This is an introductory course to computational neuroscience. The main question is how to use mathematics in order to describe the structure, dynamics and function of the neural system. We will learn examples of neural implementation of cognitive functions. A science major is a great advantage for this course but it will provide interesting insight to our up to date understanding of the brain potentially for anyone.
Some chapters of Peter Dayan and LF Abbott: Theoretical Neuroscience (Computational and Mathematical Modeling of Neural Systems) are useful.
Background info: The Encyclopeida of Computational Neuroscience is under development: http://www.scholarpedia.org/article/Encyclopedia_of_Computational_Neuroscience
We will discuss, how the mathematics can be applied to describe the neural dynamics underlying of its functions, action potentials and synaptic interactions. We will discuss the properties of voltagegated and ligand gated ionchannels and the notion of membrane potential. The equilibrium of ionic concentrations, thus the generation of resting potential will be described by the Nerstequation. The Nobelprize awarded HodgkinHuxley equations will be introduced in order to describe the action potential generation in terms of differential equations.
Theory of learning and its neural implementations: supervised, unsupervised and reinforcement learning in neural networks. Classical examples for learning neural networks: Perceptron, Hopfield network, selforganizing maps, actorcritic learning, Biological implementation of learning: from Hebb'srule to spiketime dependent plasticity.
Technological detour: windows to the brain. What information is provided by intracellular and extracellular recordings of electric activity, evoked responses, EEG (electroencephalography), MEG (magnetoencephalography), PET (positron emission tomography), fMRI (functional magnetic resonance imaging), optical imaging and light sensitive ionchannels.
The learned phenomena will be applied for an attempt to solve a puzzle of an ancient cortical area: the hippocampus. The specific anatomy and electrophysiology will be learned with special attention to the hippocampal oscillations. The basic requirements of navigational strategies and the functional correlates of the cellular activity, the possible role of place cells and gridcells in the spatial representation and the episodic memory will be reviewed.
The question of the neural code will be raised and functional models of the hippocampus will be built up by using the concept of attractor networks for the possible role of the hippocampus in navigation and episodic memory.
The description of the discussed models:
Arleo and Gerster:
Spatial cognition and neuromimetic navigation: a model of hippocampal place cell activity.
Learning activities, learning methods
Lectures and interactive discussions
Evaluation of outcomes
Learning requirements, mode of evaluation, criteria of evaluation:
- Reliable basic knowledge in the domain of informatics
mode of evaluation: examination and practical course mark
criteria of evaluation:
- Knowledge on basic concepts
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Lights, Camera, Action Potential (n.d.). In Neuroscience For Kids. Retrieved from http://staff.washington.edu/chudler/ap.html
The Sounds of Neuroscience (n.d.). In Neuroscience For Kids. Retrieved from https://faculty.washington.edu/chudler/son.html
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Kipke, D. R., Shain, W., Buzsáki, G., Fetz, E., Henderson, J. M., Hetke, J. F., & Schalk, G. (2008). Advanced neurotechnologies for chronic neural interfaces: New horizons and clinical opportunities. The Journal of Neuroscience, 28(46), 11830–11838. http://www.kfki.hu/~soma/BSCS/Kipke08.pdf
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Érdi, P. (n.d.). Computational approach to the functioning of the hippocampus. Retrieved from http://www.rmki.kfki.hu/biofiz/cneuro/tutorials/ICANN/icannall/index.html
Place cell. (2014). In Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Place_cell
Moser, E., & Moser, M.-B. (2007). Grid cells. In Scholarpedia. Retrieved from http://www.scholarpedia.org/article/Grid_cells
Arleo, A., & Gerstner, W. (2000). Spatial cognition and neuromimetic navigation: a model of hippocampal place cell activity. Biological Cybernetics 83, 287-299. http://www.kfki.hu/~soma/BSCS/Arleo00.pdf
Foster, D.J., Morris, R.G.M., & Dayan, P. (2000). A model of hippocampally dependent navigation using temporal difference learning rule. Hippocampus 10, 1-16. http://www.kfki.hu/~soma/BSCS/Foster00.pdf
Trullier, O., & Meyer, J. A (2000). Animat navigation using a cognitive graph. Biological Cybernetics 83, 271-285. http://www.kfki.hu/~soma/BSCS/trullier00.pdf