This course provides an introduction into a neural process accounts for perception, motor control, and simple forms of cognition. The vantage point is the dynamical systems approach, which emphasizes the evolution in time of behavior and of neural activation patterns as the basis for understanding how neural networks together with sensory and motor systems generate behavior and cognition. Dynamic stability, a concept shared with the classical biological cybernetics framework, is one cornerstone of the approach. Instabilities (or bifurcations) extend this framework and provide a basis for understanding flexibility, task specific adjustment, adaptation, and learning.

The course will include tutorial modules that provide some of the mathematical foundations. Theoretical concepts will be exposed in reference to a number of experimental model systems such as the perception of motion, visual and spatial working memory, movement planning, and others. In the spirit of Braitenberg´s "synthetic psychology", autonomous robots will be used to illustrate some of the ideas.

Exercises are integrated into the lectures. They consist of elementary mathematical exercises, the design of (thought) experiments and their analysis, and analysis of theoretical models and their relationship to experiment, all on the basis of the theoretical framework exposed in the main lectures. Learning to produce scientific texts with appropriate illustrations and documenting mathematical ideas is one of the learning goals of the course.

Some of the exercises refer to readings, scientific papers that students will study to do the exercises. Learning to read and understand research papers is another learning goal of the course.

Course type

Lectures

Credits

6 CP

Term

Winter Term 2015/2016

Lecture

Takes place every week on Thursday from 14:15 to 16:00 in room NB 3/57.
First appointment is on 22.10.2015

Exercise

Takes place every week on Thursday from 16:15 to 17:00 in room NB 3/57.
First appointment is on 05.11.2015

Examination

Takes place on 03.03.2016 from 14:15 to 16:15 in room NB 02/99.

This course requires some basic math preparation, typically as covered in two semesters of higher mathematics (functions, differentiation, integration, differential equations, linear algebra). The course does not make extensive use of the underlying mathematical techniques, but uses the mathematical concepts to express scientific ideas. Students without prior training in the relevant mathematics may be able to follow the course, but will have to work harder to familiarize themselves with the concepts.

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Exercises

Exercises are corrected and held by Oliver Lomp. Details on grading are available in the course rules below.

Exam

The exam will take place on the 3rd of March 2016 from 14:15 to 16:15. Please register for the exam with your degree program where appropriate or, if the program does not require that, with our secretaries. Please note the rules for how the exam is evaluated by reading the "rules for getting credit" sheet in the download list below. Note that these have changed from our last course.

Literature

The course will be based on selected chapters of a forthcoming textbook. The first two chapters are available for download in the course materials below. These and others will also serve as readings for some of the exercises. 

For the mathematical background in dynamical systems an excellent resource is a book that is available online as a free download (thanks to the author's generosity): Edward R. Scheinerman's Invitation to Dynamical Systems.  This book covers both discrete and continuous time dynamical systems, while in the course we will only make use of continuous time dynamical systems formalized as differential equations. 

Lecture slides	Chapter 1 of the textbook
Lecture slides	Rules for getting credit
Exercises	Exercise 1: Braitenberg vehicles
Lecture slides	Chapter 2 of the textbook
Lecture slides	Slides of presentation about course organization
Lecture slides	Slides of first part of Dynamical Systems Tutorial
Lecture slides	Slides of the fourth part of the Dynamic Field Theory core lecture
Lecture slides	Slides of final lecture that links DFT to neural dynamics
Exercises	Exercise 9: Dynamic Field Theory reading
Lecture slides	Exam and course results
Lecture slides	Slides of the third part of the Dynamic Field Theory core lecture
Exercises	Exercise 8: Dynamic activation fields
Lecture slides	Slides of the second part of the Dynamic Field Theory core lecture
Exercises	Paper to be read for Exercise 7
Exercises	Exercise 7: Population code
Lecture slides	Slides of the first part of the Dynamic Field Theory core lecture
Lecture slides	Slides of the second part of the Neural Dynamics core lecture
Lecture slides	Essay exercise
Lecture slides	Slides of the first part of the Neural Dynamics core lecture
Lecture slides	Slides of the tutorial on decoding and Bayes' Theorem
Exercises	Exercise 6: Neural coding
Lecture slides	Slides of the tutorial on coding, tuning curves, maps
Exercises	Exercise 5: Neurophysics tutorial
Lecture slides	Slides of the tutorial on basic neurophysics
Lecture slides	Template MATLAB simulator for exercise 4
Exercises	Exercise 4: Dynamical systems tutorial: simulator
Lecture slides	Slides of third part of Dynamical Systems Tutorial
Exercises	Exercise 3: Dynamical systems tutorial part 2
Lecture slides	Slides of second part of Dynamical Systems Tutorial
Exercises	Exercise 2: Dynamical systems tutorial part 1
Lecture slides	Slides of Braitenberg lecture
Lecture slides	Slides of introductory lecture