WSN21901 Analysis in Information Science

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Informatics and Data Science Program

Lecture Code WSN21901 Subject Classification Specialized Education

Subject Name Analysis in Information Science

Subject Name
（Katakana）アナリシス　イン　インフォーメーション　サイエンス

Subject Name in
English Analysis in Information Science

Instructor SHIMA TADASHI

Instructor
(Katakana) シマ　タダシ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Thur1-2,Fri1-2

Lesson Style Lecture Lesson Style
(More Details) 　

My teaching style in this class is heavily depend on a blackboard.

Credits 2.0 Class Hours/Week 　 Language of Instruction E : English

Course Level 5 : Graduate Basic

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords graph, Markov chain, random walk, harmonic function.

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students)

Class Objectives
/Class Outline The aim of this course is to introduce some basic concepts of the theory of stochastic processes and to show the application of them through the relationship between random walks on graphs and electrical circuits.

Class Schedule In this course, I want to show an aspect of the relation between the theory of stochastic processes and potential theory through random walks on graphs.

In my plan, the lecture starts from the very beginning of the probability theory. That is introducing the concepts of probability space and conditional probabilities.
We then treat one of the most important stochastic processes called Markov processes.
The important concepts, transition matrices, Markov properties, stopping times are introduced.
The harmonic functions are treated in connection with the absorption probability.
We then consider the Dirichlet problems on graphs.
Solutions of the Dirichlet problems are constructed by using the idea of stochastic processes.
We will then go into another subject: the correspondence between electrical networks and random walks on graphs.
From the information of a random walk on a graph, we can draw an electrical network.
The currents and voltages at vertices of the electric network are given as the probabilities or expectations under the associated random walk.
Finally, I want to apply these relations to establish the criterion for recurrence and transience of random walks on graphs.

Text/Reference
Books,etc. Random walks and electric networks, Doyle, P.G. and Snell, J.L.,
The mathematical association of America, 1984
Modern Graph Theory, Bollobas, B., Springer, 1998
Markov Chain, Norris, J.R., Cambridge University Press, 1996

PC or AV used in
Class,etc. 　

(More Details) I will distribute handouts through moodle.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Read the copies very carefully and solve exercises.

Requirements

Grading Method Your grade in the class will be determined by a report. The problem sheets for the report will be provided at the beginning of July and the deadline is the middle of Aug. (tentative)

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Informatics and Data Science Program
Lecture Code	WSN21901	Subject Classification	Specialized Education
Subject Name	Analysis in Information Science
Subject Name （Katakana）	アナリシス　イン　インフォーメーション　サイエンス
Subject Name in English	Analysis in Information Science
Instructor	SHIMA TADASHI
Instructor (Katakana)	シマ　タダシ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Thur1-2,Fri1-2
Lesson Style	Lecture	Lesson Style (More Details)
My teaching style in this class is heavily depend on a blackboard.
Credits	2.0	Class Hours/Week		Language of Instruction	E : English
Course Level	5 : Graduate Basic
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	graph, Markov chain, random walk, harmonic function.
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)
Class Objectives /Class Outline	The aim of this course is to introduce some basic concepts of the theory of stochastic processes and to show the application of them through the relationship between random walks on graphs and electrical circuits.
Class Schedule	In this course, I want to show an aspect of the relation between the theory of stochastic processes and potential theory through random walks on graphs. In my plan, the lecture starts from the very beginning of the probability theory. That is introducing the concepts of probability space and conditional probabilities. We then treat one of the most important stochastic processes called Markov processes. The important concepts, transition matrices, Markov properties, stopping times are introduced. The harmonic functions are treated in connection with the absorption probability. We then consider the Dirichlet problems on graphs. Solutions of the Dirichlet problems are constructed by using the idea of stochastic processes. We will then go into another subject: the correspondence between electrical networks and random walks on graphs. From the information of a random walk on a graph, we can draw an electrical network. The currents and voltages at vertices of the electric network are given as the probabilities or expectations under the associated random walk. Finally, I want to apply these relations to establish the criterion for recurrence and transience of random walks on graphs.
Text/Reference Books,etc.	Random walks and electric networks, Doyle, P.G. and Snell, J.L., The mathematical association of America, 1984 Modern Graph Theory, Bollobas, B., Springer, 1998 Markov Chain, Norris, J.R., Cambridge University Press, 1996
PC or AV used in Class,etc.
(More Details)	I will distribute handouts through moodle.
Learning techniques to be incorporated
Suggestions on Preparation and Review	Read the copies very carefully and solve exercises.
Requirements
Grading Method	Your grade in the class will be determined by a report. The problem sheets for the report will be provided at the beginning of July and the deadline is the middle of Aug. (tentative)
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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