AY 2014 Graduate School Course Catalog

Field of Study CS: Computer Science

2015/02/01

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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Takafumi Hayashi
担当教員名
／Instructor		 Takafumi Hayashi , Yodai Watanabe
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 情報セキュリティは、安定した安全なコンピュータ・ネットワークに必須のもの
です。
情報セキュリティは、コンピュータの一分野ではなく、政策学、法学、経済学、
心理学、社会学も含む広領域の学問・実用分野となっています。
本講義では、情報セキュリティが、コンピュータ理工学を含んだ広領域であることを念頭におきながら、情報セキュリティのfirst stepとして、様々な観点から情報セキュリティについて紹介し、情報セキュリティについて考えていきます。
具体的な事例のケーススタディなどで、多面的にセキュリティというものをとらえていきます。


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Shuxue Ding
担当教員名
／Instructor		 Shuxue Ding , Takafumi Hayashi
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 Statistical Signal Processing is very important in various applications including signal detection, noise cancellation, synchronization, communications, and instrumentations. Therefore, this course is provided as a core course for the graduate school.
This course gives a unified introduction to the theory, implementation, and applications of statistical signal processing methods. This course considers stochastic signals/systems, rather than deterministic signals/systems, as in the undergraduate course of “Digital signal processing”. Focus is on estimation theory, random signal modeling, characterization of stochastic signals and systems, nonparametric estimation, adaptive signal processing, and Kalman filtering.
授業の目的と到達目標
／Objectives and attainment
goals		 This course is designed as a fundamental common course for graduate students studying in all the fields of information system. It presents a methodology for signal processing with statistical features of the signal, which is the essence of an information system. Furthermore, the course presents implementation of each method for statistical signal processing with a computer; usually it is performed by Matlab. Finally, the course provides some applications, such as noise canceling, echo canceling, system identification, Kalman filter etc.
授業スケジュール
／Class schedule		 Chapter 1 Introduction
Chapter 2 Fundamentals of discrete-time signal processing
Chapter 3 Random variables, sequences, and stochastic process
Chapter 4 Linear nonparametric signal models
Chapter 5 Non-parametric power spectrum estimation
Chapter 6 Optimum linear filters, Wiener filter
Chapter 7 Algorithms and structures for optimum linear filters
Chapter 8 Kalman filter
Chapter 9 Least-squares filtering and prediction
Chapter 10 Adaptive filters
教科書
／Textbook(s)		 [1] Reading materials prepared by the instructor.
[2] Dimitris G. Manolakis, Vinay K. Ingle, and Stephen M. Kogon, Statistical and Adaptive Signal Processing, Artech House, Inc., 2005, ISBN 1580536107. Many MATLAB functions are included and are available from the web page of the book.
成績評価の方法・基準
／Grading method/criteria		 Attendance (20 points)
Homework (30)
Report (50 points)
履修上の留意点
／Note for course registration		 Digital signal processing (undergraduate)
Linear Systems (undergraduate)
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 Alexander D. Poularikas, and Zayed M. Ramadan, Adaptive Filtering Primer with Matlab, CRC Pr I Llc Published (Feb. 2006).


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Toshiro Watanabe
担当教員名
／Instructor		 Toshiro Watanabe , Shuxue Ding
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course provides advanced contents of applied statistics based on an undergraduate course " Probability and Statistics". Most important statistical methods are explained with many examples of data. At the same time, their mathematical foundations are given.
授業の目的と到達目標
／Objectives and attainment
goals		 Students can understand basic applied statistics such as estimation, test, regression, and analysis of variance by using Gaussian, t, F, and chi-square distributions. Moreover they can have introductory knowledge on stochastic processes.
授業スケジュール
／Class schedule
Review of Probability(確率の復習 ) I,II,III.

Sample distributions(標本分布) I,II.

Estimation and Test of mean and variance (平均と分散の推定と検定) I,II.

Test of goodness of fit(適合度検定) I,II.

Linear regression(線形回帰) I,II.

Analysis of variance (分散分析) I,II.

Stochastic processes(確率過程) I,II
教科書
／Textbook(s)		 No Text.
成績評価の方法・基準
／Grading method/criteria		 By Reports.
履修上の留意点
／Note for course registration		 Calculus, Linear algebra, Probability, Information theory.
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 Feller, W. : An Introduction to Probability Theory, Vol.1, (Wiley)
白旗慎吾 : 統計解析入門, 共立出版.
統計学入門 : 東京大学出版会.
自然科学の統計学　 : 東京大学出版会.


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開講学期
／Semester		 2014年度／Academic Year 　4学期 ／Fourth Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Masayuki Yamagami
担当教員名
／Instructor		 Masayuki Yamagami , Yodai Watanabe
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course provides basic knowledge of quantum information and quantum
computations for graduate students who want to learn modern information
and computational models.
授業の目的と到達目標
／Objectives and attainment
goals		 At the end of the course, students can acquire
1) Basin knowledge of quantum mechanics for quantum information theory.
2) Basic knowledge of quantum transportation.
3) Algorithms of quantum computers.
4) Quantum cryptography.
授業スケジュール
／Class schedule		 1. Mathematical Realization of Quantum Mechanics
2. Basic Concepts of Quantum Mechanics
3. EPR pair and measurement
4. Quantum Gates
5. Theory of Information and Communication
6. Quantum Computation
7. Shor’s Factorization Algorithm
8. Quantum Error-Correction
9. Quantum Cryptography
10. Quantum Algorithm
教科書
／Textbook(s)		 1. 量子情報理論(Sagawa and N. Yoshida, Maruzen Publishing Co. Ltd., 日本語版
[Chinese version is also available])
2. Fundamentals of Quantum Information(H. Sagawa and N. Yoshida, World
Scientific, in English)
成績評価の方法・基準
／Grading method/criteria		 Attendance 20% and reports 80%
履修上の留意点
／Note for course registration		 It is recommended to have basic knowledge of quantum mechanics. However,
the course will
accept students who do not have any knowledge of quantum mechanics but have
strong desire to learn new knowledge


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開講学期
／Semester		 2014年度／Academic Year 　1学期 ／First Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Taro Suzuki
担当教員名
／Instructor		 Taro Suzuki , Takafumi Hayashi
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 Computation is one of the most important concepts in computer science, and indicates the limit of the power of computers, which should be familiar to all people working in computer science or engineering field.
By this notion, the problems are classified into two classes, that is, the class consisting computable or solvable problems and one consisting incomputable or unsolvable problems.
授業の目的と到達目標
／Objectives and attainment
goals		 Students can be familiar to the notion of computability defined by several methods, such as Turing machines, register machines, recursive functions. Furthermore, they can understand the limit of the computers, that is, that there are problems which cannot be solved by any computer.
授業スケジュール
／Class schedule		 Meeting 1.
1. Introduction

Meetings 2 -- 5.
2. Computation Models
2.1 Turing Machine Model
2.2 Random Access Machine(RAM) Model
2.3 Recursive Function Model
2.4 While Program Model

Meetings 6 -- 9.
3. Church-Turing Thesis
3.1 The equivalence in the computation power among models
3.2 Church-Turing Thesis

Meetings 10 -- 12.
4. Universal Program
4.1 Coding of Programs
4.2 Construction of Universal Program
4.3 Interpretation of Universal Program

Meetings 13 -- 14.
5. Unsolvable Problems
5.1 Halting Problem
5.2 Reducibility
5.3 Rice's Theorem
5.4 Post's Corresponding Problem

Meeting 15.
6. Further Topics

The topis above may be changed according to the progress of the course.
教科書
／Textbook(s)		 We do not specify textbooks but introduce books related to the topics in the class. Various materials as handouts will be prepared.
成績評価の方法・基準
／Grading method/criteria		 Small quizzes will be given. A report on the topics concerning this course will be required as the final examination.
履修上の留意点
／Note for course registration		 Students enrolling this course had better to be familiar to the fundamental concepts studied in F3 Discrete Systems, F1 Algorithms and Data Structure, F8 Automata and languages, and M9 Mathematical Logic in the undergraduate program, although they are not the prerequisite courses.
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 There are so many books on this fields. Some of them will be introduced in the class.


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Qiangfu Zhao
担当教員名
／Instructor		 Qiangfu Zhao , Yong Liu
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 Most (if not all) engineering problems can be formulated as optimization problems. To solve optimization problems, different methods have been studied in mathematical programming, operations research, and so on. Conventional methods, however, are usually not efficient enough when the problem space is large and complex. Many problems faced in artificial intelligence are combinatorial optimization problems. These problems are NP-hard, and we may never find polynomial time solutions. To solve these problems efficiently, different "heuristics" have been used to "search for sub-optimal solutions".

Heuristics are search methods produced based on human intuition and creative thinking, and are often useful for finding good local solutions quickly in a restricted area. Metaheuristics are multi-level heuristics that can control the whole process of search, so that global optimal solutions can be obtained systematically and efficiently. Although metaheuristics cannot always guarantee to obtain the true global optimal solution, they can provide very good results for many practical problems. Usually, metaheuristics can enhance the computing power of a computer system greatly without increasing the hardware cost.

So far many metaheuristics have been proposed in the literature. In this course, we classify metaheuristics into two categories. The first one is "single-point" (SP) search, and the second one is "multi-point" (MP) search. For the former, we study tabu-search, simulated annealing, iterated local search, and so on. For the latter, we study evolutionary algorithms, including genetic algorithms, genetic programming, evolutionary strategy, and memetic algorithm; ant colony optimization, and particle swarm optimization. Although the efficiency and efficacy of these methods have been proved through experiments, because they were proposed based on human intuition, the theoretic foundation is still weak. Therefore, in this course, we will mainly introduce the basic idea of each method, and try to explain the physical meaning clearly. Mathematic proofs will be introduced very briefly when necessary.
授業の目的と到達目標
／Objectives and attainment
goals		 In this course, we will study the following topics:

(1) Examples of important optimization problems.
(2) Conventional optimization methods.
(3) Single-point (SP) search methods:
    * Tabu search.
    * Simulated annealing.
    * Iterated local search.
    * Guided local search.

(4) Multi-point (MP) search methods
    * Genetic algorithm (GA).
    * Genetic programming (GP).
    * Evolutionary programming (EP).
    * Memetic algorithm (MA).
    * Differential evolution (DE).
    * Particle swarm optimization (PSO) and ant colony optimization (ACO).

After this course, we should be able to

(1) Understand the basic ideas of each metaheuristics algorithm;
(2) know how to use metaheuristics for solving different problems; and
(3) become more interested in developing new algorithms.
授業スケジュール
／Class schedule		 (1) An Introduction to Optimization
    - Classification and Case Study.

(2) An Introduction to Optimization
    - An Brief Review of Conventional Search Algorithms.

(3) Tabu search
    - Tabu list, intensification, and diversification.

(4) Simulated annealing
    - Find the global optimum without remembering search history.

(5) Iterated local search and guided local search
   - Strategies for repeated search.

(6) Team work I
    - Solving problems using single point search algorithms.

(7) Presentation of team work I.

(8) Genetic algorithm
    - Basic components and steps of GA.

(9) Other Evolutionary Algorithms
    - Evolution strategies, evolutionary programming, and genetic programming.

(10) Differential evolution
    - Evolve more efficiently, but why?

(11) Memetic algorithms - I
    - Meme, memotype, memeplex, and memetic evolution.

(12) Memetic algorithms - II
    - Combination of memetic algorithm and genetic algorithm.

(13) Swarm Intelligence
    - Ant colony optimization and particle swarm optimization

(14) Team work II
    - Solving problems using multi-point search algorithms

(15) Presentation of team work II.
教科書
／Textbook(s)		 There is no text book. Teaching materials will be distributed in the class.
成績評価の方法・基準
／Grading method/criteria		 Attendance and quiz: 10 points.
Team work: 50 (25 x 2) points.
Presentation: 40 (20 x 2) points.
履修上の留意点
／Note for course registration		 * Artificial intelligence
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)
(1) M. Gendreau and J. Y. Potvin, Handbook of metaheuristics, 2nd Edition, Springer, 2010.

(2) C. Cotta, M. Sevaux, and K. Sorensen, Adaptive and multilevel metaheuristics, Springer, 2010.

(3) URL of this course: http://www.u-aizu.ac.jp/~qf-zhao/TEACHING/MH/mh.html


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開講学期
／Semester		 2014年度／Academic Year 　1学期 ／First Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Kazuto Asai
担当教員名
／Instructor		 Kazuto Asai , Takafumi Hayashi
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 The concept of graphs is considered as fundamental structures in computer
science and engineering. This course gives students in computer science wide aspects of graphs both from mathematical point of view and from engineering viewpoint.
授業の目的と到達目標
／Objectives and attainment
goals		 Although the foundation of graph theory is taught in the course "Discrete System" and some graph algorithms are taught in "Advanced Algorithms and Data Structures" in the undergraduate program, what have been taught are a few fragments of graph theory. This course intends to gives students the concepts related to graphs systematically.
授業スケジュール
／Class schedule		 Meeting 1.
1. Introduction

Meetings 2 -- 4.
2. Review
2.1 Definitions and Some Examples of Graphs
2.2 Path, Connectivity, and Distance
2.3 Traversality, Eulerian Graphs, and Hamiltonian Graphs
2.4 Planarity, Eulerian formula, and Kuratowski's Theorem
2.5 Coloring of Graphs, Vertex Coloring, Edge Coloring,
and Four Color Theorem

Meetings 5 -- 7.
3. Planarity
3.1 Subdivision, Homeomorphism, and Graph Minors
3.2 Crossing Number, Thickness, and Splitting Number

Meetings 8 -- 10.
4. Counting
4.1 Spanning Trees
4.2 Matchings
4.3 Chromatic Polynomials

Meetings 11 -- 13.
5. Cycles and Cocycles
5.1 Spanning Trees, Cycles and Cocycles
5.2 Disjoint Paths: Menger's Theorem

Meetings 14 -- 16.
6. Advanced Topics
6.1 Cayley Graphs
6.2 Matrices and Graphs
6.3 Ramsey's Theorem

* Topics in 3.or later are examples of topics, not fixed.
It can be changed by request.
教科書
／Textbook(s)		 We do not specify textbooks but introduce books related to the topics in the class. Various materials as handouts will be prepared.


成績評価の方法・基準
／Grading method/criteria		 Small quizzes will be given. A report on the topics concerning this course will be required as the final examination.
履修上の留意点
／Note for course registration		 Students enrolling this course had better to be familiar to the fundamental concepts studied in F3 Discrete Systems, F3 Algorithms and Data Structure, although they are not the prerequisite courses.


参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 There are so many books on this fields. Some of them will be introduced in the class.


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Naohito Nakasato
担当教員名
／Instructor		 Naohito Nakasato , Nobuyoshi Asai
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course mainly introduces

1. Ordinary and partial differential equations appear in science or engineering
2. Schemes to model and to discretize the differential equations , and
3. Computational techniques to get the numerical solutions.

This course starts with theory and mathematics of differential equations followed by hands-on style exercises on numerical techniques to solve various differential equations.
授業の目的と到達目標
／Objectives and attainment
goals		 A main goal of this course is to introduce basic theory of differential equations and a several most important numerical techniques and schemes to get solutions to those equations.
授業スケジュール
／Class schedule		 1 - 4 weeks Topics on Ordinary Differential Equations
5 - 15  Topics on Partial Differential Equations
教科書
／Textbook(s)		 Partial Differential Equations for Scientists and Engineers, Stanley J. Farlow, Dover Publications, 1993

Additional text books will be specified in the hand-on exercises.
成績評価の方法・基準
／Grading method/criteria		 Homework (50 points)
Report (50 points)
履修上の留意点
／Note for course registration		 Numerical Analysis (undergraduate course) and related courses.


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Hameed Saji N.
担当教員名
／Instructor		 Hameed Saji N. , Naohito Nakasato
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course provides an introduction to parallel computing including
parallel architectures and parallel programming techniques.
授業の目的と到達目標
／Objectives and attainment
goals		 The students will learn the basic parallel programming models including
shared
memory and distributed memory models. Parallel programming using MPI and
OpenMP will be a main focus. We expect to spend some time  in introducing students
to languages for the many-core architectures such as OpenCL and CUDA as well.
The course will heavily involve coding projects and weekly assignments.
授業スケジュール
／Class schedule		 1. Introduction to Parallel Architecture
2. Introduction to Parallel Programming
3. Performance considerations
4. Programming in MPI
5. Programming in OpenMP
6. Introduction to many-core architectures
7. Introduction to CUDA and OpenCL languages
成績評価の方法・基準
／Grading method/criteria		 Labs = 20%, Assignments = 10%, Project = 60%, Participation = 10%
履修上の留意点
／Note for course registration		 Computer architecture, mathematics, algorithms and programming


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Takeaki Sampe
担当教員名
／Instructor		 Takeaki Sampe , Haruo Terasaka
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course is an introductory course and provides fundamental knowledge on fluids, dynamics of fluid flows and methods for obtaining a numerical solution of the governing equations.
授業の目的と到達目標
／Objectives and attainment
goals		 In this course, the students will obtain proper understanding of properties of fluid and principles of fluid dynamics, and learn how to solve basic problems of fluid dynamics with numerical integration of the governing equations.
授業スケジュール
／Class schedule		 1. Introduction
2. Properties of fluids
3. Units, dimensional analysis, and non-dimensional quantities
4. Dynamics of fluid, Eulerian/Lagrangian description of fluid motion
5. Laminar and turbulence, advection, convection, diffusion, etc.
6. Governing equations and discritization
7. Stability, consistency, and convergence
8. Finite difference method, CFL condition
9. Advection equation, wave equation
10. Various numerical schemes for integration
11. Spectral method
12. Application to a simulation of flow in the environment
成績評価の方法・基準
／Grading method/criteria		 Assignments and reports (papers).
履修上の留意点
／Note for course registration		 ・ Calculus (undergraduate)
・ Linear algebra (undergraduate)
・ Dynamics (undergraduate)
・ Numerical analysis (undergraduate)
・ Numerical modeling and simulations (graduate course)


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開講学期
／Semester		 2014年度／Academic Year 　1学期 ／First Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Qiangfu Zhao
担当教員名
／Instructor		 Qiangfu Zhao
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 An intelligent system must have at least the following means (手段):

1)  A means to access and acquire information.

2)  A means to integrate, abstract, and be aware of the information.

3)  A means to change and to adapt to the environment based on acquired information.

The goal of neural network research is to realize an intelligent system using the human brain as a single model to realize all of the above means. There are many research topics in this area, for example

1)  How to use neural networks to represent/acquire information/knowledge?

2)  How to use neural networks to integrate, abstract, and be aware of the information?

3)  How to change a neural network to adapt to the environment?

This course introduces the basic models, learning algorithms, and some applications of neural networks. After this course, we should be able to know how to use neural networks for solving some practical problems such as pattern recognition, pattern classification, function approximation, data visualization, and so on.
授業の目的と到達目標
／Objectives and attainment
goals		 In this course, we will study the following topics:

1)  Basic neuron models: McCulloch-Pitts model, nearest neighbor model, radial basis function model, etc.

2)  Basic neural network models: multilayer neural network, self-organizing neural network, associative memory, radial basis function neural network, support vector machine, neural network tree, etc.

3)  Basic learning algorithms: delta learning rule, back propagation, winner take all, self-organizing feature map, learning vector quantization, etc.

4)  Applications: character recognition, function approximation, data visualization, etc.
授業スケジュール
／Class schedule		 1)  Introduction: A brief introduction of this course.

2)  Fundamental concepts: Neuron models and the general learning rule.

3)  Multilayer neural networks: Structure and the back propagation learning algorithm for multilayer perceptron (MLP).

4)  Team project - I: Learning of MLP for solving simple problems.

5)  Associative memory: Hopfield neural network, energy function, and convergence.

6)  Team project II: Application of Hopfield neural network to image restoration.

7)  Self-organizing neural networks: Kohonen neural network, pattern clustering, and the winner-take-all learning algorithm.

8)  Team project III: Pattern classification using self-organizing neural networks.

9)  Self-organizing feature map: Dimensionality reduction and data visualization based on the self-organizing feature map algorithm.

10)  Team project IV: Visualization of high dimensional patterns.

11)  RBF neural networks: Radial basis neural network and support vector machines.

12)  Team project V: Pattern recognition based on SVM.

13)  Neural network trees: Hybridization of neural networks and the decision tree.

14)  Team project ? VI: Pattern recognition based on neural network trees.

15)  Presentation of projects.
教科書
／Textbook(s)
No textbook. Teaching materials will be distributed in the class.
成績評価の方法・基準
／Grading method/criteria		 Attendance: 15
Projects: 60 (10 x 6)
Final presentation: 25
履修上の留意点
／Note for course registration
No special prerequisite.
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 1)  Jacek M. Zurada, Introduction to Artificial Neural Systems, PWS Publishing Company, 1995.

2)  Simon Haykin, Neural Networks: A Comprehensive Foundation, Macmillan College Publishing Company, 1994.

3)  Mohamad H. Hassoun, Foundamentals of Artificial Neural Networks,The MIT Press, 1995.

4)  Laurene Fausett, Fundamentals of Neural Networks: Architectures, Algorithms, and Applications, Prentice Hall International, Inc., 1994.

5)  B. D. Ripley, Pattern Recognition and Neural Networks, Cambridge University Press., 1996.

6)  URL of this course: http://web-ext.u-aizu.ac.jp/~qf-zhao/TEACHING/NN-I/nn1.html


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開講学期
／Semester		 2014年度／Academic Year 　4学期 ／Fourth Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Takafumi Hayashi
担当教員名
／Instructor		 Takafumi Hayashi
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course presents the basics of finite field, combinatrics based on finite field.
This course also provide the topics on sequence design, block design, and their applications to computer science
and engineering, especially communications, instrumentation, and cryptography.
授業の目的と到達目標
／Objectives and attainment
goals		 This object of this course will provide the perspective of the combinatorics and its application to computer science and science.
授業スケジュール
／Class schedule		 L1: Basics of combinatorics.
What is combinatorics. The applications of combinatrics to computer science and engineering.

L2: Finite Field
Structure of a finite field F_p and its subfields. Construction of a finite field F_p for a prime number p. Galois Field.

L3-4: Extension of a Finite field.
Structure of the extended finite field F_q, for q=p^m.
Primitive polynomial for a finite field.
Applications of finite field.

L5: Finite Geometry and its applications 1
Affine plane and finite field. Cyclic construction of points on an affine plane.

L6: Finite Geometry and its applications 2
Projective geometry and finite field.

L7: Experimental Design
Applications of experimental design to computer science and engineering.
History and examples of experimental design.
Examples of Experimental design.

L8-9: Block Design
Algorithms of Block Design Construction. Applications of block design to image processing, data mining, and networking.

L10: Block design and combinatrics.
Block design for various problems of combinatrocis.
Examples of balanced incomplete block design.

L11: Latin Square
Construction of Latin squares. Applications of Latin Square to communications, instrumentations, and cryptography.

L12: Cyclic Difference Sets
Structure of difference sets. Construction of cyclic difference set.
Applications of cyclic difference set to sequence design, communication, radar, ultrasonic imaging and positioning.
Cyclic difference set and conctucion of Hadamard matrix.

L13-14 Sequence design
Structure, properties, and construction of
shift register sequence, perfect sequence, error-correction sequence, and zero-correlation zone sequence set.

L15 Number theory and its application to computer science.
Selected topics and related algorithms.
成績評価の方法・基準
／Grading method/criteria		 Assingment


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開講学期
／Semester		 2014年度／Academic Year 　4学期 ／Fourth Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Yong Liu
担当教員名
／Instructor		 Yong Liu
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 The course introduces the basic ideas of nature-inspired
techniques to architectural, engineering, graphics, and
evolvable hardware design. The aim of this course is to
introduce some fundamental techniques and principles in
nature inspired design, and investigate their strength,
weakness, and potential applications.
授業の目的と到達目標
／Objectives and attainment
goals		 1. Understand what nature-inspired design techniques are and how
   they are applied to solve real world problems.

2. Understand the advantages and disadvantages of nature-inspired
   and other traditional design techniques and how the combined
   techniques could produce more effective solutions to real world problems.
授業スケジュール
／Class schedule		 1. Introduction.
    Give an overview of evolutionary computation, and describe
    a number of evolutionary algorithms including genetic algorithms,
    evolutionary programming, evolution strategies, and genetic
    programming.

2. Evolutionary Optimization and Fast Evolutionary Programming.
    Function optimization appears in many applications. An example
    of developing a fast evolutionary programming is given
    to explain how to find a research problem, how to develop a new
    method, and how to evaluate the new method statistically.

3. Neural Network Learning and its Evolutionary Design.
    Neural network design is a typical design problem because
    there is a learning component to it. Both direct encoding
    representations and indirect encoding representations
    are introduced in the lectures. Meanwhile, the design
    of neural network ensembles is discussed.

4. Evolutionary Game.
    Evolutionary algorithms can be used to learn game-playing
    strategies without human intervention.  Some fundamental
    questions are discussed, including how to learn a game
    without any teachers, how well the player can learn,
    and how well the evolved strategies can generalize.

5. Evolvable Hardware as Evolutionary Design of Circuits.
    Evolvable hardware refers to hardware that can change its
    architecture and behavior dynamically and autonomously
    by interacting with its environment.

6. Adaptive Evolvable Hardware.
    An example of evolvable hardware design for a controller
    is given. In order o make evolvable hardware adaptable
    online, genetic algorithms are implemented on the evolvable
    hardware chip.
教科書
／Textbook(s)		 On-line lecture notes will be available.
成績評価の方法・基準
／Grading method/criteria		 Class Attendance (10%) + Project (90%)

The students will be asked to select a project among the provided
topics, and give a presentation at the end of the course.
履修上の留意点
／Note for course registration		 C or C++ Programming
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 1. Online lectures will be provided.

2. A list of papers will be given after each lecture.


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Keitaro Naruse
担当教員名
／Instructor		 Keitaro Naruse
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 We see a number of evolving networks in our daily life, for example, hyperlink graphs in Web pages, a friend network, and so on. They look like a complete random graph. However, it has been revealed that they are in a special class of random graphs. For example, in a hyperlink graph in Web pages, the number of incoming links to each of the Web pages does not follow a normal distribution, but it distributes as the power law, in which most of the Web pages have only a small number of incoming links meanwhile some Web pages posses a huge number of links. The property is called "scale-free", and it has been shown mathematically that a scale-free network can be generated through both of "network growth" and "preferential attachment". Similarly, in a friend network, even each of you have a limited number of friends and most of the friends have same people in common, the whole friend network has a small diameter (around 6 to 7). The property is called "small world", and it is characterized as a graph with a large clustering coefficient and a short average path length in the graph theory terminology. And the small world graph can be generated by introducing a small randomness into a regular graph.
授業の目的と到達目標
／Objectives and attainment
goals		 This course provides the theory of the evolving network, in particular, properties and generative mechanisms, and where we can find them in natural and artificial networks. Furthermore, the graph theory and the statistical theory are studied as well.
授業スケジュール
／Class schedule		 #1 Introduction
#2 Scale-free networks: Overview
#3-4 Scale-free networks: Mathematical models
#5 Scale-free networks: Web networks
#6 Scale-free networks: Errors and tolerances
#7 Small world networks: Overview
#8-9 Small world networks: Mathematical models
#10 Human dynamics: Message bursts
#11 Human dynamics: Global cascades
#12-13 Human dynamics: Recommendation systems
#14 Latest issues
#15 Summary
教科書
／Textbook(s)		 None
成績評価の方法・基準
／Grading method/criteria		 By reports on numerical experiments on evolving networks, and oral presentation on related works.
履修上の留意点
／Note for course registration		 None
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 http://iplab.u-aizu.ac.jp/moodle/


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開講学期
／Semester		 2014年度／Academic Year 　1学期 ／First Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Kazuyoshi Mori
担当教員名
／Instructor		 Kazuyoshi Mori
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course is concerned with the multidimensional systems
theory. This theory includes multidimensional control system and image
processing, and so on. We will proceed precisely with mathematical
descriptions.
授業の目的と到達目標
／Objectives and attainment
goals		 This course is concerned with the multidimensional systems
theory. This theory includes multidimensional control system and image
processing, and so on. We will proceed precisely with mathematical
descriptions.
授業スケジュール
／Class schedule		 1. Scalar 2-D Input/Output Systems
2. Stability
3. Structural Stability
4. Multi-Input/Multi-Output Systems
5. Stabilization of Scalar Feedback Systems
6. Characterization of Stabilizers for Scalar Systems
7. Stabilization of Strictly Causal Transfer Matrices
8. Characterization of Stabilizers for MIMO Systems
9. Stabilization of Weakly Causal Systems
10. Stabilization of MIMO Weakly Causal Systems
教科書
／Textbook(s)		 1. Multidimensional Systems Theory (2nd Ed). D.Reidel Publishing, 2003. (Reference)
2. Schaum's Outline of Theory and Problems of Signals and Systems 3rd Ed.(Schaum's
Outlines) (Reference)
成績評価の方法・基準
／Grading method/criteria		 Final examination and/or Reports


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開講学期
／Semester		 2014年度／Academic Year 　4学期 ／Fourth Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Mohamed Hamada
担当教員名
／Instructor		 Mohamed Hamada
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 The models of computations will be introduced and the term rewriting
systems (TRS), as a universal model of computation, and its major
properties such as termination and confluence will be discussed. Term
rewriting is a branch of theoretical computer science which combines
elements of logic, universal algebra, automated theorem proving and
functional programming. Its foundation is equational logic. TRS
constitutes a Turing- complete computational model which is very close
to functional programming. It has applications in Algebra, recursion
theory, software engineering and programming languages. In general
TRSs apply in any context where efficient methods for reasoning with
equations are required.
授業の目的と到達目標
／Objectives and attainment
goals		 This course gives students the fundamental concepts of the
computational models and the concept of rewriting systems and its
applications in many areas of theoretical computer science. It also
give the students more understanding of the major properties of term
rewriting systems.
授業スケジュール
／Class schedule		 1. General Introduction
2. Computational models
3. Abstract reduction systems
4. Universal Algebra
5. Term rewriting systems
6. Unification
7. Midterm Report
8. Termination
9. Confluence
10. Completion
11. Applications
12. General review
13. Final Report and Exam
教科書
／Textbook(s)		 1. F. Baader and T. Nipkow, Term Rewriting and All That, Cambridge
University Press, 1998.
2. Other materials related to the topics will be introduced in the
class. Various materials will be prepared
成績評価の方法・基準
／Grading method/criteria		 In general the evaluation procedure will be
carried out as follows.
1. Students are expected to give some presentations/seminars.
2. Students are expected to submit up to two reports: one at midterm and one
at the final of the course.
3. Students are expected to write some programs (they can use any
programming language they like).
履修上の留意点
／Note for course registration		 As this course is given to students who have not studied the
fundamentals of term rewriting systems, there is no prerequisites. But
we expect students have some basic courses such as discrete
mathematics and/or algebra.
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 Will be given during lectures.


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開講学期
／Semester		 2014年度／Academic Year 　1学期 ／First Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Nobuyoshi Asai
担当教員名
／Instructor		 Nobuyoshi Asai
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 Not offered in AY 2014


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開講学期
／Semester		 2014年度／Academic Year 　1学期 ／First Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Nobuyoshi Asai
担当教員名
／Instructor		 Nobuyoshi Asai
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This is a topics course: several recent topics of numerical
computation will be selected and discussed in detail.
・Elements of the Hilbert space.
・The eigenvalue problem for infinite matrices.
・Application to the special function computation.
・Visualization.
・Introduction to high-performance computing.
Case studies include  to important software packages and　the Internet usage.
授業の目的と到達目標
／Objectives and attainment
goals		 To study some application of functional analysis to numerical computation.
授業スケジュール
／Class schedule		 1. Elements of the Hilbert space(1)
2. Elements of the Hilbert space(2)
3. The eigenvalue problem for infinite matrices(1)
4. The eigenvalue problem for infinite matrices(2)
5. The eigenvalue problem for infinite matrices(3)
6. The eigenvalue problem for infinite matrices(4)
7. Application to the special function computation(1)
8. Application to the special function computation(2)
9. Application to the special function computation(3)
10. Application to the special function computation(4)
11. Visualization(1)
12. Visualization(2)
13. Introduction to high-performance computing(1)
14. Introduction to high-performance computing(2)
15. Other Topics
16. Other Topics
教科書
／Textbook(s)		 A. E. Taylor, D. C. Lay, Introduction to Functional Analysis, Kriger Pub., 1980
G. F. Simmons, Intruduction to Topology and MOdern Analysis, Mc-Graw Hill, 1963
成績評価の方法・基準
／Grading method/criteria		 Quizzes or reports.
履修上の留意点
／Note for course registration		 線形代数１
線形代数２
応用代数
数値解析
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 池辺八洲彦、池辺淑子、浅井信吉、宮崎佳典、現代線形代数 -分解定理を中心として-、共立出版、２００９
池辺八洲彦、稲垣敏之、数値解析入門、昭晃堂、１９９４


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Mohamed Hamada
担当教員名
／Instructor		 Mohamed Hamada
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course gives students advanced topics in the theory of automata and languages. The characterization of language classes, which is one of the most important themes in the formal language theory, will be introduced. Especially, the homomorphic characterizations of language classes will be discussed in detail. Moreover, some applications of
formal language theory will be discussed.

授業の目的と到達目標
／Objectives and attainment
goals		 Students can be familiar to the automata and languages and recognize the importance of the theory of automata and languages, and have enough knowledge to read and understand advanced papers in this field completely.

授業スケジュール
／Class schedule		 1. Introduction

2. Review of the theory of automata and languages
Methods to describe infinite sets
Grammars as generating systems of infinite sets
Automata as recognizing systems of infinite sets
Chomsky hierarchy of language classes
Relation among grammars and automata

3. Topics on the theory of automata and languages
Subclasses languages defined by automata with restrictions
Subclasses languages defined by grammars with restrictions
Operations on languages
Homomorphic characterization of language classes

4. Applications of the theory of automata and languages
Graph languages
Application to the cryptography
教科書
／Textbook(s)		 We do not specify textbooks but introduce books related to the topics in the class. Various materials will be prepared.


成績評価の方法・基準
／Grading method/criteria		 Small quizzes will be given. A report on the topics concerning this course will be required as the final examination.


履修上の留意点
／Note for course registration		 Automata and Languages(F8) given in the undergraduate program is designated as
the only prerequisite course officially.
Moreover students who will register this course are expected to be familiar
to the fundamental notions of Discrete Systems(F3) and Algorithms and Data Structures(F1).

The ability of logical thinking is expected.

参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 There are so many good textbooks in this field. Some of them will be introduced in the class and some are given here for students' convenience.

J. Hopcroft, J. Ullman: Introduction to Automata Theory, Languages and Computation, Addison-Wesley, 1979.

A. Meduna: Automata and Languages, Theory and Applications, Springer, 1999.

P. Linz: An Introduction to Formal Languages and Automata(3 ed.),
Jones and Bartlett, 2001.

J. L. Hein: Theory of Computation, An Introduction,
Jones and Bartlett, 1996.

M. Sipser: Introduction to the Theory of Computation,
PWS Publishing Co., 1996.

N. Pippenger: Theories of Computability, Cambridge Univ. Press, 1997.

R. Greenlaw, H. J. Hoover: Fundamentals of the Theory of Computation,
Principles and Proctice, Morgan Kaufmann Pub. Inc., 1998.

A. Maruoka, Concise Guide to Computation Theory, Springer, 2011.


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開講学期
／Semester		 2014年度／Academic Year 　1学期 ／First Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Shigeru Watanabe
担当教員名
／Instructor		 Shigeru Watanabe
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 The purpose of this course is to give ideas of advanced analysis
for students who have deep understanding for undergraduate
level mathematics (Fourier analysis, complex analysis).
授業の目的と到達目標
／Objectives and attainment
goals		 Students will be able to understand Fourier analysis as an introductory theory of function spaces.

Students will be able to understand an introduction to the theory of Hilbert spaces.

Students will be able to understand Fourier expansions by orthogonal polynomials.
授業スケジュール
／Class schedule		 1. Reviews of undergraduate mathematics
2. Introductory theory of function spaces
3. Introduction to functional analysis
4. Fourier expansions by orthogonal polynomials
成績評価の方法・基準
／Grading method/criteria		 reports
履修上の留意点
／Note for course registration		 Fourier analysis, complex analysis


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Lothar M. Schmitt
担当教員名
／Instructor		 Lothar M. Schmitt
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 We present a self-contained theoretical framework for
scaled genetic algorithms over the alphabet {0,1} which
converge asymptotically to global optima as anticipated by Davis
and Principe in analogy to the simulated annealing algorithm which is also discussed. The
algorithm employs multiple-bit mutation, single-cut-point crossover (or other crossover)
and power-law scaled proportional fitness selection based upon an
arbitrary fitness function. In order to achieve asymptotic convergence
to global optima, the mutation and crossover rates have to be annealed to
zero in proper fashion, and power-law scaling is used with logarithmic
growth in the exponent. Our analysis shows that a large population size
allows for a particularly slow annealing schedule for crossover. For the
foremost described setting, a detailed listing of theoretical aspects is
presented including prerequisites on inhomogeneous Markov chains. In
particular, we focus on: (i) The drive towards uniform populations
in a genetic algorithm including the undesired effect of genetic drift. (ii) Weak and strong ergodicity of the
inhomogeneous Markov chain describing the probabilistic model for the
scaled algorithm including simulated annealing. (iii) Convergence to globally optimal solutions.
We discuss various generalizations and extensions of the core framework
presented in this exposition such as larger alphabets or other versions
of the mutation-crossover operator, in particular, the Vose-Liepins version
of mutation-crossover. This refers to work by L.M. Schmitt in
[Theoretical Computer Science 259 (2001), 1--61] and
[Technical Report 2002-2-002, Aizu University] where similar types of
algorithms are considered over an arbitrary-size alphabet, and convergence
for arbitrary fitness function under more general conditions is shown.
Finally, we present an outlook on further developments of the theory.
授業の目的と到達目標
／Objectives and attainment
goals		 Learn the mathematical theory of inhomogeneous Markov chains. Apply this to a detailed analysis of simulated annealing and genetic algorithms. Use Banach algebra techniques to obtain usable estimates for the behavior of scaled probabilistic algorithms. Show global convergence of such algorithms under certain conditions for implementation.
授業スケジュール
／Class schedule		 Introduction to Simulated Annealing and Genetic Algorithms (I).
Fundamentals of inhomogeneous Markov chains (II-III).
Simulated Annealing (IV-V).
Mutation Operator, description, estimates, weak ergodicity (VI-VII).
Crossover, description, commutation relations with mutation, estimates for mixing (VIII-IX).
Selection, description, contraction properties (X).
Convergence to uniform populations (XI).
Strong ergodicity and convergence to global maxima (XII-XIII).
Examples for convergence and non-convergence (XIV-XV).
教科書
／Textbook(s)		 Frontiers of Evolutionary Computation (Genetic Algorithms and Evolutionary Computation) Springer, A. Menon
ISBN-13: 978-1402075247
成績評価の方法・基準
／Grading method/criteria		 Attendance strictly enforced. Obligation to implement some examples of the algorithms discussed above. Final exam determines the grade.
履修上の留意点
／Note for course registration		 Calculus. Linear Algebra. Introductory probability theory.
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 Lecture material will be handed out in class. Or email L@LMSchmitt.de.


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Kazuto Asai
担当教員名
／Instructor		 Kazuto Asai
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 In this class, we deal with various topics arising from pure and applied mathematics concerning Algebraic Systems and Combinatorics. This year, we focus mainly on the theory of finite fields in the area of Algebraic Systems. The finite field F_q --- a field with finite (q) elements --- was first found by E. Galois, and so it is often called a Galois field GF(q). The structure of F_q as a field is uniquely determined by the number of elements q, and for the existence of F_q, it is necessary and sufficient for q to be a power of a prime p.

Beginning with polynomial rings, we overview the following: prime fields, finite polynomial fields, field extensions, splitting fields, structure of finite fields, primitive elements, Frobenius cycles, cyclotomic polynomials, and functions between finite fields. When we consider numbers, they are often supposed to be real or complex numbers. But here, we shall contact with more abstract numbers, rings, and fields, to develop the ability of mathematical and abstract thinking.

Finite fields are purely mathematical objects. For example, mathematicians often try to extend or modify the theory over real/complex numbers to the one over finite fields in their researches. Finite fields, however, have many application such as theory of experimental design, codes, and logical circuits, etc, which is the reason why the finite fields are very important objects for both of Scientists and Engineers.
授業の目的と到達目標
／Objectives and attainment
goals		 Polynomial rings, Prime fields, Positive characteristic, Homomorphisms and isomorphisms, Field extension, Splitting fields, Uniqueness of the q-element field, Structure of finite fields, Primitive elements, Frobenius cycles, and Cyclotomic polynomials.
授業スケジュール
／Class schedule		 1. Polynomial rings.
2. Prime fields F_p.
3. Homomorphisms and isomorphisms.
4. Finite polynomial fields and field extensions.
5. Finite fields.
6. Structure of finite fields.
7. Primitive elements.
8. Frobenius cycles.
9. Cyclotomic polynomials.
教科書
／Textbook(s)		 1. Handout: Algebraic systems and combinatorics: -- Finite fields --

2. Introduction to Finite Fields and Their Applications, Revised ed. (1994), Cambridge University Press, by R. Lidl, H. Niederreiter

3. Finite Fields (Encyclopedia of Mathematics and its Applications) (1997), Cambridge University Press, by R. Lidl, H. Niederreiter

4. Kumiawaserironto Sonoouyou (1979), Iwanami Zensho 316, by Takahashi, I. (in Japanese).
成績評価の方法・基準
／Grading method/criteria		 (related courses) Applied Algebra, Linear Algebra I,II.
履修上の留意点
／Note for course registration		 By presentation and reports.
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 ~k-asai/classes/grds/ (Directory for the class)


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Michio Honma
担当教員名
／Instructor		 Michio Honma
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course deals with several basic problems in natural sciences in order to show how the information theory and various computational methods are materialized in the analysis of practical systems.
授業の目的と到達目標
／Objectives and attainment
goals		 At the end of the course the students should be able to:
(1) explain the importance and advantages of various numerical methods in the analysis of complicated systems.
(2) design a suitable model and write programs for solving practical problems.
授業スケジュール
／Class schedule		 . Introduction
Numerical derivative, integral, and root finding
. Exercise 1
. Differential equation 1
Initial value problem
. Exercise 2
. Differential equation 2
Boundary value problem
. Exercise 3
. Matrix manipulation 1
Matrix inversion
. Exercise 4
. Matrix manipulation 2
Eigenvalue problem
. Exercise 5
. Monte Carlo method 1
Random numbers and sampling of random variables
. Exercise 6
. Monte Carlo method 2
Monte Carlo integrals and simulations
. Exercise 7
教科書
／Textbook(s)		 Handouts: Printed handouts will be distributed to students during the class.
成績評価の方法・基準
／Grading method/criteria		 Students should submit a report on the problem given in each exercise class.
履修上の留意点
／Note for course registration		 Basic physics (classical mechanics, electricity and magnetism, quantum mechanics, statistical mechanics) and programming.
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 . An introduction to computer simulation methods : applications to physical systems 2nd ed.
Harvey Gould, Jan Tobochnik
Reading, Mass. : Addison-Wesley, c1996
. Computational physics : FORTRAN version
Steven E. Koonin, Dawn C. Meredith
Redwood City, Calif. ; Tokyo : Addison-Wesley, c1990


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Akira Fujitsu
担当教員名
／Instructor		 Akira Fujitsu
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 This course provides recent developements
in high energy particle physics.
授業の目的と到達目標
／Objectives and attainment
goals		 At the end of the course the students should:

1. have basic knowledge of high energy physics
2. know how to use computer to study theory of high energy physics
授業スケジュール
／Class schedule		 1. Basic concepts of quantum field theory
2. Path integral formulation
3. Lattice field theory
4. Gauge field theory
5. Superstring theory
6. Quantum gravity
成績評価の方法・基準
／Grading method/criteria		 Reports and Examination.


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Igor Lubashevskiy
担当教員名
／Instructor		 Igor Lubashevskiy
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 The goal of the course is to demonstrate the students how randomness acts in nature, namely, in physical, chemical, biological, social, and economic systems; to acquaint the students with the basic notions of stochastic (random) processes and the numerical methods of their simulation. An essential pedagogical point of the course is that the main theoretical constructions are illustrated by “on-line” computer simulations combined with discussion of their source codes. The latter also elucidates understanding the key points in programming stochastic processes and acquaints the students with the available C & C++ numerical libraries for simulation and visualization of scientific data. Complex mathematical constructions are replaced by qualitative explanation of the corresponding basic points.
授業の目的と到達目標
／Objectives and attainment
goals		 Stochastic behaviour is exhibited by a wide variety of systems different in nature and its understanding as well as a certain skill in computer simulation of various linear and nonlinear stochastic processes is essential in many research activities, engineering applications, and statistic analysis.

It is expected that in the final phase of  

- the course the students will acquire knowledge about

- the main models of stochastic phenomena observed in physical, biological, ecological, social, economic systems,
the basic algorithms used in simulating stochastic processes,

and gain some skill in

- programming stochastic processes,

- using C & C++ numerical libraries for simulation and scientific data visualization.
授業スケジュール
／Class schedule		 (below the terms 'example' and 'computer illustration' imply “on-line” computer simulation of processes at hand)

1. Overview of the basic notions of the probability theory. Unpredictability, stochasticity, chaos. Simulation and visualization of stochastic and chaotic trajectories of particle motion (simple pedagogical examples by 'on-line' computing). Mean values, Averaging over ensemble or time, Ergodicity (examples of ergodic and non-ergodic processes)

2. Random and pseudo-random numbers, Random number generators (bad and good ones), Uniform deviates , Algorithms for generating deviates from other distributions , Quasi-random sequences, Random number generators of GNU Scientific Library (GSL)

3. Illustrative computer examples of random walks on 1D and 2D lattices, unbounded ones and with boundaries, Distribution function, Simple example of master equation and its numerical solution for one-step processes

4. Random variables, Probability distribution, Generating function, Markov process, Markovian Brownian motion, the Central Limit Theorem (qualitative derivation), the Chapman-Kolmogorov equation as a classification of random trajectories, General properties of Brownian motion in a locally homogeneous continuum and their computer illustration including lattice random walks

5. Master equation, General properties, Entropy growth, Detailed balance, Boundary conditions, Some examples of nonlinear one-step processes, Illustrative examples of Poisson processes in physical systems and chemical reactions, Computer simulation of chemical reactions based on the mater equation.

6. Assumptions about the time locality of random walks and the local medium homogeneity, the forward Fokker-Planck equation, Boundary conditions for the Fokker-Planck equation and their meaning, Numerical algorithms of solving the Fokker-Planck equations, illustrative computer examples

7. Detailed analysis of the Ornstein-Uhlenbeck process, analytic and numerical

8. The backward Fokker-Planck equation, First passage time problem, Laplace transform of the first passage time probability, Mean exit time, Distribution of exit points, Reversible and non-reversible random walks, Escaping from potential well and metastable states in physical systems, computer illustration of escaping dynamics

9. Extreme events, Extreme value theory and the first passage time problem, Characteristic examples: extreme floods, amounts of large insurance losses, equity risks, day-to-day market risk, the size of freak waves, Mutational events during evolution, large wildfires

10. The Langevin approach and its relation to the Fokker-Planck equation, the Langevin equation with additive noise, characteristic examples, methods of its numerical solution, Stochastic Runge-Kutta algorithms

11. The Langevin equation of multiplicative noise, the Ito, Stratonovich, Hanngi-Klimontovich stochastic differential equations, algorithms of their numerical solution, noise-induced phase transitions in biology, chemistry, and physics, computer illustration

12. Characteristic stochastic processes in financial systems: Arbitrage-Free Markets, the Standard Black?Scholes Model, Models of Interest Rates, Contingent Claims under Alternative Stochastic Processes, Insurance Risk

13. Characteristic stochastic processes in medicine and biology: Population Dynamics, Discrete-in-Space?Continuous-in-Time Models, Continuous Approximation of Jump, Individual-Based Models, Neuroscience elements

14. Simulation of stochastic many-particle ensembles: Monte-Carlo simulation of equilibrium systems, Monte-Carlo simulation of non-equilibrium systems, Calculations based on Monte-Carlo simulation
教科書
／Textbook(s)		 N.G. van Kampen, Stochastic processes in physics and chemistry (Elsevier, Amsterdam, 2007) 3rd ed.

C.W. Gardiner, Handbook of stochastic methods (Springer-Verlag, Berlin, 2004), 3rd ed.

W. H. Press , S.A. Teukolsky , W.T. Vetterling , B.P. Flannery, Numerical recipes, (Cambridge University Press , Cambridge, 2007) 3rd ed.

W. Horsthemke and R. Lefever, Noise-Induced Transitions (Springer,  Berlin, 1984).

V. Capasso, D. Bakstein, An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine (Birkhauser, Boston, 2005 )

GNU Scientific Library: http://www.gnu.org/software/gsl/
成績評価の方法・基準
／Grading method/criteria		 Homework Assignments: 50%; Final Examination 50%
履修上の留意点
／Note for course registration		 Calculus,
Fourier analysis,
Complex analysis,
Probability and statistics,
Thermodynamics and statistical mechanics,
Numerical analysis,
C&C++ programming


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開講学期
／Semester		 2014年度／Academic Year 　3学期 ／Third Quarter
対象学年
／Course for;		 1st year , 2nd year
単位数
／Credits		 2.0
責任者
／Coordinator		 Takahiro Tsuchiya
担当教員名
／Instructor		 Takahiro Tsuchiya , - -
推奨トラック
／Recommended track		 －
履修規程上の先修条件
／Prerequisites		 －

更新日／Last updated on 2014/09/27
授業の概要
／Course outline		 ``Considering particles that move randomly depend on geographical character of the present position, what phenomena should be happen?’’ As it may be seemed that this question is far from mathematical problems, but there is a strong connection between the problem and mathematics. In fact, Kolmogorov formulated this problem via constructing theory for stochastic process and showed these phenomena could be characterized by partial differential equations of second. Indeed, the problem explored in more detail by K. Ito in view of “sample paths” since they are described by corresponding diffusion process with the partial differential equations of second. Then this course provides basic knowledge of theory for stochastic process as above.
授業の目的と到達目標
／Objectives and attainment
goals		 To be able to understand the rich mathematical structure of a random phenomena and to develop an ability to consider from the approach taken by stochastic process.
授業スケジュール
／Class schedule		 1. Introduction
2. martingales 1
3. martingales 2
4. Stochastic integral　1
5. Stochastic integral　2
6. Ito formula 1
7. Ito formula 2
8. Stochastic differential equation 1
9. Stochastic differential equation 2
10. Stochastic differential equation 3
11. Diffusion process 1
12. Diffusion process 2
13. Diffusion process 3
14. Application 1
15. Application 2
教科書
／Textbook(s)		 確率論 (岩波基礎数学選書), 伊藤 清.
成績評価の方法・基準
／Grading method/criteria		 Reports
履修上の留意点
／Note for course registration		 M-3 微積分I又はM-4 微積分 II, M-1 線形代数 I又はM-2 線形代数 II, フーリエ解析, 複素関数論.
参考(授業ホームページ、図書など)
／Reference (course
website, literature, etc.)		 Markov process from K. Ito’s perspective, D. W. Strook.