Mean Field Theories in Neuroscience B. Cessac, Neuromathcomp, INRIA.

Slides:

Advertisements

Similar presentations

What is the neural code? Puchalla et al., What is the neural code? Encoding: how does a stimulus cause the pattern of responses? what are the responses.

Advertisements

History, Part III Anatomical and neurochemical correlates of neuronal plasticity Two primary goals of learning and memory studies are –i. neural centers.

V1 Physiology. Questions Hierarchies of RFs and visual areas Is prediction equal to understanding? Is predicting the mean responses enough? General versus.

Dynamic Causal Modelling for ERP/ERFs Valentina Doria Georg Kaegi Methods for Dummies 19/03/2008.

Neural Network of the Cerebellum: Temporal Discrimination and the Timing of Responses Michael D. Mauk Dean V. Buonomano.

III-28 [122] Spike Pattern Distributions in Model Cortical Networks Joanna Tyrcha, Stockholm University, Stockholm; John Hertz, Nordita, Stockholm/Copenhagen.

Learning crossmodal spatial transformations through STDP Gerhard Neumann Seminar B, SS 06.

Artificial Neural Networks - Introduction -

Part II: Population Models BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapters 6-9 Laboratory of Computational.

Artificial Neural Networks - Introduction -

Introduction to Mathematical Methods in Neurobiology: Dynamical Systems Oren Shriki 2009 Modeling Conductance-Based Networks by Rate Models 1.

Biological Modeling of Neural Networks: Week 11 – Continuum models: Cortical fields and perception Wulfram Gerstner EPFL, Lausanne, Switzerland 11.1 Transients.

Introduction to the mathematical modeling of neuronal networks Amitabha Bose Jawaharlal Nehru University & New Jersey Institute of Technology IISER, Pune.

Outline Formulation of Filtering Problem General Conditions for Filtering Equation Filtering Model for Reflecting Diffusions Wong-Zakai Approximation.

Supervised and Unsupervised learning and application to Neuroscience Cours CA6b-4.

Stable Propagation of Synchronous Spiking in Cortical Neural Networks Markus Diesmann, Marc-Oliver Gewaltig, Ad Aertsen Nature 402: Flavio Frohlich.

Synapses are everywhere neurons synapses Synapse change continuously –From msec –To hours (memory) Lack HH type model for the synapse.

Components of the visual system. The individual neuron.

How does the mind process all the information it receives?

A globally asymptotically stable plasticity rule for firing rate homeostasis Prashant Joshi & Jochen Triesch

Artificial Neurons, Neural Networks and Architectures

Laurent Itti: CS599 – Computational Architectures in Biological Vision, USC Lecture 7: Coding and Representation 1 Computational Architectures in.

Connected Populations: oscillations, competition and spatial continuum (field equations) Lecture 12 Course: Neural Networks and Biological Modeling Wulfram.

Biological Modeling of Neural Networks: Week 15 – Population Dynamics: The Integral –Equation Approach Wulfram Gerstner EPFL, Lausanne, Switzerland 15.1.

Unsupervised learning

Introduction to Mathematical Methods in Neurobiology: Dynamical Systems Oren Shriki 2009 Modeling Conductance-Based Networks by Rate Models 1.

Lecture 10: Mean Field theory with fluctuations and correlations Reference: A Lerchner et al, Response Variability in Balanced Cortical Networks, q-bio.NC/ ,

2 2  Background  Vision in Human Brain  Efficient Coding Theory  Motivation  Natural Pictures  Methodology  Statistical Characteristics  Models.

Lecture 11: Networks II: conductance-based synapses, visual cortical hypercolumn model References: Hertz, Lerchner, Ahmadi, q-bio.NC/ [Erice lectures]

Slide 1 Neuroscience: Exploring the Brain, 3rd Ed, Bear, Connors, and Paradiso Copyright © 2007 Lippincott Williams & Wilkins Bear: Neuroscience: Exploring.

Deriving connectivity patterns in the primary visual cortex from spontaneous neuronal activity and feature maps Barak Blumenfeld, Dmitri Bibitchkov, Shmuel.

DCM for ERPs/EFPs Clare Palmer & Elina Jacobs Expert: Dimitris Pinotsis.

Projects: 1.Predictive coding in balanced spiking networks (Erwan Ledoux). 2.Using Canonical Correlation Analysis (CCA) to analyse neural data (David Schulz).

Unsupervised learning

Lecture 9: Introduction to Neural Networks Refs: Dayan & Abbott, Ch 7 (Gerstner and Kistler, Chs 6, 7) D Amit & N Brunel, Cerebral Cortex 7, (1997)

Pencil-and-Paper Neural Networks Prof. Kevin Crisp St. Olaf College.

J. Daunizeau Wellcome Trust Centre for Neuroimaging, London, UK UZH – Foundations of Human Social Behaviour, Zurich, Switzerland Dynamic Causal Modelling:

The BCM theory of synaptic plasticity. The BCM theory of cortical plasticity BCM stands for Bienestock Cooper and Munro, it dates back to It was.

Dynamic Causal Modelling of Evoked Responses in EEG/MEG Wellcome Dept. of Imaging Neuroscience University College London Stefan Kiebel.

Artificial Neural Networks Students: Albu Alexandru Deaconescu Ionu.

Connecting neural mass models to functional imaging Olivier Faugeras, INRIA ● Basic neuroanatomy Basic neuroanatomy ● Neuronal circuits of the neocortex.

Complex brain networks: graph theoretical analysis of structural and functional systems.

Neural Networks Presented by M. Abbasi Course lecturer: Dr.Tohidkhah.

Fundamentals of Computational Neuroscience, T. P. Trappenberg, 2002.

The Unscented Particle Filter 2000/09/29 이 시은. Introduction Filtering –estimate the states(parameters or hidden variable) as a set of observations becomes.

Nens220, Lecture 11 Introduction to Realistic Neuronal Networks John Huguenard.

Spiking Neural Networks Banafsheh Rekabdar. Biological Neuron: The Elementary Processing Unit of the Brain.

Dynamic Causal Model for evoked responses in MEG/EEG Rosalyn Moran.

Biological Modeling of Neural Networks: Week 10 – Neuronal Populations Wulfram Gerstner EPFL, Lausanne, Switzerland 10.1 Cortical Populations - columns.

Bayesian inference Lee Harrison York Neuroimaging Centre 23 / 10 / 2009.

Basics of Computational Neuroscience. What is computational neuroscience ? The Interdisciplinary Nature of Computational Neuroscience.

Mean Field Methods for Computer and Communication Systems Jean-Yves Le Boudec EPFL Network Science Workshop Hong Kong July

DCM for ERP/ERF: theory and practice Melanie Boly Based on slides from Chris Phillips, Klaas Stephan and Stefan Kiebel.

Principles of Dynamic Causal Modelling

Diffusion over potential barriers with colored noise

Biointelligence Laboratory, Seoul National University

Neural Oscillations Continued

A principled way to principal components analysis

Dynamic Causal Model for evoked responses in M/EEG Rosalyn Moran.

? Dynamical properties of simulated MEG/EEG using a neural mass model

Post-Synaptic Events Graded vs Action Potentials

Computational models of epilepsy

Sensorimotor Learning and the Development of Position Invariance

OCNC Statistical Approach to Neural Learning and Population Coding ---- Introduction to Mathematical.

Introduction (2/2) in Adaptive Cooperative Systems by Martine Beckerman, ’ 7.10 B.-W. Ku.

Dynamic Causal Modelling for M/EEG

Quantum computation with classical bits

Dynamic Causal Modelling for evoked responses

Synaptic Connectivity and Neuronal Morphology

The canonical microcircuit.

Presentation transcript:

Mean Field Theories in Neuroscience B. Cessac, Neuromathcomp, INRIA

Cortical columns.

Small cylinders, of diameter 0.1~1mm, crossing cortex layers, with about neurons, from different types, strongly connected.

Cortical columns are involved in elementary sensori-motor like vision. Cortical columns.

They are composed of neurons belonging to a small number of populations interacting together. These populations belong to different cortex layers. Deep layers Layer IV Superficial layers Pyramidal Cells Inhibitory Cells Spiny Stellate Cells Thalamic Input Cortical columns.

Deep layers Layer IV Superficial layers Pyramidal Cells Inhibitory Cells Spiny Stellate Cells Thalamic Input It is possible and useful to propose phenomenological models characterizing the mesoscopic activity of cortical columns, predicting the behaviour of local field potential generated by the electric activity of neurons and to relate this behavior with measures and clinical observations (epilepsy). Cortical columns.

Cortical column paradigm Type of cortical column Definition Spatial scale Number of neurons Micro-column Mini-column Orientation column Macro-column or Hyper-column (V1) Neural Mass µm µm 600 µm (and more) 10 mm neuronsSeveral mini-columns mini-columns neurons 100XThousand neurons of the same type (pyr, stellate,…) OI pixel Our Column µm neurons Functional Anatomical Physico-functional Cortical Area Courtesy. S. Chemla.

Mean field models.

Neurons and synapses.

Pre-synaptic neuron j Post-synaptic neuron i

Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

Neurons and synapses. Pre-synaptic neuron j Post-synaptic neuron i

Neural mass model.

P populations of neurons, a =1... P

Neural mass model. Voltage-based model P populations of neurons, a =1... P

Neural mass model. Voltage-based model P populations of neurons, a =1... P Assumptions:

Neural mass model. Voltage-based model P populations of neurons, a =1... P Assumptions: Synapse response, current and noise depend only on the neuronal population.

Neural mass model. Voltage-based model P populations of neurons, a =1... P Assumptions: Synapse response, current and noise depend only on the neuronal population

Neural mass model. Voltage-based model P populations of neurons, a =1... P W W 32 W 23 W 31 W 21 Assumptions: Synapse response, current and noise depend only on the neuronal population.

Neural mass model. Voltage-based model P populations of neurons, a =1... P Synaptic weights Assumptions: Synapse response, current and noise depend only on the neuronal population. The probability distribution of synaptic efficacies depend only on pre- and post synaptic neuron' population W W 32 W 23 W 31 W 21 (independent)‏

Neural mass model. Voltage-based model P populations of neurons, a =1... P Assumptions: Synapse response, current and noise depend only on the neuronal population. The probability distribution of synaptic efficacies depend only on pre- and post synaptic neuron' population Synaptic weights (independent)‏

Dynamic mean-field theory.

Voltage-based model

Dynamic mean-field theory. Voltage-based model Stochastic (annealed)‏ Random (quenched)‏ Nonlinear

Dynamic mean-field theory. Voltage-based model

Dynamic mean-field theory. Voltage-based model

Dynamic mean-field theory. Voltage-based model Local interactions field.

Dynamic mean-field theory. Voltage-based model Local interactions field.

Dynamic mean-field theory. Voltage-based model Local interactions field. Non random synaptic weights.

Dynamic mean-field theory. Voltage-based model Local interactions field. Non random synaptic weights.

Dynamic mean-field theory. Voltage-based model Local interactions field. Non random synaptic weights.

Dynamic mean-field theory. Voltage-based model Local interactions field. Non random synaptic weights.

Dynamic mean-field theory. Voltage-based model Local interactions field. Non random synaptic weights. Dynamic mean-field equations.

Dynamic mean-field theory. Voltage-based model Local interactions field. Non random synaptic weights. Dynamic mean-field equations.

Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Naive mean-field equations. Local interactions field.

Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Naive mean-field equations. Local interactions field.

Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Naive mean-field equations. Local interactions field.

Dynamic mean-field theory. Voltage-based model Non random synaptic weights. Naive mean-field equations. Local interactions field. ?

Jansen-Ritt equations.

It is possible and useful to propose phenomenological models characterizing the mesoscopique activity of cortical columns, predicting the behaviour of local field potential generated by the electric activity of neurons and to relate this behavior with measures and clinical observations (epilepsy).

Jansen-Ritt equations. It is possible and useful to propose phenomenological models characterizing the mesoscopique activity of cortical columns, predicting the behaviour of local field potential generated by the electric activity of neurons and to relate this behavior with measures and clinical observations (epilepsy).

Jansen – Rit model (1995). Jansen-Ritt equations. It is possible and useful to propose phenomenological models characterizing the mesoscopique activity of cortical columns, predicting the behaviour of local field potential generated by the electric activity of neurons and to relate this behavior with measures and clinical observations (epilepsy).

Jansen – Rit model (1995). Jansen-Ritt equations. It is possible and useful to propose phenomenological models characterizing the mesoscopique activity of cortical columns, predicting the behaviour of local field potential generated by the electric activity of neurons and to relate this behavior with measures and clinical observations (epilepsy).

Bifurcation analysis Eigenvalues of the Jacobian of the dynamic system when the thalamic entry varies Some bifurcations of the system The bifurcations can predict neural behaviours Grimbert, Faugeras. Neural Computation 2006

Why is it working so well ?

Dynamic mean-field theory. Voltage-based model Local interaction field.

Dynamic mean-field theory. Voltage-based model Local interaction field. Random synaptic weights.

Dynamic mean-field theory. Voltage-based model Local interaction field. Random synaptic weights. Prop 1.  i is V-conditionally Gaussian with mean and covariance.

Dynamic mean-field theory. Voltage-based model Local interaction field. Random synaptic weights. DMFT

Dynamic mean-field theory. Voltage-based model Local interaction field. Random synaptic weights. DMFT where U ab is a Gaussian process with mean and covariance

Dynamic mean-field theory. Voltage-based model Local interaction field. Random synaptic weights. DMFT where U ab is a Gaussian process with mean and covariance Dynamic mean-field equations.

Dynamic mean-field theory. Simple model Random synaptic weights.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights.

Dynamic mean-field theory. Simple model Non random synaptic weights. Dynamic mean-field equations.

Dynamic mean-field theory. Simple model Non random synaptic weights. Dynamic mean-field equations.

Dynamic mean-field theory. Simple model Non random synaptic weights. Dynamic mean-field equations.

Dynamic mean-field theory. Simple model Non random synaptic weights. Dynamic mean-field equations.

Dynamic mean-field theory. Simple model Non random synaptic weights. Dynamic mean-field equations.

Dynamic mean-field theory. Simple model Non random synaptic weights. Dynamic mean-field equations.

Dynamic mean-field theory. Simple model Non random synaptic weights. Dynamic mean-field equations.

Dynamic mean-field theory. Simple model Non random synaptic weights. Dynamic mean-field equations. Naive mean-field equations.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights. Non Markovian process, depending on the whole past.

Dynamic mean-field theory. Simple model Dynamic mean-field equations. Random synaptic weights. Non Markovian process, depending on the whole past. Evolution is not ruled anymore by EDOs but by a mapping on a space of trajectories.

Dynamic mean-field theory. Voltage-based model Local interaction field. Random synaptic weights. Dynamic mean-field equations. Th. (Faugeras, Touboul, Cessac, 2008)‏

Dynamic mean-field theory. Voltage-based model Local interaction field. Random synaptic weights. Dynamic mean-field equations. Th. (Faugeras, Touboul, Cessac, 2008)‏ Existence and uniqueness of solutions in finite time. Existence and uniqueness of solutions in finite time.

Dynamic mean-field theory. Voltage-based model Local interaction field. Random synaptic weights. Dynamic mean-field equations. Th. (Faugeras, Touboul, Cessac, 2008)‏ Existence and uniqueness of solutions in finite time. Existence and uniqueness of solutions in finite time. Existence and uniqueness of stationary solutions in a specific region of the macroscopic parameters space. Existence and uniqueness of stationary solutions in a specific region of the macroscopic parameters space.

Dynamic mean-field theory. Voltage-based model Local interaction field. Random synaptic weights. Dynamic mean-field equations. Th. (Faugeras, Touboul, Cessac, 2008)‏ Existence and uniqueness of solutions in finite time. Existence and uniqueness of solutions in finite time. Existence and uniqueness of stationary solutions in a specific region of the macroscopic parameters space. Existence and uniqueness of stationary solutions in a specific region of the macroscopic parameters space. Constructive proof => Simulation algorithm. Constructive proof => Simulation algorithm.

Are there new and measurable effects here ?

How to study DMFT equations and their bifurcations ?

Are there new and measurable effects here ? How to study DMFT equations and their bifurcations ? What is synaptic weights are correlated ?