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Stochastic Processes in Neuroscience I

5

English

#20611 / #1

Seit SS 2018

Fakultät II

MA 5-1

Institut für Mathematik

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Stannat, Wilhelm

Stannat, Wilhelm

wilhelm.stannat@tu-berlin.de

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POS-Nummer PORD-Nummer Modultitel
2347949 39664 Stochastic Processes in Neuroscience I

Learning Outcomes

Participants will learn basic concepts, their theoretical foundation, and the most common models of stochastic processes used in computational neuroscience to model noisy neural systems. Participants will learn basic techniques to analyze the stochastic behavior of single neurons and neural systems both qualitatively and quantitatively. Participants will also learn basic simulation techniques for stochastic neural systems and how to evaluate simulation output. Participants will learn to adapt models to new problems as well as to develop new models of neural systems.

Content

This module provides basic knowledge about the mathematical modeling, analysis and numerical simulation of neural systems under the influence of noise using stochastic processes. Specific topics addressed are: continuous time Markov chains, diffusion approximation, mean-field theories for simple neural networks, Brownian motion, stochastic integration, stochastic differential equations , stochastic models for single neurons (stochastic integrate-and-fire models, random oscillators)

Module Components

Pflichtgruppe:

All Courses are mandatory.

Course Name Type Number Cycle Language SWS
Stochastische Prozesse in den Neurowissenschaften VL 3236 L 209 WS/SS No information 2

Workload and Credit Points

Stochastische Prozesse in den Neurowissenschaften (VL):

Workload description Multiplier Hours Total
Attendance 15.0 2.0h 30.0h
30.0h(~1 LP)

Course-independent workload:

Workload description Multiplier Hours Total
Preparation and follow-up 15.0 6.0h 90.0h
Exam Preparation 15.0 2.0h 30.0h
120.0h(~4 LP)
The Workload of the module sums up to 150.0 Hours. Therefore the module contains 5 Credits.

Description of Teaching and Learning Methods

Lecture

Requirements for participation and examination

Desirable prerequisites for participation in the courses:

Wahrscheinlichkeitstheorie I

Mandatory requirements for the module test application:

No information

Module completion

Grading

graded

Type of exam

Oral exam

Language

German/English

Duration/Extent

No information

Duration of the Module

The following number of semesters is estimated for taking and completing the module:
1 Semester.

This module may be commenced in the following semesters:
Winter- und Sommersemester.

Maximum Number of Participants

This module is not limited to a number of students.

Registration Procedures

Standard

Recommended reading, Lecture notes

Lecture notes

Availability:  unavailable

Electronical lecture notes

Availability:  available

Literature

Recommended literature
Ermentrout, Terman, Foundations of Mathematical Neuroscience, Springer 2010
Klenke, Probability Theory - a comprehensive course, Springer 2008
Lang, Lord, Stochastic Methods in Neuroscience, Oxford University Press 2009
Oksendal, Stochastic Differential Equations, Springer 2010

Assigned Degree Programs

This moduleversion is used in the following modulelists:

Miscellaneous

No information