinlan, 1994; Russle and Norvig, 1995). A neural network is usually a layered graph with the output of one node feeding into one or more nodes in the next layer. These results with a complexity in understanding the classification rules from the structure of graph and weights assigned to the links between the nodes. The Multi-layer Perceptron (MLP) is a basic feedforward artificial neural network using the back-propagation algorithm. That is, during training, information is propagated back through the network and used to update connection weights. According to Ruck et al., (1990), the multi-layer perceptron trained using the back-propagation learning algorithm approximates the optimal discriminant function defined by Bayesian theory. The output of the MLP approximates the posterior probability functions of the classes being trained. The Sigmoidial activation function is used for learning the input weight vectors in the training phase as follows:EMBED Equation.3Tuning the learning rate, the number of epochs, the number of hidden layers, and the number of neurons in every hidden layer is a very difficult task far obtaining a good performance for MLP. In each epoch the input data are used with the present weights to determine the errors, then back-propagated errors are computed and weights updated. A bias is considered for the hidden layers and output.Describing the problem how to adopt the data mining techniques is not possible without representing the data in an explicit way. Lu et al.(1995) made an effort to overcome this obstacle. They use a three-layer neural network to perform classification. ANN made up of a lot of simple computational elements (neurons), which are densely interconnected. Among the network topologies the multilayer perceptron is useful for classification purposes. Figure 3.3 shows a three-layer feedforward network, which has an input layer, a hidden layer, and an output layer. A node (neuron) in the network has a number of inputs and a single output. Every link in the network is associated with a weight. For example, node Ni has EMBED Equation.3, , EMBED Equation.3as its inputs and ai as its output. The input links of Ni has weights EMBED Equation.3, , EMBED Equation.3. A node generates its output (the activation value) by summing up its input weights, subtracting a threshold and passing the result to a non-linear function f (activation function). Outputs from neurons in a layer are fed as inputs to next layer. Thus, when an input tuple (EMBED Equation.3, , xn) is applied to the input layer of a network, an output tuple (EMBED Equation.3, , cm) is obtained, where ci has value 1 if the input tuple belongs to class ci and 0 otherwise.Their approach uses ANN to mine classification rules through three steps explained as follows:In the first step, a three-layer network is trained to find the best set of weights to classify the input data at a satisfactory level of accuracy. The initial weights are selected randomly from interval [-1, 1]. Then, these weights are updated according to the gradient of an error function. This training phase is terminated when the norm of the gradient falls below a threshold.The redundant links and nodes without any effects on performance are removed and therefore obtained pruned network.Comprehensible and concise classification rules are extracted from the pruned network in the form of: if (a1 EMBED Equation.3 v1) & (a2 EMBED Equation.3 v2) & & (an EMBED Equation.3 vn) then Cj where an ai is an input attribute value, vi is a constant like vi, and EMBED Equation.3 is a relational operator (=, EMBED Equation.3 EMBED Equation.3, <,>) and Cj is one of the class labels.k-Nearest Neighbor (kNN) Decision RuleThe k-nearest neighbor algorithm makes a classification for a given sample without making any assumptions about the distribution of the training and testing data. Each testing sample must be compared to all the samples in the training set in order to classify the sample. In order to make a decision using this algorithm, the distances between the testing sample and all the samples in the training set are first calculated. In this survey, the Euclidean distance is calculated, but, in general, any distance measurement may be used. Euclidean distance metric requires normalization of all features into the same range. At this point, the k closest neighbors of the given sample are determined where k represents an integer number between 1 and the total number of samples. The testing sample is then assigned the label most frequently represented among the k nearest samples (Duda et al., 2001). The value of k that is chosen for this decision rule has an affect on the accuracy of the decision rule. The k-nearest neighbor classifier is a nonparametric classifier that is said to yield good performance for optimal values of k. To test this, different values of k were tested in this survey. Finally, the value k =3, in kNN is chosen.Parzen Window classifierIn this approach a d-dimensional window is formed around all the training samples and then, based on the number of patterns that fit in those windows, the probability estimates of the different classes are made. This can be stated as follows (Duda et al., 2001):EMBED Equation.3where EMBED Equation.3is a d-dimensional hypercube in the feature space, and EMBED Equation.3 is a general probability distribution function. EMBED Equation.3 is the probability that the pattern fits in the given class. It is necessary to choose the form of EMBED Equation.3. In our case, the multivariate normal distribution is assumed forEMBED Equation.3. The windows are centered on the training points, hence, the mean is known, but there is no predefined method to determine the variance. Depending upon the problem under study, the variance is estimated by minimizing the error rate and maximizing the classifier performance. Therefore, it needs to be determined by trial and error. In all datasets we assume that the classes are independent and thus the covariance matrices for the Gaussian distribution are diagonal. Genetic Algorithm (GA)Many times the learning procedure is considered as a search through the space of representations. Genetic algorithm presents a powerful alternative to traditional search techniques. It has been inspired by a similar principle in nature. Evolution in nature is controlled through the following principles:Survival of the fittest: the strongest specimens have the highest chance to survive and reproduce, while the weak ones are likely to die before the reproduction stage.Reproduction: the fittest specimens recombine their genetic information, thus creating new specimens with somewhat new characteristics.Mutation leads to random changes in genetic information.The success of this search technique in the nature inspired some researchers to propose methods and develop algorithms that could be encoded in computer programs. A clear and simple introduction to the discipline of genetic algorithm has been made by Goldberg (1989). To start a successful attempt to cast a real problem in a setting that its solution is leveraged by means of a genetic algorithm, two important step are be paved: encoding the search space into chromosomes; defining a fitness function that plays the role of an evaluation function in heuristic search. The implementation of chromosome is typically in the form of bit strings.GA-AlgorithmMichalski et al. (1998) has presented the main steps of GA, that is reproduction, recombination, and mutation in the following algorithm:Construct the initial population as set of binary strings generated randomly or by some pre-specified mechanisms.Replicate the specimen in the population into a set of survivors by a mechanism that ensures that specimens with a higher fitness value have a higher chance of survival.Pair up all the survivors such that each has a mate. Next specific chunks of encoded data is swapped between mates. Mutation arises when a single bit flip-flops. If the fitness function has not improved through several cycles, stop; otherwise go to 2.Using the GA in pattern classificationAn important question arises in relation to classification: How to use Genetic Algorithm for pattern classification? There are two different approaches to applying GA in pattern recognition:Apply GA directly as a classifier. (Bandyopadhya and Murthy, 1995; Srickanth et al., 1995)Use GA as an optimization tool for resetting the parameters in other classifiers.Most application of GA in pattern recognition applies GA as an optimizer for some parameters in the classification process. Many researchers used GA in feature selection and feature extraction. GA is applied to find an optimal set of feature weights that improve classification accuracy. First, a traditional feature selection/extraction like Principal Component Analysis (PCA) is applied, then a classifier like k-NN is used to calculate the fitness function for GA. (Seidlecki, 1989; Pie et al., 1998). The combination of classifiers is another area that GA is used for optimization. Kuncheva and Jain (2000) used GA for selecting the features as well as selecting the types of individual classifiers in their design of Classifier Fusion System.Feature Selection and ExtractionFeature extraction and selection is a very important task in classification process. Why we need to use feature selection or extraction? Jain (2000) presented an insightful review of feature selection. We can denote to the benefits of feature selection and extraction as follows:Minimizing the costIn many real world applications, feature measurement to find the feature vectors is very costly, especially with a large sample size. Pie, Goodman, and Punch (1998) presented in the context of a biological pattern classification that the most important 8 out of 96 features gives 90% classification accuracy. They showed that feature selection has a great potential effect in minimizing the cost of extracting features and maintaining good classification results.Data VisualizationMany times for explanatory purposes we need to project high dimensional data in two or three dimension. The main concern is that how to protect the distance information and deployment of original data in two or three dimensions. The traditional approach in data visualization is linear projection. A more convenient choice is projecting the data onto a graph (Mori 1998). Chernoff Faces is another method that projects the feature space to cartoon face, by which one can visualize more than three features (Chenoff, 1973). Curse of DimensionalityGenerally, more features mean more information. Based on an ideal situation that we have an infinite number of training samples, the classification would be more accurate. Also, having more features from classification patterns improve the performance. Nevertheless, in real applications with a finite number of sample size, there is a maximum of performance is inversely proportional to the number of features (Duda and Heart, 1973). The demand for a large number of samples grows exponentially with the dimensionality of the feature space. This limitation is called the curse of dimensionality (Duda et al., 2001). Trunk (1979), has shown the curse of dimensionality problem through an exciting and simple example. This puts a limitation on non-parametric decision rules such as k-nearest neighbor. So, it is often desirable to reduce the dimensionality of the space by finding a new set of bases for the feature space.Feature Selection A through review of feature selection has been presented in Jain (2000). Jain et al. (1997) presented a good taxonomy of available feature selection algorithms based on pattern recognition or ANN, sub-optimal or optimal, single solution or multi-solution and deterministic or stochastic. What are the criteria for choosing a feature subset? A subset of features might be chosen in regards to the following points:The relevance to the classification result: that is we remove the irrelevant features intuitively. Langley (1994) has a useful review on relevance and feature selection.The correlation with the other features: The high correlation among features will add no more efficiency to classification, as it is explained by regression theory in statistics. If two features are highly correlated, one of the features is redundant, even though is relevant.John et al. (1994) has presented the definitions of Strong Relevance and Weak Relevance considering the correlations among feature samples. Hall and Smith (1998) formulated measure of Goodness of feature as follows:Good feature subsets contain features highly correlated (predictive of) with the class, yet uncorrelated with (not predictive of) each other.Feature Extraction Feature extraction is a linear or non-linear transformation of the original feature space. Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are the most commonly used techniques for feature extraction. PCA is an unsupervised technique, which is intended for feature extraction. The idea of the PCA is to preserve maximum variance after transformation of original features into new features. The new features are also called principal components or factors. Some factors carry more variance than other. If we limit the total variance preserved after such a transformation to some portion of original variance we can generally keep a smaller number of features. PCA performs this reduction of dimensionality by determining the covariance matrix. After PCA transformation in d-dimensional feature space the m (m < d) largest eigenvalues of the d x d covariance matrix are preserved. That is, the uncorrelated m projections in the original feature space with the largest variances are selected as the new features, thus the dimensionality reduces from d to m (Duda al et., 2001).LDA uses the same idea in the supervised learning environment. That is, it selects the m projections using the criterion that maximizes the inter-class variance while minimizes the intra-class variance (Duda al et., 2001). Chapter 4ExperimentsOur objective is to predict the students final grades based on their features, which are extracted from the homework data. We design, implement, and evaluate a series of pattern classifiers with various parameters in order to compare their performance in a real dataset of LON-CAPA system. This experiment provides an opportunity to study how pattern recognition and classification theory could be put into practice regarding to the logged data in LON-CAPA. The error rate of the decision rules is tested on one of the LON-CAPA dataset in order to compare the performance of each experiment. Results of individual classifiers, and their combination as well as error estimates are presented. The most difficult phase of the survey is properly pre-processing and preparing the data for classification. Some perl modules are developed to extract and segment the data from the logged database and visualize the useful data in statistical tables and graphical charts. More details of these tasks will be explained in part of this chapter for data acquisition and data representation. Dataset and Class LabelsAs the first step in our study, in order to have an experiment in student classification, we selected the student and course data of a LON-CAPA course, PHY183 (Physics for Scientists and Engineers I), which was held at MSU in spring semester 2002. This course integrated 12 homework sets including 184 problems. About 261 students used LON-CAPA for this course. Some of students dropped the course after doing a couple of homework sets, so they do not have any final grades. After removing those students, finally it remained 227 valid samples remained. You can see the grade distribution of the students in the following chart (figurer 4.1)We group the student regarding their final grades in several ways, which allows us classify the students in 3 ways: First: Let the 9 possible class labels be the same as students grades, as shown in table 4.1Class123456789Grade00.511.522.533.54# of students2010282343524128Percentage0.9%0.0%4.4%12.4%10.1%18.9%22.9%18.0%12.4%Second: We can label the students in relation to their grades and group them in three classes, high grades 3.5 and 4.0, middle grades 2.5 and 3, and low who has got the grades less than 2.5. 1HighGrade >= 3.56930.4%2Middle2.0 <Grade < 3.59541.8%3LowGrade <= 2.06327.8%Third: We can also categorize the students in regard to two class labels Passed grades higher than 2.0, and Failed for grades less than or equal to 2.0, as shown in table 4.3. 1Passed Grade > 2.016472.2%2FailedGrade <= 2.06327.8%Obviously, we can predict that the error rate in the first grouping should be higher than the others, because the distributions of the grades over 9 classes are so different. It is clear that we do not have enough data to model the first three classes in the training phase, and so the error rate would be high in the training phase. Before selecting any classifiers to learn the training data and choosing any model for prediction, we should discuss some pre-processing steps such as how to find the useful data from the logged data. Also, in what way we can visualize the various types of data. Well justify that the extracted data should undergo a normalization process before classification begins. Data Acquisition and Extracting the FeaturesThe problem is whether we can find the good features for classifying students! If so, we would be able to identify a predictor for any individual student after doing a couple of homework sets. With this information, we would be able to help a student use the resources better. As the first step to data mining, we want to make an initial effort to classify the students. Preprocessing student databasePreprocessing and finding the useful student data and segmenting may be a difficult task. As mentioned earlier, LON-CAPA, has two kinds of large data sets: Educational resources such as web pages, demonstrations, simulations, and individualized problems designed for use on homework assignments, quizzes, and examinations; Information about users, who create, modify, assess, or use these resources. Homework data has the following structure:resource.partid.opendate #unix time of when the local machine should let the #student inresource.partid.duedate #unix time of when the local machine should stop #accepting answersresource.partid.answerdate #unix time of when the local machine should #provide the correct answer to the studentresource.partid.weight # points the problem is worthresource.partid.maxtries # maximum number of attempts the student can haveresource.partid.tol # lots of possibilities here # percentage, range (inclusive and exclusive), # variable name, etc # 3% # 0.5 # .05+ # 3%+ # 0.5+,.005resource.partid.sig # one or two comma sepearted integers, specifying the # number of significatn figures a student must useresource.partid.feedback # at least a single bit (yes/no) may go with a # bitmask in the future, controls whether or not # a problem should say "correct" or notresource.partid.solved # if not set, problem yet to be viewed # incorrect_attempted == incorrect and attempted # correct_by_student == correct by student work # correct_by_override == correct, instructor override # incorrect_by_override == incorrect, instructor override # excused == excused, problem no longer counts for student # '' (empty) == not attempted # ungraded_attempted == an ungraded answer has been sumbitted and storedresource.partid.tries # positive integer of number of unsuccessful attempts # made, malformed answers don't count if feedback is # onresource.partid.awarded # float between 0 and 1, percentage of # resource.weight that the stundent earned.resource.partid.responseid.submissons # the student submitted string for the part.responseresource.partid.responseid.awarddetail # list of all of the results of grading the submissions # in detailed form of the specific failure # Possible values: # EXACT_ANS, APPROX_ANS : student is correct # NO_RESPONSE : student submitted no response # MISSING_ANSWER : student submitted some but not # all parts of a response # WANTED_NUMERIC : expected a numeric answer and # didn't get one # SIG_FAIL : incorrect number of Significant Figures # UNIT_FAIL : incorrect unit # UNIT_NOTNEEDED : Submitted a unit when one shouldn't # NO_UNIT : needed a unit but none was submitted # BAD_FORMULA : syntax error in submitted formula # INCORRECT : answer was wrong # SUBMITTED : submission wasn't gradedThe original data are stored with escape sequence codes like this:1007070627:msul1:1007070573%3a%2fres%2fadm%2fpages%2fgrds%2egif%3aminaeibi%3amsu%261007070573%3a%2fres%2fadm%2fpages%2fstat%2egif%3aminaeibi%3amsu%261007070574%3amsu%2fmmp%2flabquiz%2flabquiz%2esequence___1___msu%2fmmp%2flabquiz%2fnewclass%2ehtml%3aminaeibi%3amsu%261007070589%3amsu%2fmmp%2flabquiz%2flabquiz%2esequence___5___msu%2fmmp%2flabquiz%2fproblems%2fquiz2part2%2eproblem%3aminaeibi%3amsu%261007070606%3a%2fadm%2fflip%3aminaeibi%3amsu%261007070620%3a%2fadm%2fflip%3aminaeibi%3amsu%261007070627%3a%2fres%2fadm%2fpages%2fs%2egif%3aminaeibi%3amsu%261007070627%3a%2fadm%2flogout%3aminaeibi%3amsu To sense the data we use the following Perl module function: my$str; my $line; open (LOG ,$file);while ($line =<LOG>) { my ($dumptime,$host,$entry)=split(/\:/,$line); my$str = unescape($entry); my ($time,$url,$usr,$domain,$store,$dummy)=split(/\:/,$str);   my $string = escape($store);   foreach(split(/\&/,$string)){ print "$time $url$usr domain \n";   }}sub unescape {	my $str=shift;$str =~ s/%([a-fA-F0-9][a-fA-F0-9])/pack("C",hex($1) )/eg; return$str;}After passing the data from this filter we have the following results:1007070573 /res/adm/pages/grds.gif minaeibi /res/adm/pages/stat.gif1007670091 /res/adm/pages/grds.gif minaeibi /adm/flip1007676278 msu/mmp/labquiz/labquiz.sequence___2___msu/mmp/labquiz/problems/quiz1part1.problem 1007743917 /adm/logout minaeibi1008203043 msu/mmp/labquiz/labquiz.sequence___1___msu/mmp/labquiz/newclass.html minaeibi1008202939 /adm/evaluate minaeibi /adm/evaluate1008203046 /res/adm/pages/g.gif minaeibi /adm/evaluate1008202926 /adm/evaluate minaeibiThe student data restored from .db files in student directory and is fetched into a hash table. The special hash keys keys, version and timestamp were evaluated from the hash. The version will be equal to the total number of versions of the data that have been stored. The timestamp attribute is the UNIX time the data was stored. keys is available in every historical section to list which keys were added or changed at a specific historical revision of a hash. We extract some of the features from a structured homework data, which is stored as particular URLs. For example the result of solving homeworks problem by students could be extracted from resource.partid.solved, the total number of the students for solving the problem could be extracted from resource.partid.tries, and so forth. One of the difficult phase to data mining in LON-CAPA system, is gathering the student and course data, which are distributed in several locations. Finding the relevant data and segmentation phase may be complicated as well. Preprocessing Activity.logSince spring semester 2002, LON-CAPA has logged every activity of every student who has used online educational resources and their recorded paths through the web. This information is stored in activity.log which is located in a courses directory. The data stored in activity.log includes user name, time and resource URL. We can divide these data into six types of URLs, listed below, regarding their importance for data mining: 1. problems: are the most useful data. i.e. msu/mmp/kap14/kap14.sequence___33___msu/mmp/kap14/problems/cd418a.problem 2. html pages to those are some links in the problems. i.e. msu/mmp/kap14/kap14.sequence___5___msu/mmp/kap14/cd396.htm 3. The images, which are loaded in above html pages. i.e. /res/msu/mmp/kap14/picts/backsoun.gif .4. loncapa routines: i.e. /adm/navmaps,  or  /adm/roles, or  /adm/logout.5. Posted data by students: i.e. resource.0.11.submission=27.11 6. remote control gif files: i.e.: /res/adm/pages/v.gif So, the activity.log usually grows faster, when students have more access to the educational resources. We brought a sample of different types of data, which are logged in activity.log after a preprocessing phase as follows:  144) 1010955846: studentX --> /adm/navmaps 145) 1010955205: studentX --> /res/msu/mmp/kap14/picts/beta_eqn.gif 147) 1010955988: studentX --> /adm/navmaps 148) 1010955998: studentX --> msu/mmp/kap14/kap14.sequence___5___msu/mmp/kap14/cd396.htm 149) 1010955999: studentX --> /res/msu/mmp/kap14/picts/velocity_eqn3.gif 150) 1010956000: studentX --> /res/msu/mmp/kap14/picts/time_eqn.gif 151) 1010954609: studentX --> /res/adm/pages/grds.gif 152) 1010954611: studentX --> /res/msu/mmp/wordproc.gif 153) 1010954626: studentX --> /res/adm/pages/i.gif 154) 1010955717: studentX --> msu/mmp/kap14/kap14.sequence___1___msu/mmp/kap14/cd392.htm 155) 1010955717: studentX --> /res/msu/mmp/kap14/picts/backsoun.gif 156) 1010955920: studentX --> msu/mmp/kap14/kap14.sequence___3___msu/mmp/kap14/cd394.htm 157) 1010955921: studentX --> /res/msu/mmp/gifs/demo.gif 163) 1010955754: studentX --> msu/mmp/kap14/kap14.sequence___2___msu/mmp/kap14/cd393.htm 164) 1010955756: studentX --> /res/msu/mmp/kap14/picts/asound.jpg 166) 1010955999: studentX --> /res/msu/mmp/gifs2/example.gif 173) 1010955687: studentX --> /res/adm/pages/u.gif 174) 1010955688: studentX --> /res/adm/pages/e.gif 175) 1010956528: studentX --> msu/mmp/kap14/kap14.sequence___33___msu/mmp/kap14/problems/cd418a.problem 176) 1010956536: studentX --> msu/mmp/kap14/kap14.sequence___33___msu/mmp/kap14/problems/cd418a.problem 178) 1010956536: studentX --> msu/mmp/kap14/kap14.sequence___33___msu/mmp/kap14/problems/cd418a.problem 179) Sent data resource.0.11.submission=27.11 180) 1010956702: studentX --> msu/mmp/kap14/kap14.sequence___33___msu/mmp/kap14/problems/cd418a.problem Figure 4.2: A sample of  Activity.log data, which is extracted some preprocessing phase Extractable FeaturesWe can explore the following features from the data, which are stored by the LON-CAPA system: Total number of correct answers. (Success rate)Getting the problem right on the first try, vs. those with high number of tries. (Success at the first try)Total number of tries for doing homework. (Number of attempt before correct answer is derived)Hours until correct. Time at which the student got the problem correct. Usually better students get the homework completed earlier. Time spent on the problem untill solved. (Difference between time of last successful submission and the first time opened the problem).Total time spent on the problem whether got correct answer or not. (Difference between time of the last submission and the first time opened the problem).Participating in the communication mechanisms, vs. those working alone.Reading the material before attempting homework vs. attempting first and then read up on it.Submitting a lot of attempts in a short amount of time without looking up material in between, vs. those giving it one try, reading up, submitting another one, etc.Giving up on a problem versus students continuing trying up to the deadline.It might be interesting to group students with time of the first log on (beginning of assignment, middle of the week, last minute) and correlate this with the number of tries or number of solved problems. A student who gets all correct answers will not necessarily be in the successful group if they took an average of 5 tries per problem, but it should be verified from this research. At this time we were able to extract the first six features in course PHY183 SS02 that we have chosen for the classification experiment.Visualizing the data in LON-CAPA (Statistical Information)Usually, instructors or course coordinators wish to assess the students educational situation or evaluate the problems presented in the course, after the students used the educational materials. We developed some perl modules that provide the statistical information for instructors and course-coordinators. Student AssessmentWe extract from student data some reports of the current educational situation of every student as you can see in table 4.4.  A Y shows that the student has solved the problem and N shows a failure.  A - denotes an un-attempted problem. The numbers in the right column show the total number of tries of the student in solving the corresponding problems.Top of Form# Homework Set TitleResultsTries1 msu/mmp/phy183.sequence 2 msu/mmp/kap1/calckap1.sequence YYYYYYYYYYYYY 1,1,1,2,1,1,1,1,1,7,9,3,23 msu/mmp/kap2/calckap2.sequence YYNYYYYNNYYYYYYYY 10,1,0,1,1,2,1,4,5,1,1,1,3,2,1,1,14 msu/mmp/kap3/calckap3.sequence YYYYYYYYNYYYYYYYYYY 4,3,5,1,1,8,2,3,20,1,1,1,1,1,2,3,2,2,35 msu/mmp/kap4/calckap4.sequence NYYYYYYYYYYYYYYY 20,1,1,1,3,3,2,3,4,2,3,2,1,1,2,56 msu/mmp/kap5/calckap5.sequence YYYYYYYYYYY-YY 5,2,1,9,12,1,3,12,1,2,1,,1,37 msu/mmp/kap6/calckap6.sequence YYYYYYYYYYYYYY 3,2,4,2,1,1,2,1,1,9,2,3,2,28 msu/mmp/kap7/calckap7.sequence YYYYYYYYYYYYYYYYYY 4,1,3,1,10,4,1,1,2,1,1,2,1,2,1,3,1,39 msu/mmp/kap8/calckap8.sequence YYYYYYYYYYYYYYY 4,3,1,2,3,3,4,3,3,1,1,4,1,1,710 msu/mmp/kap9/calckap9.sequence YYYYN-NYYNY 1,1,1,2,1,,2,2,1,6,411 msu/mmp/kap10/calckap10.sequence YYYYYYYYYYYY 2,1,1,1,1,1,1,1,1,1,1,112 msu/mmp/kap11/calckap11.sequence ----------------- 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0Table 4.4: A sample of a student homework results and triesLON-CAPA also provides a quick review of students tries on different problems of a course.  The instructor may monitor the number of tries of every student in each map and its problems. The number of solved problems in a map is shown in the end of each map. The overall solved problems and total number of problems in the map are shown for every individual student. A small sample of this report is shown in figure 4.3.username1:msu ! 001 ! 1*11*121  8  1231.31423212  12   2111211284.131  13   231113112221 12  162 / 188username2:msu ! 003 ! 12113162  8  1+11  1  21x111 10  11211322246132  14  ############    0  149 / 188 1..9: correct by student in 1..9 tries  		 *: correct by student in more than 9 tries +: correct by override  				  -: incorrect by override .: incorrect attempted                                                      #: ungraded attempted  : not attempted 					 x: excusedFigure 4.3. Chart of map, problems, and students tries, and a quick statistics of solved problemsStatistics TableLON-CAPA presents a lot of statistical information about every problem in a table like shown in  table 4.5, we call it Stats Table. Every part of multi-part problems is distinguished as a separate problem. The multi-instance problem is also considered separately, because a particular problem or one part of it might be used in different maps. Finally, the array, which includes all computed information from all students, sorted according to the problem order, underlying homework sets order. Therefore, in this step we can compute the following statistical information:#Stdnts: 	Total number of students who take a look at the problem.(Let #Stdnts is equal to n)Tries: 	Total number of tries to solve the problem (EMBED Equation.3where EMBED Equation.3denote a student try).Mod: 	Mode, Maximum Number of Tries for solving the problem.Mean: 	Average Number of the Tries. EMBED Equation.3=EMBED Equation.3#YES: 	Number of students solved the problem correctly.#yes:	Number of students solved the problem by override. Sometimes, a student gets a correct answer after talking with the instructor. This type of correct answer is called corrected by override.%Wrng: 	Percentage of students tried to solve the problem but still incorrect. EMBED Equation.3 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/mmp/kap1/calckap1.sequence" \t "_blank" Homework Set 1 P#Homework Set Order#StdntsTriesModMean#YES#yes%WrngDoDiffS.D.Skew.D.F. 1stD.F. 2nd1 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/01_Math_1/msu-prob11.problem" \t "_blank" Calculator Skills25626731.0425600.00.040.25.70.030.002 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/01_Math_1/msu-prob10.problem" \t "_blank" Numbers256414171.6225500.40.381.65.70.110.023 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/03_Units_Scaling/msu-prob22.problem" \t "_blank" Speed256698132.7325500.40.632.21.90.060.024 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/01_Math_1/msu-prob13.problem" \t "_blank" Perimeter25638871.5225500.40.340.92.4-0.000.025 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/devolibrary/type-math/fraction-rlt-235.problem" \t "_blank" Reduce a Fraction25631541.2325600.00.190.52.30.010.006 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/devolibrary/type-math/fract-add-sub-div-p11.problem" \t "_blank" Calculating with Fractions25639371.5425500.40.350.92.00.150.027 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/01_Math_1/msu-prob04.problem" \t "_blank" Area of a Balloon254601122.3724702.80.591.81.8-0.05-0.028 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/01_Math_1/msu-prob07.problem" \t "_blank" Volume of a Balloon252565112.2424303.60.571.92.0-0.06-0.039 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/01_Math_1/msu-prob12.problem" \t "_blank" Numerical Value of Fraction25626841.0525600.00.040.23.40.01.0010 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/03_Units_Scaling/msu-prob17.problem" \t "_blank" Units2561116204.3624603.90.784.21.90.180.0311 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/06_Vectors_Scalars/msu-prob07.problem" \t "_blank" Vector versus Scalar254749112.9525101.20.662.21.1-0.05-0.0512 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/06_Vectors_Scalars/msu-prob10.problem" \t "_blank" Adding Vectors2531026204.0625001.20.763.61.80.140.0013 HYPERLINK "http://deepthought.lite.msu.edu/res/msu/physicslib/msuphysicslib/02_Math_2_Trig/msu-prob13.problem" \t "_blank" Proximity249663192.6623913.60.642.32.80.11-0.10Table 4.5: Statistics table includes general statistics of every problem of the courseS.D.: 	Standard Deviation of the students tries. EMBED Equation.3Skew.: 	Skewness of the students tries. EMBED Equation.3DoDiff: 	Degree of Difficulty of the problem. EMBED Equation.3As you see Degree of Difficulty is always between 0 and 1. This is a good factor for an instructor to determine whether a problem is difficult, and what is the degree of this difficulty. Thus, DoDiff of each problem is saved in its meta data.Dis.F.:	Discrimination Factor is an standard for evaluating how much a problem discriminates between the upper and the lower students.  First, all of the students are sorted according to a criterion. Then, %27 of upper students and %27 lower students are selected from the sorted students applying the mentioned criterion. Finally we obtain the Discrimination Factor from the following difference:Applied a criterion in %27 upper students - Applied the same Criterion in %27 lower students.Discrimination Factor is a number in interval [-1,1]. If this number is close to 1, it shows that only upper students have solved this problem. If it is close to 0 it shows that the upper students and the lowers are approximately the same in solving the problem. If this number is negative, it shows that the lower students have more successes in solving the problem, and thus this problem is very poor in discriminating the upper and lower students.We compute the Discrimination Factor from two criteria:1st Criterion for Sorting the Students: EMBED Equation.32nd Criterion for Sorting the Students: EMBED Equation.3Graphical chart Two important features of the stats table might be presented through the graphical charts. That is, a user could see the content of %wrong column and degree of difficulty of problems in the graphical chart as shown in figure 4.4 and 4.5 for homework set 1 in course PHY183 SS02. These graphical charts are produced dynamically by calling a CGI scripts, (graph.gif) which is located in /home/httpd/cgi-bin/Figure 4.4: Degree of difficulty graph 				Figure 4.5: %Wrong graphProblem AnalysisConceptual option response problems, in which the students are given several concepts that are randomly assigned to each student, are more difficult than numerical simple problems.  Instructors usually want to see the students regarding every particular concept separately. LON-CAPA provides all response option problems in one table as shown in the table 4.6. # Problem Title Resource 1 Numbers /res/msu/physicslib/msuphysicslib/01_Math_1/msu-prob10.problem 2 Speed /res/msu/physicslib/msuphysicslib/03_Units_Scaling/msu-prob22.problem 3 Units /res/msu/physicslib/msuphysicslib/03_Units_Scaling/msu-prob17.problem 4 Vector versus Scalar /res/msu/physicslib/msuphysicslib/06_Vectors_Scalars/msu-prob07.problem 5 Adding Vectors /res/msu/physicslib/msuphysicslib/06_Vectors_Scalars/msu-prob10.problem 6 Traveling Car /res/msu/physicslib/msuphysicslib/05_1D_Motion/msu-prob16.problem 7 Atwood Machine /res/msu/kashy/Testing/randomlabel/atwood3T2M.problem 8 Sliding mass concepts /res/msu/physicslib/msuphysicslib/10_Motion_W_Friction/msu-prob32.problem 9 Work, Power, Energy concept /res/msu/physicslib/msuphysicslib/12_Work_Power_Energy/msu-prob27.problem10 Bead on a Wire /res/msu/physicslib/msuphysicslib/13_EnergyConservation/msu-prob32.problem 11 Atwood Machine /res/msu/physicslib/msuphysicslib/20_Rot2_E_Trq_Accel/msu-prob23.problem 12 Flinstone Bowling /res/msu/physicslib/msuphysicslib/21_Rot3_AngMom_Roll/msu-prob38.problem Table 4.6: Option response problems in course PHY183 SS02When a particular option response problem is selected, all data about this problem is restored, for every student. Different versions of students submissions are evaluated. The results are presented in a graphical chart as well as a numerical table, as shown in Figures 4.6, and 4.7, and table 4.7. For example, if we select the analysis of:/res/msu/kashy/Testing/randomlabel/atwood3T2M.problem INCLUDEPICTURE "http://deepthought.lite.msu.edu/cgi-bin/graph.gif?Atwood_Machine&Concepts&Answers&1780&6&1342,585,1263,1087,757,1354&433,1190,512,688,1018,421" \* MERGEFORMATINET Figure 4.6: Atwood Machine option response problem in HW3 	# Concept Correct Wrong 1Two masses have same acceleration if the two the string does not stretch. 1342 433 2Weight of the two masses is greater than the tension of the string attached to the ceiling. 585 1190 3The top tension is equals the two bottom tensions. (massless pulley) 1263 512 4Tension holding the two masses are equal if mass of pulley=0 1087 688 5Sub-System accelerates upwards or downwards accordingly 757 1018 6Center of mass accelerates downward 1354 421 From:[Thu Jan 24 00:46:22 2002] To: [Mon Feb 4 23:59:59 2002]63884245Table 4.7: Table of student tries for Atwood Machine Problem according to every concept in one time interval.The data of students tries, the correct answers and the wrong answers are shown in a table 4.7. In the last row of the table you can see the time interval of this data and the overall correct and wrong answers separately. If an instructor wants to see the students tries in different time intervals, he/she could set the number of intervals from 1 to 7 time intervals, and then recompute the analysis. Thus, an instructor would be able to check whether the students have more wrong answers during the first days of opening the homework set, and how many students have tried during the first or the second interval. Since the problems are individualized he/she might be able to see how many students have tried to solve the problem after communicating with each other and understanding the concept.  The charts and tables of students tries can be shown in 2 or more time intervals. So if the homework should be done in one week, an instructor would be able to observe the distribution of students tries every day separately after choosing the 7 time intervals. ClassifiersPattern recognition has a wide variety of applications in many different fields, such that it is not possible to come up with a single classifier that can give good results in all the cases.  The optimal classifier in every case is highly dependent on the problem domain. In practice, one might come across a case where no single classifier can classify with an acceptable level of accuracy. In such cases it would be better to pool the results of different classifiers to achieve the optimal accuracy. Every classifier operates well on different aspects of the training or test feature vector. As a result, assuming appropriate conditions, combining multiple classifiers may improve classification performance when compared with any single classifier. Non-Tree ClassifiersThe scope of this survey is restricted to compare some popular non-parametric pattern classifiers and a single parametric pattern classifier according to the error estimate. Six different classifiers over one of the LON-CAPA datasets are compared in this study. The classifiers used in this study include Quadratic Bayesian classifier, 1-nearest neighbor (1-NN), k-nearest neighbor (k-NN), Parzen-window, multi-layer perceptron (MLP), and Decision Tree.  These classifiers are some of the common classifiers used in most practical classification problems. After some preprocessing operations were made on the dataset, the error rate of each classifier is reported. Finally to improve performance a combination of classifiers is presented.Combination of Multiple Classifiers (CMC)In combining multiple classifiers we want to improve classifier performance. There are different ways one can think of combining classifiers:The simplest way is to find the overall error rate of the classifiers and choose the one, which has the least error rate on the given dataset. We call it an offline CMC. This may not really seem to be a CMC, however, in general, it has a better performance than individual classifiers. The output of this combination will simply be the best performance in each column in Figures 4.9, and 4.11.The second method, which we call online CMC, uses all the classifiers followed by a vote. The class getting maximum votes from the individual classifiers will be assigned to the test sample. This method intuitively seems to be better than the previous one. However, when we actually tried this on some cases of our dataset, the results were not better than the best result in previous method. So, we changed the rule of majority vote from getting more than 50% votes to getting more than 75% votes. We got a significant improvement over offline CMC. Table 4.10 shows the actual performance of the individual classifier and online CMC over all three datasets.Woods et. al. (1995) suggested a third method, which is called DSC-LA (Dynamic Selection of Classifiers based on the Local Accuracy estimates). This method takes a particular test sample, investigates the local neighborhood of that sample using all the individual classifiers and the one, which performs best is chosen for the decision-making.Besides CMC, we also show the results for an Oracle which chooses the correct results if any of the classifiers did so, as Woods et al. (1995) has presented in his article. NormalizationHaving assumed in Bayesian and Parzen-window classifiers that the features are normally distributed, it is necessary that the data for each feature is normalized. This ensures that each feature has the same weight in the decision process. Assuming that the given data is Gaussian distributed, this normalization is performed using the mean and standard deviation of the training data. In order to normalize the training data, it is necessary first to calculate the sample mean  EMBED Equation.3  , and the standard deviation  EMBED Equation.3   of each feature, or column, in this dataset, and then normalize the data using the following equation:EMBED Equation.3This ensures that each feature of the training dataset has a normal distribution with a mean of zero and a standard deviation of one. In addition, the kNN method requires normalization of all features into the same range. However, we should be cautious in using the normalization before considering its effect on classifiers performance. Table 4.4 shows comparison of Error Rate and its Standard Deviation using the classifiers in both normalized and un-normalized data in the case of 3 classes.3-ClassesWith NormalizationWithout NormalizationClassifierError rateS.DError rateS. D.Bayes0.49240.07470.55280.03741NN0.52200.03440.58640.041KNN0.51440.04360.58560.0491Parzen0.50960.04080.7280MLP0.45240.02850.6240CMC0.29760.03990.38720.0346Oracle0.10880.03230.16480.0224Thus, we tried the classifiers with and without normalization. As you see in table 4.8 we have improvement in most classification results after normalization. Here we have two important findings:1. Parzen-Window classifier and MLP do not work properly without normalizing the data. So, we have to normalize data for using these two classifiers.2. Decision tree classifiers do not have any improvement on their classification performance, so we ignore normalization in tree classifiers. We will study the decision tree classifier later. We did not introduce the Decision Tree classifiers results in Table 4.4.Comparing 2-fold and 10-fold Cross-ValidationIn k-fold cross-validation, we divide the data into k subsets of approximately equal size. We train the data k times, each time leaving out one of the subsets from training, but using only the omitted subset to compute the error threshold of interest. If k equals the sample size, this is called "Leave-One-Out" cross-validation. (Duda et al. 2001; Kohavi, 1995). Leave-One-Out cross-validation provides an almost unbiased estimate of true accuracy, though at a significant computation cost.  In this survey we used both 2-fold and 10-fold cross validation. In 2-fold cross-validation, the order of the observations, both training and test, were randomized before every trial of every classifier. Then every sample was divided amongst the test and training data, with 50% going to training, and the other 50% going to test. This meant that testing was completely independent, as no data or information was shared between them. It is noticeable that the portion of data from each class was the same portion of classes in original dataset as well.  Then we classified the test sets after the training phase of all the classifiers on the same training and test data. We repeated this randomly cross validation ten times for all classifiers. In 10-fold cross-validation, the available data (here, the 227 students data) are divided into 10 blocks containing roughly equal number of cases and class-value distributions. For each block (10% of data) in turn, a model is developed using the data in the remaining blocks (90% of data, the training set) and then evaluated on the cases in the hold-out block (the test set). Each case is thus tested on a model that was developed without reference to it and when all the tests (10 tests) are completed, each sample in the data will have been tested exactly once. The average performance on the tests is then used to predict the true accuracy of a model developed from all the data. For values like 10 or more, this estimate is pretty reliable and is much more accurate than a resubstitution estimate. 3-Classes10-fold Cross-Validation2-fold Cross-ValidationClassifierError RateS.D.Error RateS.D.Bayes0.50.08990.55360.02191NN0.49570.06860.58320.0555KNN0.51740.08060.5760.0377Parzen0.53910.0850.49920.036MLP0.43040.08060.45120.0346CMC0.3130.0840.32240.0354Oracle0.19570.05520.14560.0462Table 4.9 shows comparison of Error Rate and its Standard Deviation of using the classifiers in both 2-fold and 10-fold cross-validation in the case of the 3-Classes. You can see that the 10-fold cross-validation in relation to individual classifier has slightly better accuracy than 2-fold cross validation, but in relation to combination of classifiers (CMC) there is no a significant difference. Therefore we selected the 10-fold cross validation for error estimation in this survey.Results, Error EstimationThe experimental results were averaged and presented in some graphical charts. They show the effect of selecting the data randomly on the average error rate.  The average of error rate and its standard deviation, which is associated with each classifier, is shown in the tables as well as the graphical chart. Each table summarizes the results of all the classifiers on our dataset. The standard deviation of error rate shows the variance of the error rate during cross validation. The error rate is measured in each round of cross validation by:EMBED Equation.3After 10 rounds, the average error rate and its standard deviation are computed and then plotted. This metric was chosen due to its ease of computation and intuitive nature. Figure 4.8 and 4.9 show the comparison of classifiers error rate when we classify the student into two categories, Passed and Failed. You can see that the best performance is for kNN with 82% accuracy, and the worst classifier is Parzen-window with 75% accuracy. CMC in the case of 2-Classes classification has 87% accuracy.It is noticeable that these processes were done after we had found the optimal k in the kNN algorithm and after we had tuned the parameters in MLP and after we had found optimal h in Parzen-window algorithm. Finding the best k for kNN is not difficult, and you can see its performance is the best in the case of 2-Classes, though is not as good as the other classifiers in the case of 3-Classes, as is shown in figure 4.11. Working with Parzen-window classifier is not simple because finding the best height for its window is not easy. The MLP classifier is the most difficult classifier to work with. Many parameters have to be set properly to make it work optimally. For example, after many trials and errors we found that the structure of the network in the case of 3-classes, the 4-3-3 (one hidden layer with 3 neurons in hidden layer) works better, and in the case of 2-classes if we have 2 hidden layer with 2 or 4 neurons in each hidden layer would lead to a better performance. There is no algorithm to set the number of epochs and learning rates in the MLP. However, sometimes MLP has the best performance in our datasets, as you can see in the Table 4.7, MLP is slightly better than the other individual classifier. In the case of 9-Classes we could not set the MLP to work properly, so we have not brought the result of MLP classifier into the final result in table 4.10.As predicted before, the error rate in 9-Classes is much higher than the other cases. The final result of the five classifiers and their combination in the case of 2-Classes, 3-Classes, and 9-Classes are shown in Table 4.8In the case of 9-classes 1-NN works better than other classifiers. Regarding the final results in Table 4.8, CMC has the better performance in relation to individual classifiers. In the case of 2-Classes it got 5% improvement, in the case of 3-Classes it got 20% improvement, and in the case of 9-Classes it got 22% improvement in relation to the best individual classifiers in the corresponding case.Error RateClassifier2-Classes3-Classes9-ClassesBayes0.23640.51430.771NN0.23180.49520.71KNN0.17730.49520.725Parzen0.250.5190.795MLP0.20450.4905-CMC0.13180.29050.49Oracle0.08180.1619-One important finding is that when our individual classifiers are working well and has a high level of accuracy; the benefit of combining classifiers is small. Thus, CMC has little improvement in classification performance, but when we have weak learner classifiers CMC has a significant improvement in accuracy.We tried to get better performance considering the degree of difficulty of problems. By choosing some specific conceptual subsets of the students data, we unfortunately did not obtain a significant increase in accuracy with this parameter. In the next section, when we explain the results of decision tree classifiers on our data set. We also will discuss the relative importance of the features, and which features have a higher correlation with category labels.Decision Tree-based softwareDecision trees have proved to be valuable tools for the description, classification and generalization of data. Many users find decision trees easy to use and understand. As a result, users more easily trust decision tree models than they do "black box" models, such as those produced by neural networks. Many tools and software have been developed to implement decision tree classification. Lim et al. (2000) has a insightful study about comparison of prediction accuracy, complexity, and training time of 33 classification algorithms; 22 decision tree, 9 statistical, and 2 neural network algorithms are compared on thirty-two datasets in terms of classification accuracy, training time, and (in the case of trees) number of leaves. In this survey we used C5.0, CART, QUEST, and CRUISE software to have tree-based classification. We also used some statistical software for multiple linear regression on our dataset. First we have a brief view of the capability, features and requirements of these software packages. Then we gather some of the results and compare their accuracy to non-tree based classifiers. C5.0Decision tree learning algorithms, for example, ID3, C5.0 and ASSISTANT (Cestnik et al., 1987), search a completely expressive hypothesis space and are used to approximate discrete valued target functions represented by a decision tree. In our experiments the C5.0 inductive learning decision tree algorithm was used. This is a revised version of C4.5 and ID3 (Quinlan 1986, 1993) and includes a number of additional options for implementation. For example, the Boosting option causes a number of classifiers to be constructed - when a case is classified, all of these classifiers are consulted before a decision is made. Boosting will often give a higher predictive accuracy at the expense of increased classifier construction time. For our experiments however, dataset boosting was not found to give any improvement in prediction accuracy. When a continuous feature is tested in a decision tree, there are branches corresponding to the conditions: Feature Value EMBED Equation.3 Threshold and Feature Value > Threshold, for some threshold chosen by C5.0. As a result, small movements in the feature value near the threshold can change the branch taken from the test. There have been many methods proposed to deal with continuous features (Quinlan, 1988; Chan et al., 1992; Ching et al., 1995). An option available in C5.0 uses fuzzy thresholds to soften this knife-edge behavior for decision trees by constructing an interval close to the threshold. This interval plays the role of margin in neural network algorithms. Within this interval, both branches of the tree are explored and the results combined to give a predicted class. Decision trees constructed by C5.0 are post pruned before they are presented to the user. The Pruning Certainty Factor governs the extent of this simplification. A higher value produces more elaborate decision trees and rule sets, while a lower value causes more extensive simplification. In our experiment a certainty factor of 25% was used. If we change the certainty factor we may obtain different results.C5.0 needs four types of files for generating the decision tree for a given data set, out of which two files are optional:The first file is the .names file. It describes the attributes and classes. The first line of the .names file gives the classes, either by naming a discrete attribute (the target attribute) that contains the class value, or by listing them explicitly. The attributes are then defined in the order that they will be given for each case. The attributes can be either explicitly or implicitly defined. The value of an explicitly defined attribute is given directly in the data. The value of an implicitly defined attribute is specified by a formula. In our case, data attributes are explicitly defined. The second file is the .data file. It provides information on the training cases from which C5.0 will extract patterns. The entry for each case consists of one or more lines that give the values for all explicitly defined attributes. The '?' is used to denote a value that is missing or unknown. Our dataset had no missing features. Also, 'N/A' denotes a value that is not applicable for a particular case. The third file used by C5.0 consists of new test cases on which the classifier can be evaluated and is the .test file. This file is optional and, if used, has exactly the same format as the .data file. We gave a .test file for our dataset. The last file is the .costs file. In applications with differential misclassification costs, it is sometimes desirable to see what affect costs have on the construction of the classifier. In our case all misclassification costs were the same so this option was not implemented.  After the program executed for the PHY183 SS02 dataset we got the output results for both the training and testing data. A confusion matrix is generated showing the misclassifications.  The confusion matrices for three types of classification in our dataset that are, 2-Classes, 3-Classes and 9-Classes are in appendix B. You can also find some rule set samples resulted from the rule-set option in C5.0, as well as a part sample of the tree produced by C5.0 in appendix B. Using 10-fold cross validation we got 79.3% accuracy in 2-Classes, 56.8% accuracy in 3-Classes, 25.6% accuracy in 9-Classes. One important and exciting experiment using C5.0 is to use a training and test set; and thus at least a 10-fold cross-validation to get a trustable result. For example, if we select one split in 3-Classes we might get about 75% accuracy in training set, and with boosting process we could get accuracy unto 90% or 95%. Unfortunately, this is overfitting, or overtraning, and we would not be able to generalize this result and this complex training model to test the unseen data.CARTCART uses an exhaustive search to identify useful tree structures of data. It can be applied to any dataset and can proceed with no parameter setting. Comparing CART analyses with stepwise logistic regressions or discriminant analysis, CART typically performs better on the learning sample. Listed below are some technical aspects of CART: CART is a nonparametric procedure and does not require specification of a functional form. CART uses a stepwise method to determine splitting rules. Thus, no advance selection of variables is necessary, although certain variables such as ID numbers and reformulations of the dependent variable should be excluded from the analysis. Also, CART performance can be enhanced by a proper feature selection and creation of predictor variables. There is no need to experiment with monotone transformations of the independent variables, such as logarithms, square roots or squares. In CART, creating such variables will not affect the trees produced unless linear combination splits are used. Outliers among the independent variables generally do not affect CART because splits usually occur at non-outlier values. Outliers in the dependent variable are often separated into nodes where they no longer affect the rest of the tree. CART does not require any preprocessing of the data. In particular continuous variables do not have to be recoded into discrete variable versions prior to analysis. While the CART default is to split nodes on single variables, it will optionally use linear combinations of non-categorical variables. For each split in the tree, CART develops alternative splits (surrogates), which can be used to classify an object when the primary splitting variable is missing. Thus, CART can be effectively used with data that has a large fraction of missing values.One of the advantages of CART is presenting the importance of independent variables in predicting both  classification mode and regression mode. Each variable in the CART tree has an importance score based on how often and with what significance it served as primary or surrogate splitter throughout the tree. The scores reflect the contribution each variable makes in classifying or predicting the target variable, with the contribution stemming from both the variables role in primary splits and its role as a surrogate splitter (Dan and Colla, 1998). In tables 4.11 and 4.12 the importance of the six features (independent variables) are scored in the case of 2-classes with Gini splitting criterion and 3-classes with Entropy splitting criterion respectively.VariableTOTCORR100.00||||||||||||||||||||||||||||||||||||||||||TRIES56.32|||||||||||||||||||||||FIRSTCRR4.58|TOTTIME0.91SLVDTIME0.83DISCUSS0.00The results in table 4.11 and 4.12 show that the most important feature which has the most correlation with the predicted variables is Total number of Correct answers, and the least useful variable is Number of Discussion. If we consider economical aspect of computation cost we could remove the less important features.In our experiment we used both 10-fold Cross-Validation and Leave-One-Out method. We found that in the case of 2-Classes and 3-Classes the error rates in training sets are not improved, but the misclassifications in the test sets are improved when we switch from 10-fold Cross-Validation to Leave-One-Out, but in the case of 9-Classes both training and testing sets are improved significantly as it shown in Table 4.13, Table 4.14, Figure 4.12, and Figure 4.13.  Why? Splitting Criterion2-Classes3-Classes9-ClassesTrainingTestingTrainingTestingTrainingTestingGini17.2%19.4%35.2%48.0%66.0%74.5%Symmetric Gini17.2%19.4%35.2%48.0%66.0%74.5%Entropy18.9%19.8%37.9%52.0%68.7%76.2%Twoing17.2%19.4%31.3%47.6%54.6%75.3%Ordered Twoing17.2%20.7%31.7%48.0%68.3%74.9%Splitting Criterion2-Classes3-Classes9-ClassesTrainingTestingTrainingTestingTrainingTestingGini17.2%18.5%36.6%41.0%46.7%66.9%Symmetric Gini17.2%18.5%36.6%41.0%46.7%66.9%Entropy17.2%18.9%35.2%41.4%48.0%69.6%Twoing17.2%18.5%38.3%40.1%47.1%68.7%Ordered Twoing18.9%19.8%35.2%40.4%33.9%70.9%Discussion:In the case of 2-Classes, there is no improvement in the training phase and a slight 1% improvement in the test phase. It shows that with Leave-One-Out method, we can have more reliable model for classifying the students. It shows that the model we obtained in training phase is approximately complete.   In the case of 3-Classes, when we switch from 10-fold to Leave-One-Out the results in the training phase becomes slightly worse, but we get about 7.5% improvement. It shows that our model was not complete in 10-fold for predicting the unseen data. So it is better to use Leave-One-Out to get a more complete model for classifying the students into three categories.In the case of 9-Classes when we switch from 10-fold to Leave-One-Out the results in both training and test sets improve significantly. However, we cannot conclude that our new model is complete; because the big difference between the results in training and testing phase shows that our model is suffering from overfitting. It means that our training samples are not enough to construct a complete model for predicting the category labels correctly. CART has a lot of useful text and graphical reports, some of which we presented in appendix B. It is noticeable that CART does not any description files to work with. You can read data as a text file or any popular database or spreadsheet.QUEST, CRUISEQUEST is a statistical decision tree algorithm for classification and data mining. The objective of QUEST is similar to that of the algorithm used in CART and described in Breiman, et al. (1984). The advantages of QUEST are that it uses an unbiased variable selection technique by default, it uses imputation instead of surrogate splits to deal with missing values, and it can easily handle categorical predictor variables with many categories. If there are no missing values in the data, QUEST can optionally use the CART greedy search algorithm to produce a tree with univariate splits. QUEST needs two text input files: 1) Data file: This file contains the training samples. Each sample consists of observations on the class (or response or dependent) variable and the predictor (or independent) variables. The entries in each sample record should be comma or space delimited. Each record can occupy one or more lines in the file, but each record must begin on a new line. Record values can be numerical or character strings. Categorical variables can be given numerical or character values. 2) Description file: This file is used to provide information to the program about the name of the data file, the names and the column locations of the variables, and their roles in the analysis. The following is our description file:phy183.dat"?"column, var, type     1  1stGotCrr  n     2  TotCorr  n     3  AvgTries  n     4  TimeCorr  n     5  TimeSpent  n     6  Discuss  n     7  Class2  x     8  Class3  d     9  Class9  x     10  Grade  xIn the first line we put the name of data file, and in the second line we put the character used to denote missing data. In our dataset we have no missing data. The position, name and role of each variable come next with one line for each variable. The following roles for the variables are permitted: c stands for categorical variable; d for class (dependent) variable; only one variable can have the d indicator; n for a numerical variable; and x which indicates that the variable is excluded from the analysis.QUEST allows both interactive and batch mode. By default it uses discriminant analysis as a method for split point selection. It is an unbiased variable selection method described in Loh and Shih (1997). However, in advanced mode, user can select exhaustive search (Breiman et al., 1984) which is used in CART. The former is the default option if the number of classes are more than 2, otherwise the latter is the default option. If the latter option is selected, the program will ask for the user to choose the splitting criterion including one of the following five methods which are studied in Shih (1999):1 Likelihood Ratio G22 Pearson Chi23 Gini4 MPI (Mean Posterior Improvement)5 Other members of the divergence family The likelihood criterion is the default option. If instead the CART-style split is used, the Gini criterion is the default option. In our case, we selected the fifth method of exhaustive search which was optimal regarding the misclassification ratio. QUEST asks for the prior for each class. If the priors are to be given, the program will then ask the user to input the priors. If unequal costs are present (like in this example), the priors are altered using the formula in Breiman et al. (1984, pp. 114-115). In our cases the prior for each class is estimated regarding the class distribution. This asks for the misclassification costs. If the costs are to be given, the program will ask the user to input the costs. In our cases the misclassification costs are equal. The user can choose either split on a single variable or linear combination of variables. We used split on a single variable.QUEST also asks for the number of SEs which controls the size of the pruned tree. 0-SE gives the tree with the smallest cross-validation estimate of misclassification cost or error. QUEST enables user to select the value of V in V-fold cross-validation. The larger the value of V, the longer running time the program takes to run. 10-fold is and 226-fold (Leave-One-Out) are used in our cases.The classification matrices based on the learning sample and CV procedure are reported. Some samples of these reports are shown in Appendix B. You can see a table gives the sequence of pruned subtrees. The 3rd column shows the cost complexity value for each subtree using the definition in Breiman et al. (1984, Definition 3.5 p. 66). The 4th column gives the current or resubstitution cost (error) for each subtree. Another table gives the size, estimate of misclassification cost and its standard error for each pruned sub-tree. The 2nd column shows the number of terminal nodes. The 3rd column shows the mean cross-validation estimate of misclassification cost and the 4th column gives its estimated standard error using the approximate formula in Breiman et al. (1984, pp. 306-309). The tree marked with an * is the one with the minimum mean cross-validation estimate of misclassification cost (also called the 0-SE tree). The tree based on the mean cross-validation estimate of misclassification cost and the number of SEs is marked with ** (See appendix B).QUEST trees are given in outline form suitable for importing into flowchart packages like allCLEAR (CLEAR Software, 1996). Alternatively, the trees may be outputted in LaTeX code. The public domain macro package pstricks (Goossens, Rahtz and Mittelbach, 1997) or TreeTEX (Bruggemann-Klein and Wood, 1988) is needed to render the LaTeX trees.CRUISE is also a new statistical decision tree algorithm for classification and data mining. It has negligible bias in variable selection. It splits each node into as many sub-nodes as the number of classes in the response variable It has several ways to deal with missing values. It can detect local interactions between pairs of predictor variables.CRUISE has most of QUEST capabilities and reports (See appendix B). We have brought the results of tree-based classification with QUEST and the CRUISE into the final reporting table (Table 4.13), which includes all tree-based and non-tree based classifiers on our dataset in the cases of 2-Classes, 3-Classes, and 9-Classes.Final ResultsThe overall results of classifiers performance on our dataset are shown in the table 4.13. Regarding individual classifier, for the case of 2-classes, kNN has the best performance with 82.3% accuracy. In the case of 3-classes and 9-classes, CART has the best accuracy of about 60% in 3-classes and 43% in 9-Classes. However, considering the combination of non-tree-based classifiers, the CMC has the best performance in all three cases. That is we got the 86.8% accuracy in the case of 2-Classes, 71% in the case of 3-Classes, and 51% in the case of 9-Classes.Error RateClassifier2-Classes3-Classes9-ClassesTree ClassifierC5.020.7%43.2%74.4%CART18.5%40.1%66.9%QUEST19.5%42.9%80.0%CRUISE19.0%45.1%77.1%Non-tree ClassifierBayes23.6%51.4%77.0%1NN23.2%49.5%71.0%kNN17.7%49.6%72.5%Parzen25.0%51.9%79.5%MLP20.5%49.1%-CMC13.2%29.1%49.0%Chapter 5Conclusions and Future WorkIn this chapter, we summarize our survey and present directions to future work on data mining aspect of LON-CAPA system, ConclusionsIn this survey we select students and course data from a LON-CAPA course, PHY183 which was held at MSU in spring semester 2002. Developing some perl modules in the pre-processing phase, allow us to extracted 6 features for 227 students and group them in three ways 2-Classes, 3-Classes, and 9-Classes. Five non-tree classifiers and four tree-based classifiers are used to segregate the students by the class labels. The error rate of the different trained models resulted from different classifiers is estimated on unseen data. A combination of multiple classifiers leads to a significant accuracy improvement in all three cases. Using multiple linear regression we realize the importance of the features. We can find that 3 of the 6 features have more correlation with the class labels in all three cases. Since the most relevant feature is a discrete variable, the tree-based classifiers are classifying more accurate in most cases.  The successful implementations of classifying the students in 2 and 3-Classes demonstrate the merits of using the LON-CAPA data for pattern recognition. However, using 10-fold Cross-Validation and Jackknife method we are able to show that these data are suffering from overfitting in the case of 9-Classes. Future workFuture perspectives on an automated system for a data mining aspect in the LON-CAPA system will focus on the following issues:Gathering more sample data by combining one course data during several semesters to avoid overfitting in the case of 9-Classes.Finding the paths that students usually choose to solve the different types of the problems from activity log to extract more relevant features.Comparing the classification results relating to groups of data i.e. regarding the different type of problems (Mathematical, Optional Response, Numerical, Java Applet, etc) .Comparing the classification results in relation to every individual problem in order to find which problem would be the best predictor.Making ANOVA to evaluate the effect of interaction between groups of problems and groups of students.Using PCA and LDA for feature extraction.Weighting features vs. feature selection.Using Genetic algorithm for extracting and weighting the features.Implementing fuzzy classification for grouping students.Clustering the student database in order to describe the student behavior and evaluating the type of problems effects on students effort.  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Norwood, NJ, Ablex Publishing. 1: 183-201Appendix A:Online Education SystemsHere are a few more profiles for comparison some institutes that have presented online delivery instructions. Based on what LON-CAPA has, there seems to be 4 major divisions:Institute Products:    (1) Assessment Tools: (e.g. WebAssign and Homework Service)                                     (2) Lecture Development Tools (e.g. Mallard)Corporate Products: (3) Complete Learning Management Systems [LMS] (e.g.Blackboard, Saba and WebCT)                                    (4) Corporate Training Systems (e.g. PeopleSoft)The University of TX World Lecture Hall also was on the list, but this is basically a collection of course lectures in html format that you can browse. Some are current and you can enroll at the hosting institution to take the course for credit or just browse through the complete course. More info to follow...WebAssignCorporate OfficesP.O. Box 8202North Carolina State UniversityRaleigh, NC  27695Web Address HYPERLINK "http://www.webassign.net" www.webassign.netEstablish Date1997Mission StatementNot AvailableNumber of UsersNearly 40,000 (2000-2001 Academic Year)Countries ReachedU.S., IsraelInstitutions LicensedSee school listing belowDelivery Capability (Web and PC?)Web Based  (NO PC)Languages AvailableEnglishCorporate PartnersNo Info AvailableService PartnersNo Info AvailableAnnual RevenuesNo Info AvailableVenture Capital (if applicable)No Info AvailableHits per MonthNo Info AvailableCapabilities/FeaturesHelp DeskInstant E-Mail NotificationRecord Keeping (for the term)Transaction Database Design (Real-time)Authentication with Institutions Database of Student ProfilesAutomated Class Registration and EnrollmentCustom Color and LayoutAdministrator Authorization to Key PersonnelProducts AvailableBasic service is to create, deliver, collect, grade, and asses student progress through the use of web-based practice exercises, quizzes, and homework assignments.Publishers contributing to the textbook and question database include:   - Addison-Wesley   - Benjamin Cummings   - Thomson Learning   - Duxbury   - Freeman   - Glencoe McGraw-Hill   - Harcourt   - Houghton Mifflin   - Prentice Hall   - WileyTextbook subjects include:   - Astrology (1 book)   - Biology (7)   - Business (2 pending)   - Chemistry (26)   - Engineering (4)   - Mathematics (8)   - Physical Science (3)   - Physics (31)(for a detailed list of books by subject matter, go to  HYPERLINK "http://www.webassign.net/info/textbooks.html" http://www.webassign.net/info/textbooks.html)If a specific textbook is not currently provided a registered user my request that one be added.  Three cost-sharing models are given for coding the questions of a new textbook including Professor/Institutional Coding, WebAssign Coding, and Joint Coding.Types of Questions:NumericalMultiple ChoiceMultiple SelectEssaySubmit FileFill in the BlankSymbolicPricing:Start-up Fee (for the first teacher in a department)	$250 first yearRenewal Fee (for the first teacher in a department)$100 per yearAdditional Teachers (in the same department)	$50 per yearTeachers may have as many classes and students as needed.Student  HYPERLINK "http://www.webassign.net/info/AccessCodeInfo.html" WebAssign Access Codes Collegiate$5 per student per class per semester (or $3.33 per quarter)Pre-College (6-12)$3 per student per class per yearTechnical Specifications:Multi-institutional server:Sun Ultra Enterprise 450 with 1280 MB memory, two processors,nine 4.2 GB drives, and two 18.0 GB drivesWeb Servers:5 Dell PowerApp Web 100sThe WebAssign program is written in Perl, interfaces with a Sybase 11.5 database, and is delivered with Apache Web Server 1.3.12. Universities and Colleges Alabama State UniversityAuburn UniversityAugustana CollegeBaylor UniversityCarroll CollegeCatholic University of AmericaChattahoochee Technical CollegeChattanooga State Technical Community CollegeChristopher Newport UniversityClarke CollegeClemson UniversityCoastal Carolina UniversityCoastal Georgia Community CollegeDe Paul UniversityDelgado Community CollegeDelta CollegeDrury UniversityDuke UniversityDuquesne UniversityEast Carolina UniversityEastern Kentucky UniversityEastern Michigan University Eastern Nazarene CollegeElizabethtown CollegeEmporia State UniversityFlorence-Darlington Technical CollegeFriday Center at UNCGainesville CollegeGeorgia Institute of TechnologyGuilford CollegeHarvard UniversityBlackboard (BB), Inc.Corporate Offices1899 L Street NW, 5th FloorWashington, DC 2003622601 North 19th Avenue, Suite 200Phoenix, AZ 85027Web Address HYPERLINK "http://www.blackboard.com" www.blackboard.comEstablish DateJune 1997Mission StatementTransforming the Internet into a powerful environment for teaching and learningNumber of Users1900 CustomersCountries ReachedOffices in:Australia, Canada, Germany, Greece, Netherlands, United KingdomInstitutions LicensedListed below.Delivery Capability (Web and PC?)Web based delivery.Languages AvailableMultiple (See digital content partner Parlo)Corporate PartnersPartner Groups include:   Digital Commerce:	Barnes & Noble (Booksellers)	CampusTech (Software Seller  multi-seat licensing)	Edudex (Non-print educational materials, e.g. video)	NowDocs (e-Document receipt, print, delivery)	Obik (Career intelligence company, e.g. career guidance)	SurfDiensten (Dutch Institution education material 	purchasing non-profit corp)   Digital Content:	Academic Systems (Math and English Programs)	 HYPERLINK "mailto:AOL@School" AOL@School (K-12 Content)	Apex Learning (K-12 Content)	Atomic Dog Publishing (Higher education content)	Caliber (Corporate curriculum)	Economy.com (Financial/Business Information)	edu (College recruiting tools)	Harcourt College Publishers	Houghton Mifflin	John Wiley & Sons, Inc.	Kaplan (Test Prep)	Labyrinth Publications (Computer skills content)	McGraw-Hill	MetaText (eBooks provider  owned by NetLibrary)	Parlo (Language courses)	Pearson Education	Thomson Learning	W.W. Norton	XanEdu.com   Technology:	Dell.com	Embanet (Application hosting and management site)	FT Knowledge (Management, Business, Finance)	Griffity University (Australia)	HorizonLive (Web-base video delivery)	iGroup (Asian print, software, e-services delivery)	IMS Global Learning Consortium, Inc. (developing open 	interoperability specifications)	Infinet (Educational software apps developers)	iORMYX (eCommerce solutions provider)	K-World (Web portal developer)	KPMG LLP (Consulting company)	Microsoft Corporation	netLibrary (eBooks, Internet based content management)	Oracle	PeopleSoft (LMS)	Saba (Human capital management and development 	solutions)	Smarthinking (Online tutorial and educational assistance)	Stoas (Netherlands based multimedia and training systems 	developer)	Sun Microsystems	Swapdrive (Internet based file management)	Tegrity, Inc. (Develop group-learning processes)	Trevantis [by Lectora] (Content development software)	VA Linux Systems (Linux based web-services provider)	Yellowbrix (Automated information provisioning)Service PartnersSee above12/19/01  Questionmark offers testing services through the Blackboard Building Blocks (BB) Initiative.11/15/01  Blackboard forms Government Solutions Group, assisting government groups to expand their online learning and training solutions.10/29/01  Campus Pipeline partners with Blackboard, linking the backoffice operations of Campus Pipeline with the service offerings of Blackboard 5.10/29/01  Blackboards BB program provides the industrys first open set of Application Programming Interfaces (APIs) and developer services for creating extensions to Blackboard. From institution-developed innovations that extend Blackboard into new pedagogical frontiers, to commercial applications from 3rd party providers who speed their growth through Blackboards platform technology and client base, Building Blocks represents a springboard for innovation in the e-Education market.Annual RevenuesVenture Capital (if applicable)More than $100 MillionFrom investors that include AOL Time Warner Inc., The Aurora Funds Inc., The Carlyle Group, Dain Rauscher Wessels, Dell Computer Corporation, Internet Capital Group, Kaplan Ventures, Merrill Lynch KECALP, Microsoft Corporation, Morgan Keegan, Novak Biddle Venture Partners, Oak Hill Capital Partners, L.P., and Pearson Education.Hits per MonthNot AvailableCapabilities/FeaturesBlackboard 5 Learning System: Customizable (e.g. Kaplan, Bigchalk.com, Pearson Education)Blackboard Community Portal System: Blackboard Transation SystemCommerce and Access Solutions Integration with student ID cards (debit accounts) Future integration with cell phones, PDAs, etc. Blackboard Optim 9000 Blackboard EnvisionBuilding Blocks Initiative: An initiative focused on allowing customers (instructors, students, institutions, etc.) to build on the existing BB platform by integrating proprietary and 3rd party software, content, and services. Early adopters include Carnegie Mellon University and Princeton University.Products AvailableNo physical products offered other than through Corporate Partners.Course and Portal Clients:Adelaide University Australia InternationalArizona State University Higher EducationArkansas Tech University AR, USA Higher EducationAvon Old Farms School CT, USA K-12Belfast Institute of Further and Higher Education United Kingdom InternationalBook Promotion and Service Thailand InternationalBristol-Myers Squibb NJ, USA Corporate/Association HYPERLINK "http://company.blackboard.com/clients/cases/viewcs.cgi?csid=2016849" California State University at Dominguez Hills CA, USA Higher EducationCalvin College MI, USA Higher EducationCarnegie Mellon University PA, USA Higher EducationCase Western Reserve University OH, USA Higher EducationCherry Creek School District CO, USA K-12City College Manchester United Kingdom InternationalCity of Sunderland College United Kingdom InternationalCity University of Hong Kong Hong Kong InternationalColumbia University Teachers College NY, USA Higher EducationCornell University NY, USA Higher EducationDallas County Community College District TX, USA Higher EducationDuke University NC, USA Higher EducationEducation Queensland Australia InternationalErasmus Universitet of Rotterdam Netherlands International HYPERLINK "http://company.blackboard.com/clients/cases/viewcs.cgi?csid=66866702" Estrella Mountain Community College AZ, USA Higher EducationFlorida State University FL, USA Higher EducationFT Knowledge United Kingdom InternationalGeorgetown University DC, USA Higher EducationGriffith University Australia InternationalHouston Independent School District TX, USA K-12Huddersfield University United Kingdom InternationalInstituto Tecnologico Y De Estudios Superiores De Monterrey (ITESM) Mexico InternationalJames Madison University VA, USA Higher EducationJohns Hopkins University MD, USA Higher EducationWebCTUsage Statistics: Institutional use: 2,273 Active Users: Countries Reached: 76 Page Views per Month: Institutions Using Bb Web: Launch Date: e-Learning Platforms Release: WebCTs Vision:(Found at  HYPERLINK "http://www.webct.com" www.webct.com)WebCT's vision is to work in concert with leading institutions to go beyond online course delivery and actually transform the educational experience. To that end, we will deliver state-of-the-art educational technology that supports a full range of teaching and learning styles and optimizes intellectual and technical resources. WebCT (WCT) provides users with access to e-Packs - Publisher content that is WCT-ready - Content Partners include: - McGraw Hill - Pearson - Pearson Canada - Thomson Learning - Bedford, Freeman & Worth Publishing - EMC Paradigm - Vivendi - John Wiley & Sons - Jones & Barlett - Mayfield Publishing - W.W. Norton & Company- Licensed materials that users have trial-access to for 30 days. Upon expiration, users can adopt the e-Pack - The e-Pack can be downloaded to an institutions server as long as they have a valid WebCT license - OR, the e-Pack can be hosted on WebCTs servers - An e-Pack example: Title: College Accounting 1-12 Description: For use with WebCT 3.x This e-Pack is a companion website for EMCParadigm's Paradigm College, Accounting 1-12 textbook. This Class Connection features: Course objectives, Syllabi, Assignments, Chapter-specific Self-tests, Glossary, and course Resources, featuring links to book-specific extra material and file downloads. Author: Dansby, Kaliski, Lawrence Publisher: EMC Paradigm Publishing Availability: *Available Now! Student Access Code Price:$31.19 (if purchased at WebCT.com)	- COBALT, the next generation of WebCT (to be released 1st Quarter 2002), will include:		- Best-of-breed learning tools		- Robust content management capabilities		- Dynamic learning information management		- Complete personalization of the learning experience		- Enterprise-class platform architecture		Leveraging Technology to Transform the Educational Experience  A Web CT White Paper		June 2001	- COBALT will incorporate two forms of data mining:	- Content Management:		- An institution will only have access to content available on their server/platform			- Internally developed content			- Content e-Packs		- Content will be tagged and stored with the intent of future reuse, reassembling, and sharing		- Content will be tracked and monitored to:			- Identify the use of content and improve pedagogical approaches			- Control the use and reuse of copyrighted or licensed material		- Additional key points re: COBALTs content management- A New Media Library will be included for managing audio, video, graphics and other media content- A commercially developed search-engine will be the first of its type to be utilized in a system developed for content management- COBALT will be developed to comply with major standards including: SCORM, IMS Content and Assessment Specifications Suport- The enhanced File Manger and method for developing a hierarchy for content will improve the storing and sharing of content across educational sections.- Role based access will allow instructors to designate scope of access by the role of a particular operater (e.g. Learner vs. Teaching Assistant vs. Instructor)		- An institution or instructor will also be able to mine for information re: the student population- Students are encouraged to utilize the notes and chat functions of class space.  Data is collected and then analyzed to identify areas for improvement- Student records are available, in a single location, for trend and regression analysis- Additional tracking information will be collected as students engage with the COBALT Learning Platform  this information can be used by the instructor to monitor and enhance the acquisition of deep knowledge	- The Benefits of COBALT:- For Students:		Easily accessed, personalized, high quality education			- For Faculty:		The power to offer superior courses as efficiently as possible		- For Administrators: A cost-effective platform for improving quality and reaching more students			- For CIOs:	An integrated, manageable, scalable platform that will meet critical e-learning 									needs, today and tomorrow		Leveraging Technology to Transform the Educational Experience  A Web CT White Paper		June 2001.Appendix B: Some Tree Classifiers OutputC5.0Using C5.0 for classifying the students: This result shows the error rate in each fold in 10-fold cross-validation, and confusion matrix.In 2-classes (Passed, Failed) Fold            Rules     ----      ----------------            No      Errors   0         9       18.2%   1         9       22.7%   2        12       27.3%   3         5       30.4%   4         8       17.4%   5         7       21.7%   6        10       13.0%   7         8       17.4%   8         4       17.4%   9         8       21.7%  Mean     8.0       20.7%SE       0.7        1.6%In 3-classes (High, Middle, Low) we got the following results:Fold        Decision Tree   ----      ----------------            Size      Errors     0         7       36.4%   1        12       45.5%   2         6       45.5%   3         7       47.8%   4        10       34.8%   5         9       34.8%   6         6       47.8%   7         8       43.5%   8        10       47.8%   9         9       47.8%  Mean     8.4       43.2%  SE       0.6        1.8%In 9-classes we got the following results:Fold        Decision Tree   ----      ----------------            Size      Errors     0        57       81.8%   1        51       63.6%   2        55       63.6%   3        61       78.3%   4        48       73.9%   5        56       73.9%   6        58       69.6%   7        53       87.0%   8        56       78.3%   9        56       73.9%  Mean    55.1       74.4%  SE       1.2        2.4%           (a)   (b)   (c)   (d)   (e)   (f)   (g)   (h)   (i)    <-classified as          ----  ----  ----  ----  ----  ----  ----  ----  ----                         1           1                            (a): class 1             1           3     2     2     2                      (b): class 2             1     2     7     6     2     7     3                (c): class 3                   4     2     5     2     4     3     3          (d): class 4                   2     5     3    12    11     8     2          (e): class 5                         7     5     9    15     9     7          (f): class 6                         4     6     3    15     5     8          (g): class 7                         1     1     7     3     2    14          (h): class 8                                                                  (i): class 9Here, there are a sample of rule sets resulted the from C5.0 in 3-class classificationRule 1: (8, lift 2.9)        FirstCorrect > 64        FirstCorrect <= 112        TotalCorrect > 181        AvgTries > 1270        TotalTimeSpent <= 87.87        Discussion <= 0        ->  class High  [0.900]Rule 2: (5, lift 2.8)        FirstCorrect > 93        FirstCorrect <= 99        TotalCorrect > 181        AvgTries <= 1270        Discussion <= 14        ->  class High  [0.857]Rule 3: (15/2, lift 2.7)        FirstCorrect <= 112        TotalCorrect > 181        Discussion > 0        Discussion <= 14        ->  class High  [0.824]Rule 4: (8/1, lift 2.6)        FirstCorrect <= 112        TotalCorrect > 174        TotalCorrect <= 180        AvgTries <= 1768        Discussion <= 0        ->  class High  [0.800]Rule 5: (3, lift 2.6)        FirstCorrect > 112        FirstCorrect <= 117        TotalCorrect > 180        TotalTimeSpent > 14.01        Discussion <= 1        ->  class High  [0.800].Rule 15: (3/1, lift 2.2)        FirstCorrect <= 112        TotalCorrect > 180        TotalCorrect <= 181        Discussion <= 0        ->  class Low  [0.600]Here, there are a sample of rule sets resulted the from C5.0 in 2-class classificationRules:Rule 1: (158/25, lift 1.2)        TotalCorrect > 165        ->  class Passed  [0.838]Rule 2: (45/8, lift 1.1)        Discussion > 1        ->  class Passed  [0.809]Rule 3: (7, lift 3.2)        FirstCorrect <= 78        TotalCorrect <= 165        ->  class Failed  [0.889]Rule 4: (2, lift 2.7)        TotalCorrect <= 165        AvgTries > 669        Discussion > 1        Discussion <= 4        ->  class Failed  [0.750]Rule 5: (47/15, lift 2.4)        TotalCorrect <= 165        ->  class Failed  [0.673]Default class: PassedEvaluation on hold-out data (22 cases):                Rules               ----------------            No      Errors             5    3(13.6%)   <<And a sample of tree which is produced by C5.0 in one of the folds in 3 classes:TotalCorrect <= 165::...AvgTries > 850: Low (13/2):   AvgTries <= 850::   :...Discussion > 2::       :...TotalTimeSpent <= 20.57: Low (2):       :   TotalTimeSpent > 20.57: Middle (3/1):       Discussion <= 2::       :...TotalTimeSpent > 22.63: Low (8):           TotalTimeSpent <= 22.63::           :...AvgTries <= 561: Low (7/1):               AvgTries > 561::               :...TotalCorrect > 156: Low (2):                   TotalCorrect <= 156::                   :...TotalCorrect <= 136: Low (3/1):                       TotalCorrect > 136: Middle (6)TotalCorrect > 165::...AvgTries <= 535:    :...TotalCorrect <= 177: Low (5)    :   TotalCorrect > 177: High (5/2)    AvgTries > 535:    :...FirstCorrect > 112:        :...TotalCorrect <= 172: Middle (6)        :   TotalCorrect > 172:        :   :...TotalCorrect > 180: Middle (38/13)        :       TotalCorrect <= 180:        :       :...TimeTillCorr <= 23.47:        :           :...TotalCorrect > 178: High (2)        :           :   TotalCorrect <= 178:        :           :   :...TotalCorrect <= 174: High (4/2)        :           :       TotalCorrect > 174: Middle (8/1)        :           TimeTillCorr > 23.47:        :           :...FirstCorrect > 129: Middle (2)        :               FirstCorrect <= 129:        :               :...TotalCorrect > 175: Low (7/1)        :                   TotalCorrect <= 175:        :                   :...FirstCorrect <= 118: Low (2)        :                       FirstCorrect > 118: High (2)        FirstCorrect <= 112:        :...TotalTimeSpent > 87.87: Middle (5/1)            TotalTimeSpent <= 87.87:            :...TotalCorrect <= 169: High (5/1)                TotalCorrect > 169:                :...TotalCorrect <= 174: Middle (8)                    TotalCorrect > 174:                    :...Discussion > 7: Middle (5/1)                        Discussion <= 7:                        :...TotalCorrect <= 177: High (5/1)                            TotalCorrect > 177:                            :...TotalCorrect <= 181:                                :...AvgTries <= 1023: High (3)                                :   AvgTries > 1023: Middle (9/2)                                TotalCorrect > 181:                                :...Discussion > 0: High (15/2)                                    Discussion <= 0:                                    :...FirstCorrect > 99: Middle (5/1)                                        FirstCorrect <= 99:                                        :...FirstCorrect > 89: High (7/1)                                            FirstCorrect <= 89:                                            :...AvgTries <= 1355: Middle (4)                                                AvgTries > 1355: [S1]Evaluation on hold-out data (22 cases):            Decision Tree             ----------------            Size      Errors              32    7(31.8%)   <<CARTSome of CART report for 2-Classes using Gini criterion:	File:	PHY183.XLS	Target Variable:	CLASS2	Predictor Variables:	FIRSTCRR, TOTCORR, TRIES, SLVDTIME, TOTTIME, DISCUSSTree SequenceTreeNumberTerminalNodesCross-ValidatedRelative CostResubstitutionRelative CostComplexity1230.873  0.0990.317-1.0002220.984  0.1040.3171.00E-0053151.016  0.1040.3970.003490.762  0.0890.4760.004570.778  0.0910.5080.004650.841  0.0930.5560.0077**30.667  0.0900.6190.009820.714  0.0880.6830.018911.000  6.73E-0051.0000.088			*  Minimum Cost			** Optimal Classification tree topology for: CLASS2Error CurveGains for 2Gains Data for 2NodeCasesClass 2% of NodeClass 2%Class 2Cum %Class 2Cum %Pop%PopCasesin NodeCumliftLiftPop13570.0055.5655.5622.0322.03502.5222.5222770.0011.1166.6726.434.41102.5222.52232112.5733.33100.00100.0073.571671.0000.453Variable Importance Variable TOTCORR100.00||||||||||||||||||||||||||||||||||||||||||TRIES56.32|||||||||||||||||||||||FIRSTCRR4.58|TOTTIME0.91SLVDTIME0.83DISCUSS0.00Misclassification for Learn DataClassNCasesN Mis-ClassedPctErrorCost11641810.980.112632133.330.33Misclassification for Test DataClassNCasesN Mis-ClassedPctErrorCost11642112.800.132632133.330.33Some of CART report for 3-Classes using Twoing criterion: (10-fold Cross-Validation):Tree SequenceTreeNumberTerminalNodesCross-ValidatedRelative CostResubstitutionRelative CostComplexity1420.802  0.0500.230-1.0002380.808  0.0500.2360.0013370.808  0.0500.2380.0014360.794  0.0500.2420.0035350.786  0.0500.2470.0036270.778  0.0500.2890.0047240.762  0.0500.3110.0058230.762  0.0500.3190.0059220.761  0.0500.3270.00510210.731  0.0490.3360.00611180.734  0.0490.3660.00712140.727  0.0490.4070.00713130.740  0.0490.4180.00714110.732  0.0490.4440.00915**100.694  0.0490.4570.0091680.720  0.0500.5000.0141760.743  0.0500.5450.0151850.741  0.0500.5740.0191940.728  0.0500.6050.0212030.745  0.0500.6610.0372120.758  0.0350.7510.0602211.000  0.0001.0000.166Classification tree topology for: CLASS3Error CurveGains for 1Gains Data for 1NodeCasesClass 1% of NodeClass 1%Class 1Cum %Class 1Cum %Pop%PopCasesin NodeCumliftLiftPop9480.005.805.802.202.2052.6322.6322480.005.8011.594.412.2052.6322.63263162.0044.9356.5226.4322.03502.1382.0404857.1411.5968.1232.606.17142.0901.88071327.0818.8486.9653.7421.15481.6180.8915112.501.4588.4157.273.5281.5440.41110211.762.9091.3064.767.49171.4100.3878211.112.9094.2072.697.93181.2960.366148.005.80100.0094.7122.03501.0560.263300.000.00100.00100.005.29121.0000.000Variable Importance Variable TOTCORR100.00||||||||||||||||||||||||||||||||||||||||||TRIES40.11||||||||||||||||FIRSTCRR24.44||||||||||TOTTIME23.22|||||||||SLVDTIME21.67||||||||DISCUSS14.44|||||Misclassification for Learn DataClassNCasesN Mis-ClassedPctErrorCost1692231.880.322953435.790.363631523.810.24Misclassification for Test DataClassNCasesN Mis-ClassedPctErrorCost1693550.720.512955254.740.553632133.330.33Some of CART report for 9-Classes using Entropy criterion: (10-fold Cross-Validation)Different tree topologies for: CLASS-9Entropy 			Gini				 TwoingDescriptive Statistics in CART for 3-Classes   Variable             N         Mean           SD          Min          Max          Sum  ------------------------------------------------------------------------------------------- Overall   FIRSTCRR          227.00      106.242       20.462       47.000      150.000    24117.000    TOTCORR           227.00      171.678       18.155       80.000      184.000    38971.000    TRIES             227.00      977.987      450.898      265.000     3095.000   222003.000     SLVDTIME          227.00       36.620       24.837        2.590      130.870     8312.700      TOTTIME           227.00       37.948       25.434        3.000      130.870     8614.170    DISCUSS           227.00        1.330        3.034        0.000       23.000      302.000 CLASS3 = 1   FIRSTCRR           69.00      103.145       19.598       57.000      149.000     7117.000   TOTCORR            69.00      179.290        7.900      141.000      184.000    12371.000   TRIES              69.00     1088.406      439.742      487.000     2227.000    75100.000    SLVDTIME           69.00       39.060       22.209        2.590       98.840     2695.130    TOTTIME            69.00       39.764       22.797        3.000       99.200     2743.720   DISCUSS            69.00        1.493        2.988        0.000       14.000      103.000 CLASS3 = 2   FIRSTCRR           95.00      108.505       20.973       54.000      150.000    10308.000    TOTCORR            95.00      175.453       12.412      118.000      184.000    16668.000    TRIES              95.00      984.937      443.874      392.000     3095.000    93569.000   SLVDTIME           95.00       36.866       27.353        4.100      130.870     3502.240    TOTTIME            95.00       37.916       27.865        4.130      130.870     3602.010   DISCUSS            95.00        1.537        3.596        0.000       23.000      146.000 CLASS3 = 3   FIRSTCRR           63.00      106.222       20.482       47.000      147.000     6692.000   TOTCORR            63.00      157.651       24.763       80.000      184.000     9932.000   TRIES              63.00      846.571      446.210      265.000     2623.000    53334.000   SLVDTIME           63.00       33.577       23.605        4.870      107.100     2115.330    TOTTIME            63.00       36.007       24.561        5.920      114.210     2268.440    DISCUSS            63.00        0.841        1.953        0.000        9.000       53.000A Sample of CART tree for 3-Classes using Entropy criterion: (10-fold Cross-Validation)QUEST  Summary of numerical variable: FirstCorr       Size        Obs        Min        Max       Mean         Sd        226        226  0.470E+02  0.150E+03  0.106E+03  0.204E+02    Summary of numerical variable: TotCorr       Size        Obs        Min        Max       Mean         Sd        226        226  0.960E+02  0.184E+03  0.172E+03  0.171E+02    Summary of numerical variable: AvgTries       Size        Obs        Min        Max       Mean         Sd        226        226  0.193E+01  0.169E+02  0.551E+01  0.246E+01    Summary of numerical variable: TimeCorr       Size        Obs        Min        Max       Mean         Sd        226        226  0.249E+01  0.942E+02  0.280E+02  0.185E+02    Summary of numerical variable: TimeSpent       Size        Obs        Min        Max       Mean         Sd        226        226  0.260E+01  0.942E+02  0.281E+02  0.185E+02    Summary of numerical variable: Discuss       Size        Obs        Min        Max       Mean         Sd        226        226  0.000E+00  0.140E+02  0.912E+00  0.201E+01  Result for 2-classes  Summary of response variable: Class2                class   frequency              Failed      62              Passed     164                  -------------                   2     226    Options for tree construction  Learning sample  estimated priors are               Class     prior              Failed    0.27434              Passed    0.72566  Size and CV misclassification cost and SE of subtrees:  Tree   #Tnodes     Mean       SE(Mean)    1       26      0.1947     0.2634E-01    2*      16      0.1903     0.2611E-01    3       13      0.1947     0.2634E-01    4       12      0.2035     0.2678E-01    5        6      0.1947     0.2634E-01    6**      4      0.1947     0.2634E-01    7        3      0.2301     0.2800E-01    8        2      0.2434     0.2854E-01    9        1      0.2743     0.2968E-01  CART 0-SE tree is marked with *CART SE-rule using CART SE is marked with **use 10-fold CV sample pruning  SE-rule trees based on number of SEs = 1.00    subtree  # Terminal  complexity  current  number    nodes       value        cost     1        26        0.0000     0.0885     2        16        0.0022     0.1106     3        13        0.0029     0.1195     4        12        0.0044     0.1239     5         6        0.0052     0.1549     6         4        0.0111     0.1770     7         3        0.0177     0.1947     8         2        0.0354     0.2301     9         1        0.0442     0.2743  Classification tree:        Node 1: TotCorr <= 156.9        Node 2: Failed      Node 1: TotCorr > 156.9        Node 3: TotCorr <= 168.8          Node 18: Discuss <= 1.279            Node 20: Failed          Node 18: Discuss > 1.279            Node 21: Passed        Node 3: TotCorr > 168.8          Node 19: Passed    Classification matrix based on learning sample              predicted class  actual class   Failed   Passed        Failed       35       27        Passed       13      151  Classification matrix based on 10-fold CV              predicted class  actual class   Failed   Passed        Failed       33       29        Passed       15      149  Result for 3-classes  use 10-fold CV sample pruning  SE-rule trees based on number of SEs = 1.00    Size and CV misclassification cost and SE of subtrees:  Tree   #Tnodes     Mean       SE(Mean)    1       47      0.5354     0.3318E-01    2       30      0.5265     0.3321E-01    3       24      0.5354     0.3318E-01    4       10      0.4735     0.3321E-01    5*       9      0.4425     0.3304E-01    6        8      0.4513     0.3310E-01    7        6      0.4602     0.3315E-01    8**      4      0.4735     0.3321E-01    9        2      0.4823     0.3324E-01   10        1      0.5796     0.3283E-01    CART 0-SE tree is marked with *  CART SE-rule using CART SE is marked with **  Following tree is based on **    Structure of final tree      Node Left node Right node   Split variable   Predicted class    1        2         3        TotCorr    2  * terminal node *                         Low    3       26        27        1stGotCrr   26       28        29        TotCorr   28  * terminal node *                         Middle   29  * terminal node *                         High   27  * terminal node *                         Middle    Number of terminal nodes of final tree = 4  Total number of nodes of final tree = 7    Classification tree:        Node 1: TotCorr <= 165.5        Node 2: Low      Node 1: TotCorr > 165.5        Node 3: 1stGotCrr <= 117.5          Node 26: TotCorr <= 181.5            Node 28: Middle          Node 26: TotCorr > 181.5            Node 29: High        Node 3: 1stGotCrr > 117.5          Node 27: Middle    Classification matrix based on learning sample              predicted class  actual class     High      Low   Middle          High       34        4       31           Low        2       34       26        Middle       21       11       63    Classification matrix based on 10-fold CV              predicted class  actual class     High      Low   Middle          High       27       10       32           Low        4       37       21        Middle       25       15       55Bagging (Leave-one-out method)    estimated priors are               Class     prior                High    0.30531                 Low    0.27434              Middle    0.42035  minimal node size: 2  use univariate split  use (biased) exhaustive search for variable and split selections  use the divergence famliy  with lambda value:   0.5000000          use 226-fold CV sample pruning  SE-rule trees based on number of SEs = 1.00    Size and CV misclassification cost and SE of subtrees:  Tree   #Tnodes     Mean       SE(Mean)    1       67      0.5354     0.3318E-01    2       61      0.5354     0.3318E-01    3       31      0.5177     0.3324E-01    4       24      0.5000     0.3326E-01    5*      10      0.4204     0.3283E-01    6        9      0.4425     0.3304E-01    7**      8      0.4469     0.3307E-01    8        6      0.5000     0.3326E-01    9        4      0.4956     0.3326E-01   10        2      0.4823     0.3324E-01   11        1      0.5796     0.3283E-01    CART 0-SE tree is marked with *  CART SE-rule using CART SE is marked with **  Following tree is based on **    Structure of final tree      Node Left node Right node   Split variable   Predicted class    1        2         3        TotCorr    2  * terminal node *                         Low    3       32        33        1stGotCrr   32       34        35        TotCorr   34       36        37        TotCorr   36  * terminal node *                         High   37  * terminal node *                         Middle   35       70        71        TimeCorr   70  * terminal node *                         High   71  * terminal node *                         Middle   33      104       105        TimeCorr  104  * terminal node *                         Middle  105      132       133        TotCorr  132  * terminal node *                         Low  133  * terminal node *                         Middle    Number of terminal nodes of final tree = 8  Total number of nodes of final tree = 15  Number of terminal nodes of final tree = 10Total number of nodes of final tree = 19    Classification tree:        Node 1: TotCorr <= 165.5        Node 2: Low      Node 1: TotCorr > 165.5        Node 3: 1stGotCrr <= 117.5          Node 26: TotCorr <= 181.5            Node 28: TotCorr <= 169.5              Node 30: High            Node 28: TotCorr > 169.5              Node 31: Middle          Node 26: TotCorr > 181.5            Node 29: TimeCorr <= 52.44              Node 56: High            Node 29: TimeCorr > 52.44              Node 57: Middle        Node 3: 1stGotCrr > 117.5          Node 27: TimeCorr <= 24.49            Node 80: Middle          Node 27: TimeCorr > 24.49            Node 81: TotCorr <= 180.5              Node 104: Low            Node 81: TotCorr > 180.5              Node 105: 1stGotCrr <= 130.0                Node 110: TimeCorr <= 27.16                  Node 112: Low                Node 110: TimeCorr > 27.16                  Node 113: Middle              Node 105: 1stGotCrr > 130.0                Node 111: High  Classification matrix based on learning sample              predicted class  actual class     High      Low   Middle          High       38        5       26           Low        3       47       12        Middle       13       13       69    Classification matrix based on 226-fold CV              predicted class  actual class     High      Low   Middle          High       31        9       29           Low        5       43       14        Middle       19       19       57Result for 9-classes   Classification tree:       Node 1: TotCorr <= 104.0        Node 2: 0      Node 1: TotCorr > 104.0        Node 3: TotCorr <= 165.5          Node 4: 3        Node 3: TotCorr > 165.5          Node 5: TotCorr <= 181.5            Node 44: TimeCorr <= 2.565              Node 46: 8            Node 44: TimeCorr > 2.565              Node 47: TimeCorr <= 71.06                Node 48: AvgTries <= 3.145                  Node 50: 4                Node 48: AvgTries > 3.145                  Node 51: 1stGotCrr <= 77.00                    Node 56: 5                  Node 51: 1stGotCrr > 77.00                    Node 57: AvgTries <= 12.52                      Node 58: TimeCorr <= 40.50                        Node 60: 5                      Node 58: TimeCorr > 40.50                        Node 61: 6                    Node 57: AvgTries > 12.52                      Node 59: 3              Node 47: TimeCorr > 71.06                Node 49: 3          Node 5: TotCorr > 181.5            Node 45: AvgTries <= 2.630              Node 108: 4            Node 45: AvgTries > 2.630              Node 109: 1stGotCrr <= 111.5                Node 110: 1stGotCrr <= 55.50                  Node 112: 5                Node 110: 1stGotCrr > 55.50                  Node 113: TimeCorr <= 57.44                    Node 114: AvgTries <= 5.330                      Node 116: 6                    Node 114: AvgTries > 5.330                      Node 117: 8                  Node 113: TimeCorr > 57.44                    Node 115: 6              Node 109: 1stGotCrr > 111.5                Node 111: 6            predicted class  actual class        0        2        3        4        5        6        7        8             0        1        0        0        0        0        0        0        0             2        1        0        8        0        0        1        0        0             3        0        0       21        2        2        3        0        0             4        0        0        7        5        8        2        0        1             5        0        0        6        0       32        3        0        2             6        0        0        5        0       19       24        0        4             7        0        0        2        1       16       15        0        7             8        0        0        2        0        3        4        0       19  elapsed time: 386.25 seconds  (user: 386.14, system: 0.11)CRUISEHere, some output results of CRUISE for 3-classes:  CV misclassification cost and SE of subtrees:  Subtree      CV R(t)           CV SE       # Terminal Nodes (largest)    0.549823         0.3313E-01          82      1       0.539823         0.3315E-01          70      2       0.544248         0.3313E-01          67      3       0.539823         0.3315E-01          59      4       0.526549         0.3321E-01          56      5       0.544248         0.3313E-01          41      6       0.553097         0.3307E-01          38      7       0.553097         0.3307E-01          23      8       0.561947         0.3300E-01          21      9       0.557522         0.3304E-01          15     10       0.535398         0.3318E-01           9     11       0.504425         0.3326E-01           8     12*      0.460177         0.3315E-01           6     13       0.504425         0.3326E-01           2     14       0.579646         0.3283E-01           1  * denotes 0-SE Tree  ** denotes given-SE Tree * tree is same as ** tree   Following tree is based on **   Splits of the Tree:     Node      Split variable     1  TotCorr       2  * terminal *         3  TotCorr         8  TotCorr           24  * terminal *             25  * terminal *           9  TotCorr           27  * terminal *             28  TimeCorr             84  * terminal *               85  * terminal *     Tree Structure:    Node 1: TotCorr <=  163.156        Node 2: Terminal Node, predicted class = Low       Class label :   High    Low Middle       Class size  :      3     28     11   Node 1: TotCorr >  163.156        Node 3: TotCorr <=  171.059          Node 8: TotCorr <=  168.639            Node 24: Terminal Node, predicted class = Low           Class label :   High    Low Middle           Class size  :      2      7      1       Node 8: TotCorr >  168.639            Node 25: Terminal Node, predicted class = Middle           Class label :   High    Low Middle           Class size  :      3      4      9     Node 3: TotCorr >  171.059          Node 9: TotCorr <=  183.206            Node 27: Terminal Node, predicted class = Middle           Class label :   High    Low Middle           Class size  :     34     18     53       Node 9: TotCorr >  183.206            Node 28: ABS(TimeCorr -  35.4849    ) <=  19.1162              Node 84: Terminal Node, predicted class = High             Class label :   High    Low Middle             Class size  :     22      4     11         Node 28: ABS(TimeCorr -  35.4849    ) >  19.1162              Node 85: Terminal Node, predicted class = Middle             Class label :   High    Low Middle             Class size  :      5      1     10    Detailed Description of the Tree:     Nodes      No.     Subnode    Split     Split          Split   label    cases      label     stat.    variable        value       1     226          2        F      TotCorr      <=   163.16                              3                            <   infinity                      # obs   mean/mode of TotCorr            Class   High :  69      179.290                Class    Low :  62      158.903                Class Middle :  95      175.453            2      42        **** terminal, predicted class: Low                         # obs            Class   High :   3            Class    Low :  28            Class Middle :  11        3     184          8        F      TotCorr      <=   171.06                              9                            <   infinity                      # obs   mean/mode of TotCorr            Class   High :  66      180.576                Class    Low :  34      175.176                Class Middle :  84      179.226            8      26         24        F      TotCorr      <=   168.64                             25                            <   infinity                      # obs   mean/mode of TotCorr            Class   High :   5      167.600                Class    Low :  11      167.182                Class Middle :  10      169.800           24      10        **** terminal, predicted class: Low                         # obs            Class   High :   2            Class    Low :   7            Class Middle :   1       25      16        **** terminal, predicted class: Middle                         # obs            Class   High :   3            Class    Low :   4            Class Middle :   9        9     158         27        F      TotCorr      <=   183.21                             28                            <   infinity                      # obs   mean/mode of TotCorr            Class   High :  61      181.639                Class    Low :  23      179.000                Class Middle :  74      180.500           27     105        **** terminal, predicted class: Middle                         # obs            Class   High :  34            Class    Low :  18            Class Middle :  53       28      53         84  Levene   ABS(TimeCorr - 35.5    ) <=19.116                             85                            <   infinity                      # obs   mean/mode of TimeCorr            Class   High :  27      34.7652                Class    Low :   5      36.5700                Class Middle :  21      36.1519           84      37        **** terminal, predicted class: High                         # obs            Class   High :  22            Class    Low :   4            Class Middle :  11       85      16        **** terminal, predicted class: Middle                         # obs            Class   High :   5            Class    Low :   1            Class Middle :  10   Number of nodes in maximum tree        =     153 Number of nodes in final tree          =      11 Number of terminal nodes in final tree =       6   Classification Matrix :         Predicted class                                High    Low Middle  Actual class #obs   Prior ---------------------          High   69   0.305       22      5     42           Low   62   0.274        4     35     23        Middle   95   0.420       11     12     72   Total obs = 226,    # correct = 129  Resubstitution misclassification cost =   0.4292      S.E. of resubstitution misclassification cost =   0.3055E-01   Cross-validation error cost from pruning =   0.4602      S.E. of CV misclassification cost =   0.3315E-01  Elapsed system time in seconds:  5.54 In appendix A, there are more profiles of some institutes that have presented online delivery instructions. ID3 got this name because it was the third version of interactive dichotomizer procedure.  This name has been got from administration office of Michigan State University for evaluating the exams problem. Here we expanded this expression to homework problems as well. The first five classifiers are coded in MATLABTM 6.0, and for the decision tree classifiers we have use some available software packages such as C5.0, CART, QUEST, CRUISE. We will discuss the Decision Tree-based software in the next section. In this section we deal with non-tree classifiers. We have not implemented this method in this survey yet. All the code was written in MATLABTM 6.0 Weak learner means that the classifier has accuracy only slightly better than chance (Duda et al., 2001) It is the commercial version of the C4.5 decision tree algorithm developed by Ross Quinlan. See5/C5.0 classifiers are expressed as decision trees or sets of if-then rules. RuleQuest provides C source code so that classifiers constructed by See5/C5.0 can be embedded in your own systems.  CART(tm) (Classification And Regression Trees) is a data mining tool exclusively licensed to Salford Systems (http://www.salford-systems.com). CART is the implementation of the original program by Breiman, Friedman, Olshen, and Stone. We used CART version 5.02 under windows for our classification.  QUEST (Quick, Unbiased and Efficient Statistical Tree) A classification tree restricted to binary splitsCRUISE (Classification Rule with Unbiased Interaction Selection and Estimation) A classification tree that splits each node into two or more sub-nodes These new software are developed by Wei-Yin Loh at the University of Wisconsin-Madison, Shih at university of Taiwan, and Hyunjoong Kim at University of Tennessee. These are vastly-improved descendant of an older algorithm called FACT. 		        Survey /  PAGE 111Interpretation/ EvaluationData MiningKnowledgeTransformationPreprocessing / CleaningPatternsTransformed DataSelectionPreprocessed DataTarget DataDataFigure 3.1: Steps of the KDD Process (Fayyad et al., 1996)Bayesian Classificationg1EvaluationLikelihoodFunctionsPatternDecisiong2xjMaximumSelectorngmFeatureExtractionaj{j=j,n}gi{i=i,m}Figure 3.2: the Bayesian Classification Process (Adapted from Wu et al.,  1991)Figure 3.3: A Three Layer Feedforward Neural Network [Lu et al., 1995]Input LayerHidden LayerOutput LayerFigure 4.7: Graphical chart of student tries for                  Atwood Machine Problem according                  to every concept in 1 interval time.A frictionless, massless pulley is attached to the ceiling, in a gravity field g. Mass Ma is greater than mass Mb. The tensions Tx,Ty, Tz, and the constant g are magnitudes. (For each, select: Greater than, Less than, Equal to, True, or False)   EMBED Word.Picture.8All machines in the network are connected with each other through two-way persistent TCP/IP connections. The network has two classes of servers: library and access servers. A library server can act as a home server that stores all personal records of users, and is responsible for the initial authentication of users when a session is opened on any server in the network. For authors, it also hosts their construction area and the authoritative copy of every resource that has been published by that author. Library servers can be used as backups to host sessions when all access servers in the network are overloaded. An Access Server is a machine that hosts student sessionsExpert ModelCommunication ModuleStudent ModelPedagogical ModuleLearnerFigure 2.3: A schema of distributed data in LON-CAPATable 4.3: selecting 2 class labels regarding to students grades in course PHY183  SS02Table 4.8: Comparing Error Rate  of classifiers with and without  Normalization in the case of 3 classes Table 4.10: Comparing the Performance of classifiers, in all cases: 2-Classes, 3-Classess, and 9-ClassesUsing 10-fold Cross-Validation in all cases.Table 4.2: selecting 3 class labels regarding to students grades in course PHY183  SS02Table 4.1: selecting 9 class labels regarding to students grades in course PHY183  SS02Figure 4.1: Graph of distribution of grades in course PHY183  SS02Table 4.9: Comparing Error Rate  of classifiers 2-fold and 10-fold Cross-Validation in the case of 3 classes Figure 4.8: Comparing Error Rate of classifiers with 10-fold Cross-Validation in the case of 2-Classes Figure 4.9: Comparing Error Rate of classifiers with 10-fold Cross-Validation in the case of 2-ClassesFigure 4.10: Comparing Error Rate of classifiers with 10-fold Cross-Validation in the case of 3-Classes Figure 4.11: Comparing Error Rate of classifiers with 10-fold Cross-Validation in the case of 3-Classes (a)   (b)   (c)    <-classified as----  ----  ---- 29    30    10    (a): class High 18    62    15    (b): class Middle  5    20    38    (c): class Low(a)   (b)    <-classified as----  ----147    17    (a): class Passed 30    33    (b): class FailedTable 4.14: Comparing the Error Rate of CART, between  2-Classes, 3-Classess, and 9-ClassesUsing Leave-One-Out method all learning and testing test.Table 4.11: Variable Importance in 2-Classes Using Gini CriterionVariable TOTCORR100.00||||||||||||||||||||||||||||||||||||||||||TRIES58.61||||||||||||||||||||||||FIRSTCRR27.70|||||||||||SLVDTIME24.60||||||||||TOTTIME24.47||||||||||DISCUSS9.21|||Table 4.12: Variable Importance in 3-Classes Using Entropy CriterionTable 4.13: Comparing the Error Rate in CART, between 2-Classes, 3-Classess, and 9-ClassesUsing 10-fold Cross-Validation in all learning and testing test.Figure 2.2: Components of an ITSTable 4.13: Comparing the Error Rate of all classifiers on PHY183 dataset in the cases of   2-Classes, 3-Classess, and 9-Classes                                                                                                                                                                                                                                                                                                                                                                                                                                       9  :  ;  <  A  N  P  i  l  u            	  	  	  	  #	  8	  źҦ҇sfTD                 hy h4+ 5CJ( OJ QJ aJ  #hy hX, 5CJ( OJ QJ ^J aJ$hy 5CJ OJ QJ ^J h4+ 5CJ OJ QJ ^J h4+ 5CJ h4+ 5CJ OJ QJ h4+ 5OJ QJ h4+ 5CJ OJ QJ h4+ CJ OJ QJ h4+ CJ OJ QJ h4+ 5OJ QJ \ h4+ 5CJ OJ QJ \ h4+ OJ QJ h4+ CJ h4+ CJ( OJ QJ h4+ CJ( OJ QJ h4+ OJ QJ h4+             : ; < = > ? @ A N O P _ i j k l  $a$  d  dh   ~= z9 !v%        _0 l                   # 8 9 : ; 2  $d a$   gdX,  d gdy  $a$ 8 9 : ;   K  # G O q s y | }     - 1   8 <           ԼԼԲԲ墕v h4+ CJ \] hTf CJ hy h4+ 5CJ( OJ QJ aJ hX, 5CJ OJ QJ aJ hy hX, 5CJ( OJ QJ aJ h4+ B*CJ ph h4+ CJ h h4+ B*CJ ph h4+ 6CJ h4+ CJ h4+ 5CJ OJ QJ hn 5CJ OJ QJ aJ hy 5CJ OJ QJ aJ *2 3 <                     $ d a$gdX,  $ a$gdX,  $ a$gdy  & F d  d  $d a$     j! k! l! !$  !$b$  d            6%  &  (  (  (  ƷtfYMG
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h4+ CJ UVh4+ 6CJ
h4+ CJ  j    h4+ CJ Uj h4+ EHU %              ç  ħ  ʧ  ˧    a  z  {          >  ?      ̩  ͩ          F  G  c  e              a  b  u            ֲ      ؿؿظءث               h4+ 6OJ  QJ  h4+ OJ  QJ   h4+ 6B*CJ ph     h4+ B*CJ ph    h4+ 5CJ OJ QJ ^J h4+ 5CJ h4+ 6CJ ] h4+ 6CJ H* h4+ 6CJ
h4+ CJ  j    h4+ CJ Uj h4+ EHUj:@
h4+ CJ UV 1a  b  u  [              ֲ  T  U    Y  յ                                                                                                                                                                                                                                                             
& F* h88d ^8  d   $ & F  S   d ^  a$  d   $ & F' d a$  $ & F  n d a$   $d a$         Ƴ  ǳ                       "  T  U  Y  Z  c  d  y  z  |                      Ĵ  Ŵ  ƴ  
/  0  1  V  W  \  ]  _    p  q  r  s  t                      䶦   j h4+ CJ EHOJ  QJ  Uj	:@
h4+ OJ  QJ  UVj    h4+ OJ  QJ  Uh4+ H*OJ  QJ  h4+ CJ
OJ  QJ   h4+ OJ  QJ   h4+ 6OJ  QJ  h4+ 6H*OJ  QJ  A          е  ѵ  ҵ      +  ,  b  c                A  B  R  S  T  U  q  r  s  t                      ŷ  Ʒ    ˾شاشؐشyo   j" h4+ EHUj:@
h4+ CJ UVj  h4+ EHUj:@
h4+ CJ UVj h4+ EHUj
:@
h4+ CJ UVj    h4+ CJ Uh4+ 5CJ OJ QJ ^J
h4+ CJ  h4+ 6CJ
h4+ CJ
h4+ CJ
h4+ 6OJ  QJ  h4+ OJ  QJ   h4+ 6H*OJ  QJ  +      E  u                               4                                                                                                                                                                                                                                                        $a$  $ & F     d ^  a$     d  ' d     $ *$    $d a$   $d a$  $ & F   d ^  a$         M  N  ^  _    a  e  f  g  h  i  j  z  {  |  }  ~                        ָ  ׸                      )  ĺu          j, h4+ EHUj:@
h4+ CJ UVj* h4+ EHUj:@
h4+ CJ UVj( h4+ EHUj:@
h4+ CJ UVj& h4+ EHUj:@
h4+ CJ UVj$ h4+ EHUj:@ h4+ CJ UVj h4+ CJ U h4+ CJ h4+ 6CJ ,) * + , 0 1 A B C D K L \ ] ^ _ c d t u v w x y ¹ ù Ĺ ش؝؆|oe^ h4+ 6CJ j9 h4+ EHUj:@ h4+ CJ UVj7 h4+ EHUj:@ h4+ CJ UVj 5 h4+ EHUj:@ h4+ CJ UVj93 h4+ EHUj:@ h4+ CJ UVj0 h4+ EHUj:@ h4+ CJ UV h4+ CJ j h4+ CJ Uj. h4+ EHUj:@ h4+ CJ UV$Ĺ  Ź  ƹ  ǹ  ׹  ع  ٹ  ڹ  ۹  ܹ               1  2  3  4  D  E  F  G  T  e  u  v            ˺  ̺  ܺ  ݺ  ĺzk                              j:@
h4+ OJ  QJ  UVj    h4+ OJ  QJ  Uh4+ OJ  QJ   j&A h4+ EHUj5*@
h4+ UVj#? h4+ EHUj:@
h4+ CJ UVj = h4+ EHUj:@
h4+ CJ UVj; h4+ EHUj:@
h4+ CJ UVj    h4+ CJ U
h4+ CJ  h4+ 6CJ  $ݺ ޺ ߺ " # H I  w x   Ͽ п 0 1 ȸ׫ۢۜwpۢf j h4+ CJ Uh4+ 6CJ h4+ 6B*CJ ph h4+ B*CJ ph h4+ 56CJ OJ QJ ^J h4+ CJ h4+ 6OJ QJ h4+ 5CJ OJ QJ ^J jbE h4+ CJ EHOJ QJ U j :@ h4+ OJ QJ UVh4+ h4+ OJ QJ j h4+ OJ QJ U jC h4+ CJ EHOJ QJ U #     O P e f v w x y 6 K Ƽدؘхxn_ h4+ 5CJ OJ QJ ^J aJ j3P h4+ EHUj#:@ h4+ CJ UVh4+ 6CJ H* jRN h4+ EHUj":@ h4+ CJ UVj0L h4+ EHUj!:@ h4+ CJ UVj6I h4+ EHUjh*@ h4+ UVh4+ 6CJ h4+ CJ j h4+ CJ Uj4G h4+ EHUj :@ h4+ CJ UV$4  5  6  K    \            n  o    3  6  :                                                                                                                                                                                                                d   $ & F   d ^  a$   $d a$   $   d a$  $ & F  7   d ^  a$  $d a$ $& F- h *$ ^$ *$   $ & F d a$    K        &  A  O                K  N  X  o          X  d    S  T  U  V  W  [  \                 1  ýðsss                               h4+ 6B*H*OJ  QJ  ph    h4+ 6B*OJ  QJ  ph     h4+ B*OJ  QJ  ph    &h4+ 5B*CJ OJ QJ ^J aJ ph     h4+ 5CJ OJ QJ aJ
h4+ CJ  h4+ B*CJ ph    h4+ 6B*CJ ph     "h4+ 5B*CJ OJ QJ aJ ph     h4+  h4+ 6OJ  QJ  h4+ OJ  QJ  '1  2  B  C  D  E                     #  $% & , - 1 3 5 6 9 : B C I J L 񸪛wg񪸪YYYYY j h4+ UmH nH u jS h4+ 6B*EHUph %j(P@ h4+ CJ OJ QJ UVaJ h4+ 6OJ QJ h4+ OJ QJ h4+ 6B*H*OJ QJ ph h4+ 6B*OJ QJ ph h4+ B*OJ QJ ph jQ h4+ 6B*EHUph %jP@ h4+ CJ OJ QJ UVaJ h4+ 6B*ph j h4+ 6B*Uph : C J M O Q R K m  M N $d 7$8$ H$a$  $ & F   d ^  a$   $d a$ 5 d    $d a$  d  L  M  N  O  P  Q  x  y                            K  L  \  ]  ^  _  b  f  g  k  m      zzshVzz   #jW h4+ 6B*CJ EHUph    j@
h4+ UVh4+ CJ h h4+ B*ph    h4+ 6B*ph     #jU h4+ 6B*CJ EHUph    jʑ@
h4+ UVj    h4+ 6B*CJ Uph    h4+ 6B*CJ ph     j    h4+ UmH nH u "h4+ B*CJ mH nH ph    sH	u j    h4+ UmH nH sH	u h4+ B*CJ ph     !                                                  xox\JxCx          h4+ CJ h #j^ h4+ 6B*CJ EHUph    %j6@
h4+ 6B*CJ UVph    h4+ 6CJ h  h4+ CJ h
h4+ CJ  h4+ 5CJ OJ QJ j\ h4+ B*EHUph     j*Q@
h4+ UVh4+ B*ph    j    h4+ B*Uph     h4+ B*CJ ph    j    h4+ 6B*CJ Uph    jZ h4+ 6B*EHUph    j(P@
h4+ UVh4+ 6B*CJ ph        )  *  +  ,  [    5        P  i      M  Y  j
d  M  N      #        &  6      O  ƴƦƞƦƦ~rjjj                       h4+ 0J OJ  QJ   h4+ OJ  QJ   h4+ B*CJ aJ ph    'j    h4+ 0J0 CJ PJ UaJ nHtHh4+ B*CJ aJ ph   h4+ CJ aJ  h4+ CJ PJ aJ nHtH "h4+ 5B*CJ OJ QJ ^J ph     h4+ B*CJ ph    jb h4+ CJ EHUh  j6@
h4+ CJ UVh  h4+ CJ h j    h4+ CJ Uh !    e  g                                                                                                                                                                                                                                                                      2 $d a$ 2 $d a$ ( $d a$   $dh a$
&F  n  d 7$8$ H$ d 7$ 8$H$    $ & F d 7$ 8$H$ a$  $d a$ $d 7$8$ H$a$ O  _          o  p                                                ӼǦӇyǚjW                    %j' A
h4+ CJ OJ  QJ  UVaJ h4+ 6CJ OJ  QJ  ]aJ  jcf h4+ CJ EHUh  %jY A
h4+ CJ OJ  QJ  UVaJ h4+ CJ OJ  QJ  aJ  h4+ CJ aJ  jc h4+ CJ EHUh  j A
h4+ UVj    h4+ CJ Uh  h4+ CJ h h4+ 6CJ ]h h4+ 5\^J  h4+ OJ  QJ   h4+ 6OJ  QJ  ]                T  U                                &  '  (  )  [  \  l  m  n  o  ߹ߣߘqfX  jp h4+ CJ EHUh  jo A
h4+ UVjn h4+ CJ EHUh  j A
h4+ UVjm h4+ CJ EHUh  j A
h4+ UVh4+ CJ aJ  jwj h4+ CJ EHUh  j A
h4+ UVh4+ 6CJ OJ  QJ  ]aJ  h4+ CJ OJ  QJ  aJ  h4+ CJ h j    h4+ CJ Uh  j~h h4+ CJ EHUh "o  t  u
%  &  ^  _  o  p  q  r            Ⱥ~vmv]                 h4+ B*CJ OJ  QJ  aJ ph    h4+ 5\^J  h4+ OJ  QJ   jx h4+ CJ EHUh  j A
h4+ UVjv h4+ CJ EHUh  j A
h4+ UVh4+ 6CJ ]h jt h4+ CJ EHUh  jo A
h4+ UVjr h4+ CJ EHUh  j A
h4+ UVj    h4+ CJ Uh  h4+ CJ h  !      $7 8 I  $        I  J  K  S  k  '                                                                                                                                                                                                                                                                     $d a$
&F    $d a$  d 
&F   	
&F  S  ( $d a$ ( $d a$ 
&F d 7$8$ H$   ! " # 7 8 I  $      I  J  S    ĸĀnnf^nZnTNn
h4+ CJ
h4+ CJ  h4+  h4+ CJ aJ  h4+ OJ  QJ   #h4+ B*CJ OJ QJ ^J aJ ph    h4+ B*CJ OJ  QJ  aJ ph    jz h4+ CJ EHUh  %jA
h4+ CJ OJ  QJ  UVaJ h4+ CJ h j    h4+ CJ Uh  h4+ B*CJ OJ  QJ  aJ ph    h4+ CJ OJ  QJ  aJ  "h4+ CJ OJ  PJ QJ  aJ nHtH h4+ CJ PJ aJ nHtH                                      H L      ! " ʸݒyyiVDi  #jj} h4+ 6B*CJ EHUph    %j6@
h4+ 6B*CJ UVph    j    h4+ 6B*CJ Uph    h4+ 6CJ h4+ 5CJ OJ QJ h4+ CJ \
h4+ CJ  h4+ CJ OJ QJ  h4+ 6B*CJ ph     h4+ B*CJ ph    "h4+ 5B*CJ OJ QJ ^J ph     h4+ CJ aJ  h4+ 6CJ ]aJ  h4+ CJ aJ  h4+ CJ OJ  QJ  aJ  h4+ 6CJ OJ  QJ  ]aJ '    A                   #                                                                                                                                                                                                                                                                                      $d a$   $d a$   $ & F d 7$ 8$H$ a$  $d d d [$\$a$ ( $d a$ ( $
& F d a$ "                                        ) ʽ֣֮֮ւsfʽ֮h4+ 6B*CJ H*ph j h4+ B*EHUph "j(:@ h4+ B*CJ UVph j h4+ B*EHUph j@ h4+ UV j h4+ B*CJ Uph h4+ 6B*CJ H*ph h4+ 6B*CJ ph h4+ B*CJ ph j h4+ UmH nH u h4+ 5B*CJ ph h4+ CJ (     ,  -    ~  ( ) P % & ? F [    $d a$ $
&F     d ^    a$ & F   d ^   d $
& F d a$  $d a$ ) * + , 1 2 B C D E   X Y i j k l r s                   ƻƠƕРyn_РyƠyƠy j h4+ B*EHUph j@ h4+ UVh4+ 6B*CJ H*ph jχ h4+ B*EHUph j>@ h4+ UVh4+ 6B*CJ ph j h4+ B*EHUph jw@ h4+ UVh4+ B*CJ ph j h4+ B*CJ Uph j߃ h4+ B*EHUph "j):@ h4+ B*CJ UVph "                          !  " $ % & / 0 1 3 4 D E F G I J K U V a b c d  ǻזǻ{זǻkזזזj@ h4+ 6B*EHUph    jo h4+ 6B*EHUph    j^@
h4+ UVh4+ B*CJ ph    j h4+ 6B*EHUph    js^@
h4+ UVh4+ 6B*CJ ph     j    h4+ 6B*CJ Uph    h4+ B*CJ H*ph     h4+ 6B*CJ H*]ph     h4+ 6B*CJ ]ph     *                            	  ( P ̙~scV             h4+ 5CJ OJ QJ h  j֔ h4+ 6B*EHUph    j@
h4+ UVj h4+ 6B*EHUph    jg@
h4+ UVh4+ B*CJ ]ph     j h4+ 6B*EHUph    j^@
h4+ UVh4+ 6B*CJ ph     j    h4+ 6B*CJ Uph    h4+ B*CJ ph    h4+ B*CJ H*ph     h4+ 6B*CJ ]ph     P f  9 > Q    % & ? R T F G W X Y Z [ a b r s t u     ÷Ç}pd}}W                    j6@
h4+ CJ UVj h4+ CJ EHUj6@
h4+ CJ UVj    h4+ CJ Uh4+ 6CJ OJ QJ #j h4+ 6B*CJ EHUph    %j6@
h4+ 6B*CJ UVph    h4+ 6B*CJ ph     j    h4+ 6B*CJ Uph    h4+ 5CJ OJ QJ h4+ 5CJ OJ QJ h  h4+ 6CJ
h4+ CJ  h4+ CJ h            i j z { | } ~            
   # + \ E ˿زؙ{wh\h\h\w     h4+ B*CJ \ph     h4+ 6B*CJ \]ph     h4+  "h4+ 5B*CJ OJ QJ ^J ph     j h4+ CJ EHUj6@
h4+ CJ UVjI h4+ CJ EHUj6@
h4+ CJ UVjJ h4+ CJ EHUj6@
h4+ CJ UV
h4+ CJ  h4+ 5CJ OJ QJ j    h4+ CJ Ujz h4+ CJ EHU #    # \    {   9                                                                                                             k            k            k                     $ & F  p@ H d a$  $ & F  p@ H d a$   $ p@ H d a$ A    $ & F  p@ H d a$   $ & F  p@ H d a$   $ & F  p@ H d a$ A      $ & F  p@ H d a$ E U     {   1 # 7# P$ d$ 5& H& U( m(  * * * * <+ , , , - - - - i. m. y. . / йаynnnn                  h4+ 6>*CJ \]aJ  h4+ >*CJ \aJ  h4+ CJ aJ h h4+ 6CJ aJ h  h4+ CJ aJ h h4+ 5CJ OJ QJ ^J aJ h4+ 5CJ OJ QJ h4+ CJ \aJ h4+ 5CJ OJ QJ aJ h4+ B*CJ ph    h4+ B*CJ \ph     "h4+ 5B*CJ OJ QJ ^J ph     h4+ CJ \h4+  h4+ 6]"9    {  (  )  # # 7# O$ P$ d$ t  $
&F  p@H   d a$ $
&F  p@H    d a$ $   p@H    d a$  $
& F  p@H   d a$ $
&F  p@H    d a$  $ p@H    d a$  $
& F  p@H   d a$ d$ 4& 5& H& T( U( m( 	,
, , , , @- A- - i. ~/ / Y0                                                                                                                                                                                                                                  $ & F  p@ H d a$   $ & F  p@ H d a$  $  p@ H d a$   $ & F  p@ H d a$   $ p@ H d a$ / / / / 80 K0 [0 0 0 0  1 1 3 4 4 =4 >4 b4 c4 d4 e4 f4 g4 4 4 15 25 65 75 .6 /6 06 16 ;6 F6 ȿ}m]            h} h4+ 5CJ( OJ QJ aJ  h} h} 5CJ( OJ QJ aJ  h} 5CJ( OJ QJ aJ  h} 5CJ  OJ QJ aJ h4+ 5CJ  OJ QJ aJ h4+ CJ OJ QJ ^J aJ h h4+ 6CJ ]aJ h h4+ CJ aJ h h4+ CJ aJ  h4+ 5CJ OJ QJ ^J aJ *h4+ CJ \aJ  h4+ CJ \aJ h4+ 6CJ \]aJ  "Y0 Z0 0 0 0  1 M5 N5 -6 .6 06 16 ;6 G6 H6 8 8                                                                                                                                                                                                         $d 7$ 8$H$ a$gd} $d 7$8$ H$a$
$d a$gd}    $ & F  p@ H d a$  $ p@ H d a$   $ p@ H d ^a$   $ p@ H d a$ F6 G6 H6 \6 c6 8 8 %9 &9 '9 (9 09 9 9 9 A: I: V: Z: : : : :  = != "= #= = = = = > h> û߻û߳߳ߨyuhh^                        h4+ OJ QJ ^J  h4+ 5OJ QJ \^J  h}  j    h4+ UmH nH tHu h4+  j h4+ Uh4+ 6OJ  QJ  ] h4+ OJ  QJ   h4+ 5CJ OJ QJ h% CJ aJ  hX, CJ aJ  h CJ aJ  h4+ CJ aJ h h4+ 6CJ ]aJ  h4+ CJ aJ  h} CJ aJ  h} h4+ 5CJ, OJ QJ aJ$8 : : = "=$= %= &= = = = = > > > > 	> > > > >                                                                                                                                                                                                                                                          $$ & #$/ If a$b$ +   d   !  $a$  d  $
&F  7 d a$gdz2  $d 7$8$ H$a$gd  > > > > >  > "> &> (> ,> .> 2> 4> 5> C> E> G> J> M> P> S> V> Y> \> ]> h>                                                                                                                                                                                                                                                                                                                           Ffѵ    FfG    Ff    $$ & #$/ If a$b$ h> m> r> w> }> > > > > > > > > e? g? l? y? |? ?  $$d  $1$If a$	  $$If   a$ $! d a$ ! d   Ffa  $$ & #$/ If   a$b$ h> q> r> v> w> |> }> > > > > > > > > > > > > > > > > ? ?  ? 9? <? e? g? l? y? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ɸɰyyu     h4+  h4+ CJ aJ
h4+ CJ  h4+ 5OJ QJ \^J   h4+ 5CJ OJ QJ \^J aJ  h4+ 6CJ ]aJ  h4+ CJ aJ   h4+ 5CJ OJ QJ \^J aJ  h4+ 5CJ \aJ  &j    h4+ OJ QJ U^J mH nH u h4+ OJ QJ ^J  h4+ CJ OJ QJ ^J aJ -? ? ? ? ? ? ? O            F            F            F            F            F                                              	  $$If   a$ kd $$If T l 4       r k | s d    0        6    4  l a f4T ? ? ? ? ? ? ? O F F F F F $$If a$  kd $$If    T l 4            u r k
|s                d                                                                 0                                6                                                            4 
l a  f4T  ? ? ? ? }@ @ @ Q            I            I            I            5            5               $$ & #$/ If a$b$  $d a$ kdq $$If T l 4      r k | s d    0        6    4  l a f4T ? ? ? ? ? @ @ 7@ =@ }@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ B B B B B uog_g_W_ hZ CJ aJ h4+ CJ aJ hz2 CJ aJ h4+ CJ j h4+ UmH nH u h4+ h4+ CJ h4+ CJ aJ h4+ 5CJ OJ QJ \^J aJ h4+ CJ OJ QJ ^J aJ h4+ 6CJ \]aJ h4+ CJ \aJ h4+ 5CJ OJ QJ ^J aJ h4+ 5CJ aJ h4+ 5CJ OJ QJ %j h4+ 5OJ QJ UmH nH u @ @ @ @  $$ & #$/ If   a$b$   $ & #$/ If   b$ @ @ @ @ @ @ F 2 2 2 2  $$ & #$/ If   a$b$  kdX $$If    T l 4            r 	
Su                                                 -                                 6   0                                6                                                             4 
l a  e4f4T  @ @ @ @             2            *                                            $d a$  kda $$If    T l 4            r 	
Su                                                 -                                 6   0                                6                                                             4 
l a  e4f4T    $$ & #$/ If a$b$ @ @ @ @ B B B C C C /E 0E OE E F F F $! d a$ $
& F8 d a$ $
&F d     @&	  $ & F  7 d a$gdz2    $d a$  $  p@ H d a$gdZ   $  p@ H d a$     $d a$  B B B B C C C C C C C C C /D 8D D D D D 0E OE E
F F F F G G [S \S S U 7V ĵ𗏈{qme[                  h4+ CJ OJ  QJ   h4+ OJ  QJ   h4+  h4+ CJ OJ QJ  h4+ 5CJ
h4+ CJ  h4+ CJ h h4+ CJ aJ  h4+ CJ OJ QJ aJ  h4+ CJ aJ h h4+ 6CJ aJ h4+ 5CJ OJ QJ \aJ  h4+ 5CJ OJ QJ \ h4+ 5CJ OJ QJ h4+ 5CJ OJ QJ h  h4+ CJ \h4+ CJ aJ  h CJ aJ  F G \G }G G G 8H yH H H 0I sI I I I I I J gJ J J AK K K L AL L L M                                                                                                                                                                                                                                                                                                                                                            2    $d a$ M JM M M N _N tN N N O bO O O P -P oP P P :Q Q Q Q #R oR R R S [S \S                                                                                                                                                                                                                                                                                                                                                           $  @& 2 \S ]S S U 7V KV ^V uV V V W &W GW qW vW xW yW W W W W W +X ,X Y Z 5  ( $    a$ (    $d a$ 7V W +X ,X Z Z Z Z Z Z Z Z Z [ ([ Y[ ][ \ \ \ ] ] ] *] ^ ^ (^ ^ L_ U_ W_ [_ _ l_ _ _ _   O Ԭssg hz2 h4+ 5>*CJ hz2 h4+ 5>*CJ hz2 h4+ CJ h4+ 6CJ aJ h4+ CJ aJ h h4+ CJ OJ QJ aJ h4+ aJ h4+ CJ aJ h4+ CJ OJ QJ aJ h4+ 6OJ QJ aJ h4+ 6CJ aJ h4+ CJ aJ h4+ OJ QJ h4+ h h4+ CJ h mH sH h4+ CJ OJ QJ h 'Z ^ ^ (^ _ +a a a b Fi Gi i i i j Ej $
& F6 d a$  d  $a$  ^ &$d %d &d 'd N    O    P    Q    gdz2   d       gdz2  $! d a$ $& F d   @&  $d a$ $ 7 d a$ O Q T ^      a (a .a >a Ea Ra Xa ca ha sa xa a a a a a b b b Bc Dc nc pc c c d d Wd d d d Ue We e e e e .f 0f @f f } h4+ 5CJ h4+ 5CJ h4+ CJ h4+ 5CJ h4+ 6CJ h4+ CJ h4+ >*CJ h4+ OJ QJ h4+ CJ hz2 h4+ 6>*CJ hz2 h4+ >*CJ hz2 h4+ 6CJ hz2 h4+ 5CJ hz2 h4+ 5CJ hz2 h4+ CJ hz2 h4+ CJ 1f f f f g sg g g g g g g g g Ch Eh Uh ^h bh ch h h h h Di Fi Gi Qi i i o [p p p q q ߳sja h4+ OJ QJ h h4+ CJ aJ h h4+ CJ OJ QJ aJ h4+ OJ QJ aJ h4+ CJ aJ h4+ CJ h4+ CJ OJ QJ aJ h4+ CJ h h4+ 5CJ h h4+ 5CJ OJ QJ \^J aJ h4+ 6>*CJ h4+ 5>*CJ h4+ 5>*CJ h4+ CJ h4+ 5CJ h4+ 5CJ h4+ 6CJ h4+ CJ #Ej j k l l l \m n Nn o o [p p q q q q Is  d   $
&F     @&	 $& F  7 ;d ^;a$    $d a$   $hd ^ha$  $ & F6 d a$ q q q Is Us Xs ys s s 	t t ct xt t t u *u ku {u u u v )v lv yv v v 8w Bw uw vw y y <y =y Ny Ry cy fy vy xy zy y y y y y y y y y y ȿ    h4+ B*	eh  ph   r       h4+ B*eh  ph   r      h4+ eh  r     h4+ CJ h h4+ CJ h h4+ h mH	sH	h4+ CJ h h4+ 5CJ h
h4+ CJ  h4+ 5OJ QJ ^J 	h4+ 5
h4+ CJ  h4+  h4+ OJ QJ 3Is Us Xs ks ss ys zs                                                             9                       kdj $$If                 \ L B6$        ~          0          4   aj $$If a$ '3 L$d %d &d 'd N  O  P  Q  L zs }s s s s s s s s s c kdN $$If       \ L B6$        ~	        0                                            4 
 aj	  dh $If s s s t t ?t l c c c c dh $If      kd. $$If                \ L B6$        ~          0          4   aj ?t @t Ct ct xt t l c c c c dh $If      kd $$If                \ L B6$        ~          0          4   aj t t t t t t l c c c c dh $If      kd $$If                \ L B6$        ~          0          4   aj t t t u *u Gu l c c c c dh $If      kd $$If                \ L B6$        ~          0          4   aj Gu Hu Ku ku {u u l c c c c dh $If      kd $$If                \ L B6$        ~          0          4   aj u u u u u u l c c c c dh $If      kd $$If                \ L B6$        ~          0          4   aj u u u v )v Gv l c c c c dh $If      kdn $$If                \ L B6$        ~          0          4   aj Gv Hv Lv lv yv v l c c c c dh $If      kdN $$If                \ L B6$        ~          0          4   aj v v v v v v l c c c c dh $If      kd. $$If                \ L B6$        ~          0          4   aj v v v w w 7w l c c c c dh $If      kd $$If                \ L B6$        ~          0          4   aj 7w 8w 9w uw vw y y y l g b  X X V   $d a$ 5  $a$  $a$ kd $$If       \ L B6$        ~	        0                                            4 
 aj y y y y { { j{ k{ |{ | | P| ^| } } } ~ ~ ~ ~ L~ M~ ]~ ^~ _~ ~ f~ g~ w~ ƾth[R                    h4+ 6CJ H* j    h4+ 6CJ H*Uj h4+ CJ EHUj+:@
h4+ CJ UV
h4+ CJ  j    h4+ CJ Uh4+ 6CJ aJ h  h4+ CJ aJ h h4+ 5CJ h  h4+ 6CJ h  h4+ CJ h h4+ OJ QJ  h4+ CJ h
h4+ CJ  h4+ 5CJ h4+   h4+ B*	eh  ph   r       h4+ B*eh  ph   r     y Fz ~z z { { i{ j{ k{ |{ } ~ ~ ~  T   j                                                                                                                                                                                                                                P   $ & F; d a$  $ & F; a$   $d a$ $& F d   @&  $dh a$  $a$ '  $d  %d &d 'd  N     O    P    Q     ]  w~ x~ y~ z~ ~ ~ ~ ~ ~ ~ ~ ~ ~            ! T Y     j k { | } ~  ƽƶͬͬ͆͟zƽͶvͬi]  j h4+ CJ EHUj0:@
h4+ CJ UVh4+  j h4+ CJ EHUj/:@
h4+ CJ UVj h4+ CJ EHUj.:@
h4+ CJ UVj    h4+ CJ Uh4+ 5CJ h4+ 5CJ h  h4+ CJ h
h4+ CJ  j    h4+ 6CJ H*Uj h4+ 6CJ EHH*Uj-:@
h4+ 6CJ H*UV $j          " ' - 4 9 ? H Q R T         $If      Ff? 	  $$If   a$   $a$    ݀ ހ ߀    Q S T U ́ ́ ΁ ߁                                              ľĩľľĩľ j h4+ CJ Uh4+ 0J CJ j h4+ CJ U h4+ CJ j h4+ CJ U h4+ CJ h4+ 5CJ OJ QJ ^J aJ h4+ 0J j h4+ Uj h4+ Uh4+ =                    Â Ȃ ɂ ˂ S W [ ^  Ff  Ff  $If                Â ǂ Ȃ ʂ ˂ ̂ J K L Q R S V W Z [ ] ^ b c f g h i l m q r u v y z ~          
               ! $ % ) * - . 1 2 7 j h4+ CJ Uh4+ 0J CJ j h4+ CJ U h4+ CJ j h4+ CJ U h4+ CJ h4+ M^ c g i m r v z           ! % * . 2 8 = > @ ф  Ff   Ff  $If    7 8 < = ? @ A    τ Є ф Ԅ Մ ؄ ل ڄ ۄ ߄                                            ą Ņ ȅ Ʌ ͅ ΅ ҅ Ӆ Յ օ ׅ N                        j h4+ CJ Uh4+ 0J CJ  j h4+ CJ U
h4+ CJ  j    h4+ CJ Uh4+
h4+ CJ Iф Մ ل ۄ                     Ņ Ʌ ΅ Ӆ                                                                                                                                                                                                                                                                                                                                                                 Ff'    $If Ӆ ԅ օ c g k n s w y }        ( , 0 3 8 < > B G K  Ff?  $If      Ff<  N O P a b c f g j k m n r s v w x y | }                 & ' ( + , / 0 2 3 7 8 ; < = > A B F G J K N O T U Z [ ] ^ _ և ׇ ؇     ڶj h4+ CJ Uj h4+ CJ U
h4+ CJ  h4+
h4+ CJ  h4+ 0J CJ  j    h4+ CJ Uj h4+ CJ U HK O U [ \ ^      
       $ % (      ň ǈ  FfE   FfB  $If              	
            # $ ' ( )               Ĉ ň ƈ ǈ ʈ ˈ ψ Ј ӈ Ԉ ׈ ؈ ܈ ݈      g h i } ~              j3, h4+ CJ Uh4+ 0J CJ j"$ h4+ CJ U
h4+ CJ  j    h4+ CJ Uh4+
h4+ CJ Mǈ ˈ Ј Ԉ ؈ ݈                   I M R U                                                                                                                                                                                                                                                                                                                                                       Ffk0    FfV(   $If                 7 8 9 G H I L M Q R T U Y Z ] ^ _  c d h i l m p q u v z { ~                     " # ' ( + , / 0 4 5 : j]< h4+ CJ Uh4+ 0J CJ jH4 h4+ CJ U h4+ CJ j h4+ CJ U h4+ CJ h4+ MU Z ^  d i m q v { |         # ( , 0 5 ; < =   $a$   Ff@  Ff8  $If    : ; = F       ɋ ʋ ڋ ۋ ܋ ݋ ދ     	      $ & : L M ] ^ _  a T [ \ q r  s j h4+ 0J0 CJ UjtK h4+ CJ EHUj3:@ h4+ CJ UVj=G h4+ CJ EHUj2:@ h4+ CJ UVjjD h4+ CJ EHUj1:@ h4+ CJ UVj h4+ CJ Uh4+ 6CJ h4+ 5CJ h4+ CJ h h4+ CJ h4+ 5CJ h4+ h4+ CJ *   ɋ ދ   L a T  A  < y   ȑ b  $d a$ $
&F d a$  $h^ha$  $hha$ 6 d $hd ha$ $
& F; d a$ P  $d a$  $a$ $
& F; a$  $dh a$  A < J d e u v w x y         ȑ b c d e o       𗐆zqicqicX h4+ CJ OJ QJ h h4+ aJ h4+ CJ aJ h4+ 5CJ aJ j c h4+ CJ Uh j*S h4+ CJ Uh4+ CJ h h4+ 5CJ OJ QJ ^J aJ h jP h4+ CJ EHUj5:@ h4+ CJ UV jM hX, hX, CJ EHU j{A hX, UVnHtHj h4+ CJ Uh4+ 6CJ h4+ CJ h4+ 6CJ aJ b e    & ) 8 B $$If a$  $If  $d a$ & F  d   d   d   & B O  M   e   ə ʙ  ( ! W X Y Z        N Q R o N    ۹}uumu}ffۋ[f h4+ 5 h4+ CJ h4+ 5CJ j h4+ Uj h4+ Uj h4+ UmH nH u h4+ 5CJ OJ QJ ^J aJ h4+ 56CJ ]aJ h4+ 6CJ h4+ CJ h4+ aJ h4+ 5aJ h4+ <CJ OJ QJ aJ h h4+ CJ OJ QJ aJ h4+ h4+ 5CJ OJ QJ ^J aJ h4+ CJ h4+ CJ OJ QJ h #B C F O  u o o e (   $If     $If kdq $$If T       F $                  0                            6                4 
 a  T       O            I            I            I                                                                                        $If kdr $$If T       F $                  	                        0                            6                4 
 a  p            T      3 O            I            I            I                                                                                        $If kds $$If T       F $                  	                        0                            6                4 
 a  p            T  3 4 7 M  O            I            I            ?
(     $If  $If      kdt $$If    T              F 
$                  0      6    4   a p T      O I I I  $If      kdu $$If    T              F 
$                  0      6    4   a p T     I O I I C + $If     $If kdv $$If T       F $                  	                        0                            6                4 
 a  p            T  I J M ]  O            I            I            I                                                                                        $If kdw $$If T       F $                  	                        0                            6                4 
 a  p            T       O            I            I            I                                                                                        $If kdx $$If T       F $                  	                        0                            6                4 
 a  p            T      e O            I            I            :                                                         3 $&d If P  $If      kdy $$If    T              F 
$                  0      6    4   a p T e f j z Ƙ O I I I  $If      kdz $$If    T              F 
$                  0      6    4   a p T Ƙ ǘ ˘ ۘ % O I I I  $If      kd{ $$If    T              F 
$                  0      6    4   a p T % & * =  O I I I  $If      kd| $$If    T              F 
$                  0      6    4   a p T      O I @ @ $$If a$  $If kd} $$If T       F $                  	                        0                            6                4 
 a  p            T    ș ə ʙ ! W X O            J            J            B            B            B            B                        $d a$   $a$   kd~ $$If    T              F 
$                  0      6    4   a p T X    Q R U ^ g n $$If a$  $  @&   $a$ n o q   ǜ l f f f f  $If      kd $$If                \  sh)"                 0                                            4 
 a ǜ Ȝ ʜ ' , 2 <            6            6            6            6                                 $If kd $$If       \  s h )"                    ( 0          4   ap( 2 3 5 {   < 6 6 6 6  $If     kdĆ $$If                \  sh)"                 	     (                          0                                            4 
 ap(                      ǝ ͝ ҝ <            6            6            6            6                                 $If kd $$If       \  s h )"                    ( 0          4   ap( ҝ ӝ ՝    < 6 6 6 6  $If     kdF $$If                \  sh)"                 	     (                          0                                            4 
 ap(                      A G L <            6            6            6            6                                 $If kd $$If       \  s h )"                    ( 0          4   ap( L M N    < 6 6 6 6  $If     kdȋ $$If                \  sh)"                 	     (                          0                                            4 
 ap(                           2 3 4 l            j            j            j            j            e            j            e            j            j                                          d       kd	 $$If                \  sh)"                 0                                            4 
 a
     2 4 6 B 6 K   |   ϧ ѧ       z 2 U ±¥}iZK                h4+ 5CJ OJ QJ ^J aJ h4+ 5B*CJ \aJ ph    'j    h4+ 0J0 6B*CJ UaJ ph    h4+ B*CJ ]aJ ph     h4+ 6B*CJ aJ ph     h4+ B*CJ aJ ph    h4+ B*CJ aJ ph    h4+ 5CJ OJ QJ \^J aJ  h4+ CJ aJ   h4+ 5CJ OJ QJ \^J aJ  h4+ CJ aJ  h4+
h4+ CJ  h4+ OJ  QJ   	h4+ 5
h4+ CJ 4 B 4 5 6 K   1 2 \   u v   g h                                                                                                                                                                                                                                        $ d ^a$  $ & F d a$   $d a$  $ & F d a$   $ & F d 7$ 8$H$ a$ $d 7$8$ H$a$   $ & F d 7$ 8$H$ a$ U \       . I O j   d e g ï Ư  '       8 9 L M 浰棛zlW (jڮq@ h4+ CJ UVaJ mH nH u j h4+ CJ EHUaJ (jJq@ h4+ CJ UVaJ mH nH u j h4+ CJ UaJ h4+ CJ aJ h4+ 5CJ OJ QJ aJ h4+ h j h4+ 0J0 Uh h4+ B*CJ aJ h ph h4+ 6CJ ]aJ h h4+ 6CJ aJ h h4+ CJ aJ h h4+ 5CJ OJ QJ ^J aJ h h   '  ̲  ƴ ٴ  $$If a$	 d 7$8$ H$$d 7$8$ H$a$   $ & F d 7$ 8$H$ a$ $d 7$8$ H$a$   $d a$ 	M N O   Ȳ ɲ ʲ ˲ ̲  Ŵ ƴ ش ٴ    
 ˽݌~sdUdUPF9               h4+ 5OJ QJ \^J  h4+ OJ QJ ^J  	h4+ ;h4+ ;CJ OJ QJ ^J aJ h4+ 5CJ OJ QJ ^J aJ h4+ ;OJ QJ ^J h4+ OJ QJ ^J nHtH h4+ OJ  QJ   'jG h4+ 6B*CJ EHUaJ ph    (jq@
h4+ CJ UVaJ mH nH u h4+ 6B*CJ aJ ph     #j    h4+ 6B*CJ UaJ ph    h4+ CJ aJ  j    h4+ CJ UaJ j h4+ CJ EHUaJ     
   l            f            f            ]            ]            ]                                                                                            	  $$If   a$ $If      kdu $$If   l 4       F  $$f P  t 0       6    4  4  l a f4     " ) 0 7 > ? C J Q X ^ _ c j q x                ĵ ˵ ҵ ٵ ڵ          e  𤝔} h4+ 5CJ OJ QJ aJ h h4+ OJ QJ h4+ CJ aJ h h4+ 5CJ j h4+ UmH nH u h4+ 5CJ OJ QJ \^J aJ h4+ CJ OJ QJ ^J aJ h4+ 5CJ OJ QJ \^J aJ h4+ CJ OJ QJ ^J aJ h4+ h4+ 5OJ QJ ^J 1  " ) 0 7 > L F = = = = If a If kd3 If l        r  $$f                $   $
t$0       6     4  4  l a > ? C J Q X ^ L C C C C C $$If a$  kd $$If   l       ;r  $$f      t 0       6     4  4  l a ^ _ c j q x  L C C C C C If a kd If l       ;r  $$f                $   $
t$0       6     4  4  l a        L C C C C C $$If a$  kd $$If   l       ;r  $$f      t 0       6     4  4  l a        L C C C C C If a kdǗ If l       ;r  $$f                $   $
t$0       6     4  4  l a    ĵ ˵ ҵ ٵ L C C C C C $$If a$  kd $$If   l       ;r  $$f      t 0       6     4  4  l a ٵ ڵ      L C C C C C If a kd If l       ;r  $$f                $   $
t$0       6     4  4  l a     Ŷ [ L J B = 0   d ^   d  $d a$  kdv $$If l       ;r   $$f      t 0       6     4  4  l a [ e f  ú ĺ n o      If a  d 7 8 H   & F |d ^|a  d a  vd ^v         ʹ   Ǻ ͺ  ' (   4 M o r y   پ     󰠰ttj\ h4+ OJ QJ ^J nHtH h4+ CJ OJ QJ h4+ 6OJ QJ ]h h4+ 5OJ QJ \h h4+ OJ QJ h h4+ 6CJ aJ h j h4+ 0J0 CJ UaJ h h4+ CJ aJ h h4+ 5B*CJ \aJ ph h4+ B*CJ ]aJ ph h4+ 6B*CJ aJ ph h4+ 6B*CJ ]aJ ph h4+ B*CJ aJ ph              ' . 5 < = A H O U \ ] d k q x ~                      ̥̥̥̥̥̥̥̥̥̥̥̥̥̥ᕍ h4+ CJ aJ j h4+ UaJ mH nH u "h4+ CJ OJ QJ ^J aJ nHtH (h4+ 5CJ OJ QJ \^J aJ nHtH (h4+ 5CJ OJ QJ \^J aJ nHtH h4+ PJ nHtH (h4+ 5CJ OJ QJ \^J aJ nHtH1       r i i i i i If a kd[ If l       F  P   t 0       6   4  4  l a        L C C C C C If a kd If l       ;r & P W ^   t 0       6     4  4  l a    ' . 5 < L C C C C C If a kd If l       ;r &$$P$W                $^$                $ t 0       6     4  4  l a < = A H O U \ L C C C C C $$If a$  kdƝ $$If   l       ;r &$$P W ^   t 0       6     4  4  l a \ ] d k q x ~ L C C C C C If a kd If l       ;r &$$P                $W$^                $$
t   0                                    6                                                              4   4 
l a   ~       L            C            C            C            C            C                                        	  $$If   a$ kd $$If l       ;r & $$P W ^   t 0       6     4  4  l a        L C C C C C If a kdc If l       ;r &$$P$W                $^$                $ t 0       6     4  4  l a        L C C C C C $$If a$  kdB $$If   l       ;r &$$P W ^   t 0       6     4  4  l a       g L D D D 9 D 2  & F d a 2 d a kd! If l       ;r &$$P                $W$^                $$
t   0                                    6                                                              4   4 
l a     g h i j k l   ! " # $ H N U [      ½皌}i^^NFB h4+ jw h4+ U j h4+ UaJ mH nH u h4+ 6CJ ]aJ 'jz h4+ 6B*CJ EHUaJ ph jHA h4+ UVnHtHh4+ 6B*CJ aJ ph #j h4+ 6B*CJ UaJ ph h4+ 5CJ OJ QJ \^J aJ h4+ h j  h4+ CJ UaJ 0j h4+ 5OJ QJ U\^J aJ mH nH u h4+ CJ aJ h4+ 5CJ OJ QJ \^J aJ g h k l  %   !        q r      $$ &#$/ If   a$  $a$  $d a$ 2 $d a$ 2 $d a$           q r      ; < B U V Z h m n r y                 čččnčnččnččn h4+ 5CJ OJ QJ \^J aJ h4+ CJ OJ QJ ^J aJ h4+ 5CJ OJ QJ aJ h4+ 5CJ OJ QJ \aJ h4+ CJ aJ h h4+ CJ aJ h h4+ CJ aJ h h4+ j> h4+ Uj h4+ Uh &j h4+ CJ UaJ mH nH tHu h4+ CJ aJ h4+ 6CJ aJ +   ' 1 ; u u u u  $$ &#$/ If   a$x kdI $$If l       e0  ! w 0              4  4  l a ; < B I P U a O O O O  $$ &#$/ If   a$ kdnJ $$If l       e\  n ! m m  0              4  4  l a U V Z a h m a O O O O  $$ &#$/ If   a$ kd K $$If l       \  n ! m m  0              4  4  l a m n r y   a O O O O  $$ &#$/ If   a$ kdK $$If l       \  n ! m m  0              4  4  l a       a O O O O  $$ &#$/ If   a$ kdL $$If l       \  n ! m m  0              4  4  l a       a O O O O  $$ &#$/ If   a$ kd2M $$If l       \  n ! m m  0              4  4  l a       a O O O O  $$ &#$/ If   a$ kdM $$If l       \  n ! m m  0              4  4  l a       a O O O O  $$ &#$/ If   a$ kdN $$If l       P \  n ! m m  0              4  4  l a       a O O O O  $$ &#$/ If   a$ kdEO $$If l       \  n ! m m  0              4  4  l a                - . a u      M N O  5 v ಭ|eWOOWOW h4+ CJ aJ h4+ CJ PJ aJ nHtH ,h4+ 5B*CJ OJ QJ \]^J aJ ph$j    h4+ 0J0 6CJ U]aJ h  h4+ 6CJ ]aJ h h4+ CJ aJ h h4+ OJ  QJ  h 	h4+ h j    h4+ UmH nH u h4+ 5CJ OJ QJ \aJ   h4+ 5CJ OJ QJ \^J aJ  h4+  h4+ CJ OJ QJ ^J aJ  h4+ 5CJ OJ QJ aJ        a            O            O            O            O                                                                                   $$ &#$/ If a$  kdO $$If   l       \ 	n!
m                m                                0                                                                                          4   4 
l a        - .  a            Y            Q            I            Q            I            Q                                   $d   *$    $d a$   $dh a$  kdP $$If   l       \ 	n!
m                m                                0                                                                                          4   4 
l a     t v {        Z                                                                                                                                                                                                                               $ & F d 7$ 8$H$ a$$ d    *$7$ 8$H$    $d d d [$\$a$  d d d [$\$
&F 8d   $d 7$ 8$H$ a$ $
&F         d ^    a$ v z {   J R  5 C D T U V W b h     H b     c j   q w سإyfTسإسسسس "jXQ h4+ 6B*EHU]ph %j< A h4+ CJ OJ QJ UVaJ h4+ 6B*]ph j h4+ 6B*U]ph h4+ 6OJ PJ QJ ]nHtH h4+ OJ PJ QJ nHtH h4+ 6CJ PJ ]aJ nHtH 'j h4+ 0J0 CJ OJ QJ U^J aJ h4+ CJ PJ aJ nHtH h4+ 5CJ \ h4+ 5CJ OJ QJ \^J aJ w   H I J K      ] c           8 = V W [ i          ͹ͥtffff hZ CJ PJ aJ nHtH h*7k CJ PJ aJ nHtH #h4+ B*CJ PJ aJ nHph tH h4+ 5CJ PJ \aJ nHtH &h4+ CJ OJ PJ QJ ^J aJ nHtH &h4+ CJ OJ PJ QJ ^J aJ nHtH &h4+ CJ OJ PJ QJ ^J aJ nHtH h4+ 6CJ PJ ]aJ nHtH h4+ CJ PJ aJ nHtH& V W 6 7 <  @ / \ ] Z [ X Z c d $$7$ 8$H$ If   a$ $7$8$ H$a$   $ b d 7$ 8$H$ a$$   *$7$ 8$H$    $d d d [$\$a$ ( $d a$
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&F  (   $d 7$ 8$H$ a$gd}Z $d 7$8$ H$a$   $ 1           % ) 5 6 < @ A    Z [ X ±䛆v_vWSGSW h4+ B*CJ aJ ph h4+ h4+ CJ aJ ,j h4+ 0J0 B*CJ OJ QJ UaJ ph h4+ B*CJ OJ QJ aJ ph )h4+ 5B*CJ OJ QJ \^J aJ ph +h4+ B*CJ OJ PJ QJ ^J nHph tH h}Z h4+ CJ PJ aJ nHtH h}Z h}Z CJ PJ aJ nHtH h4+ 6CJ PJ ]aJ nHtH h4+ CJ PJ aJ nHtH h}Z CJ PJ aJ nHtHX Y        O P % & X Y Z             D E T x y z |          ֯o j h4+ UmH nH tHu h4+ CJ OJ QJ ^J aJ h4+ 5CJ OJ QJ \^J aJ h4+ h4+ 5CJ OJ QJ aJ 'h4+ B*OJ PJ QJ ^J nHph tHh4+ OJ QJ h4+ 6CJ ]aJ h4+ CJ aJ h4+ CJ OJ QJ ^J aJ &j h4+ CJ UaJ mH nH tHu+d e f n u  l kd*S $$If < 4F Q          S              4  < a p    $$7$ 8$H$ If   a$        5 ] kdT $$If < F Q          S         4  < a $$7$ 8$H$ If   a$ ] kdT $$If < F Q          S         4  < a        ] kd U $$If < F Q          S         4  < a $$7$ 8$H$ If   a$        5 ] kd4V $$If < F Q          S         4  < a $$7$ 8$H$ If   a$ ] kdU $$If < F Q          S         4  < a       O P % & x x f x Y  d  7$ 8$H$ ^ $ b d   *$ 7$8$ H$ $ b d 7$8$ H$a$	  $7$ 8$H$ a$ ] kdV $$If < F Q          S         4  < a $$7$ 8$H$ If   a$ & : D N X Y Z c k t V kdLW $$If l       e\ $$    0       6      4  4  l a $$If a$ 	t |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            	  $$If   a$     & $$If a$   kdX $$If   l       ֞ $-$                                K                                K                                J                0                                    6                                                                                        4   4 
l a                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        	  $$If   a$     & $$If a$   kdY $$If   l       ֞ $-$                                K                                K                                J                0                                    6                                                                                        4   4 
l a                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        	  $$If   a$     & $$If a$   kdZ $$If   l       ֞ $-$                                K                                K                                J                0                                    6                                                                                        4   4 
l a                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         	  $$If   a$    & & $$If a$   kd[ $$If   l       ֞ $-$                                K                                K                                J                0                                    6                                                                                        4   4 
l a   & , 2 8 > D                                                                                                                                                                                                                                                                                                                                                                                                                                                                                	  $$If   a$ D E T Z & $$If a$   kd\ $$If   l       ֞ $-$                                K                                K                                J                0                                    6                                                                                        4   4 
l a   Z  f l r x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                	  $$If   a$ x y { | &$            $ kd"] $$If l       P ֞ $- $  K  K  J 0       6    4  4  l a | } ~       I kd&^ $$If l       e\ $$    0       6      4  4  l a $$If a$   d  7$8$ H$^         $$If a$     &                                       	  $$If   a$ kd^ $$If l       ֞ $- $  K  K  K 0       6    4  4  l a       $$If a$ 
     , > D E M S Y _ q r y                        H  I  딌~se   h4+ CJ OJ QJ ^J aJ  h4+ 6CJ ]aJ  h4+ CJ OJ QJ ^J aJ  h4+ CJ aJ  h4+ 5CJ \aJ  jq h4+ Ujd h4+ U h4+ 5CJ OJ QJ \^J aJ  j    h4+ UmH nH tHu h4+ CJ OJ QJ ^J aJ  h4+ 5CJ OJ QJ aJ h4+   h4+ 5CJ OJ QJ \^J aJ '    & &                                       	  $$If   a$ kd_ $$If l       ֞ $- $  K  K  K 0       6    4  4  l a & , 2 8 > D $$If a$ D E M S &                                       	  $$If   a$ kd $$If l       ֞ $- $  K  K  K 0       6    4  4  l a S Y _ e k q $$If a$ q r y  &                                       	  $$If   a$ kda $$If l       ֞ $- $  K  K  K 0       6    4  4  l a       $$If a$     &                                       	  $$If   a$ kdb $$If l       ֞ $- $  K  K  K 0       6    4  4  l a       $$If a$     &            $ d  kdc $$If l       P ֞ $- $  K  K  K 0       6    4  4  l a       J  K  ; K   Y Z  $d 7$8$ H$a$  d (
&F dh    b d 7$8$ H$ $ b d 7$8$ H$a$   $ b hd 7$ 8$H$ ^ha$ $
& F  b d 7$8$ H$a$   $ b dh 7$ 8$H$ a$ I  J  ; < I J K ; C      b c           )  *  m   L  һtdVHh4+ CJ OJ QJ ^J aJ h4+ CJ OJ QJ ^J aJ h4+ OJ PJ QJ ^J nHtH &h4+ CJ OJ PJ QJ ^J aJ nHtH h4+ 5CJ \aJ h4+ 6CJ ]aJ h4+ CJ aJ )h4+ 5B*CJ OJ QJ \^J aJ ph -j h4+ 0J0 5CJ OJ QJ U\^J aJ h4+ 5CJ OJ QJ \^J aJ h4+ h4+ OJ QJ h4+ 5CJ OJ QJ \^J aJ           , > P b c m      $ N O K L                                                                                                                                                                                                                                                                                                                       	  d 7$8$ H$ d 7$ 8$H$   $d 7$ 8$H$ a$ 7$ 8$H$  L N O     _ g h   D v    R W     a f             ) * 0 6 ̾}}o}o                  h4+ CJ OJ QJ ^J aJ  h4+  h4+ 5CJ OJ QJ aJ h4+ 5CJ OJ QJ \aJ  h4+ 5CJ OJ QJ ^J aJ #h4+ B*CJ PJ aJ nHph    tHh4+ CJ OJ
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aJ  h4+ CJ aJ (  ^ _     C D                                                                                                                                                                                                                                                                                              	  $$If   a$ 7$ 8$H$  2 $d a$2 $ & F  dh a$	  d 7$8$ H$ d d  7$ 8$H$   $d 7$ 8$H$ a$        ~ ~ ~ ~ $$If a$x  kd} $$If   l       e0 	!
x                0                                                                  4   4 
l a        # ) ^            U            U            U            U            U                                                                            	  $$If   a$ kdI~ $$If l 4      e\  n ! m m  0              4  4  l a f4 )  *  +  0  6  <  B  K B B B B B $$If a$  kd  $$If   l 4      r 	n!                                  m                m                                0                                                                                                      4   4 
l a  f4 6 B C J \ ] e w x | } ~               	
     ' ( ) + , . 8 T U zq                      h4+ 5CJ aJ ht h4+ 5CJ( OJ QJ aJ  ht hH 5CJ( OJ QJ aJ  haY 5CJ  OJ QJ aJ h4+ 5CJ OJ QJ h4+ CJ PJ aJ nHtH j    h4+ UmH nH tHu h4+ CJ OJ QJ ^J aJ  h4+ 5CJ OJ QJ aJ h4+   h4+ 5CJ OJ QJ \^J aJ (B C D J P V \ K            B            B            B            B            B                                      	  $$If   a$ kd $$If l 4      r  n !    m m  0              4  4  l a f4 \  ]  ^  e  k  q  w  K B B B B B $$If a$  kd $$If   l 4      r 	n!                                  m                m                                0                                                                                                      4   4 
l a  f4 w x y z { | } K            B            B            B            B            B                                      	  $$If   a$ kdL $$If l 4      P r  n !    m m  0              4  4  l a f4 }  ~       K B B B B B $$If a$  kd $$If   l 4      r 	n!                                  m                m                                0                                                                                                      4   4 
l a  f4        K            B            B            B            B            B                                      	  $$If   a$ kdԂ $$If l 4      r  n !    m m  0              4  4  l a f4         K B B B B B $$If a$  kd $$If   l 4      r 	n!                                  m                m                                0                                                                                                      4   4 
l a  f4        K            B            B            B            B            B                                      	  $$If   a$ kd\ $$If l 4      r  n !    m m  0              4  4  l a f4           K B B B B B $$If a$  kd  $$If   l 4      r 	n!                                  m                m                                0                                                                                                      4   4 
l a  f4 	
      K            B            B            B            B            B                                      	  $$If   a$ kd $$If l 4      r  n !    m m  0              4  4  l a f4           !  '  K B B B B B $$If a$  kd $$If   l 4      P r 	n!                                  m                m                                0                                                                                                      4   4 
l a  f4 ' ( * + , - K            B            B            :            /
$d a$gdH  2 $dh a$   d d [$\$  kdl $$If   l 4      r 	n!                                  m                m                                0                                                                                                      4   4 
l a  f4 - . 8 T U    S  T  " " " F# # W$  $
& F d a$gdl<  $
& F d a$gdFJ $d a$gdaY $d a$gd(M $d a$gd]A  $
&F d a$gd >@ $d a$gdt  $d a$ $d a$gdH U              [  q         $ D g k | T                  ! J! K! ! ! " 	" )" _" k" " " " " " ƽ       h(M CJ \aJ h ? CJ \aJ h]A CJ \aJ h_ CJ \aJ hTf CJ \aJ h_ CJ aJ  h4+ CJ aJ  h4+ CJ \aJ #ht h4+ 5CJ OJ QJ ^J aJ #ht ht 5CJ OJ QJ ^J aJ ht CJ \aJ ht ht CJ \aJ  1" " " " " " " " " " # # F# # W$$ $$ $ % % d% q% r% {% l& m& n& o& ' ' "' *' =' N' ' ' ' ' ' ' Ⱦ|pfh4+ CJ OJ QJ h4+ CJ OJ QJ aJ h4+ 5CJ OJ QJ aJ hTf 5CJ OJ QJ aJ hTf 6CJ \]hU 6CJ \]h 6CJ \]h4+ 6CJ \]hl< 6CJ \]hFJ 6CJ \]h4+ CJ \aJ h(M CJ \aJ #h >@ h4+ 5CJ OJ QJ ^J aJ hV4 CJ \aJ (W$ % % % & I& & & R' ' ' ' 0( ( w) ) 1* * 9+                                                                                                                                                                                                                                                          	%     ^     	% ^
$d a$gd_   $ & F d a$gdU   $ & F d a$gd   $ & F d a$  $ & F d a$gd  ' ' ( ( ) ) ) * G* * * * + }+ + + + , , , , - - - "- $- Q- - - - . . Q. R. . . / / / / / / / 0 Ǽްޠ{sެn h4+ H*h4+ OJ QJ h4+ CJ h4+ nHtH h4+ 6PJ ]nHtH h4+ PJ nHtH h4+ 6CJ h4+ 6h4+ h4+ CJ OJ QJ aJ h4+ 6CJ ]aJ h4+ CJ aJ h4+ 6CJ OJ QJ ]aJ h4+ CJ OJ QJ aJ h4+ CJ OJ QJ h4+ 6CJ OJ QJ +9+ + , , - - #-$- - - Q. R. / / / / h0 i0 0 0 K1                                                                                                                                                                                                                                                    $ b 7$ 8$H$ a$  ~= z9 !v%   ^ ( $^a$ (  ^  7$ 8$H$  	% ^  0 d0 e0 h0 0 #1 |1 1 1 1 1 92 U2 n2 2 3 3 3 \4 4 4 4 4 4 5 =5 ]5 l5 m5 5 H6 c6 d6 x6 6 6 6 6 7 Y7 p7 q7 7 8  8 G8 K8 S8 x8 8 8 8 8 8 8 ,9 i9 9 9 9 9 9 %: F: ĶĶհըհը h4+ B*ph    h4+ OJ  QJ
h4+ CJ  h4+ CJ PJ aJ nHtH  h4+ 6CJ PJ ]aJ nHtH h4+ 6CJ h4+ 6CJ OJ  QJ  h4+ CJ OJ  QJ   	h4+ H*h4+  	h4+ 6 ?K1 L1 1 1 T2 U2 3 ~3 3 4 4 4 4 5 m5 n5 c6 d6 6 6 7  7                                                                                                                                                                                                                                                                         ~=z9!v%  	 ^   	 ^ # $d    ^a$   $^a$  7 7 7 F8 G8 8 8 9 9 E: F: 1; 2; &< '< < < = = > > > > o? p? f@                                                                                                                                                                                                                                                                                                                      7$8$ H$^  ^ $^a$ F: J: R: : : : }; ; 9< ;< < < O= Y= Z= [= ]= v= x= = = = 3> 4> ;> >> k> l> > > > > > "? #? %? Q? ? ? ? ? ? @ @ 5@ n@ v@ z@ @ A A A A A 9B QB B B YC fC hC C ND XD YD ZD \D uD wD D LE VE XE E E$F ]F
h4+ 0JD  h4+ 0JD 6] h4+ H*] 	h4+ ]h4+ 6H* h4+ 6] 	h4+ 5	h4+ 6h4+  h4+ B*ph     Lf@ g@ @ @ A !A A +B ,B RB SB B B C C D D E E CF DF |F }F                                                                                                                                                                                                                                                                                    $^a$  $7$ 8$H$ ^a$ $7$8$ H$^a$  7$8$ H$$^a$ ]F mF F F QG G %H cH H H H I I @I kI I I I J vJ J J J J K K K K K kL L M M M M M M M N )N 4N 5N 6N N N N N N N N N O ,O -O .O EO zO O O h4+ CJ h4+ 6B*ph h4+ B*ph h4+ 6H*] h4+ 6] h4+ 5h4+ 0JD 6] h4+ 0JD h4+ 6CJ OJ QJ ] h4+ CJ OJ QJ ]h4+ CJ OJ QJ h4+ ]h4+ h4+ 6 :}F F F G G H H WI J J J J J K K K L L L L M M 5N  $^a$ $^a$ % ^%  Z ^  $a$ $^a$ 5N 6N N N -O .O O O gP hP P P CQ DQ R ~R =S S T 9U U JV W fW % ^ %   ^   d d [$\$  $a$ 7$ 8$H$    $^a$ O O 2P VP P P Q /Q DQ Q Q KR tR uR vR R R =S }S S S S CT U .U /U 0U 9U ]U U U U  V V JV V V V V ,W HW fW pW rW W W W  X X ౢౢ{  j0 h4+ 6U j    h4+ 6U 	h4+ H*h4+ >*CJ OJ  QJ  h4+ 6CJ OJ  QJ  ]aJ  h4+ CJ OJ  QJ  aJ  h4+ 6CJ OJ  QJ  ] h4+ 5CJ OJ  QJ  h4+ 6CJ OJ  QJ  h4+ CJ OJ  QJ   h4+ 6] 	h4+ 6h4+  	h4+ 5 0fW gW X X {X |X Y Y UZ VZ Z Z [ [ 0\ 1\ \ \ ] ] ^ ^ ^                                                                                                                                                                                                                                                                                $a$   $a$ 	  ^  7$8$ H$ $^a$ % ^ $^a$ X X ZX pX |X X X UY Y Y 4Z JZ tZ Z Z Z S[ r[ [ [ \ -\ [\ \ \ h] ] ] ] ] O^ ^ ^ ^ ^ ^ ^ ^ n_ _  ynfnh4+ CJ aJ h4+ 5CJ \aJ #h4+ 5>*CJ OJ QJ \^J aJ h4+ 5CJ0 OJ QJ \^J aJ0 #h4+ B* CJ PJ aJ nHph tH h4+ 5h4+ 5CJ h4+ 6h h4+ h h4+ H*h4+ 6CJ OJ QJ h4+ 6CJ OJ QJ ] h4+ CJ OJ QJ h4+ 6h4+ j h4+ 6U(^ ^ _  w b b b b$b 2b Rb eb                                                                                                                                                                                                    \  kd$ $$If l 4       $ h%        0                                            4 
l a  f4  $If  ^   $ d     @&	   $a$  & b b b b rb sb b b b b b c c kh lh h h h h h i i Fj Oj Uk Vk k k k k k 1l Kl Ll hl l l l l ˺˺˺銂tfh4+ 0J) 67OJ  QJ  ]h4+ 0J) 57OJ  QJ  \h4+ OJ  QJ   h4+ 6OJ  QJ  ] j֖ h4+ Uh4+ 5\ j h4+ Uh4+ 6>*]
h4+ 0J  jT h4+ Uj    h4+ Uh4+ 5CJ \aJ  h4+ 5CJ( \aJ(  h4+  h4+ 5CJ \aJ  h4+ CJ aJ (eb fb rb b                                                                                                                                                                                                                                                                        $If l kd $$If l       0 j$                  0                                                        4 
l a   b b b b                                                                                                                                                                                                                                                                        $If l kd7 $$If l       0 j$                  0                                                        4 
l a   b b b b                                                                                                                                                                                                                                                                        $If l kd׌ $$If l       0 j$                  0                                                        4 
l a   b b b c                                                                                                                                                                                                                                                                        $If l kdw $$If l       0 j$                  0                                                        4 
l a   c c 0c =c                                                                                                                                                                                                                                                                        $If l kd $$If l       0 j$                  0                                                        4 
l a   =c >c Tc mc                                                                                                                                                                                                                                                                        $If l kd $$If l       0 j$                  0                                                        4 
l a   mc nc c c                                                                                                                                                                                                                                                                        $If l kdW $$If l       0 j$                  0                                                        4 
l a   c c c c                                                                                                                                                                                                                                                                        $If l kd $$If l       0 j$                  0                                                        4 
l a   c c c c                                                                                                                                                                                                                                                                        $If l kd $$If l       0 j$                  0                                                        4 
l a   c c c
d                                                                                                                                                                                                                                                                        $If l kd7 $$If l       0 j$                  0                                                        4 
l a   
d d d -d                                                                                                                                                                                                                                                                        $If l kdב $$If l       0 j$                  0                                                        4 
l a   -d .d Nd d                                                                                                                                                                                                                                                                        $If l kdw $$If l       0 j$                  0                                                        4 
l a   d ad pd d                                                                                                                                                                                                                                                                        $If l kd $$If l       0 j$                  0                                                        4 
l a   d d d d d d e De pe e e                                                                                                                                                                                                                                     $If l kd $$If l       0 j$                  0                                                        4 
l a
e e e mf nf f f f f g g )g 7g Mg g kg lg                                                                                                                                                                                                       $If l kdW $$If l       0 j$                  0                                                        4 
l a   lg g g g g g g h "h 4h h h i i i i i                                                                                                                                                                                                     l  kd6 $$If   l             0 j$        0            4  l a  $If    i i j j j *j <j Ej Fj Oj Pj j j k k Lk Mk k k 0l 1l Kl Ll hl l l l l l                                                                                                                                                                                                                                                                                                                                                    ,            l l {m m p p p p q  q Gq Hq Iq [q \q r r t t t t t t t w y I d ڄ ۄ , - . \ ] B C     ޮޣޕޮފޅ~ޮsޮh    j h4+ Uj h4+ Uh4+ 5\ 	h4+ H*jԞ h4+ Uh4+ 6>*]
h4+ 0J  j h4+ Uj    h4+ Uh4+ 5CJ \aJ  h4+ 5CJ( \aJ(  #h4+ B*	CJ PJ aJ nHph   tHh4+  h4+ 0J- 57\h4+ OJ  QJ   h4+ 0J) 7OJ  QJ   (l {m m p p p p p p p p q                                                                                                                                                                                                                   a  kd $$If   l 4             $h%    0              4  l a f4 $If     7$8$ H$ $a$ ,   q q q ]q  $If    q  kdM $$If   l             0 &$         0              4  l a ]q ^q mq wq  $If    q  kdԙ $$If   l             0 &$         0              4  l a wq xq q q  $If    q  kdt $$If   l             0 &$         0              4  l a q q q q  $If    q  kd $$If   l             0 &$         0              4  l a q q r r [r  $If    q  kd $$If   l             0 &$         0              4  l a [r \r rr r  $If    q  kdT $$If   l             0 &$         0              4  l a r r r r  $If    q  kd $$If   l             0 &$         0              4  l a r r r r  $If    q  kd $$If   l             0 &$         0              4  l a r r s 's <s Zs s s s .t t t t t u Ou  $If    q  kd4 $$If   l             0 &$         0              4  l a Ou ou u u u u v v Kv Xv v v v v v v v v .w \w }w w w 2x bx x x x x y  $If    y y 1y my y y  z ,z ^z z z z z { { {                                                                                                                                                                                                 q  kd $$If   l             0 &$         0              4  l a  $If    { { { | | | | ~ ~ ~ ~                                                                                                                                                                                                                          q  kd7 $$If   l             0 &$         0              4  l a  $If
~ ~ ~ ~ +                                                                                                                                                                                                                                                         $If q kdנ $$If l       0 &$                  0                                                            4 
l a   + , ; I                                                                                                                                                                                                                                                              $If q kdw $$If l       0 &$                  0                                                            4 
l a   I J  ~      ! W     ׁ                                                                                                                                                                                                  $If q kd $$If l       0 &$                  0                                                            4 
l a   ׁ     H                                                                                                                                                                                                                                                   q  kd $$If   l             0 &$         0              4  l a  $If    H I d     m  ڄ x  ܅  E                         z            z            z            z            z            z            z            z            z            z            z            z                 ^    ?!   ^ q  kdW $$If   l             0 &$         0              4  l a E ~   1 a  Ӈ  B ׈  < o  ҉  e  ъ ӊ Ԋ ڊ ۊ    5 N   7$ 8$H$    ^   ъ Ԋ ي ڊ   ۋ ܋ ݋    : o   ď Ə ݏ ߏ  1 9 : S X b ~     ܑ   7    r v }                                    	h4+ H*h4+ B*ph h4+ 6] h4+ 5\ h4+ 5B*\ph h4+ OJ  QJ   h4+ 6CJ OJ  QJ  ]aJ
h4+ 0J  j h4+ Uh4+ 5CJ$\aJ$  h4+ 5CJ( \aJ(  #h4+ B*	CJ PJ aJ nHph   tHh4+  j    h4+ U *N k ~     : ; o   Í ύ    0 < R f ~  
 o                                                                                                                                                                                                                                                                                                                                           ~=z9!v%  (           ޏ . U {  ݑ ޑ 7 X     k w x   œ  > S   & i                                                                                                                                                                                                                                                                                                                                                         	  |^|         F  E  q r  %   d q r s t u v                                                                                                                                                                                                                                                                                               $a$  7$8$ H$  ^   ^  ^  ^   ^ v y        4 7 @ S  ȷlbSAS- 'h4+ B* OJ PJ QJ ^J nHph tH#h4+ 5>*CJ PJ \aJ nHtH h4+ >*CJ PJ aJ nHtHh4+ PJ nHtH 8h4+ 5>*B* CJ$ OJ PJ QJ \^J aJ$nHph tH & *h4+ 5>*CJ( OJ QJ \^J aJ( h4+ 5>*OJ QJ \^J aJ( h4+ OJ QJ ^J h4+ 5CJ( OJ QJ \^J aJ( h4+ 5CJ OJ QJ \^J aJ( h4+ 5CJ0 OJ QJ \^J aJ0 )h4+ 5B* CJ PJ \aJ nHph tH     4 S n     ܝ   - H c ~    О d  7$ 8$H$ 	  d 7$8$ H$ d 7$ 8$H$   $d 7$ 8$H$ a$C $    7$8$ H$[$ \$a$     ʞ Ϟ О Ҟ      *          ʠ ͠ ֠ נ  ϻϤϻϒqcGϻϤϻσqc   7j    h4+ B*	OJ PJ QJ U^J mH nH ph   tHuh4+ CJ PJ aJ nHtH #h4+ 5>*CJ PJ \aJ nHtHh4+ >*CJ PJ aJ nHtH#h4+ B*	CJ PJ aJ nHph   tH-h4+ 5B*OJ PJ QJ \^J nHph    tH'h4+ B*	OJ PJ QJ ^J nHph   tH'h4+ B*OJ PJ QJ ^J nHph    tH7j    h4+ B*OJ PJ QJ U^J mH nH ph    tHu О    * + H e     ՟   & A \ w    ɠ ʠ                                                                                                                                                                                                                                                                                                                                 d  7$8$ H$^ d 7$ 8$H$    d  7$8$ H$   / L M h    ԡ   % @ [ \ w     % t ã  a   N d  7$ 8$H$   L ^ b q v y {  % 9 ? E K c t |     ã ˣ ף ݣ      , 2 J P a o      Ĥ ֤ ܤ     + 1 7 = N b    ۥ  E ׬׬׬׬׬׬׬׬׬׬׬׬׬׬׬                      h4+ CJ PJ aJ nHtH 'h4+ B*OJ PJ QJ ^J nHph   tH-h4+ 5B*OJ PJ QJ \^J nHph    tH'h4+ B*OJ PJ QJ ^J nHph    tH'h4+ B*	OJ PJ QJ ^J nHph   tH :N     E F \ v   Ŧ     4 N i    ֧ ק   ' > W                                                                                                                                                                                                                                                                                                                                                             	  d  7$8$ H$E F         \ u  ū  5  Ԭ * R S  ŭ ƭ   1 5 ӋӋӋӋӋӋӋw_G /h4+ B* CJ OJ PJ QJ ^J aJ nHph tH/h4+ B*CJ OJ PJ QJ ^J aJ nHph tH'h4+ B*OJ PJ QJ ^J nHph tH'h4+ B* OJ PJ QJ ^J nHph tHh4+ CJ PJ aJ nHtH &h4+ CJ OJ PJ QJ ^J aJ nHtH "h4+ CJ OJ PJ QJ aJ nHtH 'h4+ B*OJ PJ QJ ^J nHph tH/h4+ B*CJ OJ PJ QJ ^J aJ nHph tH W w x   Ǩ    4 5 K f    ԩ      2 M i   $   *$7$ 8$H$ 	  d  7$8$ H$        9 [ \ u    ū     5 Q h     Ԭ d  7$ 8$H$    d  7$8$ H$^ Ԭ    ) * R S n    ŭ ƭ ǭ ȭ ɭ ʭ   1 P e }  ۮ   d  7$ 8$H$    d  7$8$ H$^ 5 P T e m }    ۮ     , E U p     ԯ    8 k o         0 4 P X     ӱ    5 I q    ز    < P v      > B     P T   " & [ _   /h4+ B* CJ OJ PJ QJ ^J aJ nHph tH/h4+ B*CJ OJ PJ QJ ^J aJ nHph tH R  E p     W k   ̰   ( H {  ˱  - i  в  4 n  ܳ d  7$ 8$H$  ܳ  6 g     < q  ֵ  ; z   0 e   3 s    / L i                                                                                                                                                                                                                                                                                                                                                             	  d  7$8$ H$                  & \ j k  ? @ A D P Q U a b 绩sbQ jq h4+ B*CJ UaJ ph jf h4+ B*CJ UaJ ph jv h4+ B*CJ UaJ ph h4+ CJ OJ QJ ^J aJ h4+ OJ QJ ^J h4+ 5OJ QJ \^J #h4+ 5>*CJ$ OJ QJ \^J aJ$& *h4+ 5>*CJ( OJ QJ \^J aJ( /h4+ B* CJ OJ PJ QJ ^J aJ nHph tH/h4+ B*CJ OJ PJ QJ ^J aJ nHph tH i         [ \ j k w    ̺ $$7$ 8$H$ If   a$ $7$8$ H$a$
$$7$8$ H$a$  7$8$ H$ b 7$ 8$H$    $a$	  d  7$8$ H$̺ ͺ Ϻ Һ   ? 1 1 1 1 $$7$ 8$H$ If   a$ kdH $$If T < 4r H L         @    @    @    2           4  < a p2      T         n kdT $$If T < r H L         @    @    @         4  < a T $$7$ 8$H$ If   a$     % + 1 | n n n n n $$7$ 8$H$ If   a$ kd $$If T < r H L         @    @    @         4  < a T 1 2 4 6 D J P | n n n n n $$7$ 8$H$ If   a$ kdx $$If T < r H L         @    @    @         4  < a T P Q S U c i o | n n n n n $$7$ 8$H$ If   a$ kd  $$If T < r H L         @    @    @         4  < a T o p r t    | n n n n n $$7$ 8$H$ If   a$ kd $$If T < r H L         @    @    @         4  < a T        | n n n n n $$7$ 8$H$ If   a$ kd. $$If T < r H L         @    @    @         4  < a T     » Ȼ λ | n n n n n $$7$ 8$H$ If   a$ kd $$If T < r H L         @    @    @         4  < a T λ ϻ ѻ ӻ    | n n n n n $$7$ 8$H$ If   a$ kdR $$If T < r H L         @    @    @         4  < a T       ? @ B C D P | v v v v k b b v v k $7$8$ H$a$
$$7$8$ H$a$  7$8$ H$kd $$If T < r H L         @    @    @         4  < a T P R S T U a c d e f g x }      ż Ӽ ܼ      Ff6 $$7$ 8$H$ If   a$ $$7$ 8$H$ a$ 7$ 8$H$ 	  $7$ 8$H$ a$ b g w x   H i þ  ;             , -   c    |        nb h4+ B*CJ aJ ph jK  h4+ B*CJ UaJ ph j[ h4+ B*CJ UaJ ph /j h4+ B*CJ UaJ mH nH ph tHu j5 h4+ B*CJ UaJ ph j; h4+ B*CJ UaJ ph jD h4+ B*CJ UaJ ph h4+ CJ OJ QJ ^J aJ h4+ 5OJ QJ \^J h4+ OJ QJ ^J &         $$7$ 8$H$ If   a$   kd $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T    # ) / 5 : = C I $$7$ 8$H$ If   a$ I J kd $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T J L O U [ b i o s y  $$7$ 8$H$ If   a$     $7$8$ H$a$   kdT $$If    T < 
d$d$d#                                                                                            (                              (                              (                              (                              4 
< a  T                                                                                                S                                    kd $$If    T < 4F Q	                   S        	                                                              4 
< a  p                     T    $$7$8$ H$If a$	  $7$ 8$H$ a$ $$7$ 8$H$ a$ 7$ 8$H$  	                                                                                                                                                                                                                                                                              \  kd $$If    T < F Q	                   S                                              4 
< a  T    $$7$8$ H$If a$                                                        7                             \  kd $$If    T < F Q	                   S                                              4 
< a  T    $$7$8$ H$If a$ \  kd| $$If    T < F Q	                   S                                              4 
< a  T   $ % & / 4 5 \ kd $$If T < F Q          S       4  < a T $$7$ 8$H$ If   a$ 5 6 > C D E 7 \ kd $$If T < F Q          S       4  < a T $$7$ 8$H$ If   a$ \ kd, $$If T < F Q          S       4  < a T E F G H i j p x    $$7$ 8$H$ If   a$ $$7$ 8$H$ a$ 7$ 8$H$ 	  $7$ 8$H$ a$       ? 1 1 1 1 $$7$ 8$H$ If   a$ kdL $$If T < 4r O z +        H    g    +    2           4  < a p2      T         n kd $$If T < r O z +        H    g    +         4  < a T $$7$ 8$H$ If   a$    ¾ þ      | s m m b s T T T $$7$ 8$H$ If   a$ $$7$ 8$H$ a$ 7$ 8$H$ 	  $7$ 8$H$ a$ kd> $$If T < r O z +        H    g    +         4  < a T       1 kd $$If T < 4r O z +        H    g    +    2           4  < a p2      T $$7$ 8$H$ If   a$    % & ( + . 4 9 n kd0 $$If T < r O z +        H    g    +         4  < a T $$7$ 8$H$ If   a$ 9 : ; < = > ? @    | s g g g g g g g \ $$7$ 8$H$ a$  b 7$ 8$H$ 	  $7$ 8$H$ a$ kd $$If T < r O z +        H    g    +         4  < a T     ߿   $$7$ 8$H$ If   a$ $7$8$ H$a$  
   ! ?            1            1            1            1                        $$7$8$ H$If a$   kd $$If    T < 4r HL                   @         @         @      
2                                                                                                 4 
< a  p2                                   T  ! ( ) + . < B H             n                                                                                                                                                                            kd $$If    T < r HL                   @         @         @                                                                      4 
< a  T    $$7$8$ H$If a$ H I K N \ b h |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kdF $$If    T < r HL                   @         @         @                                                                      4 
< a  T  h i k n |   |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kd $$If    T < r HL                   @         @         @                                                                      4 
< a  T         z            l            l            l            l            l                                                                                                                             $$7$8$ H$If a$   kdj $$If    T <  r HL                   @         @         @                                                                      4 
< a  T         |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kd  $$If    T < r HL                   @         @         @                                                                      4 
< a  T         |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kd $$If    T < r HL                   @         @         @                                                                      4 
< a  T         |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kd$ $$If T < r H L         @    @    @         4  < a T      " ( | n n n n n $$7$ 8$H$ If   a$ kd $$If T < r H L         @    @    @         4  < a T ( ) , / = C I | n n n n n $$7$ 8$H$ If   a$ kdH $$If T < r H L         @    @    @         4  < a T I J M P ^ d j | n n n n n $$7$ 8$H$ If   a$ kd $$If T < r H L         @    @    @         4  < a T j k n q    | n n n n n $$7$ 8$H$ If   a$ kdl $$If T < r H L         @    @    @         4  < a T        | n n n n n $$7$ 8$H$ If   a$ kd $$If T < r H L         @    @    @         4  < a T        | n n n n n $$7$ 8$H$ If   a$ kd $$If T < r H L         @    @    @         4  < a T        | n n n n n $$7$ 8$H$ If   a$ kd" $$If T < r H L         @    @    @         4  < a T        | n n n n n $$7$ 8$H$ If   a$ kd $$If T < r H L         @    @    @         4  < a T    $ * 0 |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kdF $$If    T < r HL                   @         @         @                                                                      4 
< a  T  0 1 4 6 D J P |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kd $$If    T < r HL                   @         @         @                                                                      4 
< a  T  P Q T V d j p |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kdj $$If    T < r HL                   @         @         @                                                                      4 
< a  T  p q t v    |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kd $$If    T < r HL                   @         @         @                                                                      4 
< a  T         |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kd $$If    T < r HL                   @         @         @                                                                      4 
< a  T         |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kd  $$If    T < r HL                   @         @         @                                                                      4 
< a  T       	       |            q            q            h            q            h            b            q            h            h            h                   7$8$ H$$7$8$ H$a$
$$7$8$ H$a$   kd $$If    T < r HL                   @         @         @                                                                      4 
< a  T   - 2 @ R \ j t z                                                                                                                                                                                                                                                                                                                                                                      FfW    $$7$8$ H$If a$	  $7$ 8$H$ a$   kd $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T            $$7$ 8$H$ If   a$   kd $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T          " ( $$7$ 8$H$ If   a$ ( ) kdu $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T ) + - 3 9 ? E J M S Y $$7$ 8$H$ If   a$ Y Z kd/ $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T Z \ _ e k q w }    $$7$ 8$H$ If   a$   kd $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T            $$7$ 8$H$ If   a$   kd $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T            $$7$ 8$H$ If   a$   kd] $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T            $$7$ 8$H$ If   a$   kd $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T    ! & + 2 8 > A G M $$7$ 8$H$ If   a$ M N kd $$If T <  d$	d$ d#                                          ( ( ( ( 4  < a T N P R W \ c j o r x ~ $$7$ 8$H$ If   a$ ~    $7$8$ H$a$   kd $$If    T < 
d$d$d#                                                                                            (                              (                              (                              (                              4 
< a  T                                                                                                S                                    kdE $$If    T < 4F Q	                   S        	                                                              4 
< a  p                     T    $$7$8$ H$If a$	  $7$ 8$H$ a$ $$7$ 8$H$ a$ 7$ 8$H$  	                                                                                                                                                                                                                                                                              \  kd# $$If    T < F Q	                   S                                              4 
< a  T    $$7$8$ H$If a$       !                                                 7                             \  kdC $$If    T < F Q	                   S                                              4 
< a  T    $$7$8$ H$If a$ \  kd $$If    T < F Q	                   S                                              4 
< a  T  ! ' 1 2 ; A J                                                                                                                                                                                                                                                                        \  kd $$If    T < F Q	                   S                                              4 
< a  T    $$7$8$ H$If a$ J K S Y _                                                  7                                  \  kd  $$If    T < F Q	                   S                                              4 
< a  T    $$7$8$ H$If a$ \  kdc  $$If    T < F Q	                   S                                              4 
< a  T   a b c                                                                                                                                                                                                                                                                                                                                                                                                   $$7$8$ H$If a$
$$7$8$ H$a$  7$8$ H$$7$8$ H$a$
      ?            1            1            1            1                        $$7$8$ H$If a$   kd $$If    T < 4r Oz +                  H         g         +      
2                                                                                                 4 
< a  p2                                   T                      n                                                                                                                                                                            kd $$If    T < r Oz +                  H         g         +                                                                      4 
< a  T    $$7$8$ H$If a$        |            n            n            n            n            n                                                                                                                                 $$7$8$ H$If a$   kdu $$If    T < r Oz +                  H         g         +                                                                      4 
< a  T            / |            s            m            m            b            s            T            T            T                          $$7$8$ H$If a$
$$7$8$ H$a$  7$8$ H$$7$8$ H$a$   kd1 $$If    T < r Oz +                  H         g         +                                                                      4 
< a  T  	/ 9 > ? A D                         1                                                kd $$If    T < 4r Oz +                  H         g         +      
2                                                                                                 4 
< a  p2                                   T    $$7$8$ H$If a$ D G M R S U X [ a f                                     n                                                                                                                                          kd# $$If    T < r Oz +                  H         g         +                                                                      4 
< a  T    $$7$8$ H$If a$ 	f g i l o u z z            l            l            l            l            l                                                                                                                             $$7$8$ H$If a$   kd $$If    T <  r Oz +                  H         g         +                                                                      4 
< a  T  z { |         |            s            g            a            V            T            T            T            T                        
$$7$8$ H$a$  7$8$ H$ b 7$ 8$H$ 	  $7$ 8$H$ a$ kd $$If T < r O z +        H    g    +         4  < a T       ! " O P    p  -   H I U   m  (   7$ 8$H$   7$8$ H$    O     a b g h i   µµ{iZF/ ,h4+ 5CJ OJ PJ QJ \^J aJ nHtH &h4+ CJ OJ PJ QJ ^J aJ nHtH h4+ 5OJ QJ \^J aJ0 #h4+ 5>*CJ0 OJ QJ \^J aJ0 & *h4+ 5>*CJ0 OJ QJ \^J aJ0 h4+ 5CJ. OJ QJ \^J aJ. )j h4+ 5CJ. OJ QJ U\^J aJ. h4+ 5OJ QJ \^J &h4+ CJ OJ PJ QJ ^J aJ nHtH ,h4+ 5CJ OJ PJ QJ \^J aJ nHtH$h4+ 5OJ PJ QJ \^J nHtH   N  	 f    -   E             h i                                                                                                                                                                                                                                                                                                                                    $a$   $a$    b 7$8$ H$ 7$ 8$H$  i     F     <     2 5      U                                                                                                                                                                                                                                                                                                                                                       	  d  7$8$ H$ 7$ 8$H$     l m ) k n     ( 1 2 3  V W     I z j u ~    < мvvvvvvb                                     &h4+ CJ OJ PJ QJ ^J aJ nHtH $h4+ 5OJ PJ QJ \^J nHtH h4+ PJ ^J nHtH h4+ OJ PJ QJ ^J nHtH ,h4+ 5CJ OJ PJ QJ \^J aJ nHtH &h4+ CJ OJ PJ QJ ^J aJ nHtH ,h4+ 5CJ OJ PJ QJ \^J aJ nHtH /h4+ 5>*CJ OJ PJ QJ \^J aJ nHtH    5 U r u        W     ( R |      J K d  7$ 8$H$   7$8$ H$K i      C m     ? i l m        : ] y   d  7$ 8$H$   7$8$ H$       ) J k n        2 3 S    d  7$ 8$H$  $d    7$ 8$@& H$     ~=z9!v% 7$8$ H$ 7$ 8$H$     : d     6            " a     H ~                                                                                                                                                                                                                                                                                                                                                                  7$8$ H$    * - L  ~      @ Z ]     * T W      ~= z9 !v% 7$ 8$H$   7$8$ H$   I j k       / r        D m     ?  $     7$8$ @&	H$ 7$ 8$H$  ? i     ; >          : o     W     O w                                                                                                                                                                                                                                                                                                                                                                7$8$ H$w     ? B n        ( L r      7 ] {    d  7$ 8$H$   7$8$ H$  ( D i     . X w z {     F p s v     = g d  7$ 8$H$  g h i       
  > a      8 b     < _                                                                                                                                                                                                                                                                                                                                   7$8$ H$d  7$ 8$H$    d  7$8$ H$ _     ) D f     % C o     @ m      G   L  7$ 8$H$  L   Q   < = D E x {     S        + a    9 o                                                                                                                                                                                                                                                                                                                               d  7$8$ H$^  $a$ d  7$ 8$H$   7$8$ H$< = C D E x       n o " # R U J K    о~j~\\NF\A\\\ h4+ H*h4+ CJ aJ j h4+ 0J0 CJ UaJ h4+ j h4+ 0J0 U&h CJ OJ PJ QJ ^J aJ nHtH &h4+ CJ OJ PJ QJ ^J aJ nHtH )h4+ 5B*CJ PJ \aJ nHph tH-h4+ 5B*OJ PJ QJ \^J nHph tH#h4+ 5>*CJ0 OJ QJ \^J aJ0 & *h4+ 5>*CJ0 OJ QJ \^J aJ0 5h4+ 5B*CJ OJ PJ QJ \^J aJ nHph tH o    ' B ] _          # A U s        5 _  7$ 8$H$  _      , Z      D F i    $ & K    " $	 a	 	 	                                                                                                                                                                                                                                                                                                                                                                7$8$ H$    %  '  g    2  e      3  R  q      < o     H   7$ 8$H$      O Q     	  J i      S      W v                                                                                                                                                                                                                                                                                                                                                                   7$8$ H$  ! e    ) + h      % D c       ; = o     7$ 8$H$   : m o     G z   n " I J     ? @ m o                                                                                                                                                                                                                                                                                                         (  	$ *$ 7$8$ H$$d 7$8$ H$a$	  $7$ 8$H$ a$ / / $a$ 7$ 8$H$             " @ A B F J m o p q v   r ]  ^  _    j  s  t  z  {  ~zrh^X^
h4+ 0J  j    h4+ 0J Uh4+ OJ QJ ^J  h4+ OJ QJ  h  h4+ CJ aJ  h4+ CJ aJ  h4+ 5CJ OJ  QJ  \aJ  j    h4+ 0J0 CJ UaJ h4+ CJ aJ  h4+ CJ H*OJ  QJ  aJ h4+ CJ OJ  QJ  aJ  h4+ B*ph   h4+ PJ nHtH h4+ 6] j    h4+ 0J0 Uh4+  h4+ CJ H*
h4+ CJ ! r _                                                                                                                                                                                                                                                                                                                                                                                	   $a$  h]h  &        (  {  ~                          ! ! ! !  ! !! 4! >! p! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ૞}}૞૞Ì h4+ 6CJ h4+ OJ  QJ   h4+ 6CJ h4+ 6CJ OJ  QJ  h4+ 6CJ H*OJ  QJ   h4+ 6CJ OJ  QJ
h4+ CJ  h4+ 5\ 	h4+ 6h4+ 5CJ
h4+ CJ  h4+ 56 h  h4+
h4+ 0J  j    h4+ 0J Uh 0J mH nH u 1  ! ! ! !  ! !! -! .! 3! 4! o! p! ! ! ! ! ! ! ! ! ! ! ! ! ! !                                                                                                                                                                                                                                                                                                                            (      ( $  a$   $a$         $a$ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! " " 	" " " " f" g" " "                                                                                                                                                                                                                                                                                                                                           $a$ (         ( $  a$ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! " " " 	"
" " " G" T" g" q" " " " " " " " " " " " r# s# t# u# j$ k$ m$ n$ $ Ÿбתױױױx j h4+ CJ Uj h4+ U h4+ CJ h4+ CJ h4+ 5CJ h4+ 5\ h4+ aJ h4+ 6H* h4+ 6CJ h4+ 6CJ H*OJ QJ h4+ 6CJ OJ QJ h4+ 6CJ h4+ 6h4+ 6CJ H*OJ QJ h4+ 6CJ OJ QJ h4+ h4+ OJ QJ -" " " " " " " # =# s# t# u# j$ $$ $ -' .' ;' <' Q' R' ' a' t' u' }'   $dh a$ 5 5    $a$ $ $$ $$ $$ $$ 7% E% S% ^% & & ' ,' -' .' ;' <' Q' R' ' a' t' u' }' ~' ' ' ' ' ( ( ( >( B( G( O( P( ]( y( ( źźźŮ֥֥֖֝֝֝։}vvvo   h4+ 5CJ h4+ 5\ 	h4+ 5h4+ \aJ h4+ 5aJ
h4+ CJ  h4+ 5CJ h4+ OJ QJ  h4+ 5OJ QJ h4+ 6CJ ]aJ h h4+ 6CJ aJ h  h4+ CJ aJ h h4+ CJ aJ  h4+
h4+ CJ  j    h4+ CJ Uj&: h4+ Uj9:@
h4+ CJ UV +}' ~' ' ' ( ( x( y( ( ) ) i) j) ) ) * * v* w* * * G+ H+ + + , , ?,                                                                                                                                                                                                                                                                                                                                               d  7$8$ H$^  $a$  ( ( ( ( ( ( ( ( ) ) j) s) ) ) * * * 8* >* C* [* w* * * * * * =+ F+ H+ S+ + + + + , , , P, S, _, s, v, |, , , , , , , , , , , , κΦκΔκ h4+ PJ nHtH #h4+ B* CJ PJ aJ nHph tH'h4+ B*OJ PJ QJ ^J nHph tH'h4+ B*OJ PJ QJ ^J nHph tH'h4+ B* OJ PJ QJ ^J nHph tH h4+ CJ h4+ 5CJ h4+ 5\ h4+ h4+ 5 6?, P, s, , , , , , , , - #-$- - - - - - - . 	. .                                                                                                                                                                                                                                                                                               $$7$8$ H$If a$  $$    7$8$ A$H$ a$  $a$  d 7$ 8$H$    d  7$8$ H$^ , , - - - #-$- .- 0- [- d- f- p- v- - - - - - - - - . . . . / / / / &/ (/ R/ [/ ]/ g/ m/ w/ }/ / / / ׿oj   	h4+ \ j	E h4+ B*CJ UaJ ph     h4+ 5OJ QJ ^J &h4+ CJ OJ PJ QJ ^J aJ nHtH h4+ 5OJ QJ \^J  h4+ 5\ 	h4+ 5h4+ 5CJ h4+  'h4+ B*OJ PJ QJ ^J nHph    tH'h4+ B*	OJ PJ QJ ^J nHph   tH'h4+ B*OJ PJ QJ ^J nHph   tH ). . . . F. {            m            m            m                                                                                                                                                                 $$7$8$ H$If a$   kd@ $$If    T < 4F Q	                   S        	                                                              4 
< a  p                     T  F. G. M. S. l. m. v.                                                 7                             \  kd9B $$If    T < F Q	                   S                                              4 
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< a  T  v. |. . . . . .                                                                                                                                                                                                                                                                        \  kdB $$If    T < F Q	                   S                                              4 
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TРkm Nl4v^}w%@*MO|U*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]U CO'ot| 艩Ǧ5+B!fݭ0Hpjb%/ M e;W.Pn:B1Vr qegÜ^夲ߊ튬s#凓|n58k_~YXI%ε_g &ƮPﱢTsi_?"4_͍FdFRZ4;A4#YA?'/)&;zF +2)" U򟗿'&|cW^u/ j}F5CV֒?3]2K}KXdh,}4pvT*_ O 㡊S /_ bw } o|'[ My_>(zG)WWb 8kew?7yF ,2<\k:?2\-Xkvх SEr'( *ƭ 8[p;>Ya9s~:N]XuhKJWvlciG"'˟W 8JڹX;mQK 4j/8/-qX 5 CЭ E.|#&* \PB 8 86ubI~(N@4iȪ lԴVKLԿ+)= YAS[Ժߧ*2YbСVT> 8+G/3yEoO8E攱{9|w%լM Ǭ^y@Z P Uߊm+Sҿo+IH~Cz7Vm  %y#PЀqWSпUϖ~e}w}R? \+NF'dWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]S" I9C# 24 % !_6y{N%LnrB  Asϓ\C\~R{ 0%wkc]>b> }inX6m:d mvQDR(*"( P ;v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*U _ 1 0 8 4 4 3 9 0 3 6    F O tO  O l e     C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   6 _ 1 0 8 4 4 3 9 0 3 7      F tO tO  O l e     C o m p O b j    f      F Microsoft Equation 3.0 DS Equation Equation.3 9q    f     1 n  i    x  i  i = 1 n  i  "    O b j I n f o    E q u a t i o n N a t i v e  _ 1 0 8 4 4 3 9 0 3 8    F tO tO  O l e     C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   _ 1 0 8 4 4 3 9 0 3 9   %  F tO tO    F Microsoft Equation 3.0 DS Equation Equation.3 9q           x " i   x "C  i  "  2 i = 1 k "      F Microsoft Equation 3.0 DS Eq O l e     C o m p O b j    f  O b j I n f o     E q u a t i o n N a t i v e   6 uation Equation.3 9q      o   1       F Microsoft Equation 3.0 DS Equation Equation.3 9q     H 4   2  _ 1 0 8 4 4 3 9 0 4 0  "  F tO tO  O l e     C o m p O b j  ! # f  O b j I n f o    E q u a t i o n N a t i v e  6 _ 1 0 8 4 4 3 9 0 4 1   * '  F tO tO  O l e    C o m p O b j  & ( ! f      F Microsoft Equation 3.0 DS Equation Equation.3 9q      o   k       F Microsoft Equation 3.0 DS Equation Equation.3 9q  O b j I n f o  ) #  E q u a t i o n N a t i v e  6 _ 1 0 8 4 4 3 9 0 4 3  ,  F tO tO  O l e  %   C o m p O b j  + - & f  O b j I n f o  . (  E q u a t i o n N a t i v e  ) 6 _ 1 0 8 4 4 3 9 0 4 4   C 1  F tO tO     s    i       F Microsoft Equation 3.0 DS Equation Equation.3 9q     s    i     O l e  *   C o m p O b j  0 2 + f  O b j I n f o  3 -  E q u a t i o n N a t i v e  . 6 _ 1 0 8 4 4 3 9 0 4 5  6  F tO tO  O l e  /   C o m p O b j  5 7 0 f  O b j I n f o  8 2     F Microsoft Equation 3.0 DS Equation Equation.3 9q     s    i       F Microsoft Equation 3.0 DS Equation Equation.3 9q   E q u a t i o n N a t i v e  3 6 _ 1 0 8 4 4 3 9 0 4 6  4 > ;  F tO tO  O l e  4   C o m p O b j  : < 5 f  O b j I n f o  = 7  E q u a t i o n N a t i v e  8 6 _ 1 0 8 4 4 3 9 0 4 7  @  F tO tO  O l e  9     o   1       F Microsoft Equation 3.0 DS Equation Equation.3 9q     H 4   2       F Microsoft Equation 3.0 DS Eq C o m p O b j  ? A : f  O b j I n f o  B <  E q u a t i o n N a t i v e  = 6 _ 1 0 8 4 4 3 9 0 4 8  9 M E  F tO tO  O l e  >   C o m p O b j  D F ? f  O b j I n f o  G A  E q u a t i o n N a t i v e  B 6 uation Equation.3 9q      o   k       F Microsoft Equation 3.0 DS Equation Equation.3 9q    7 <  d" _ 1 0 8 4 4 3 9 0 4 9  J  F tO tO  O l e  C   C o m p O b j  I K D f  O b j I n f o  L F  E q u a t i o n N a t i v e  G ) _ 1 0 8 4 4 3 9 0 5 0  H R O  F tO tO  O l e  H   C o m p O b j  N P I f      F Microsoft Equation 3.0 DS Equation Equation.3 9q     P7    i       F Microsoft Equation 3.0 DS Equation Equation.3 9q  O b j I n f o  Q K  E q u a t i o n N a t i v e  L 6 _ 1 0 8 4 4 3 9 0 5 1  T  F tO tO  O l e  M   C o m p O b j  S U N f  O b j I n f o  V P  E q u a t i o n N a t i v e  Q 6 _ 1 0 8 4 4 3 9 0 5 2  /  Y  F tO tO      o   i       F Microsoft Equation 3.0 DS Equation Equation.3 9q      |q   i     O l e  R   C o m p O b j  X Z S f  O b j I n f o  [ U  E q u a t i o n N a t i v e  V 6 _ 1 0 8 4 4 3 9 0 5 3  ^  F tO tO  O l e  W   C o m p O b j  ] _ X f  O b j I n f o   Z     F Microsoft Equation 3.0 DS Equation Equation.3 9q      B   i       F Microsoft Equation 3.0 DS Equation Equation.3 9q   E q u a t i o n N a t i v e  [ 6 _ 1 0 8 4 4 3 9 0 5 4  \ f c  F tO tO  O l e  \   C o m p O b j  b d ] f  O b j I n f o  e _  E q u a t i o n N a t i v e   6 _ 1 0 8 4 4 3 9 0 5 5  h  F tO tO  O l e  a    P7    i       F Microsoft Equation 3.0 DS Equation Equation.3 9q     (9 <   i       F Microsoft Equation 3.0 DS Eq C o m p O b j  g i b f  O b j I n f o  j d  E q u a t i o n N a t i v e  e 6 _ 1 0 8 4 4 3 9 0 5 6  a u m  F tO tO  O l e  f   C o m p O b j  l n g f  O b j I n f o  o i  E q u a t i o n N a t i v e  j 6 uation Equation.3 9q     (9 <   i       F Microsoft Equation 3.0 DS Equation Equation.3 9q     P7    i  _ 1 0 8 4 4 3 9 0 5 7  r  F tO tO  O l e  k   C o m p O b j  q s l f  O b j I n f o  t n  E q u a t i o n N a t i v e  o 6 _ 1 0 8 4 4 3 9 0 5 8  p z w  F tO tO  O l e  p   C o m p O b j  v x q f      F Microsoft Equation 3.0 DS Equation Equation.3 9q    (9 <        F Microsoft Equation 3.0 DS Equation Equation.3 9q  O b j I n f o  y s  E q u a t i o n N a t i v e  t ) _ 1 0 8 4 4 3 9 0 5 9  |  F tOO  O l e  u   C o m p O b j  { } v f  O b j I n f o  ~ x  E q u a t i o n N a t i v e  y _ 1 0 8 4 4 3 9 0 6 0  k  F OO    ҄ I I    p ( x |  i  ,  i  ) P (  i  ) i = 1 k "      F Microsoft Equation 3.0 DS Equation Equation.3 9q    O l e  |   C o m p O b j   } f  O b j I n f o     E q u a t i o n N a t i v e  )  (9 <        F Microsoft Equation 3.0 DS Equation Equation.3 9q     (9 <   1       F Microsoft Equation 3.0 DS Eq_ 1 0 8 4 4 3 9 0 6 1    F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  6 _ 1 0 8 4 4 3 9 0 6 2    F OO  O l e    C o m p O b j   f uation Equation.3 9q      B   2       F Microsoft Equation 3.0 DS Equation Equation.3 9q     h \k   k   O b j I n f o    E q u a t i o n N a t i v e  6 _ 1 0 8 4 4 3 9 0 6 3    F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  6 _ 1 0 8 4 4 3 9 0 6 5    F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  6      F Microsoft Equation 3.0 DS Equation Equation.3 9q     P7    i       F Microsoft Equation 3.0 DS Equation Equation.3 9q _ 1 0 8 4 4 3 9 0 6 6    F OO  O l e    C o m p O b j   f  O b j I n f o        (9 <   i       F Microsoft Equation 3.0 DS Equation Equation.3 9q      o   i    E q u a t i o n N a t i v e  6 _ 1 0 8 4 4 3 9 0 6 7    F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  6 _ 1 0 8 7 3 1 8 5 8 1    F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  l _ 1 0 8 4 4 3 9 0 6 9    F OO    F Microsoft Equation 3.0 DS Equation Equation.3 9q    P      P (  i  ) = 1 i = 1 k "      F Microsoft Equation 3.0 DS Equation Equation.3 9q  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  )    (9 <        F Microsoft Equation 3.0 DS Equation Equation.3 9q    (9 <     _ 1 0 8 4 4 3 9 0 7 0  W  F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  ) _ 1 0 8 4 4 3 9 0 7 1    F OO  O l e    C o m p O b j   f    F Microsoft Equation 3.0 DS Equation Equation.3 9q    (    F  C  K        F Microsoft Equation 3.0 DS Equation Equation.3 9q  O b j I n f o    E q u a t i o n N a t i v e  D _ 1 0 8 7 3 1 8 6 3 2    F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  _ 1 0 8 4 4 3 9 0 7 3    F OO    2    1 "( 1 / )  x " k    2 k "( 1 / )   x " i    2 i "      F Microsoft Equation 3.0 DS Equation Equation.3 9q  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  \    @ yI I   x " k    2      F Microsoft Equation 3.0 DS Equation Equation.3 9q    @I nI   k  _ 1 0 8 4 4 3 9 0 7 4    F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  8 _ 1 0 8 4 4 3 9 0 7 5   ~  F OO  O l e    C o m p O b j   f      F Microsoft Equation 3.0 DS Equation Equation.3 9q     mI yI        F Microsoft Equation 3.0 DS Equation Equation.3 9q  O b j I n f o    E q u a t i o n N a t i v e  , _ 1 0 8 9 3 5 9 8 8 0    =  F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  6 _ 1 0 8 9 3 5 9 9 1 2    F OO    n     i       F Microsoft Equation 3.0 DS Equation Equation.3 9q   n     i     O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  6 _ 1 0 8 9 3 1 1 1 7 8    F OO  O l e    C o m p O b j   f  O b j I n f o       F Microsoft Equation 3.0 DS Equation Equation.3 9q    n/ h 1  p ( x |  i  )      F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e  K _ 1 0 8 9 3 1 1 1 3 0  8  F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  _ 1 0 8 9 3 6 0 1 7 0   )  F OO  O l e      n x    p (  i  | x ) =  p ( x |  i  ) p (  i  ) p ( x )      F Microsoft Equation 3.0 DS Equation Equation.3 9q    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  _ 1 0 8 5 0 2 7 9 8 3  e  F OO  n 0   g  i  = m a x  j  { g  i  } , j = 1 , . . . , m .      F Microsoft Equation 3.0 DS Equation Equation.3 9q        g  i  ( x ) O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e   = ( "1 / 2 ) ( x " i  )  t " "1 ( x " i  ) "( 1 / 2 ) l n | "| + l n p (  i  )      F Microsoft Equation 3.0 DS Equation Equation.3 9q  _ 1 0 8 5 0 2 7 9 8 2    F OO  O l e    C o m p O b j   f  O b j I n f o    E q u a t i o n N a t i v e  , _ 1 0 9 0 5 7 5 6 1 7  V  F OO  O l e    C o m p O b j   f   mI yI  "      F Microsoft Equation 3.0 DS Equation Equation.3 9q   z (   i ( N ) = " P (  j  ) j " l o g  2  P (  j  )  O b j I n f o    E q u a t i o n N a t i v e  _ 1 0 9 0 5 7 5 9 6 1     F OO  O l e              " % ( + 0 5 8 9 : = @ C H M R W \ a f k p u x y z }      F Microsoft Equation 3.0 DS Equation Equation.3 9q   z' 0   P (  j  )      F Microsoft Equation 3.0 DS Eq C o m p O b j    f  O b j I n f o     E q u a t i o n N a t i v e   C _ 1 0 9 0 5 7 6 1 6 7    F OO  O l e     C o m p O b j    f  O b j I n f o     E q u a t i o n N a t i v e   6 uation Equation.3 9q   z     j       F Microsoft Equation 3.0 DS Equation Equation.3 9q   z    i ( N ) = i _ 1 0 9 0 5 8 2 6 7 3    F OO  O l e     C o m p O b j    f  O b j I n f o      E q u a t i o n N a t i v e   _ 1 0 9 0 5 8 2 7 1 9      F OO  O l e     C o m p O b j     f ( N ) "P  L  i ( N  L  ) "( 1 "P  L  ) i ( N  R  )      F Microsoft Equation 3.0 DS Equation Equation.3 9q   z hx o  N  L                                                                                                        /                 ; <       O b j I n f o     E q u a t i o n N a t i v e   6 _ 1 0 9 0 5 8 2 7 6 4      F OO  O l e         F Microsoft Equation 3.0 DS Equation Equation.3 9q   z    N  R       F Microsoft Equation 3.0 DS Equation Equation.3 9q  C o m p O b j     f  O b j I n f o      E q u a t i o n N a t i v e   6 _ 1 0 9 0 5 8 2 8 9 5    F OO  O l e     C o m p O b j      f  O b j I n f o     E q u a t i o n N a t i v e  ! C   z'    i ( N  L  )      F Microsoft Equation 3.0 DS Equation Equation.3 9q   z' U O  i ( N  R  )_ 1 0 9 0 5 8 2 9 4 0       F OO  O l e  #   C o m p O b j     f  O b j I n f o   &  E q u a t i o n N a t i v e  ' C _ 1 0 9 0 5 8 3 1 5 1    F OO  O l e  )   C o m p O b j    * f      F Microsoft Equation 3.0 DS Equation Equation.3 9q   z    P  L       F Microsoft Equation 3.0 DS Eq O b j I n f o   ,  E q u a t i o n N a t i v e  - 6 _ 1 0 9 0 5 8 3 9 8 5      F OO  O l e  .   C o m p O b j    / f  O b j I n f o    1  E q u a t i o n N a t i v e  2 - _ 1 0 9 0 5 8 6 6 2 3  !  F OO uation Equation.3 9q   z    i      F Microsoft Equation 3.0 DS Equation Equation.3 9q   z    i ( N ) =  P  O l e  3   C o m p O b j    " 4 f  O b j I n f o  # 6  E q u a t i o n N a t i v e  7 (  j  ) j "i " P (  i  ) = 1 " P  2 j " (  j  )      F Microsoft Equation 3.0 DS Equation Equation.3 9q    O  DJ  f ( x ) =  1 _ 1 0 8 5 0 2 7 9 7 4  t &  F OO  O l e  ;   C o m p O b j  % ' < f  O b j I n f o  ( >  E q u a t i o n N a t i v e  ? k _ 1 0 8 9 4 0 6 2 1 5  +  F OO  O l e  A   C o m p O b j  * , B f 1 + e  ( "x )      F Microsoft Equation 3.0 DS Equation Equation.3 9q    n    x  1 i      F Microsoft Equation 3.0 DS Eq O b j I n f o  - D  E q u a t i o n N a t i v e  E ; _ 1 0 8 4 4 3 9 0 8 0  0  F O O  O l e  F  W y 9mE<WR.syh0uM.i^Fc]ŹFX MSz\/!y~g?VN-VDRj#Dάꊳ_ew ǾZ/̟]s\mNz66pvRby?ߜ|ҿ-&hn?,י.tO-+kRmBK;wkk36+ޫHYH.ʽsʟy=_'|k_۰?4;tAfT Y^ z(X3Z&}_Igmz,)ӹYa)]Ҍ3^v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*/GV? +'9gǏO=Oz_Y_N oC5 +9oV^u~?{a[ _'W_Mv*/SLUZG C~  ??}kЮއ.U޼=Wkw%O}eԽz=z~=O^~f C5 ) Q S~=n=V;WTJTI L~~ __x^]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثWb]v*UثW D d  h  B    S A ?        2 m _/bBl/ I   !A _/bBl/  @ x |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗ/djgb* F\:3+!5C2 d^penR~\ /͂#c 60:0ͭ䂺 CFD@a {aĤ\Y\PnϜ2(c -GK D d    B    S A ?        2  5< Bĵ    ! 5< Bĵ   8   xOP]˯B" 1&A:0bRĂ (8D$G]X EzG+kޏ}A@0z8pЉ11m[D3lTeЙvDo JyK0O Vk"+T  A}C-i&qbVD1+~և\bPGԭ6yШ <o6j<0Zs+E K^rxCzN|]q(拖YI.r*)Lp}zqI路Rd cn )h\k ur>Mu>moO .Ar,Zq~ȮĽa+Jմ l qg Ǭb D d    N    s *  A ?      ?    2   .\NnQ   q ! .\NnQX    xSKA~v EDZÃQv( \Pz 7ms] .{:u06ofBw}}f 8  DȘ:#y6r#n]:<yGa *U Q,| V0c䈜BH0= uЫɈr_'6V FҶyP,φHլ jXP: H?i<2'c(:_y(/NS:vν)O}H T:e\E?euΛɛRt;gEwf߂/ wq[rqX3 q'륯wN־~pqM!6p"~~Q=oi BVi8K93p)iz{C|fuIQa+ D d  T  B    S A ?        2 r π 4qI N   !F π 4qI    K  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C  0d @Hfnj_jBP~nb 횷ߗq]ab F\E.7f P d^penR~ %Y0@|yF\Ps}v&"0=0adbR ,.Ie(_Œvd>PƆ b#383 FF D d  ,T  B    S A ?        2 p zڮ L  & !D zڮ    K  xcdd> @c112BYL%bL0Yn &B@?6  5 bn ĒʂT +~3);a&br<5o//gZT T 0j]nT 1 <(ȼܤ Z痀f1ps @VrA]!ؙPÄI)5%G\v.Fl@9v]  I  D d  ,h  B    S A ?        2 m %S9vsn^ I  , !A %S9vsn^꾤  @  |  xcdd> @c112BYL%bL0Yn &B@?6  5=bn ĒʂT+~3);a~&br<5o//?4NHq=̮<&yI9 Y.͂#c 60:0ͭ䂺 CFD@a {aĤ\Y\P9Md>PƆ b#32 H[ D d  h  B    S A ?        2 n s J  / !B s  @ x |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗ/djgb* F\:3+!5C2 d^penR~\ /͂#c 60:0ͭ䂺 CFD@a {aĤ\Y\PnϜ2(c .G D d  h  B    S A ?       2 n s J  3 !B s  @ x |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗ/djgb* F\:3+!5C2 d^penR~\ /͂#c 60:0ͭ䂺 CFD@a {aĤ\Y\PnϜ2(c .G D d  h  B    S A ?       2 n s J  7 !B s  @ x |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗ/djgb* F\:3+!5C2 d^penR~\ /͂#c 60:0ͭ䂺 CFD@a {aĤ\Y\PnϜ2(c .G D d  T  B    S A ?       2 o  epQF* K  ; !C  epQF*    K  xMOJC1ƿV_Z w-x /*<B @ o#t-\tVĭ/ 4 &K)Py؁dQ1QPZڴ: Oˉg<uQ5lú14z,eI z8/6Noά7{wFQvPn6(^.>iVDZ-6Yʟȓ]vgk7Q<Wȯ_KnIp\mTp }ģb8(fs^ 9~M΢w* Ed D d  ,T  B    S A ?       2 o %=1<_ ܅I K  @ !C %=1<_ ܅I    K  xcdd> @c112BYL%bL0Yn &B@?6  5 bn ĒʂT +~3);a&br<5o//T T 0j]nT 1 <(ȼܤ E.K@ ss+LE@a {aĤ\Y\P%͕d>PƆ b#32 "F D d  ,h  B    S A ?       2 o E9]= K  E !C E9]=  @  |  xcdd> @c112BYL%bL0Yn &B@?6  5=bn ĒʂT+~3);a~&br<5o//?T T 0jufWBkd ȼܤ b痀f1ps @VrA]!#t]"0=0adbR ,.Ie(ő2(c ~I D d    B    S A ?        2 : OİT?z%2   J  ! OİT?z%2L @  h R xMPAQ ZA  xBB"71MGbv=M~i}=O1Q=ϳFVk7(+M Oǐ(覙 9ɠ'vo>S(Y/^lÌL '# 1򾸈AX 0-j*v XUBvϑV;1;l/֤{ R >3 D d  h  B    S A ?        2 o "d]t9M(8E K    !C "d]t9M(8E  @  |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗsrE00p1 s i#!2/27)?;%Y0@|yFy\Ps}6 b(L8L+KRs]XAl!v1203 3 ;GU D d  h  B    S A ?        2 m n9P'@ I  ! !A n9P'@彤  @  |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗ_deb* F\:3+!5C2 d^penR~5f.K@ s+l:.P p021)W2 53t1g0Cbdf@ TGq D d  h  B    S A ?        2 m ?EyFb I  "# !A ?EyFb  @  |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗwsqb* F\-:3+!5C2 d^penR~P׾K@ s+l:.P p021)W2gO[2(c .I7 D d  h  B    S A ?        2 o "d]t9M(8E K  %% !C "d]t9M(8E  @  |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗsrE00p1 s i#!2/27)?;%Y0@|yFy\Ps}6 b(L8L+KRs]XAl!v1203 3 ;GU D d  h  B    S A ?        2 n -RR#SSL * J  *' !B -RR#SSL *  @  |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗwsqb* F\-:3+!5C2 d^penR~P׾K@ s+l:.P p021)W2gO[2(c /bIz D d  h  B    S A ?        2 o G}CZ&eZ K  .) !C G}CZ&eZ  @ R |  xcdd> @c112BYL%bL0Yn &F! KA?H  Z @MO7# !L a A 37X/\!(?71v %9Xt9Ư !2/27)?"+%Y0@|yFQ\Ps}6 b(L8L+KRsﰧdgbaǹ H D d  h  B    S A ?        2 m ?S߯]=+ I  3+ !A ?S߯]=+  @ R |  xcdd> @c112BYL%bL0Yn &F! KA?H  Z @MO7# !L a A 37X/\!(?71v 1s20p1 s i#_@:3+!5C2 d^penR~ +K@s +l:.P p021)W2se3t1g0Cbdf@ 'G D d  h  B    S A ?        2 o "d]t9M(8E K  6- !C "d]t9M(8E  @  |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗsrE00p1 s i#!2/27)?;%Y0@|yFy\Ps}6 b(L8L+KRs]XAl!v1203 3 ;GU D d    B    S A ?        2 < O=v WPyU   ;/ ! O=v WPyUL   !  xcdd^ @c112BYL%bL0Yn  B@?6 uZ7# La A 27)?8 ǥ巁BrZHq%02VX F;D@~=321)Wd.b# af@ 732p D d    B    S A ?        2  nƳ!Yzx   1 ! nƳ!Yzx @   | xJ@ggӴIFAOAPP/ gEl_BjC A^< zPГoիqwv4Fdfl8  Lrb8(gE&IBH^]đuMق=Hbv-Fpk<جwjV0o'#p& j/m +"ZU@.yҺ Y +^F-5 l.FT&3e7</.yV u' 6|% wkez<%rWx-SֳIђ+yI!vk%԰Õ)Ym5 % ϩ>.tj\!OtKCڝ0R+sO D d    B    S A ?        2 < O=v WPyU   }3 ! O=v WPyUL   !  xcdd^ @c112BYL%bL0Yn  B@?6 uZ7# La A 27)?8 ǥ巁BrZHq%02VX F;D@~=321)Wd.b# af@ 732 D d  T  B    S A ?        2 o ħAˀ K  O5 !C ħAˀڤ   R K  xcdd> @c112BYL%bL0Yn &F! KA?H  Z @MG7# ! L a A 37X/\!(?71v ˝f10p1 Us i#@Z+!5e\p,y ><F0nn(J.>;vP p021)W2si3t1g0Cbdf@ G D d  T  B    S A ?        2 q  cNT %We\ M  T7 !E cNT %We\    K  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C  0d @Hfnj_jBP~nb 횷ߗ+qrdb F\3UBk3(2/27)?aW%Y0@|yFQ\Ps}v&"0=0adbR ,.Ie(J{2(c H D d  h  B    S A ?       2 o Fw:r9"!@ K  [9 !C Fw:r9"!@  @  |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗrY20p1 s i#@:+!5C2 d^penR~Я$/͂#c 60-䂺 CFD@a {aĤ\Y\Pvd>PƆ b#383 SH! D d  h  B    S A ?       2 n -RR#SSL * J  ; !B -RR#SSL *  @  |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗwsqb* F\-:3+!5C2 d^penR~P׾K@ s+l:.P p021)W2gO[2(c /bIz D d  h  B    S A ?       2 m ޭio5 I  d= !A ޭio5  @ R |  xcdd> @c112BYL%bL0Yn &F! KA?H  Z @MO7# !L a A 37X/\!(?71v %9Xt9Ư !2/27)?"+%Y0@|yFQ\Ps}6 b(L8L+KRsﰧdgbaǹ HV D d  h  B    S A ?       2 m n9P'@ I  g? !A n9P'@彤  @  |  xcdd> @c112BYL%bL0Yn &B@?6 17TobIFHeA*C 0l? @Hfnj_jBP~nb 횷ߗ_deb* F\:3+!5C2 d^penR~5f.K@ s+l:.P p021)W2 53t1g0Cbdf@ TGqj D d    P   ! S A ?       "    2  {מ{8p__   jA ! {מ{8p__  @ 4  h xcdd @c112BYL%bpu<L,؅,56~) @ k#/g UXRY loN A 27)?(pˊ7k30 I] Hqd2g < y?b7L0\[;!2BmƊl.½ Q! ~ Ay Ĺ){+a/3LSY |tf/@*?ylv!Ƚ,sa|!p|hl pN"\1]=<Ĥ\Y\ t0 .?2~ D d    B   " S A ?       ! 2 < O=v WPyU   C ! O=v WPyUL   !  xcdd^ @c112BYL%bL0Yn  B@?6 uZ7# La A 27)?8 ǥ巁BrZHq%02VX F;D@~=321)Wd.b# af@ 732 D d    B   # S A ?       " 2 < O=v WPyU   E ! O=v WPyUL   !  xcdd^ @c112BYL%bL0Yn  B@?6 uZ7# La A 27)?8 ǥ巁BrZHq%02VX F;D@~=321)Wd.b# af@ 732 D d  |  B    S A ?       # 2 l + -x{ H  xG !@ + -x{    0  xcdd @c112BYL%bL0Yn &! KA?H  Z @@UXRYP vo0L ZZpmظ00p1 s i#. -ޕ6Ok<F0nF1 PsΫ5ѕd[%4T!6 b(8+KRsʥN3t1g~f@ X D d  4  P   % S A ?       "    2 V  N\,OtZi 2  zI !* N\,OtZi @ X 8  xڥT=OA[9X )D#HDHG((99hL"ARtQ~@Nih %&JIk{3ޭ .x *&}.[)hHJ TAo@[&׋F){ATkLe|.E9"r q93ז O9*0ď/ D(-Dj-4XtqSKIQ i>n2'opWC[ T1x]dq,븈YG%IuK:fyQ+p/ցFG;̜ϲg3 *sR. w b >{'9Z Oy>@bYfcdUs|s?WZ;Zת;XcџgnO"< ёw⣅hs̭DSwh X" D d  H  B   & S A ?       % 2  C ?\W 5t h  tL ! C ?\W 5tx @   @C . xKPǿwIզ?@B vrE[\!賅4,:O(]^Ā^xqϻ.* }ab,oi82ӎf\u:O]ٰ:v'{Ȗ%j8{(F 8W5t&-~FGM>2/gq's0ޅ8Nfp<dO<RB@X{Xґ%##M(>a75+py'Sz_zKמܴ^cX]bntd ؓ Y# D d  @h  B   ' S A ?       & 2 K @иm0Y A '  N !  @иm0Y A  @  | xMPKjA}U3@jpNlB=hHH: 2;%td@ꚉICUzՄ?W-YӣD;Ӄ";_^)ےuI.KB:JuOl:F%?Ɉo,Y'>wғ[oj*yOA !ex.|wRJ3ƍVݖ;|2'4wέ43 D d  @  B   ( S A ?       ' 2   Y%®qtU5S  wP ! Y%®qtU5S   R  x5O P =I}'qtp_&Pp(إ[GG?A =5I념pn #JSGQ"C6dNcCL^TgbZIeTITIM!?K lׂ.EO H_z{ZC3Z5 ؍VmHӸi.o82' D d  h  P   ) S A ?       "    ( 2 T *cg㌰#V 0  )R !( *cg㌰#V  @ H | xcdd> @c112BYL%bpu<LL,56~) @ k7 zP5< %! 3);aV&br<Яb@Vgu  m 3b^?@W&0; Eظ?ma (䂺 C.]  p021)Wx ], 0v] q (=> D d  h  P   * S A! ?       "    ) 2 T c*PˢKo> 0  !T !( c*PˢKo>  @ H | xcdd> @c112BYL%bpu<LL,56~) @ k7 zP5< %! 3);aV&br<Яb@Vgu  m 3b^?@W&0; E3ظc7L( RQ^u=؇]=0adbR ,.I@X  .>6( D d  h  P   + S A" ?       "    * 2   .},j   V !X .},jr  @  | & xcddddba V d,FYzP1n: &B@?b ʞㆪaM,,HeH @201d++&1~-b p i#O, J _盁Q O?>Fc >,ۛYF1K*b '27)?(µ8701TWrAc ]=8gdbR ,.I@X sdo D d  <   P   , S A# ?       "    + 2  w){T;"rK   AX ! w){T;"rK  @ Hb   xڝS;K@DsD/EQ("X Xji AFOc")vV{D {>tavgfA( 0 |1+S#D!y.qS1й4mx]j@?\ W;c3h=Jj}c! Ģowe2Cyvmqy|C*Q 0 v 緣-X|{ L3Q䚴ύh# gW Îfi xSz6u}JGOi kH>EEK6;E'n3) -Oj|J!H^UݤN^wt|G7E<o-ֶ7!f}Ӯv_ފ :N%?´[76&[L%sy t)kn=8԰"8KEix D d  h  P   - S A! ?       "    , 2 T c*PˢKo> 0  Z !( c*PˢKo>  @ H | xcdd> @c112BYL%bpu<LL,56~) @ k7 zP5< %! 3);aV&br<Яb@Vgu  m 3b^?@W&0; E3ظc7L( RQ^u=؇]=0adbR ,.I@X  .>6^ D d  ( |  P   . S A ?       "    - 2  SۗU   \ ! SۗU @  1 0 \ xڝ1K@߻4FED8uV(V-P G A'x({{< 19=VD D<WW-u>;RFNf!'1etOY'l,-AlI7M^;|?- , c2"|r !R>iVE.qP" [\|urj}q0悧8I[⣒A CwIъ Q C\B/1)rc7UQg3ܼޑEI<dlu{IJDl(O=[j+p  D d  /|  N   / s *  A% ?      ?   . 2 | hD \-, X  <_ !P hD \-, #  h7 0  xOQpe9AN % Z^ gb)'XBIL,,,,06Ɯ;W nv3ٙ' ( R2%d]4rYnM+J2#c0d+kGO16^.5ee}"~S B\BvkΝtW6pS!TtXMG <XFȟFO/Iyx:<n:M<sWɚc?z wQ~fxy.IM C~=y๴KFg.ͻ܂ :_f|Nh~g+Ms D ɳ[]]Zl7+_VOgj8z'Crߤ5 %DZ /U")_}&{g_KCk 2:zh#òEK{2ب.4y/ڳ. ' D d  ,  B   0 S A& ?       / 2   @,Y*}-6h  Zb ! @,Y*}-6h   x  xcddbb V dX@FE%"LPL0}<L0Qcgb qP2 憪aM,,Hep  g11W&00r i#F+ \PӸ62uCĤ\Y\ .w P 3?@* D d  @ 0  P   1 S A' ?       "    0 2  ދ:-" r   d ! ދ:-" r     k  xڥSO@~wm - d0:@  %*lC,& +Db޽k/ P}~ Pity#4d1KK^(0a N! ,Sa9!'{YӿFPRmW:td޼fHuPٿ@5c@v<GX39^/踧vFx#;t:~".)&8r,gf_Kdg3CRNLb?Ok=b8c_VrUvu4|퀷f5} OK , ?'oϣf[h8yߨQ7]#|G5QE _'=g%ŭIof1  D d  |  P   2 S A( ?       "    1 2 w 0?bARw9 S  f !K 0?bARw9R @   0  xcddddba V d,FYzP1n: &! KA?H1  Z00sC0&dT20 KXB2sSRsxC1XP] Hq502d4+a|5*!+Hܞ@**H!2 R\&I9 @\ Ĺqe\D.v0o8N+KRsA<.f8 ;]U D d  @|  P   3 S A) ?       "    2 2 U ;BWxpi 1  h !) ;BWxpi    0 xcdd> @c112BYL%bpu<L L LB@?b  b熪aM,,He( I? 01d++&1~-bF: p i#Y!2/27)?(ZՍ<F0nn HEy%\ BtAÄI)5batCbd 9*<ܘ D d  T  P   4 S A* ?       "    3 2  @W:W*u   j ! @W:W*u   e% XJ  xڕ?H@߻&6Vq CPtRڊ8IJ.:;888uprI0]' 6pK޽ B &@\: G !s]WFyעc) M00G|2 eѾ'~iJ2'~-H z[Vޱʻv ͏Ni9=!;:>?Q<L)x^K8F~N կӽz-ׯeZ8ʎϖs]jrgq{@Q(zdoŨ_RMσS"z/uV {qԍ|R8r*05M%\pi0z{5!N1dlu[xJ7b D d  hT  P   5 S A+ ?       "    4 2 @ ='\?,sVqtp;   Sm ! ='\?,sVqtp; @  | XJ xcdd> @c112BYL%bpu<L LLB@?b =47# ! lo&'0L ZZ\  X. 0VuTBkGyF  J.>% #RpeqIj. n  = D d  hT  P   6 S A, ?       "    5 2 @ U$F2:_   7o ! U\]F2:_ @  | XJ xcdd> @c112BYL%bpu<L LLB@?b =47# ! lo&'0L ZZ\  X. 0VuUBkGyF  J.>% #RpeqIj. n  S= D d  lT  P   7 S A- ?       "    6 2 c _0Iv ?  q !7 _0Iv     XJ  xcddfedba V d,FYzP1n: &B@?b 030 UXRY 7S?&,eabM-VK-WMcZ.  ,@R F\ JQ 1_?|Fg <cDw7#w?Ϭ䂆8d!@ゑI)5b2B16?1Q^ D d  T  P   8 S A. ?       "    7 2 c [RCHTbՔ ?  "s !7 [RCHTbՔ    @2 XJ  xcddfedba V d,FYzP1n: &&! KA?H1  ZㆪaM,,He @201d++&1~-b p i#FSff%ר f>#I3p{ 01TUDwCe l zgVrAC S v 0y{qĤ\Y\ te P D d  ,T  P   9 S A/ ?       "    8 2 @ 7E, y   )u ! 7E, y    XJ xcdd> @c112BYL%bpu<L L,56~) @ k/ t jx|K2B* RvfRv,L ! ~ Ay _ŀ΀H9 @ڈ#XO%ļ?mtc 䂺 C.]  p021)Wx ], 0v] q > D d  hT  P   : S A+ ?       "    9 2 @ ='\?,sVqtp;   w ! ='\?,sVqtp; @  | XJ xcdd> @c112BYL%bpu<L LLB@?b =47# ! lo&'0L ZZ\  X. 0VuTBkGyF  J.>% #RpeqIj. n  = D d  ,  P   ; S A0 ?       "    : 2 O  A,ߏ3 +  x !# A,ߏ3̒    H xcdd> @c112BYL%bpu<L 0 Yjl R A@1 ^ 4jx|K2B* R vfjv,L ! ~ Ay _ŀ΀H9 @ڈ+Q3<W@W&0; ֱrE7L@2׊¥ z.! v 0y{aĤ\Y\ t0 !v120= D d  0  P   < S A1 ?       "    ; 2 & ݠc1k\ݸn0   z ! ݠc1k\ݸn0   x k  xڥK1_kwE Т]qH[qpBmmur\ :8PA u:ADƞP wM{| h၅--VM}~ 6#Ԛq0 CrZWm% ckZj2@~O a+r#+RzTz  4NSoV̙>1L AU3V zd]Џ2Evd^u"{^|vr ftOU=EbM\r#g@fyv}Z˴֯qh8~o=E~{cz6| v8GNEǭ˒<ߝꋏWA2|]}[FDx8;a<]0rF L D d  l  N   = s *  A2 ?      ?   < 2  7f=:4=& *   } ! 7f=:4=& *   p  xcdd>d@9,&FF( TN! KA?H1  @1@0&dT0p E1At 2Babb Yٜ wfRQ9A 37X/\!(?71AD<+ 8U 5l= 0~9;Q 1 y3p{W0S4 L @DBoؿ#\L'ǌ{&??I9 @B^W 8t\ g+mA|J.hnp-F&&\A D,Ġt O |  D d  C o m p O b j  / 1 G f  O b j I n f o  2 I  E q u a t i o n N a t i v e  J ; _ 1 0 8 4 4 3 9 0 8 1  . y 5  F O O uation Equation.3 9q     (  x  n i      F Microsoft Equation 3.0 DS Equation Equation.3 9q     Ģ  w  1 i  O l e  K   C o m p O b j  4 6 L f  O b j I n f o  7 N  E q u a t i o n N a t i v e  O ; _ 1 0 8 8 8 4 5 7 3 5   :  F O O  O l e  P   C o m p O b j  9 ; Q f  O b j I n f o  < S       F Microsoft Equation 3.0 DS Equation Equation.3 9q      d  w  n i      F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e  T ; _ 1 0 8 9 4 0 6 2 7 0   G ?  F O O  O l e  U   C o m p O b j  > @ V f  O b j I n f o  A X  E q u a t i o n N a t i v e  Y 7 _ 1 0 8 9 4 0 6 3 6 8  D  F O O  O l e  Z     n  4.  x  1       F Microsoft Equation 3.0 DS Equation Equation.3 9q   n  <   c  1     C o m p O b j  C E [ f  O b j I n f o  F ]  E q u a t i o n N a t i v e  ^ 7 _ 1 0 8 9 4 9 4 6 4 3  B Q I  F O O  O l e  _   C o m p O b j  H J  f  O b j I n f o  K b  E q u a t i o n N a t i v e  c )    F Microsoft Equation 3.0 DS Equation Equation.3 9q   W          F Microsoft Equation 3.0 DS Equation Equation.3 9q  _ 1 0 8 9 4 9 4 7 0 0  N  F O O  O l e  d   C o m p O b j  M O e f  O b j I n f o  P g  E q u a t i o n N a t i v e  h ) _ 1 0 8 9 4 9 5 1 4 3   L S  F O O  O l e  i   C o m p O b j  R T j f  W          F Microsoft Equation 3.0 DS Equation Equation.3 9q   W    d",      F Microsoft Equation 3.0 DS Eq O b j I n f o  U l  E q u a t i o n N a t i v e  m - _ 1 0 8 9 4 9 5 2 5 3   X  F O O  O l e  n   C o m p O b j  W Y o f  O b j I n f o  Z q  E q u a t i o n N a t i v e  r ) _ 1 0 8 5 0 2 7 9 8 1    ]  F O O uation Equation.3 9q   W    e"      F Microsoft Equation 3.0 DS Equation Equation.3 9q    pI   p  n  ( x ) O l e  s   C o m p O b j  \ ^ t f  O b j I n f o  _ v  E q u a t i o n N a t i v e  w =  1 n    1 v  n  i = 1 n "  ( x "x  i  ) h  n       F Microsoft Equation 3.0 DS Equation Equation.3 9q     =   v  n  _ 1 0 8 5 0 2 7 9 8 0  b  F O O  O l e  {   C o m p O b j  a c | f  O b j I n f o  d ~  E q u a t i o n N a t i v e   6 _ 1 0 8 5 0 2 7 9 7 9  o [ g  F O O  O l e     C o m p O b j  f h  f                                                       F Microsoft Equation 3.0 DS Equation Equation.3 9q    9         F Microsoft Equation 3.0 DS Equation Equation.3 9q  O b j I n f o  i   E q u a t i o n N a t i v e   ) _ 1 0 8 5 0 2 7 9 7 7  l  F O O  O l e     C o m p O b j  k m  f  O b j I n f o  n   E q u a t i o n N a t i v e   C _ 1 0 8 5 0 2 7 9 7 6    j q  F O O    ' S   p  n  ( x )      F Microsoft Equation 3.0 DS Equation Equation.3 9q    9     O l e     C o m p O b j  p r  f  O b j I n f o  s   E q u a t i o n N a t i v e   ) _ 1 0 8 5 0 2 7 9 7 5   v  F OO  O l e     C o m p O b j  u w  f  O b j I n f o  x        F Microsoft Equation 3.0 DS Equation Equation.3 9q    9         F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e   ) _ 1 0 8 4 4 3 9 0 8 3  {  F OO  O l e     C o m p O b j  z |  f  O b j I n f o  }   E q u a t i o n N a t i v e   X _ 1 0 8 4 4 3 9 0 8 5   3    F OO  O l e      r< I I    x  i  i = 1 n "      F Microsoft Equation 3.0 DS Equation Equation.3 9q   r mI yI  x  i   C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   8 _ 1 0 8 4 4 3 9 0 8 6    F OO  O l e     C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   0      F Microsoft Equation 3.0 DS Equation Equation.3 9q   r I I  2x  I      F Microsoft Equation 3.0 DS Equation Equation.3 9q _ 1 0 8 4 4 3 9 0 8 7       F OO  O l e     C o m p O b j     f  O b j I n f o        fK     1 n   x  i  i = 1 n "      F Microsoft Equation 3.0 DS Equation Equation.3 9q    fp @   1 0 0 *   ( E q u a t i o n N a t i v e   g _ 1 0 8 4 4 3 9 0 8 8    F OO  O l e     C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   _ 1 0 8 4 4 3 9 0 8 9      F @O@O  O l e    n "( # Y E S + # y e s ) n   )      F Microsoft Equation 3.0 DS Equation Equation.3 9q    f 0     1 n "1   ( x  i  "2x  )  2 i                                 ! " #  % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : G = > ? @ A C B D E   H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _  a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~    h  P   > S A3 ?       "    = 2 Q s[=l<Y3wƍZ -  0 !% s[=l<Y3wƍZ  @  | xcdd @c112BYL%bpu<LL ,56~) @ k;' P5< %! 3);aV&br<Яb@Vgu  mA3b^?c .a Dw'5\J.hpC b ; ֌LLJ% H X, -NX D d  |  B   ? S A4 ?       > 2 h ZZ*O[ D  % !< ZZ*O[    0  xcdd @c112BYL%bL0Yn B@?6 Ā깡jx|K2B* Rͤ  YB2sSRsn׼-| W  P.P16 ֙Y 30yk~?Kܞ~ **l:.P p121)W23qcgba~ q,C YI D d  ,h  B   @ S A5 ?       ? 2 m .FgzLBN I  # !A .FgzLBN  @  |  xcdd @c112BYL%bL0Yn &B@?6  5}bn ĒʂT +~3);a~&br<5o//ƥT T0ufVBkGy?#c .t P^NGv'\F LZVrAC rca"+ kF&&\\i ] ـr06  PY D d  @|  P   A S A6 ?       "    @ 2 I 3TmȻ}~m %  & !  3TmȻ}~m    0 xcdd @c112BYL%bpu<L L LB@?b  熪aM,,HeH I? 01d++&1~-bF: p i#/ >W 1 y3p{0:0TWrA}1D.v0o8+KRsA<.@ .Ff8 i? D d  h  P   B S A7 ?       "    A 2 D K<ԍ{iy    ! K<ԍ{iy  @ H | xcdd> @c112BYL%bpu<LL,56~) @ k;7 P5< %! 3);aR&br<Яb@ Vu  mcX 1 <Fc .[Qu=؇]=0adbR ,.I@X  > D d  h  P   C S A8 ?       "    B 2 D A'&66G,dQ    ! A'&66G,dQ  @  | xcdd> @c112BYL%bpu<LL ,56~) @ k;' P5< %! 3);aR&br<Яb@ Vu  mtcX 1 <Fc .4\u=؇]=0adbR ,.I@X  >s D d    P   D S A9 ?       "    C 2 , ʱ }a%! V    !  ʱ }a%! V: @   H xEN=Q;_w'^"Rh5 =!\RBhTgߺ%vf% ф=9gRD.Sѐ HFM2姞 a5K/>um* 3fh(LyjR \;Bތ.O7eWݝ[xX)W_SYi 0> D d    P   E S A: ?       "    D 2 - ]}c[t    ! ]}c[t: @   H xENQ=3cQJ#_TlAlNP J;7;{!@ ц=y)2DlQԧf _iHuAB-k/*f|t*g Fx9I7!h/]' bB2x4H} {BJތ|me)nq2|]twb] F)G_S ~1OT0 D d    P   F S A: ?       "    E 2 - ]}c[t    ! ]}c[t: @   H xENQ=3cQJ#_TlAlNP J;7;{!@ ц=y)2DlQԧf _iHuAB-k/*f|t*g Fx9I7!h/]' bB2x4H} {BJތ|me)nq2|]twb] F)G_S ~1OT0 D d    P   G S A: ?       "    F 2 - ]}c[t   U ! ]}c[t: @   H xENQ=3cQJ#_TlAlNP J;7;{!@ ц=y)2DlQԧf _iHuAB-k/*f|t*g Fx9I7!h/]' bB2x4H} {BJތ|me)nq2|]twb] F)G_S ~1OT0 D d  ,  P   H S A; ?       "    G 2 P  rK̿ݪd ,  & ! rK̿ݪd     xcdd> @c112BYL%bpu<L0 Yjl R A@3 N t jx|K2B* Rvfjv ,L ! ~ Ay _ŀH9 @ڈˁ^J,1 Ma(w رp5b7L@2ׄbq%\ BtAÄI)5batCbd y=N D d    P   I S A< ?       "    H 2 . 3ׁG +PH    ! 3ׁG +PH: @   R xcdd @c112BYL%bpu<LB@?b P5< %! 35;aR&&ܤ r&f+_ŀ΀H9 @ڈˁdJ.-\@TCĤ\Y\ tev0@Af8 s[1m D d    N   J s *  A= ?      ?   I 2 P O ޔ!'Hn ,   ! O ޔ!'Hn      x/A߼ݮv[Z%"B,Q AF"DH8#&J:mĩNC?@CI\ŅfT#eپ}f }/g!!Eq nv"8(tÂ!FuZgtLEUD~ug}N@zPdkfPS|]Aw |'닲~pĊEމ[ȤB4s,\tKĭM8Ә V_#,3k D:p<j|E9Z8N|\w l#ӻ^T\_'2mp Up#x\G|?>􀫋dsz6 k9k"o[QD#RVf-uzOs Ϥ[[;M wPk_j_Qn5OJ}6ClMKqcVV :AMYt) z]Cb¬Al֭ D d  h  <   K C  A>       J 2 P q;0+^G ,  ޙ ! q;0+^G  @ x | xcdd> @c112BYL%bpu<LL ,56~) @ k' zP5< %! 3);aV&br<1@pT9 P.P16z3b^?c 60-䂺 CF=0adbR ,.I Ӊr!v120CF} D d    <   L C  A?       K 2 @ QZ{HWc SW    ! QZ{HWc SW<   ! x xcdd @c112BYL%bpu<L ,56~) @ KH+ :P5< %! 35;aV&&ܤ r(7e1@pT9 P\Hq100ܛU F;=321)Wx\ ] ]O4NC( q .l2 D d  lh  <   M C  A@       L 2 o #=bl+.KrZD K   !C #=bl+.KrZD   @ p |  xcddfedba V d,FYzP1n: &B@?b 030<UXRY 7S?&,eabM-VK-WMcs>Q. N300 Us i#F9fVJ 3d>#dOȄ =Y ~ jF} y\P,8xa&#RpeqIj.ŠV "1h:(G3ı Z D d    <   N C  A?       M 2 @ QZ{HWc SW    ! QZ{HWc SW<   ! x xcdd @c112BYL%bpu<L ,56~) @ KH+ :P5< %! 35;aV&&ܤ r(7e1@pT9 P\Hq100ܛU F;=321)Wx\ ] ]O4NC( q .l2 D d    <   O C  A?       N 2 @ QZ{HWc SW   ] ! QZ{HWc SW<   ! x xcdd @c112BYL%bpu<L ,56~) @ KH+ :P5< %! 35;aV&&ܤ r(7e1@pT9 P\Hq100ܛU F;=321)Wx\ ] ]O4NC( q .l2 D d   0   P # AA    O "  =SPC".Z  - @= =SPC".Z9  S K D1 xmhTWɌM:w~mRƴ~,ê,ۡDn(u Z1X*"Pea~ֵ-}s余fɻs9{{̍upqS @o /^ w ǐ'҃R8 C 5!&7M!=؎#xYR .Ghg{SaMq}՞d*5m ]EE7;㹘:lݶDc ;ń <|[Ki Y(} ;n/9|n':ʷհV_d'}^Y0wO[8~yCs G71|O{J}GM=t89^ʅ _D 9ߛt2sq/A{a K:uJMs&c6vT~Y|H-}23؄6}aGHR}j[{,HO~gJ wJ9׻N31ݎ|_s_܉sy3gys'n}HƧ9\?;<Q<99ߜKͽ XHgJ v#2^ ]>4}d _&Nn,3(J>F Q y?4z4|^KQKb>_Y?M{H) cn#'6WKF:d!+U٣ |QYu8SpxUVoJ϶˶oiK"lvX}Cڐm]4>H)g.AEu-KҸӬ uf}b덣U7& 7+N3?d+fO ML[6,k< 3NRB~mZ{AP ~FAbk^fMʼ oS>Sǎ8lOm6n aOᷴZeݾy wu[/oFWo#mԺ{eٓi]mlx֚a46 [/262/W.؍) IBDv# z Ժqmذ~pm^=482zՏ}'0N'4^Dq՛C<uN«'mnlH6 +mz.#\E2«He ׺W5NQ?ce?mG؄̻\. ckiנz ~@&W3NذI@'|짍yڌ}1N5^D\ߦuN«'mnl8^qm>VRȼ T+o)iƫH_'rv!ޥuN«'mnlXwm>V\~jh8x5S?Ӯ4it^3 @'>cѠ [Vδ{.?t-OM . 61ݮߍ  iʬypQcwv- 'Ҹ 2-TBtZ+~cs r?(CK Z)xm P rw7= (w3<3δV>m]7 pNfwjA6jv!Rݛ?Yזyկmax ? z CSw zF3?-)AO交3ٳ &fKC).:?K /AiK?s O?#,C [JؿCٿ!K P~1?aXϽ|1unssJ;rdC [bSZ 1M1HR_73 f& RL=|? s%^G|ѥB紆ql|oKҜYk'cJc pJ?]W&@SOt=I=7 \e_{b^ ss&n^5Us[ z oҧ+c|~fg,<oN92{#ub r^KXd-u&=oމ s@=k8\s4gM4<QoӸu>o.<YPO)5e6XJHGO\ '0NM9jg~V>: 1T^gǊ Ӻ śNIf  !v h5 5 5=5=55555 5 #v #v #v=#v#v#v#v#v #v :V l t 6   0       6 , 5 5555555 5 e48kdm If l        Tq F Y!          t 6   0       6  ( ( ( ( 4  4  l a e4NIf  !v h5 5 5=5=55555 5 #v #v #v=#v#v#v#v#v #v :V l t 6   0       6 , 5 5555555 5 e48kd If l        Tq F Y!          t 6   0       6  ( ( ( ( 4  4  l a e4NIf  !v h5 5 5=5=55555 5 #v #v #v=#v#v#v#v#v #v :V l t 6   0       6 , 5 5555555 5 e48kd If l        Tq F Y!          t 6   0       6  ( ( ( ( 4  4  l a e4TIf  !v h5 5 5=5=55555 5 #v #v #v=#v#v#v#v#v #v :V l t 6   0       6 , , 5 5555555 5 e48kd  If l        Tq F Y!          t 6   0       6  ( ( ( ( 4  4  l a e4 If  !v h5 s5d555#v s#vd#v#v#v:V l 4 0        6 , 5 s5d5554  f4T If  !v h5 s5d555#v s#vd#v#v#v:V l 4u 0        6 , 5 s5d5554  f4T If  !v h5 s5d555#v s#vd#v#v#v:V l 40        6 , 5 s5d5554  f4T If  !v h5 u555-5#v u#v#v#v-#v:V l 46   0        6 , ,,5 u555-54  e4f4T If  !v h5 u555-5#v u#v#v#v-#v:V l 46   0        6 , ,,5 u555-54  e4f4T If [!v h5 55~ 5 #v #v#v~ #v :V   0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj If [!v h5 55~ 5 #v #v#v~ #v :V  0       , 5 55~ 5 /   4  4   aj D d  0  B   Q S AB ?       P 2  >q4w\ \   !T >q4w\P  @ m  " xcddVgdbe V dX, XĐ ɁYRcgb 63G 憪aM,,Hex V_C&,Bܤ &@Q muɜ)T 0X-A,@! ~ Ay 0@Lb4ؤ<~& 6I lRHt{f# \и h 0y{1Ĥ\Y\ 1 ug0 >YG D d  h  B   R S AC ?       Q 2 < 1ඇunE%&   ( ! 1ඇunE%&h  @ R | xPQ=3Kb#jБ> >bEN+|ZSTj5wvdrgΝs% {r%Y֢DcRC S]/&Y;_EƒJ},1CT0ZDasubϨN2*Co&Xuґ}NoUU SiJ{8CG sUEAM̭! 1*d J: D d    B   S S AD ?       R 2 ; S;Ã(Jc S    ! S;Ã(Jc SL   ! x x5OQ=3Kb㑈j | 4:M(JЩ>A3*VXsgs9K+@R96()D!P7-B3* j#4"r zJ;":IcNv19l<m͑/6)rSEeAD&߈{&'ɰ'K sFk !+kÊSXVWo'b/L_?E-m D d    N   T s *  AE ?      ?   S 2   ɩ:    ! ɩ:P  @ ]  m x=KAggOϜC@0 v!?Kc - &Eu{g}fn 䵠 a8YļM⒘"+Mj}r!V";"uGeHcbP(7+y{oE)4{]̳%7>t*IC~ A 췃%n l\;#Synovy+_;U^5/p~թh=P ynX5vcmsV cwG]YG wKqsx: :W lyJ1l4=_Y,c={i g~ D d  l  N   U s *  AF ?      ?   T 2  b}cX@|{f   8 ! b}cX@|{fP   h p  xRJAݻ%3Q"_ JJ-LI"r X K kBVVQH "=v웷 hp<8cbKk)_r ͞ʠ2yS0X[h Inq\<{))*Q-rٝn= .tM4: P0I3ɚF"=Ndssvi8" (^[>qE_s u++ /0g SIX y;z}Rޱ qj\6䴿5n8l˷ƫ@*Ys"܍.8;S,: =nf/zCLXKL oh b D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / m m p / k a p 1 / c a l c k a p 1 . s e q u e n c e If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V  0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   akd If       8h ! 2/ + !            A        X    d    A                            0      8 8 8 8 4   a- D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 1 _ M a t h _ 1 / m s u - p r o b 1 1 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kd  If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ - D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 1 _ M a t h _ 1 / m s u - p r o b 1 0 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kd If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ ; D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 3 _ U n i t s _ S c a l i n g / m s u - p r o b 2 2 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kd  If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ - D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 1 _ M a t h _ 1 / m s u - p r o b 1 3 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kd# If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ 5 D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / d e v o l i b r a r y / t y p e - m a t h / f r a c t i o n - r l t - 2 3 5 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌  C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   _ 1 0 8 4 4 3 9 0 9 0    F @O@O = 1 n "         F Microsoft Equation 3.0 DS Equation Equation.3 9q    f      1 n   ( x  i  "2x  )  3 i = 1 n "  S . D . ( )  3  O l e     C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e    =   1 n   ( x  i  "2x  )  3 i = 1 n "    1 n "1   ( x  i  "2x  )  2 i = 1 n "  ( )  3      F Microsoft Equation 3.0 DS Equation Equation.3 9q _ 1 0 8 4 4 3 9 0 9 1       F @O@O  O l e     C o m p O b j     f  O b j I n f o        rԈ I I  1 "  (  # Y E S + # y e s   x  i  i = 1 n "   )      F Microsoft Equation 3.0 DS Equation Equation.3 9q   E q u a t i o n N a t i v e   _ 1 0 9 2 1 4 2 9 7 1     F @O@O  O l e     C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   _ 1 0 8 4 4 3 9 0 9 3     F @O@O  O l e     ,¯ h       " P a r t i a l  C r e d i t  A w a r d e d    x  i  i = 1 n "      F Microsoft Equation 3.0 DS Equation Equation.3 9q   C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   _ 1 0 8 1 1 9 1 7 5 4     F @O@O  rԀ I ̚I     ( " # Y E S + # y e s )   x  i  i = 1 n " a      F Microsoft Equation 3.0 DS Equation Equation.3 9q    LI ~I                                                                                  R 0                                               kd. If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ ? D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / d e v o l i b r a r y / t y p e - m a t h / f r a c t - a d d - s u b - d i v - p 1 1 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kdC If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ - D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 1 _ M a t h _ 1 / m s u - p r o b 0 4 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kdF If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ - D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 1 _ M a t h _ 1 / m s u - p r o b 0 7 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kdI If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ - D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 1 _ M a t h _ 1 / m s u - p r o b 1 2 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kdL  If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ ; D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 3 _ U n i t s _ S c a l i n g / m s u - p r o b 1 7 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kd]% If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ ? D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 6 _ V e c t o r s _ S c a l a r s / m s u - p r o b 0 7 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kdr- If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ ? D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 6 _ V e c t o r s _ S c a l a r s / m s u - p r o b 1 0 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kd5 If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌ 7 D y K   y K h t t p : / / d e e p t h o u g h t . l i t e . m s u . e d u / r e s / m s u / p h y s i c s l i b / m s u p h y s i c s l i b / 0 2 _ M a t h _ 2 _ T r i g / m s u - p r o b 1 3 . p r o b l e m If !v h5 555A55X5d5A5 5 5 5 5 5#v #v#v#vA#v#vX#vd#vA#v #v #v #v #v #v:V             ֌ 0       , 5 555A55X5d5A5 5 5 5 5 5/   4  4   ap֌ kd= If       8h ! 2/ + !            A        X    d    A                                       ֌ 0      8 8 8 8 4   ap֌  D d     N   V s *  AG ?      ?   U 2 1 ዦQ F?'[9G   D ! ዦQ F?'[9G @  h 8  xTJAsgb&H T4>A0 >jA!hT0Ng-]gNsι̲ '@@3+V K2f+A5X. %"É:j  I}U]h jIRauAn ZOH;v-8tVUJqL;I Pɬf3;E{ :qJs2R>҇ꗜq wƊ^Z9he gz'IϾ8uŭ {?'rj-+ g.Y,s;LsK;'ߔ<YWm|1+K=ΊEF*<=وs xhvM02cZǼD26/w F¾ij>{蕟ph7 D d  '  N   W 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GHcsTE c<I@(YqT<E n& E K87D5.IcQ8]zI4u@'c]shqDuWUO-ssȟ#,8Gt@ #N7,ᘞUX7G!, mLlWCALlWxG 8o H"% ;Unq4E,[L*[ [K5zI'bI|}2-6o?\MZ8^>PrB zņ }dm4/ /*^n1@ @}= wLo- Ƕc]Xm?FD @}xq J::G1\'pd/ '@8 p=zsc'@8 p=zsc'@8@ņg'qmC[@6 nPc'@Hp8bF'± sz@8zu1# 9= =κIp  g]@8vd@ +畷+aru9gş wX4bW-wu;|y!v hmXLC+'o8U)2c@N- XF#Жycɍv!yc!!KkنN Bɠ\@:MZtb[,u@e!Е+c DZ8"h (cmnC(;7kٖYYf5)3n{e!C W}RT>w&LņUp/=mE .xTpcsÐņn.8ʮ˔YZ>Tv L=_PۿKT7CG]9Sn58bq U8E±V)^v0 0\eeTG#&Xaub (Uw]cuٔGkm\Q<bXc;Ӻp; 3UIciM|B!Cj8YfXNSa=-C)r2 ]~Lz@ 9*G r G r G r G r G r G r G r G r G r 7 IENDB If !v h5 5 5#v #v #v:V  0      6 , 5  /   4  4   T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p T If !v h5 5 5#v #v #v:V     0      6 , 5  /   4  4   p  O l e     C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   , _ 1 0 8 1 1 9 2 1 5 4      F @OO  O l e     C o m p O b j     f  O b j I n f o          F Microsoft Equation 3.0 DS Equation Equation.3 9q    I I         F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e   , _ 1 0 8 1 1 9 2 0 8 1     F OO  O l e     C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e   d _ 1 0 9 0 9 3 0 8 1 6       F OO  O l e       H I yI  x  i  =  x  i  "       F Microsoft Equation 3.0 DS Equation Equation.3 9q    .  <  E r r o r  R  C o m p O b j     f  O b j I n f o     E q u a t i o n N a t i v e    _ 1 0 9 1 3 6 9 2 7 6     F OO a t e  i n  e a c h  r o u n d  =  T o t a l  m i s s c l a s s i f i e d  o f  t e s t  e x a m p l e s  T o t a l  n u m b e r  o f  t e s t  e x a m p l e s      F Microsoft Equation 3.0 DS EqT  D d     \    s 8 A         g r a p h   b  v)g)+lɽg   H  n  v)g)+lɽgPNG  IHDR   Y PLTE   T bKGD  H cmPPJCmp0712 Om 0IDATxv ༽];At{z@ cWMU'2No q pӽ(Z ~p"q5ǫqб^ݿţ=}r[~ x ' U :Y޴}|>[>;~\ ?6!#T~*ǋūa\':V_p]zY7 w1C򡯘S8|>B|q!t1.}5j|}搯_3,R_Z# 888וӣrp: rT zU&uv|6]خ[u &sGp wA | 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h5  555#v  #v#v#v:V     ( 0       , 5  555/   4  4   ap( ?If !v h5  555#v  #v#v#v:V     ( 0       , 5  555/   4  4   ap( If !v h5  555#v  #v#v#v:V  0       , 5  555/   4  4   a D d   B   ] S AN ?       ] 2  ="%Z'O  - ! ="%Z'O   R  x5O; P Vbi. xA4RZzbayafg + R>Sb! d!uߩ! ƘO陈^RaǉUm}.1?|-n-q^# A3k9[1=,#1ReT Eϴ# D d   B   ^ S AO ?       ^ 2  VY3U[i5  ݏ ! VY3U[i5   R ! x5O; P V"V" @A!iҥKdafg ; R>Qb!sdj!u&/kݤas(O c~Z<[b1m /g@^ ̑L܊ѷiy2˛ߥ-x?^t". D d  Ll  B   _ S AP ?       _ 2  ~}6 QçN t   !l ~}6 QçNR    : x}QJP=&6,j@BCu +,4VfQPo }i7rɻ2m<TMK1NmdɱWxkՃUl0"T{z O4Sa{p/,b0_lu;n]&|mw2G.j oogdpy Úsק5 >g z__&Y|\ǽ}LZgvNo4?q:/fj n KK^u\k I~ UR If  !v h5 l55#v l#v#v:V l 4 t 0       6 , 5 f5P59 f4 If  !v h5 l5555#v l#v#v#v#v:V l  t 0       6, 5 f555 59 9 If  !v h5 l5555#v l#v#v#v#v:V l ; t 0       6, 5 f555 59 9 If  !v h5 l5555#v l#v#v#v#v:V l ; t 0       6, 5 f555 59 9 If  !v h5 l5555#v l#v#v#v#v:V l ; t 0       6, 5 f555 59 9 If  !v h5 l5555#v l#v#v#v#v:V l ; t 0       6, 5 f555 59 9 If  !v h5 l5555#v l#v#v#v#v:V l ; t 0       6, 5 f555 59 9 If  !v h5 l5555#v l#v#v#v#v:V l ; t 0       6, 5 f555 59 9 If  !v h5 l5555#v l#v#v#v#v:V l ; t 0       6, 5 f555 59 9 If  !v h5 B55c#v B#v#vc:V l  t 0       65 P559  If  !v h5 B5P5s5152#v B#vP#vs#v1#v2:V l ; t 0       6,5 P5W5^559  If  !v h5 B5P5s5152#v B#vP#vs#v1#v2:V l ; t 0       6, 5 P5W5^559  If  !v h5 B5P5s5152#v B#vP#vs#v1#v2:V l ; t 0       6, 5 P5W5^559  If  !v h5 B5P5s5152#v B#vP#vs#v1#v2:V l ; t 0       6, 5 P5W5^559  If  !v h5 B5P5s5152#v B#vP#vs#v1#v2:V l ; t 0       6, 5 P5W5^559  If  !v h5 B5P5s5152#v B#vP#vs#v1#v2:V l ; t 0       6, 5 P5W5^559  If  !v h5 B5P5s5152#v B#vP#vs#v1#v2:V l ; t 0       6, 5 P5W5^559  If  !v h5 B5P5s5152#v B#vP#vs#v1#v2:V l ; t 0       6, 5 P5W5^559 zG D d   0    # AQ     b F  EȻۓ _ F  D  n F EȻۓ _PNG  IHDR 0  sRGB FsIDATx^]z++-M̚Σc~H 仓%A!?  joh     ~   * !0 @  |   T BRa(    @ @ P  @H  P I @ @    3@  Yv9͟]2qd+IQ3 % udZ N՞rY[CU GGn8U4 &GJ>4sWQ^!-WVJ!Yd'H1AN-ܴ+Q׊H5yǟlOy/H ɭhXa*U, "шc0ܜeA ^X DTǛc2Dgci,(By> { RNtNFX BH]eU)bv<ܔ[}Mӗ]/2W J˚I(Ғ%~7+P@8[ "M9A ߖ;K#4Gz CoȖL6Gtx)hq4s&9Zn+9q[e, Q&I6 DYb(r %U*I6]FMԟVkc]}VPԅ gqAl=9uG%{划u GH։:+hrSOyJNX Еwj6.ںZ۱%N ^ٝhjĆMVb\着eU>#QOxC\uf?}_E1\/V,bDͭ |zv(_l@"&e! 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55K55K55JIf  !v h5 ! 5 5d5 5d5 5b#v ! #v #vd#v #vd#v #vb:V l 0       6 , 5 55K55K55JIf  !v h5 ! 5 5d5 5d5 5b#v ! #v #vd#v #vd#v #vb:V l P 0       6 , 5 55K55K55J If  !v h5 ! 5o 5m 5k #v ! #vo #vm #vk :V l e0       6 , 5 5If  !v h5 ! 5 5d5 5d5 5b#v ! #v #vd#v #vd#v #vb:V l 0       6 , 5 55K55K55KIf  !v h5 ! 5 5d5 5d5 5b#v ! #v #vd#v #vd#v #vb:V l 0       6 , 5 55K55K55KIf  !v h5 ! 5 5d5 5d5 5b#v ! #v #vd#v #vd#v #vb:V l 0       6 , 5 55K55K55KIf  !v h5 ! 5 5d5 5d5 5b#v ! #v #vd#v #vd#v #vb:V l 0       6 , 5 55K55K55KIf  !v h5 ! 5 5d5 5d5 5b#v ! #v #vd#v #vd#v #vb:V l 0       6 , 5 55K55K55KIf  !v h5 ! 5 5d5 5d5 5b#v ! #v #vd#v #vd#v #vb:V l P 0       6 , 5 55K55K55K D d E  0   f # AW    f " & Da .ZW   4e @= Da .ZW4B l  'Y ; x\}lTw>> ΥS5 *R1VD_ט:QJ( rj%q*"%JNEEB)Ý7<;sg;m μ~b_X<f = zCs,-k㡏 Sv1& 0-TeHVYdI&}Qֽ>8*NǉCN>*.9+X·s nh[8 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        , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 4P 0         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 4P 0         + , 5  5m5f4 If  !v h5  5 5m5m5#v  #vm#v:V l 40         + , 5  5m5f4 D y K    h t t p : / / w w w . w b t s y s t e m s . c o m / y K 6 h t t p : / / w w w . w b t s y s t e m s . c o m / 0 P OGR M F LES W OF E  W w If  !v h5 h%#v h%:V l 40         5 h%/   4  f4 If  !v h5 5#v #v:V l 0         5 5/   4  D y K    w w w . w e b a s s i g n . n e t y K 4 h t t p : / / w w w . w e b a s s i g n . n e t / If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  If  !v h5 5#v #v:V l 0         5 5/   4  ? D y K   - h t t p : / / w w w . w e b a s s i g n . n e t / i n f o / t e x t b o o k s . h t m l y K Z h t t p : / / w w w . w e b a s s i g n . n e t / i n f o / t e x t b o o k s . h t m l If  !v h5 5#v #v:V l 0         5 5/   4  D y K   y K d h t t p : / / w w w . w e b a s s i g n . n e t / i n f o / A c c e s s C o d e I n f o . h t m l If  !v h5 h%#v h%:V l 40         5 h%/   4  f4 If  !v h5  5#v  #v:V l 0         5  5/   4  D y K    w w w . b l a c k b o a r d . c o m y K 6 h t t p : / / w w w . b l a c k b o a r d . c o m / n @ a If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  D y K   A O L @ S c h o o l y K  m a i l t o : A O L @ S c h o o l n N If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4  If  !v h5  5#v  #v:V l 0         5  5/   4   D y K   y K h t t p : / / c o m p a n y . b l a c k b o a r d . c o m / c l i e n t s / c a s e s / v i e w c s . c g i ? c s i d = 2 0 1 6 8 4 9  D y K   y K h t t p : / / c o m p a n y . b l a c k b o a r d . c o m / c l i e n t s / c a s e s / v i e w c s . c g i ? c s i d = 6 6 8 6 6 7 0 2 ; D y K    w w w . w e b c t . c o m y K , h t t p : / / w w w . w e b c t . c o m / If  !v h5 55@5@5@#v #v@:V < 4 2        5 5@/   4  4  < p2      T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T  D d   X  0   h # AY    h " l 5 TTkw;T H   @=@ 5 TTkw;T  r  g v  xڝSJAq(M  KSk/?;<;]N#c0ޞꩭq m|3@9_ԀgLȷ0yߖh@CJq0~ |+w8Jy ) 07V\P383ۄoޣb2|. z5e>Lz[֖StUR--TAxZ7s oj="z2æ@xMJI|8P] C4 D d    0   i # AZ    i "   >- rRF c   @=[ >- rRFXP  ǝ^  ) x\klUfm)Rjۢ bR+EcE"kE<4M@| j& E@|5!d7ӻv q:ιs ̜3ٽBhXM429(e06cW0#@T%~Pt#R5lZ |1ޯʍD/ȕP| ɯl0B hIFyD ԉ3 SMA<Uƞݕv44(OS"*>.Hh:}0-wL0r|ǆ ЮUGBgҬ#!ukM].oC~o8Hk ?bê yoY{'<,: :ldFKY JR CFQrZPZqtQu&rνVX^V&K (n2xV~U9LǽyqRٹڜ6oz{^4^˛ǯ1fDP+8u8D~25~r;66&w1r~>4Ey^ ֑OAǪOEZݪIHYomϕ>gρj++A\& S*;GǭS.U.m_,^ˤi*4#Wp{q6ggr-ߢ; ~7 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o'sVtssQB>W&d1߃fbU5BuP-Y 2iP>~8KYLj3LHn2ǓJs7g_6xn J K ֯xMZ? ~n0 mONūns lYp!gqHqP 4Yp考 (XT ,Xw,6 xoQ0 jLcRs<_{t.v̟ygs#oF뙃M wȁ?7*ln9xނ 9FŢn9F͍3Xpp9FS՞ZTaW8]5FK;ףtO߄*/EQ!H nh,oK?Mݚ^&]Ǯ'KFTqus~Or{e6}Cɽ99<0 .;]'˟LKȷBь+G~fAÞN5 NY \6ڭ݂}~y F7bݫȐBw};skg6^)_=m/0)>WuJ ⵈw-"<\9Eg1TZWfbtZ !gqHqP 4YpZ 2 T2,8w-Ebv WgYpZopZ<'miN4~__\#uOj_ZZW7s G\S1sq~~~˵݇6̡k iSc Pms/՚TkA--}>| _ jjϠIf  !v h5 55555555 5 #v #v :V < 4  d             5 5 /   4  4  < pd           T kd If T < 4 d d d#                                          d            ( ( ( ( 4  < a pd           T If  !v h5 55555555 5 #v #v :V <   5 5 /   4  4  < T If  !v h5 55555555 5 #v #v :V <   5 5 /   4  4  < T If  !v h5 55555555 5 #v #v :V <   5 5 /   4  4  < T If  !v h5 55S#v #v#vS:V < 4        5 55S/   4  4  < p    T If  !v h5 55S#v #v#vS:V <   5 55S/   4  4  < T If  !v h5 55S#v #v#vS:V <   5 55S/   4  4  < T If  !v h5 55S#v #v#vS:V <   5 55S/   4  4  < T If  !v h5 55S#v #v#vS:V <   5 55S/   4  4  < T If  !v h5 55S#v #v#vS:V <   5 55S/   4  4  < T If  !v h5 55S#v #v#vS:V <   5 55S/   4  4  < T 4If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V < 4 2        5 +55H5g5+/   4  4  < p2      T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <   5 +55H5g5+/   4  4  < T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <   5 +55H5g5+/   4  4  < T 4If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V < 4 2        5 +55H5g5+/   4  4  < p2      T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <   5 +55H5g5+/   4  4  < T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <   5 +55H5g5+/   4  4  < T If  !v h5 55@5@5@#v #v@:V < 4 2        5 5@/   4  4  < p2      T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <    5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T If  !v h5 55@5@5@#v #v@:V <   5 5@/   4  4  < T  D d  = \z  0   k # A\    k " s yNEdV F O   @=G yNEdV F  # x  xڽV=KA5QTB_8*HElJ0Xi3Vj:*ARZiffp7۷yvg6 v0 1>0S x×i>B G> ?%HMccH 91 N175094ad0zU4gy!^6x5O6 ^ca+z8ow"uRKyb?& /fz~"x~YbW|M짪x?X~qRB8ǋY//d?i@+og~5!%Z[[%>Ƭ1֛MSWP [ x]5Ʃ0zp|1wmsm 鏨Hi YxZ?s⍴.y-n-g>{XW=355ޫyn +sr͸x]g[^m _e6u|u?onk\Wuk{xÕ:>־/Mǹe D d    0   l # A]    l " v s^q5 R   @=J s^q59  ǝ^   x[}lEwףKJh b%~ | QjJH! Q #PPsw7}ݻoי7ovޛy7;c QH\]&q?Rl<@aK U3 ƠlVU1E W :>AjX ڐ laVE)cBZ̿~8a.C =|՘VX _^laCøqfN-;aQ\ c9'֍KE=}v~ c 5=;7P_{޻HfǗniw, ^5nQ{_*[w!8 fc|!wpx 8Ipy0 F ̰ 8z0XH xe& YϘ@B p^#Z8O:+i>xbрsG}<h~ jyz>:І|=; J4)>_W6@a*}D6l#(KiSpdSDkګ|-UiЦ=m ag~ O9_v8Hت|L#]LyX}>ξZg23̍XS70 [e ķ/ܶo۬BT\(6uBNȗ r!_,䋅TKXȋ|O?a7MfsX F1hN!B~Ro -!/2ʉk|w y3B~O y ('^7 y3c/F<Vb.egQ,iGjAKkw5'˪ hT 0 4Y .bY/zTnTAV i#~ zp),[<MalZY o4]HUHo#kw"Q#"-x/tCF:Ԡ^>>>>??UOid^x/ts<R{y]p]9'ϱ+ α1=uaݳ<]fXu* ՆX܊BRֵu/PU6L+5 ݧQW g{<ꚃO.x/tfcz}x/t_f] c:O=l̥uXv4Vؾ5<i9a} t+~')T\7(s.8fFn j< 0 uסxcC<*RWū QW+Hoz^dx4^Oǧh w!_s!ҏIT#sA8,a : b0l,r n3p!(Xִ0h1c@2',Ƣa٧R^H5teO{m1ha8syEao>׬:ﺅBN?oJ걳A@cף01+ФQ*W:1h*J =pFP_=P0cҾnoo_}m;v ]rzש9ߢq܄lZ,m#-3}~-\{]94oOx1="%m*[]va܈6،Waڊ%;4 gENLp xdPy(y^jBB< }4gEEW]ЩU5v~v~ԻH<gҍnuĥ!h|I%O6/ͅHDƏ<8] D d  r   0   m # A^    m "  f[Ae {   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      r    6              r    6               r    6               r    6               r    6               r    6               r    6               r    6             r    6             r    6             r    6             r    6             r    6               r    6               r    6               r    6              r    6              r    6              r    6              r    6              r    6               r    6               r    6               r    6               r    6               r    6               r    6             r    6             r   ! 6            B     S       ?                          - ! ^    t  =    t   %   t   % O  t   %   t  J %   t   %   t  % b  t   W  N t  W  N t    ]  t   G  t      t     t      t     t      t  O    t      t  =  7  t   X ? O t   X  O t   X  O t  w X  O t  " X  O t  O X p O t  " X  O t  X e O t  X - O t    Q t   S t / : z  .          / : < = C L T V \ c d h n q    .                                         @  ̫u    - p  @  G   T i m e s N e w R o m a n 5   S y m b o l 3&    A r i a l "  q  h ҁeҁe          20    A h m a d  A h m a d  O b j I n f o      O b j e c t P o o l   O O  O l e P r e s 0 0 0    c \ W o r d D o c u m e n t   q     , { 4    &  &   Word Microsoft Word     Courier New  -      @ Times New Roman  -        -  "  -   ?      -  "  -    ?        @ Times New Roman  -      -    ' -   "  -     -  -    -  -   ~  >  -  -    ~  >      @ Times New Roman  -    & >  . 2 & >   1 &  .    -    ' -  -    b  -  -     a    -    & a  . 2 & a   )   .  T{ -    ' -  -    y  -  -     y    -    & y  .  2 & y   The - & !  .  T{ -    ' -  -   E  -  -    D    -    &  . 2 &  acceleratio ! ! ! !  !  !   &  .  T{ -    ' -  -   d  -  -    c #   -    & # . 2 & #  n &  .  T{ -    ' -  -    G -  -     G   -    & G .  2 & G   (   .  T{ -    ' -  -    p -  -     p   -    & p .  2 & p  magnitude : ! % &   & & !  .  T{ -    ' -  -     -  -        -    &  . 2 &   )   .  T{ -    ' -  -     -  -        -    .  T{ -    ' -  -   y  -  -    y    -    {  .  2 {   of&   .  T{ -    ' -  -   y  -  -    y    -    {  .  2 {   Mb C &   .  T{ { K .  2 { K  is ....         .  T{ {  .  2 {   that of  & !   &   .  T{ -    ' -  -   @y  -  -    ?y    -    {  .  2 {   Ma. C !   .  T{ -    ' -  -   Py ! -  -    Oy !   -     ! T{ -    ' -  -  7 >  -  -   6 >    -     >  .  2 >   2) &    .  T{   .  2   Tz+Ty - ! * . %   .  T{  n .  2 n  is ....         .  T{   .  2   Tx- %  .  T{  d . 2 d  .   .  T{ -    ' -  -  7 _ -  -   6 _   -     _ T{ -    ' -  -  u>  -  -   u>    -    &>  .  2 &>   3) (Mb&    B &  .  T{ & . 2 &  )g is ....  %          .  T{ & .  2 &  Tz- !  .  T{ &S . 2 &S  .   .  T{ -    ' -  -  S -  -   S   -    .S T{ -    ' -  -  ty>  -  -   sy>    -    z>  .  2 z>   4) (Mb&    B &  .  T{ z . & 2 z  )g + (Ma)g is .... %  *   C !  %         .  T{     -  >  .  2 >   Tx- %  .  T{   . 2    .   .  T{ -    ' -  -  }yO -  -   }yO   -    O T{ -    ' -  -  6>  -  -   5>    -    >  .  2 >   5) &    .  T{   .  2    Tz - !   .  T{   .  2    is ....         .  T{  .  2   Ty-   .  T{  . 2   .   .  T{ -    ' -  -  6 -  -   5   -     T{ -    ' -  -  >  -  -   >    -    &>  . 2 &>  6) The center &   - & !  ! ! &  !   .  T{ -    ' -  -   -  -      -    & . 2 &  -   .  T{ -    ' -  -    -  -      -    & . 2 &  o &  .  T{ -    ' -  -  " -  -   !   -    & . 2 &  f   .  T{ -    ' -  -  7 -  -   7   -    & . 2 &  -   .  T{ -    ' -  -   -  -      -    & .  2 &  mass of Mb: !  &   C &  .  T{ -    ' -  -  z  -  -   z    -    {  . " 2 {   and Ma does not ! & &  C !  & & !  % &   .  T{     -    .  2   accelerate! ! ! !  !  !  !  .  T{ -    ' -  -  z} -  -   z|   -    | T{ -    ' -  Y     -  bjbjWW   = =     ]     & & & & & 2 & F b b b b b               > 1         1  b b  b     d * b  b            :   b N  ?x& &    1)The acceleration (magnitude) of Mb is .... that of Ma. 2) Tz+Ty is .... Tx. 3) (Mb)g is .... Tz. 4) (Mb)g + (Ma)g is .... Tx. 5) Tz is .... Ty. 6) The center-of-mass of Mb and Ma does not accelerate    ! #  & ' ) - / : < = ? A C L N O Q R T W Y l n r t u w                             & ( ) - B*CJ h nH  B*CJ h nH  j UmH  >   " # % & ( ) . / ; < > ? B C M N P Q S T X Y m n s t v w                                   ! " #  % & ' ( ) - . / : ; < = > ? A B C L M N O P Q R S T W X Y l m n r s t u v w                           dw                             '                   & ' ( ) * + , ' ( * + , -   N N!"""#""%  S u m m a r y I n f o r m a t i o n (   ~   D o c u m e n t S u m m a r y I n f o r m a t i o n 8    1 T a b l e      aI  S u m m a r y I n f o r m a t i o n (                                                                                                                                    Oh +'0 P              0  8  @  H    s  s  Ahmad f  hma  Normal  Ahmad  1 ma  Microsoft Word 8.0 @ @ TV@ TV        ՜. +,D ՜. +,,  h  p  |          MSU       j       Title     6  >   _PID_GUID   A N { 7 A 0 0 C A 2 1 - 6 8 9 B - 1 1 D 6 - B A 3 2 - 0 0 C 0 4 F A 3 B A C F } S#v #v#vS:V <   5 55S/   4  4  < T If  !v h5 55S#v #v#vS:V <   5 55S/   4  4  < T If  !v h5 55S#v #v#vS:V <   5 55S/   4  4  < T 4If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V < 4 2        5 +55H5g5+/   4  4  < p2      T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <   5 +55H5g5+/   4  4  < T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <   5 +55H5g5+/   4  4  < T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <   5 +55H5g5+/   4  4  < T 4If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V < 4 2        5 +55H5g5+/   4  4  < p2      T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <   5 +55H5g5+/   4  4  < T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <    5 +55H5g5+/   4  4  < T If  !v h5 +55H5g5+#v +#v#vH#vg#v+:V <   5 +55H5g5+/   4  4  < T  D d   O  0   n # A_    n " l :b׷aif H   @=@ :b׷aifL  7. 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[<fƵ00ۦ q?0면.kk Ed;RrO86 6my,c4+MWa<f~ L|-[p7܂1n=-REܢ2j宙͹W !Ub&,TɶAw S,^1n0dLlT_/x9]%G/AmC%G/o6}]m\?H^9^^%M4~B-J$$GX}Ip*:Mٗ&d
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o_R9iϘR#lߦ1Uo(<|pΰ,g+=2"W/(=+3폢_]R|>ޕ?ߐK7DKD                                                                                                                                                                        [              8  @ 8           N o r m a l       _HmH	sH	tH	B @  B          	 H e a d i n g   1     $$@& a$ CJ aJ < @  < H e a d i n g 2   $@& CJ aJ H @  H          	 H e a d i n g   3     $$@&a$ 5CJ \aJ N @  N H e a d i n g 4   $$d @&a$ 5CJ \aJ B @  B          	 H e a d i n g   5     $@& 5CJ \aJ F @  F H e a d i n g 6   $$d @&a$ 5\B @  B          	 H e a d i n g   7     $@& 5CJ \aJ @ @  @ H e a d i n g 8   $$@&a$ 5\F 	@  F          	 H e a d i n g   9    	 $$@&a$ 56\]D A@ D   D e f a u l t P a r a g r a p h F o n t V i@ V  T a b l e N o r m a l :V  4  4  l a  ( k (   N o L i s t  0 U@ 0 H y p e r l i n k  >*B*< O  <  H 3   $d d @& 5CJ \aJ < O  <           H 4     $d d @& 5CJ \aJ @ O  @  H 1   $d d @& 5CJ0 KH$\aJ0 < O  <  H 2   $d d @& 5CJ$\aJ$ 8 O  8           A d d r e s s      6CJ ]aJ b O Rb           P r e f o r m a t t e d   (  #   ~=z9!v%            OJ QJ . X@ a.           E m p h a s i s    6]@ V@ q@           F o l l o w e d H y p e r l i n k    >*B*D B@ D          	 B o d y   T e x t     $a$ CJ OJ QJ aJ B C@ B           B o d y   T e x t   I n d e n t     $a$  : Q@ :           B o d y   T e x t   3      CJ aJ 4 O  4           H 5     $d d @& 5\4 @ 4  F o o t e r  ! . )@ . P a g e N u m b e r 4 @ 4  H e a d e r  ! * W@ *  S t r o n g  5\. (@ . L i n e N u m b e r @ Y  @  D o c u m e n t M a p  ! -D  OJ QJ f O 2f  t i t l e + " $$$$   *$@& a$  5CJ OJ QJ \aJ T O BT  a u t h o r # $d  *$a$  CJ OJ QJ aJ P O  P           a b s t r a c t    $$d *$a$  CJ OJ QJ aJ d O Rd           r e f e r e n c e i t e m    % $  *$^ a$  CJ OJ QJ aJ L #   L   T a b l e o f F i g u r e s  & p^p : O r:  c o n t e n t ' d d  CJ aJ L ^@ L N o r m a l ( W e b ) ( d d  CJ OJ QJ aJ < O <  w a 1 0 1  7>* CJ OJ QJ Y( aJ d$@ d           E n v e l o p e   A d d r e s s   ! * @&+D/ ^@  CJ aJ : %@ :           E n v e l o p e   R e t u r n    +   4 O 4           w a 1 0
, d d  OJ QJ 8 O 8           w a 1    7>* CJ OJ QJ Y( aJ  4 O 4           b i g t e x t    5CJ$\aJ$ 6 @ 6          F o o t n o t e   T e x t    /   @ &@ @          F o o t n o t e   R e f e r e n c e    H* J O J           B u l l e t   I t e m    1 $d *$a$  CJ aJ t e@ "t  H T M L P r e f o r m a t t e d 7 2 2 ( Px  4 #\'*.25@9 h \@ h  z - T o p o f F o r m  3 $&d a$& <CJ OJ QJ _HaJ h mH sH tH \ ]@  \   z - B o t t o m o f F o r m  4 $$d a$ <CJ OJ QJ aJ  R ORR           F i r s t   P a r a g r a p h    5  CJ OJ  QJ  aJ mHsH\ R@ b\           B o d y   T e x t   I n d e n t   2    6 $hdh ^ha$ CJ aJ B O  B           p 1 a    7 $d *$a$  CJ OJ QJ aJ t O  t f i g u r e l e g e n d 0 8 $$ & F?     *$^    a$ CJ OJ QJ aJ | O r|  h e a d i n g 1 < 9 $$$$ & FG d *$@& ^a$ 5CJ OJ QJ \aJ x O rx  h e a d i n g 2 7 : $$$
&FG @ d  *$@&^a$  5CJ OJ QJ \aJ  O r           h e a d i n g 3   ? ; $$$ & FG  xd  *$@&^xa$  5CJ OJ QJ \aJ O N u m b e r e d I t e m  < & F>T    . O   I t e m = $
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F     d *$>T   - ^ a$ CJ OJ QJ aJ x O rx           h e a d i n g 4   7 > $$$ & FG p d  *$@&^a$  6CJ OJ QJ ]aJ > O>  h e a d i n g 5  ? & F: @& < Z@ < P l a i n T e x t  @ OJ QJ aJ b P@ b B o d y T e x t 2 " A $ p@H    d a$ B*CJ \ph L @ "L H T M L A d d r e s s  B  6B*CJ ]aJ ph ^ O 2^  c 8  C d d [$\$/ 5B* CJ OJ PJ QJ \^J aJ nHph tH  O A  h <    <   T O C 1 E x x 5;\aJ P .   P  T O A H e a d i n g  F x  5CJ OJ QJ \^J aJ 6    6   T O C 2 G  ^  :aJ 8    8   T O C 3 H ^ 6]aJ 2    2   T O C 4 I X^X aJ 2    2   T O C 5 J  ^  aJ 2    2   T O C 6 K ^ aJ 2    2   T O C 7 L ^ aJ 2    2   T O C 8 M x^x aJ 2    2   T O C 9 N @^@ aJ T ,   T   T a b l e o f A u t h o r i t i e s  O  8^ 8 X S@ X  B o d y T e x t I n d e n t 3  P $hd ^ha$ CJ :   :   I n d e x 1  Q  8^ 8 :   :   I n d e x 2  R 8^8 :   :   I n d e x 3  S X8^X8 :   :   I n d e x 4  T  8^ 8 :    :   I n d e x 5  U 8^8 :    :   I n d e x 6  V 8^8 :    :   I n d e x 7  W x8^x8 :    :   I n d e x 8  X @8^@8 :    :   I n d e x 9  Y 8^8 6 !  6  I n d e x H e a d i n g  Z B M q  d    @ I (         n     {     ) 4 D ^ h j |   ( 1 ; ? C Z ^ t    ( 5 C Q         -     = Y + 6 4 x K   2 T  (                     $               )               ,               -               /               0               2               3               6               7               8               :               =               @               A               C                                                                                                                        z               y               x               w               |                                                                                                                                                                                                                                                                                                                                                                         )   4   D   ^   h   j   |                      (  1  ;  ?  C  Z  ^  t        (  5  C  Q                  -          =	  	  	  Y

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 F [      # \    {   9    {  ( )   7 O P d 4 5 H T  U  m  	$$ $$ $ @% A% % i& ~' ' Y( Z( ( ( ( ) M- N- -. .. 0. 1. ;. G. H. 0 0 2 2 5 "5$5 %5 &5 5 5 5 5 6 6 6 6 	6 6 6 6 6 6 6 6 6  6 "6 &6 (6 ,6 .6 26 46 56 C6 E6 G6 J6 M6 P6 S6 V6 Y6 \6 ]6 h6 m6 r6 w6 }6 6 6 6 6 6 6 6 6 e7 g7 l7 y7 |7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 }8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 : : : ; ; ; /= 0= O= = > > > ? \? }? ? ? 8@ y@ @ @ 0A sA A A A A A B gB B B AC C C D AD D D E JE E E F _F tF F F G bG G G H -H oH H H :I I I I #J oJ J J K [K \K ]K K M 7N KN ^N uN N N O &O GO qO vO xO yO O O O O O +P ,P Q R V V (V W +Y Y Y Z Fa Ga a a a b Eb b c d d d \e f Nf g g [h h i i i i Ik Uk Xk kk sk yk zk }k k k k k k k k k k k 	l l ?l @l Cl cl xl l l l l l l l l m *m Gm Hm Km km {m m m m m m m m m n )n Gn Hn Ln ln yn n n n n n n n n o o 7o 8o 9o uo vo q q q Fr ~r r s s is js ks |s u v v v w Tw w x jx x x x x y y y y y "y 'y -y 4y 9y ?y Hy Qy Ry Ty y y y y y y y y y z z z z z z z z z z z z z z z z z z z z z S{ W{ [{ ^{ c{ g{ i{ m{ r{ v{ z{ { { { { | | | | | | !| %| *| .| 2| 8| =| >| @| | | | | | | | | | | | | } } } } } } } } } } } } } } } } } } c~ g~ k~ n~ s~ w~ y~ }~ ~ ~ ~ ~ ~ ~ ~ ( , 0 3 8 < > B G K O U [ \ ^      
       $ % (      ŀ ǀ ˀ Ѐ Ԁ ؀ ݀                   I M R U Z ^  d i m q v { |         # ( , 0 5 ; < =    Ƀ ރ   L a T  A  < y   ȉ b e    & ) 8 B C F O         3 4 7 M         I J M ]         e f j z Ɛ ǐ ː ې % & * =       ȑ ɑ ʑ ! W X    Q R U ^ g n o q   ǔ Ȕ ʔ ' , 2 3 5 {     Ǖ ͕ ҕ ӕ Օ      A G L M N           2 3 4 B 4 5 6 K   1 2 \   u v   g h   '  ̪  Ƭ ٬         " ) 0 7 > ? C J Q X ^ _ c j q x                ĭ ˭ ҭ ٭ ڭ         Ů [ e f  ò Ĳ n o     ϸ и ۸             ' . 5 < = A H O U \ ] d k q x ~              ƹ ͹ Թ ۹     ͻ  g h k l  %   !        q r       ' 1 ; < B I P U V Z a h m n r y                                     - .   t v {       Z       V W 6 7 <  @ / \ ] Z [ X Z c d e f n u                         O P % & : D N X Y Z c k t |                             & , 2 8 > D E T Z  f l r x y { | } ~                        & , 2 8 > D E M S Y _ e k q r y                       J K ; K   Y Z           , > P b c m    $ N O K L   ^	 _	     C D                 # ) * + 0 6 < B C D J P V \ ] ^ e k q w x y z { | } ~                             	
          ! ' ( * + , - . 8 T U    S T    F  W     I   R    0    w! ! 1" " 9# # $ $ % % #% $% % % Q& R& ' ' ' ' h( i( ( ( K) L) ) ) T* U* + ~+ + , , , , - m- n- c. d. . . / / / / F0 G0 0 0 1 1 E2 F2 13 23 &4 '4 4 4 5 5 6 6 6 6 o7 p7 f8 g8 8 8 9 !9 9 +: ,: R: S: : : ; ; < < = = C> D> |> }> > > ? ? @ @ WA B B B B B C C C D D D D E E 5F 6F F F -G .G G G gH hH H H CI DI J ~J =K K L 9M M JN O fO gO P P {P |P Q Q UR VR R R S S 0T 1T T T U U V V V V W X wX Z Z Z Z$Z 2Z RZ eZ fZ rZ Z Z Z Z Z Z Z Z Z [ [ 0[ =[ >[ T[ m[ n[ [ [ [ [ [ [ [ [ [ [
\ \ \ -\ .\ N\ \ a\ p\ \ \ \ \ \ \ ] D] p] ] ] ] ] m^ n^ ^ ^ ^ ^ _ _ )_ 7_ M_ _ k_ l_ _ _ _ _ _ _  " 4   a a a a a a b b b *b <b Eb Fb Ob Pb b b c c Lc Mc c c 0d 1d Kd Ld hd d d d d d {e e h h h h h h h h i i i ]i ^i mi wi xi i i i i i i j j [j \j rj j j j j j j j j k 'k <k Zk k k k .l l l l l m Om om m m m m n n Kn Xn n n n n n n n n .o \o }o o o 2p bp p p p p q q 1q mq q q  r ,r ^r r r r r s s s s s t t t t v v v v v v v +x ,x ;x Ix Jx x ~x x x x x y !y Wy y y y y y z z z { H{ I{ d{ { { { | m| | | x} } } ~ E~ ~~ ~ ~ 1 a    B ׀  < o  ҁ  e  т ӂ Ԃ ڂ ۂ  	  5 N k ~     : ; o   Å υ    0 < R f ~  
 o    އ . U {  ݉ މ 7 X     k w x   ŋ  > S   & i      F  E  q r  %   d q r s t u v      4 S n     ܕ   - H c ~    Ж    * + H e     ՗   & A \ w    ɘ ʘ   / L M h    ԙ 
 % @ [ \ w     % t Û  a   N     E F \ v   Ş     4 N i    ֟ ן   ' > W w x   Ǡ    4 5 K f    ԡ      2 M i           9 [ \ u    ţ     5 Q h     Ԥ    ) * R S n    ť ƥ ǥ ȥ ɥ ʥ   1 P e }  ۦ    E p      W k   ̨   ( H {  ˩   - i  Ъ  4 n  ܫ  6 g     < q  ֭  ; z   0 e   3 s    / L i         [ \ j k w    ̲ Ͳ ϲ Ҳ             % + 1 2 4 6 D J P Q S U c i o p r t             ³ ȳ γ ϳ ѳ ӳ         ? @ B C D P R S T U a c d e f g x }      Ŵ Ӵ ܴ         	       # ) / 5 : = C I J L O U [ b i o s y                         $ % & / 4 5 6 > C D E F G H i j p x                  ¶ ö             % & ( + . 4 9 : ; < = > ? @       ߷       ! ( ) + . < B H I K N \ b h i k n |             ¸ ȸ ɸ ˸ θ ܸ             " ( ) , / = C I J M P ^ d j k n q              ǹ ͹ ι ӹ ֹ            $ * 0 1 4 6 D J P Q T V d j p q t v             ĺ ʺ к Ѻ Һ   	       - 2 @ R \ j t z              ǻ Ȼ ʻ ̻ һ ׻ ݻ               " ( ) + - 3 9 ? E J M S Y Z \ _ e k q w }                  Ǽ ̼ Ҽ ؼ ݼ                 ! & + 2 8 > A G M N P R W \ c j o r x ~             ߽          ! ' 1 2 ; A J K S Y _  a b c             ž ƾ Ⱦ ˾ ξ Ծ پ ھ ܾ ߾             / 9 > ? A D G M R S U X [ a f g i l o u z { | ҿ ӿ             ! " O P  	  p  -   H I U   m  (     N  	 f    -   E             h i     F     <     2 5      U         5 U r u        W     ( R |      J K i      C m     ? i l m        : ] y         ) J k n        2 3 S      : d     6            " a     H ~      * - L  ~      @ Z ]      * T W      I j k       / r        D m     ? i     ; >          : o     W     O w     ? B n        ( L r      7 ] {     ( D i     . X w z {     F p s v     = g h i       
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 = s t u j    - . ; < Q R  a t u } ~       x  y    ! ! i! j! ! ! " " v" w" " " G# H# # # $$ ?$ P$ s$$ $$ $$ $$ % #% $% % % % % % % & & & & & & F& G& M& S& l& m& v& |& & & & & & & & & & & & & & & & & ' ' ' ' ' w' ' ' ' ' 7( ]( ^( a( 0 0 0 0 0 0 0 ( 0 ( 0 ( 0 ( 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 0  0 70 0 #0 80 70 0 10 0 0  0  0  0  0   0  0  0  0  0   0  0  0  0  0   0  0  0  0  0   0  0  0  0  0   0  0  0  0  0   0  0  0  0  0   80 80 +0 0 ( ;0 70 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 50 G% 80 G% 0 G% 80 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 0 G% 3 <0 G% 3 <0 G% 3 <0 G% 3 <0 G% 0 G% 0 G% 0 G%  :0 10 4 70 4 70 4 0 4 0 4 0 4 70 4 0 4 0 4 70 4 70 4 70 4 10 4 10 4 10 4 10 4 10 4 0 4 0 4  0 4 0 4 0 4  0 lB 4 0 4 0 4  0 lB 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4  0 lB 4 0 4 0 4 0 4 0 4  0 lB 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4  0 lB 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4  0 lB 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4  0 4 0 4 0 4 0 4 0 4 0 4 X 0 4 X 0 4 X 0 4 X 0 4 X 0 4 X 0 4 X 0 4 X 0 4 X 0 4 X 0 4 X 0 4 0 { 0 { X 0 4 0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 |  0 | 0 | 0 |  0 | 0 | 0 | X 0 ! 4 (  0 4 (  0 4 (  0 4 0 ( X 0 ! ( 0 0 0 0 X 0 ( X 0 (  0 ! 0 (  0 4 ( # 0 4 0 v  0 ! v 0 v X 0 v 0 Ő 0 Ő  0 Ő 0 Ő 0 Ő 0 Ő 0 Ő 0 Ő  0 Ő 0 Ő 0 Ő 0 Ő 0 Ő  0 , Ő 0 Ő 0 Ő 0 Ő 0 Ő 0 Ő 0 Ő 0 Ő$  0       Ő             $0 Ő$  0      Ő               0       Ő               0       Ő                0       Ő                0       Ő              0   ,  Ő                0       Ő            '  0       Ő             '  0      Ő            '  0      Ő            '  0      Ő              0       Ő              0       Ő              0   ,  Ő               0       Ő              0       Ő             * 0       Ő             * 0      Ő            * 0      Ő            * 0      Ő               0       Ő               0       Ő                0       Ő              0   ,  Ő                0       Ő               0       Ő                0       Ő                0       Ő               $0 Ő '0 Ő  0 , Ő$0       Ő              0       Ő                0       Ő              0   ,  Ő                0       Ő               0       Ő                0       Ő                0       Ő               $0 Ő 0 Ő 0 Ő 0 Ő 0 Ő  0 Ő$0       Ő            - $0 Ő -$0      Ő                0       Ő               0       Ő               0       Ő              0      Ő                0       Ő               0       Ő              0      Ő               0       Ő              0       Ő               0       Ő               0       Ő               0       Ő                0       Ő               50       Ő               50       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő              0     Ő                0       Ő               0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő                0       Ő              0      Ő               0       Ő              0       Ő             0       Ő               0       Ő               0       Ő               (0       Ő               (0       Ő               (0       Ő               20       Ő               20       Ő               0       Ő             0      Ő               (0       Ő              (0       Ő               (0       Ő               (0       Ő            8 0      v               (0       8                           	
                                               !  "  #  $ % & ' ( ) * + , - . / 0 1 2 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _  a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~   8 0 v 8 0 v 0 0 8 0 v 0  0  8 0 v 0 0 8 0 v 8 0 v (0 K (0 K (0 K (0 K (0 K (0 K (0 K 0 K 0 K  0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K  0 K 0 K 0 K  0 K 0 K 0 K 0 K 0 K  0 K A0 K 0 K 0 K 0 K A0 K 0 K  0  K 0 K 0 K 0 K 0 K 0 K 0 K  0  K 0 K 0 K 0 K 0 K 0 K 0 K  0 K 0 K 0 K  0 K 0 K 0 K  0 K 0 K 0 K  0 K 0 K 0 K 0 K 0 K  0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K  0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K  0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K 0 K +0 K 0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K 0 K 0 K 0 K  0 K  0 K  0 K  0 K  0 K   0 K  0 K  0 K  0 K  0 K  0 K   0 K  0 K  0 K  0 K  0 K  0 K   0 K 0 K 0 K 0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K   0 K  0 0 8 0 8 0 8 0 8 0 8 0 8 0 8  0 8 0 8 0 8  0 ; 8 0 8 8 0 8 8 0 8 0 8 0 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 20 8 0 8 0 8 0 8 (0 8 (0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 50 8 0 8 (0 8 (0 8 0 8 0 8  0 ; 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8  0 ; 8 0 8 6 0 8 6 0 8 6 0 8 6 0 8 6 0 8 6 0 8 6 0 8 6 0 8 6 0 8 6 0 8 0 8 0 8 ( 0 8 0 [h 0 [h  0 [h [h 0 [h 0 [h 30 [h  0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h  0 [h  0 [h  0 [h  0 [h   0 [h 0 [h 50 [h 0 [h 0 [h 0 [h 0 [h 0 [h 0 [h 0 [h 0 [h 0 [h 0 [h 0 [h  0 [h [h 0 [h ; 0 [h 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N       D          Ԕ          ?           "           5               B
   &
N       D          Ԕ          ?           "           4               B
   
N       D          Ԕ          ?           "           (               
   ,
<        ,           ?           "           :                    n   2
   *
0            ?           "           8            6   
   9
 "           G            V   
   .
C                  "           <            6   
   5
 "           C            \   B
   ?
S    D               "           M            6   
   1
 "           ?            \   B
   >
S    D               "           L            \   B
   ;
S    D               "           I            \   B
   4
S    D               "           B            \   B
   <
S    D               "           J            N   B
   B
S    D                   P            x   
   C
<        C           ?               Q                       
   0
<        0           ?           "           >                       
   2
<        2           ?           "           @                       
   A
<        A           ?           "           O                       
   @
<        @           ?           "           N                       
   8
<        8           ?           "           F                       
   -
<        -           ?           "           ;                       
  `