Hiroshima University Syllabus |

Japanese

Academic Year 2020Year 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

EnglishAnalysis 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：IAS C709 Lesson Style Lecture Lesson Style

【More Details】My teaching style in this class is heavily depend on a blackboard. Credits 2 Class Hours/Week Language on 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

ProgramCriterion referenced

EvaluationClass Objectives

/Class OutlineThe 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.At the first class, I will distribute handouts. Suggestions on

Preparation and

ReviewRead 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.