Our brain is an information processing device that interprets sensory stimuli to learn about the external world and make intelligent decisions. To understand how the brain achieves all these functions we develop computational models and compare their predictions to neuronal activity recorded during behavior. During this course we introduce the toolkit of information theory, dynamical systems and machine learning to discover the principles underlying sensory coding, decision making, learning and memory. The course starts with discussing how the activity of neural populations represent and transform sensory information in order to control behavioral responses. Then we study the excitability of neurons and networks both at the biophysical and at the dynamical level. Finally we investigate the mathematical basis of learning and memory in the nervous system. Besides the lectures focusing on the core principles and concepts of computational neuroscience, the course also includes optional programming exercises in python allowing students to test their knowledge on real data. The course is recommended for biology students ready to learn mathematics or programming to build quantitative models of the nervous system, and physics, math, informatics or engineering students interested in information processing in the brain.

Syllabus:

• Sept 11: Introduction, use of modeling in neuroscience research, Marr’s levels of analysis, basics of neural computation
• Sept 18: Hodkin-Huxley model of neurons
• Sept 25: Dendritic integration and signal propagation, synapses
• Oct 2: Simplified models: integrate-and-fire, state space models, FitzHugh-Nagumo model, rate models
• Oct 9: Neural encoding of stimuli
• Oct 16: Decoding of neural activity
• Nov 6: Decision making, causality
• Nov 13: Reinforcement learning
• Nov 20: Synaptic plasticity, supervised learning
• Nov 27: Memory and hippocampus, Hopfield networks
• Dec 4: Unsupervised learning, dimensionality reduction

Selected  suggested and recommended literature:

Selected chapters from Pléh Csaba – Kovács Gyula – Gulyás Balázs (szerk): Kognitív idegtudomány. Osiris, Budapest Érdi Péter – Lengyel Máté: Matematikai modellek az idegrendszer-kutatásban. p 126-148. Fiser József – Nádasdy Zoltán: Neurális kódolás térben és időben. p 171-201 Nádasdy Zoltán – Fiser József: A tanulás biológiai és mesterséges neurális hálói p 389 Káli Szabolcs – Acsády László: A hippocampusfüggő memória neurobiológiai alapjai p 359