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Stochastic Processes: Data Analysis and Computer Simulation †

About the course †

Course Number

TBA

Brief Description

The course deals with how to simulate and analyze stochastic processes, in particular the dynamics of small particles diffusing in a fluid.

Full Description

The motion of falling leaves or small particles diffusing in a fluid is highly stochastic in nature. Therefore, such motions must be modeled as stochastic processes, for which exact predictions are no longer possible. This is in stark contrast to the deterministic motion of planets and stars, which can be perfectly predicted using celestial mechanics. This course is an introduction to stochastic processes through numerical simulations, with a focus on the proper data analysis needed to interpret the results. We will use the Jupyter (iPython) notebook as our programming environment. It is freely available for Windows, Mac, and Linux through the Anaconda Python Distribution. The students will first learn the basic theories of stochastic processes. Then, they will use these theories to develop their own python codes to perform numerical simulations of small particles diffusing in a fluid. Finally, they will analyze the simulation data according to the theories presented at the beginning of course. At the end of the course, we will analyze the dynamical data of more complicated systems, such as financial markets or meteorological data, using the basic theory of stochastic processes.

What You’ll Learn

Basic Python programming

Basic theories of stochastic processes

Simulation methods for a Brownian particle

Application: analysis of financial data

Learner Testimonial

TBA

Course Dates

TBA

Course Length

6 weeks

Estimated Effort

2-3 hours per week

Prerequisites

Basic mathematics expected of a 2nd year undergraduate student (differential and integral calculus and linear algebra).

Language

Content: English

Videos: English

Course Level

Intermediate

Certificate Type and Price

TBA

XSeries

No

Course Staff

Ryoichi Yamamoto

Ryoichi is a full Professor at the Transport Phenomena Lab in the department of Chemical Engineering at Kyoto University. He received his B.Eng. and M.Eng in Chemical Engineering from Kobe University and his Ph.D. in Molecular Engineering from Kyoto University in 1988, 1992, 1996, respectively.

Areas of Expertise:

Soft Matter Science

Computational Science

Transport Phenomena

Major Works:

Hydrodynamic interactions of self-propelled swimmers, John J. Molina, Yasuya Nakayama, and Ryoichi Yamamoto.

Dynamics of Highly Supercooled Liquids; Heterogeneity, Rheology, and Diffusion, Ryoichi Yamamoto and Akira Onuki.

Connect:

website: http://www-tph.cheme.kyoto-u.ac.jp/index.php?en%2FFrontPage

facebook:https://www.facebook.com/groups/1158492977603546/

Lectures †

• Week1: Python programming for beginners [ Go? ]

• Week2: Distribution function and random number [ Go? ]

• Week3: Brownian motion 1: basic theories [ Go? ]

• Week4: Brownian motion 2: computer simulation [ Go? ]

• Week5: Brownian motion 3: data analyses [ Go? ]

• Week6: More complicated stochastic processes [ Go? ]

Useful Information †

• Download Python and set up programming environment on your [Windows/Mac/Linux] PC [ Go ]

• Python 3 official documentation [ Go ]

• Jupyter official website [ Go ]

• Related online resources

• edX "Introduction to Computer Science and Programming Using Python" [ Go ]

• What I have done for performing my slide presentations

• Install anaconda "Anaconda3-4.2.0-MacOSX-x86_64.pkg" downloaded from https://repo.continuum.io/archive/ .
• Install RISE by following the instructions found in https://github.com/damianavila/RISE . Be careful that RISE doesn't support Python 3.6 yet.
• Install notebook extensions by following the instructions found in http://qiita.com/Tsutomu-KKE@github/items/1326e05eb992a8aa849d . Then you can use a spell checker etc...
• Replace "main.css" and "main.js" found in ~/anaconda/share/jupyter/nbextensions/rise/ with the same fine you can find in (dropbox)/00common/RISE_customize/ . This is needed to fit slides with bigpad.
• Launch *.ipynb using Safari, display full screen, click the "RISE presentation icon"