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Basics of ComputationalNeuroscience

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Lecture: Computational Neuroscience, Contents

1) IntroductionThe Basics – A reminder:

1) Brain, Maps, Areas, Networks, Neurons, and SynapsesThe tough stuff:

2,3) Membrane Models3,4) Spiking Neuron Models5) Calculating with Neurons I: adding, subtracting, multiplying, dividing5,6) Calculating with Neurons II: Integration, differentiation6) Calculating with Neurons III: networks, vector-/matrix- calculus, assoc. memory6,7) Information processing in the cortex I: Neurons as filters7) Information processing in the cortex II:Correlation analysis of neuronal connections7,8) Information processing in the cortex III: Neural Codes and population responses8) Information processing in the cortex IV: Neuronal maps

Something interesting – the broader perspective9) On Intelligence and Cognition – Computational Properties?

Motor Function10,11) Models of Motor Control

Adaptive Mechanisms11,12) Learning and plasticity I: Physiological mechanisms and formal learning rules12,13) Learning and plasticity II: Developmental models of neuronal maps13) Learning and plasticity III: Sequence learning, conditioning

Higher functions14) Memory: Models of the Hippocampus15) Models of Attention, Sleep and Cognitive Processes

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Literature (all of this is very mathematical!)

General Theoretical Neuroscience:

„Theoretical Neuroscience“, P.Dayan and L. Abbott, MIT Press (there used to be a version of this on theinternet)

„Spiking Neuron Models“, W. Gerstner & W.M. Kistler, Cambridge University Press. (there is a version on the internet)

Neural Coding Issues: „Spikes“ F. Rieke, D. Warland, R. de Ruyter v. Steveninck, W. Bialek, MIT Press

Artificial Neural Networks: „Konnektionismus“, G. Dorffner, B.G. Teubner Verlg. Stuttgart

„Fundamentals of Artificial Neural Networks“, M.H. Hassoun, MIT Press

Hodgkin Huxley Model: See above „Spiking Neuron Models“, W. Gerstner & W.M. Kistler, Cambridge University Press.

Learning and Plasticity: See above „Spiking Neuron Models“, W. Gerstner & W.M. Kistler, Cambridge University Press.

Calculating with Neurons: Has been compiled from many different sources.

Maps: Has been compiled from many different sources.

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What is computational neuroscience ?

The Interdisciplinary Nature of Computational Neuroscience

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Neuroscience:

Environment

Stimulus

Behavior

Reaction

Different Approaches towards Brain and Behavior

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Psychophysics (human behavioral studies):

Environment

Stimulus

Behavior

Reaction

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Environment

Stimulus

Neurophysiology:

Behavior

Reaction

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Environment

Stimulus

Theoretical/Computational Neuroscience:

Behavior

Reaction dx

)(xf

U

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Levels of information processing in the nervous system

Molecules0.1m

Synapses1m

Neurons100m

Local Networks1mm

Areas / „Maps“1cm

Sub-Systems10cm

CNS1m

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CNS (Central Nervous System):

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Cortex:

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Where are things happening in the brain.

Is the informationrepresented locally ?

The Phrenologists viewat the brain(18th-19th centrury)

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Results from human surgery

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Results from imaging techniques – There are maps in the brain

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Visual System:More than 40 areas !

Parallel processing of „pixels“ andimage parts

Hierarchical Analysis of increasinglycomplex information

Many lateral and feedbackconnections

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Primary visual Cortex:

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Retinotopic Maps in V1: V1 contains a retinotopic map of the visual Field. Adjacent Neurons represent adjacent regions in theretina. That particular small retinal region from which a single neuron receives its input is called the receptivefield of this neuron.

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

V1 receives information from both eyes. Alternatingregions in V1 (Ocular Dominanz Columns) receive(predominantely) Input from either the left or the right eye.

Each location in the cortex represents a different partof the visual scene through the activity of manyneurons. Different neurons encode different aspects of the image. For example, orientation of edges, color, motion speed and direction, etc.

V1 decomposes an image into these components.

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Orientation selectivity in V1:

Orientation selective neurons in V1 changetheir activity (i.e., their frequency forgenerating action potentials) depending on the orientation of a light bar projected ontothe receptive Field. These Neurons, thus, represent the orientation of lines oder edgesin the image.

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Their receptive field looks like this:

stimulus

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Superpositioning of maps in V1: Thus, neurons in V1 are orientationselective. They are, however, also selective for retinal position and ocular dominance as well as forcolor and motion. These are called„features“. The neurons aretherefore akin to „feature-detectors“.

For each of these parameter thereexists a topographic map.

These maps co-exist and aresuperimposed onto each other. In this way at every location in thecortex one finds a neuron whichencodes a certain „feature“. Thisprinciple is called „full coverage“.

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Local Circuits in V1:

Selectivity is generated byspecific connections

stimulus

Orientation selectivecortical simple cell

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Layers in the Cortex:

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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Local Circuits in V1:

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

LGN inputs Cell types

Spiny stellatecell Smooth stellate

cell

Circuit

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Considerations for a Cortex Model• Input

– Structure of the visual pathway• Anatomy of the Cortex

– Cell Types– Connections

• Topography of the Cortex– „X-Y Pixel-Space“ and its distortion– Ocularity-Map– Orientation-Map– Color

• Functional Connectivity of the cortex– Connection Weights– Physiological charateristics of the neurons

At least all these things need to beconsidered when making a „complete“cortex model

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At the dendrite the incomingsignals arrive (incoming currents)

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

At the soma currentare finally integrated.

At the axon hillock action potentialare generated if the potential crosses the membrane threshold

The axon transmits (transports) theaction potential to distant sites

At the synapses are the outgoingsignals transmitted onto the dendrites of the targetneurons

Structure of a Neuron:

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Different Types of Neurons:

Unipolarcell

Bipolarcell

(Invertebrate N.) Retinal bipolar cell

dendrite

axon

soma

Spinal motoneuronHippocampalpyramidal cell

Purkinje cell of thecerebellum

axonsoma

dendrite

Different Typesof Multi-polarCells

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Cell membrane:

K+

Cl-

Ion channels:

Membrane - Circuit diagram: