Introduction to neurodynamics and neuroinformatics 1000-1M09WNN

Plan of lecture
1) General introduction to neurobiology:
- review of brain, neural, and synaptic structure;
2) Dynamics of a single neuron:
- basic electrical and chemical properties of neurons and synapses;
- Hopfield model, threshold of activity;
- "Integrate-and-fire" model;
- Hodgkin-Huxley model;
- model of a synapse; excitatory and inhibitory synapses;
3) Dynamics of neural networks:
- firing-rate network models;
- network of "integrate-and-fire" neurons;
- network synchronization - what is it good for?;
- synaptic plasticity, memory and learning in neural networks;
4) Information theory in neural networks:
- how information is encoded in neural activities?
- entropy in neural networks;
- mutual information;
- Fisher information, accuracy of coding;
5) Examples of neural modeling (if time allows).

Requirements
I expect that students know how to solve analytically linear differential equations. The plus is to know (although it is not required) how to solve numerically non-linear differential equations and their sets (e.g. the method of Runge-Kutta in Matlab, C, or Fortran) - I will devote to this topic some time during the lecture. It is required also some basic knowledge of linear algebra (matrix and its transformations), and elementary knowledge of probability concepts and the Gauss distribution.