Circular symmetry of solutions of the neural field equation

Size: px
Start display at page:

Download "Circular symmetry of solutions of the neural field equation"

Transcription

1 Neural Field Dynamics Circular symmetry of solutions of the neural field equation take 287 Hecke Dynamically Selforganized Max Punk Institute Symposium on Nonlinear Glacier Dynamics 2005 in Zermatt

2 Neural Field Dynamics Outline Introduction Neural field equation The 1D-Case Extensions to 2D Arising problems Simplification of the interaction kernel Proof of circularity Conclusions Outlook

3 Neural Field Dynamics OK, OK! Just Kidding... Not again. And now for something (not completely) different!

4 Localization of Neural Activity a new episode Hecke Schrobsdorff, Vincent David, Joachim Hass, Marc Timme, Michael Herrmann, Theo Geisel Max Planck Institute for Dynamics and Selforganization Symposium on Nonlinear Dynamics 2005 in Zermatt

5 Outline 1 Introduction 2 Numerical Findings 3 Description of the Model 4 Existence of neural breathers 5 Recent results

6 Outline 1 Introduction 2 Numerical Findings 3 Description of the Model 4 Existence of neural breathers 5 Recent results

7 Outline 1 Introduction 2 Numerical Findings 3 Description of the Model 4 Existence of neural breathers 5 Recent results

8 Outline 1 Introduction 2 Numerical Findings 3 Description of the Model 4 Existence of neural breathers 5 Recent results

9 Outline 1 Introduction 2 Numerical Findings 3 Description of the Model 4 Existence of neural breathers 5 Recent results

10 Introduction Introduction Individual Units

11 Introduction Introduction Localized Excitations

12 Numerical Findings Motivation

13 Description of the Model Model of one unit v vth v vreset t Mirollo-Strogatz Neurons (here: leaky integrate and fire) resting potential v threshold potential v th refraction potential v reset

14 Description of the Model Network structure delta coupling spatial organization in a chain equal synaptic weights ǫ only to the two nearest neighbours, all excitatory ǫ ǫ ǫ ǫ synaptic delay τ v i 2 v i 1 v i v i+1 v i+2 network size arbitrary, only localized activations are of interest no learning

15 Description of the Model Network structure delta coupling spatial organization in a chain equal synaptic weights ǫ only to the two nearest neighbours, all excitatory ǫ ǫ ǫ ǫ synaptic delay τ v i 2 v i 1 v i v i+1 v i+2 network size arbitrary, only localized activations are of interest no learning

16 Description of the Model Network structure delta coupling spatial organization in a chain equal synaptic weights ǫ only to the two nearest neighbours, all excitatory ǫ ǫ ǫ ǫ synaptic delay τ v i 2 v i 1 v i v i+1 v i+2 network size arbitrary, only localized activations are of interest no learning

17 Existence of neural breathers Existence ( ) vreset v For τ > ln 1 + th v v th the spike-pattern below exists and is stable for [ 1 ( ǫ v th v + (v th v reset )e γ2τ) [,(1 e γτ )(v th v ) 2 unit τ 2τ 3τ 4τ time

18 Existence of neural breathers Proof v i vth1 v 1 vreset1 vth2 v 2 vreset2 vth3 v 3 vreset3 vth4 v 4 vreset4 vth5 v 5 vreset5 vth6 v 6 vreset6 vth7 v 7 vreset7 vth8 v 8 vreset8 τ 2τ 3τ t

19 Existence of neural breathers Return map Let the crossing of v th be preserved. Return map: ( ) ( ) ( t3,i+1 t3,i max(t3,i, t = F = 5,i ) + 2τ max(t 3,i, t 5,i ) + 2τ t 5,i+1 t 5,i ) This is already linear. No dependence of the concrete potentials because of the fix v reset

20 Existence of neural breathers Return map Let the crossing of v th be preserved. Return map: ( ) ( ) ( t3,i+1 t3,i max(t3,i, t = F = 5,i ) + 2τ max(t 3,i, t 5,i ) + 2τ t 5,i+1 t 5,i ) This is already linear. No dependence of the concrete potentials because of the fix v reset

21 Existence of neural breathers Return map Let the crossing of v th be preserved. Return map: ( ) ( ) ( t3,i+1 t3,i max(t3,i, t = F = 5,i ) + 2τ max(t 3,i, t 5,i ) + 2τ t 5,i+1 t 5,i ) This is already linear. No dependence of the concrete potentials because of the fix v reset

22 Existence of neural breathers Resynchronization v i vth3 v 3 vreset3 vth4 v 4 vreset4 vth5 v 5 vreset5 vth6 v 6 vreset6 τ τ + τ 2τ 2τ + τ 3τ + τ t

23 Recent results Larger patterns unit τ 2τ 3τ 4τ time

24 Recent results larger patterns v intern vthintern v intern vresetintern 3ǫ ǫ τ 2τ 3τ t t

25 Recent results No Resynchronization unit τ 2τ 3τ 4τ time

26 Outlook Outlook I A more general network structure should be considered (Hi Marc!). Inner neurons outer neurons boundary neurons

27 Outlook Outlook II With a good understanding of breezers, a simulational model of associating in PFC is imaginable (Hi Michael!). IT V4 PFC

28 Summary Summary Localized excitation is possible in very simple models. With leaky integrate n fire neurons their existence and stability can be investigated analytically.

Localized Excitations in Networks of Spiking Neurons

Localized Excitations in Networks of Spiking Neurons Localized Excitations in Networks of Spiking Neurons Hecke Schrobsdorff Bernstein Center for Computational Neuroscience Göttingen Max Planck Institute for Dynamics and Self-Organization Seminar: Irreversible

More information

Effects of Interactive Function Forms and Refractoryperiod in a Self-Organized Critical Model Based on Neural Networks

Effects of Interactive Function Forms and Refractoryperiod in a Self-Organized Critical Model Based on Neural Networks Commun. Theor. Phys. (Beijing, China) 42 (2004) pp. 121 125 c International Academic Publishers Vol. 42, No. 1, July 15, 2004 Effects of Interactive Function Forms and Refractoryperiod in a Self-Organized

More information

Balance of Electric and Diffusion Forces

Balance of Electric and Diffusion Forces Balance of Electric and Diffusion Forces Ions flow into and out of the neuron under the forces of electricity and concentration gradients (diffusion). The net result is a electric potential difference

More information

Computing with Inter-spike Interval Codes in Networks of Integrate and Fire Neurons

Computing with Inter-spike Interval Codes in Networks of Integrate and Fire Neurons Computing with Inter-spike Interval Codes in Networks of Integrate and Fire Neurons Dileep George a,b Friedrich T. Sommer b a Dept. of Electrical Engineering, Stanford University 350 Serra Mall, Stanford,

More information

Phase Response. 1 of of 11. Synaptic input advances (excitatory) or delays (inhibitory) spiking

Phase Response. 1 of of 11. Synaptic input advances (excitatory) or delays (inhibitory) spiking Printed from the Mathematica Help Browser 1 1 of 11 Phase Response Inward current-pulses decrease a cortical neuron's period (Cat, Layer V). [Fetz93] Synaptic input advances (excitatory) or delays (inhibitory)

More information

CSE/NB 528 Final Lecture: All Good Things Must. CSE/NB 528: Final Lecture

CSE/NB 528 Final Lecture: All Good Things Must. CSE/NB 528: Final Lecture CSE/NB 528 Final Lecture: All Good Things Must 1 Course Summary Where have we been? Course Highlights Where do we go from here? Challenges and Open Problems Further Reading 2 What is the neural code? What

More information

Consider the following spike trains from two different neurons N1 and N2:

Consider the following spike trains from two different neurons N1 and N2: About synchrony and oscillations So far, our discussions have assumed that we are either observing a single neuron at a, or that neurons fire independent of each other. This assumption may be correct in

More information

CISC 3250 Systems Neuroscience

CISC 3250 Systems Neuroscience CISC 3250 Systems Neuroscience Systems Neuroscience How the nervous system performs computations How groups of neurons work together to achieve intelligence Professor Daniel Leeds dleeds@fordham.edu JMH

More information

Most Probable Escape Path Method and its Application to Leaky Integrate And Fire Neurons

Most Probable Escape Path Method and its Application to Leaky Integrate And Fire Neurons Most Probable Escape Path Method and its Application to Leaky Integrate And Fire Neurons Simon Fugmann Humboldt University Berlin 13/02/06 Outline The Most Probable Escape Path (MPEP) Motivation General

More information

Effects of Interactive Function Forms in a Self-Organized Critical Model Based on Neural Networks

Effects of Interactive Function Forms in a Self-Organized Critical Model Based on Neural Networks Commun. Theor. Phys. (Beijing, China) 40 (2003) pp. 607 613 c International Academic Publishers Vol. 40, No. 5, November 15, 2003 Effects of Interactive Function Forms in a Self-Organized Critical Model

More information

Dynamical Synapses Give Rise to a Power-Law Distribution of Neuronal Avalanches

Dynamical Synapses Give Rise to a Power-Law Distribution of Neuronal Avalanches Dynamical Synapses Give Rise to a Power-Law Distribution of Neuronal Avalanches Anna Levina 3,4, J. Michael Herrmann 1,2, Theo Geisel 1,2,4 1 Bernstein Center for Computational Neuroscience Göttingen 2

More information

Decoding. How well can we learn what the stimulus is by looking at the neural responses?

Decoding. How well can we learn what the stimulus is by looking at the neural responses? Decoding How well can we learn what the stimulus is by looking at the neural responses? Two approaches: devise explicit algorithms for extracting a stimulus estimate directly quantify the relationship

More information

Computational Explorations in Cognitive Neuroscience Chapter 2

Computational Explorations in Cognitive Neuroscience Chapter 2 Computational Explorations in Cognitive Neuroscience Chapter 2 2.4 The Electrophysiology of the Neuron Some basic principles of electricity are useful for understanding the function of neurons. This is

More information

TIME-SEQUENTIAL SELF-ORGANIZATION OF HIERARCHICAL NEURAL NETWORKS. Ronald H. Silverman Cornell University Medical College, New York, NY 10021

TIME-SEQUENTIAL SELF-ORGANIZATION OF HIERARCHICAL NEURAL NETWORKS. Ronald H. Silverman Cornell University Medical College, New York, NY 10021 709 TIME-SEQUENTIAL SELF-ORGANIZATION OF HIERARCHICAL NEURAL NETWORKS Ronald H. Silverman Cornell University Medical College, New York, NY 10021 Andrew S. Noetzel polytechnic University, Brooklyn, NY 11201

More information

3 Detector vs. Computer

3 Detector vs. Computer 1 Neurons 1. The detector model. Also keep in mind this material gets elaborated w/the simulations, and the earliest material is often hardest for those w/primarily psych background. 2. Biological properties

More information

DEVS Simulation of Spiking Neural Networks

DEVS Simulation of Spiking Neural Networks DEVS Simulation of Spiking Neural Networks Rene Mayrhofer, Michael Affenzeller, Herbert Prähofer, Gerhard Höfer, Alexander Fried Institute of Systems Science Systems Theory and Information Technology Johannes

More information

Simple neuron model Components of simple neuron

Simple neuron model Components of simple neuron Outline 1. Simple neuron model 2. Components of artificial neural networks 3. Common activation functions 4. MATLAB representation of neural network. Single neuron model Simple neuron model Components

More information

(Feed-Forward) Neural Networks Dr. Hajira Jabeen, Prof. Jens Lehmann

(Feed-Forward) Neural Networks Dr. Hajira Jabeen, Prof. Jens Lehmann (Feed-Forward) Neural Networks 2016-12-06 Dr. Hajira Jabeen, Prof. Jens Lehmann Outline In the previous lectures we have learned about tensors and factorization methods. RESCAL is a bilinear model for

More information

Dynamical systems in neuroscience. Pacific Northwest Computational Neuroscience Connection October 1-2, 2010

Dynamical systems in neuroscience. Pacific Northwest Computational Neuroscience Connection October 1-2, 2010 Dynamical systems in neuroscience Pacific Northwest Computational Neuroscience Connection October 1-2, 2010 What do I mean by a dynamical system? Set of state variables Law that governs evolution of state

More information

Mathematical Models of Dynamic Behavior of Individual Neural Networks of Central Nervous System

Mathematical Models of Dynamic Behavior of Individual Neural Networks of Central Nervous System Mathematical Models of Dynamic Behavior of Individual Neural Networks of Central Nervous System Dimitra Despoina Pagania 1, Adam Adamopoulos 1,2 and Spiridon D. Likothanassis 1 1 Pattern Recognition Laboratory,

More information

Learning Spatio-Temporally Encoded Pattern Transformations in Structured Spiking Neural Networks 12

Learning Spatio-Temporally Encoded Pattern Transformations in Structured Spiking Neural Networks 12 Learning Spatio-Temporally Encoded Pattern Transformations in Structured Spiking Neural Networks 12 André Grüning, Brian Gardner and Ioana Sporea Department of Computer Science University of Surrey Guildford,

More information

Synchrony in Neural Systems: a very brief, biased, basic view

Synchrony in Neural Systems: a very brief, biased, basic view Synchrony in Neural Systems: a very brief, biased, basic view Tim Lewis UC Davis NIMBIOS Workshop on Synchrony April 11, 2011 components of neuronal networks neurons synapses connectivity cell type - intrinsic

More information

1 Balanced networks: Trading speed for noise

1 Balanced networks: Trading speed for noise Physics 178/278 - David leinfeld - Winter 2017 (Corrected yet incomplete notes) 1 Balanced networks: Trading speed for noise 1.1 Scaling of neuronal inputs An interesting observation is that the subthresold

More information

Neuron. Detector Model. Understanding Neural Components in Detector Model. Detector vs. Computer. Detector. Neuron. output. axon

Neuron. Detector Model. Understanding Neural Components in Detector Model. Detector vs. Computer. Detector. Neuron. output. axon Neuron Detector Model 1 The detector model. 2 Biological properties of the neuron. 3 The computational unit. Each neuron is detecting some set of conditions (e.g., smoke detector). Representation is what

More information

Stability of the splay state in pulse-coupled networks

Stability of the splay state in pulse-coupled networks Krakow August 2013 p. Stability of the splay state in pulse-coupled networks S. Olmi, A. Politi, and A. Torcini http://neuro.fi.isc.cnr.it/ Istituto dei Sistemi Complessi - CNR - Firenze Istituto Nazionale

More information

Probabilistic Models in Theoretical Neuroscience

Probabilistic Models in Theoretical Neuroscience Probabilistic Models in Theoretical Neuroscience visible unit Boltzmann machine semi-restricted Boltzmann machine restricted Boltzmann machine hidden unit Neural models of probabilistic sampling: introduction

More information

7 Rate-Based Recurrent Networks of Threshold Neurons: Basis for Associative Memory

7 Rate-Based Recurrent Networks of Threshold Neurons: Basis for Associative Memory Physics 178/278 - David Kleinfeld - Fall 2005; Revised for Winter 2017 7 Rate-Based Recurrent etworks of Threshold eurons: Basis for Associative Memory 7.1 A recurrent network with threshold elements The

More information

Information Theory and Neuroscience II

Information Theory and Neuroscience II John Z. Sun and Da Wang Massachusetts Institute of Technology October 14, 2009 Outline System Model & Problem Formulation Information Rate Analysis Recap 2 / 23 Neurons Neuron (denoted by j) I/O: via synapses

More information

Phase-locking in weakly heterogeneous neuronal networks

Phase-locking in weakly heterogeneous neuronal networks Physica D 118 (1998) 343 370 Phase-locking in weakly heterogeneous neuronal networks Carson C. Chow 1 Department of Mathematics and Center for BioDynamics, Boston University, Boston, MA 02215, USA Received

More information

Fast classification using sparsely active spiking networks. Hesham Mostafa Institute of neural computation, UCSD

Fast classification using sparsely active spiking networks. Hesham Mostafa Institute of neural computation, UCSD Fast classification using sparsely active spiking networks Hesham Mostafa Institute of neural computation, UCSD Artificial networks vs. spiking networks backpropagation output layer Multi-layer networks

More information

On the Dynamics of Delayed Neural Feedback Loops. Sebastian Brandt Department of Physics, Washington University in St. Louis

On the Dynamics of Delayed Neural Feedback Loops. Sebastian Brandt Department of Physics, Washington University in St. Louis On the Dynamics of Delayed Neural Feedback Loops Sebastian Brandt Department of Physics, Washington University in St. Louis Overview of Dissertation Chapter 2: S. F. Brandt, A. Pelster, and R. Wessel,

More information

Liquid Computing in a Simplified Model of Cortical Layer IV: Learning to Balance a Ball

Liquid Computing in a Simplified Model of Cortical Layer IV: Learning to Balance a Ball Liquid Computing in a Simplified Model of Cortical Layer IV: Learning to Balance a Ball Dimitri Probst 1,3, Wolfgang Maass 2, Henry Markram 1, and Marc-Oliver Gewaltig 1 1 Blue Brain Project, École Polytechnique

More information

Mathematical Methods for Neurosciences. ENS - Master MVA Paris 6 - Master Maths-Bio ( )

Mathematical Methods for Neurosciences. ENS - Master MVA Paris 6 - Master Maths-Bio ( ) Mathematical Methods for Neurosciences. ENS - Master MVA Paris 6 - Master Maths-Bio (2014-2015) Etienne Tanré - Olivier Faugeras INRIA - Team Tosca November 26th, 2014 E. Tanré (INRIA - Team Tosca) Mathematical

More information

Hopfield Neural Network and Associative Memory. Typical Myelinated Vertebrate Motoneuron (Wikipedia) Topic 3 Polymers and Neurons Lecture 5

Hopfield Neural Network and Associative Memory. Typical Myelinated Vertebrate Motoneuron (Wikipedia) Topic 3 Polymers and Neurons Lecture 5 Hopfield Neural Network and Associative Memory Typical Myelinated Vertebrate Motoneuron (Wikipedia) PHY 411-506 Computational Physics 2 1 Wednesday, March 5 1906 Nobel Prize in Physiology or Medicine.

More information

Simple Neural Nets for Pattern Classification: McCulloch-Pitts Threshold Logic CS 5870

Simple Neural Nets for Pattern Classification: McCulloch-Pitts Threshold Logic CS 5870 Simple Neural Nets for Pattern Classification: McCulloch-Pitts Threshold Logic CS 5870 Jugal Kalita University of Colorado Colorado Springs Fall 2014 Logic Gates and Boolean Algebra Logic gates are used

More information

Ranking Neurons for Mining Structure-Activity Relations in Biological Neural Networks: NeuronRank

Ranking Neurons for Mining Structure-Activity Relations in Biological Neural Networks: NeuronRank Ranking Neurons for Mining Structure-Activity Relations in Biological Neural Networks: NeuronRank Tayfun Gürel a,b,1, Luc De Raedt a,b, Stefan Rotter a,c a Bernstein Center for Computational Neuroscience,

More information

Mathematical Models of Dynamic Behavior of Individual Neural Networks of Central Nervous System

Mathematical Models of Dynamic Behavior of Individual Neural Networks of Central Nervous System Mathematical Models of Dynamic Behavior of Individual Neural Networks of Central Nervous System Dimitra-Despoina Pagania,*, Adam Adamopoulos,2, and Spiridon D. Likothanassis Pattern Recognition Laboratory,

More information

7 Recurrent Networks of Threshold (Binary) Neurons: Basis for Associative Memory

7 Recurrent Networks of Threshold (Binary) Neurons: Basis for Associative Memory Physics 178/278 - David Kleinfeld - Winter 2019 7 Recurrent etworks of Threshold (Binary) eurons: Basis for Associative Memory 7.1 The network The basic challenge in associative networks, also referred

More information

Supporting Online Material for

Supporting Online Material for www.sciencemag.org/cgi/content/full/319/5869/1543/dc1 Supporting Online Material for Synaptic Theory of Working Memory Gianluigi Mongillo, Omri Barak, Misha Tsodyks* *To whom correspondence should be addressed.

More information

Basic elements of neuroelectronics -- membranes -- ion channels -- wiring

Basic elements of neuroelectronics -- membranes -- ion channels -- wiring Computing in carbon Basic elements of neuroelectronics -- membranes -- ion channels -- wiring Elementary neuron models -- conductance based -- modelers alternatives Wires -- signal propagation -- processing

More information

Causality and communities in neural networks

Causality and communities in neural networks Causality and communities in neural networks Leonardo Angelini, Daniele Marinazzo, Mario Pellicoro, Sebastiano Stramaglia TIRES-Center for Signal Detection and Processing - Università di Bari, Bari, Italy

More information

Synchrony in Stochastic Pulse-coupled Neuronal Network Models

Synchrony in Stochastic Pulse-coupled Neuronal Network Models Synchrony in Stochastic Pulse-coupled Neuronal Network Models Katie Newhall Gregor Kovačič and Peter Kramer Aaditya Rangan and David Cai 2 Rensselaer Polytechnic Institute, Troy, New York 2 Courant Institute,

More information

Short Term Memory and Pattern Matching with Simple Echo State Networks

Short Term Memory and Pattern Matching with Simple Echo State Networks Short Term Memory and Pattern Matching with Simple Echo State Networks Georg Fette (fette@in.tum.de), Julian Eggert (julian.eggert@honda-ri.de) Technische Universität München; Boltzmannstr. 3, 85748 Garching/München,

More information

Basic elements of neuroelectronics -- membranes -- ion channels -- wiring. Elementary neuron models -- conductance based -- modelers alternatives

Basic elements of neuroelectronics -- membranes -- ion channels -- wiring. Elementary neuron models -- conductance based -- modelers alternatives Computing in carbon Basic elements of neuroelectronics -- membranes -- ion channels -- wiring Elementary neuron models -- conductance based -- modelers alternatives Wiring neurons together -- synapses

More information

Fast neural network simulations with population density methods

Fast neural network simulations with population density methods Fast neural network simulations with population density methods Duane Q. Nykamp a,1 Daniel Tranchina b,a,c,2 a Courant Institute of Mathematical Science b Department of Biology c Center for Neural Science

More information

Heteroclinic cycles between unstable attractors

Heteroclinic cycles between unstable attractors Heteroclinic cycles between unstable attractors Henk Broer, Konstantinos Efstathiou and Easwar Subramanian Institute of Mathematics and Computer Science, University of Groningen, P.O. 800, 9700 AV Groningen,

More information

Reducing neuronal networks to discrete dynamics

Reducing neuronal networks to discrete dynamics Physica D 237 (2008) 324 338 www.elsevier.com/locate/physd Reducing neuronal networks to discrete dynamics David Terman a,b,, Sungwoo Ahn a, Xueying Wang a, Winfried Just c a Department of Mathematics,

More information

Tuning tuning curves. So far: Receptive fields Representation of stimuli Population vectors. Today: Contrast enhancment, cortical processing

Tuning tuning curves. So far: Receptive fields Representation of stimuli Population vectors. Today: Contrast enhancment, cortical processing Tuning tuning curves So far: Receptive fields Representation of stimuli Population vectors Today: Contrast enhancment, cortical processing Firing frequency N 3 s max (N 1 ) = 40 o N4 N 1 N N 5 2 s max

More information

Fast and exact simulation methods applied on a broad range of neuron models

Fast and exact simulation methods applied on a broad range of neuron models Fast and exact simulation methods applied on a broad range of neuron models Michiel D Haene michiel.dhaene@ugent.be Benjamin Schrauwen benjamin.schrauwen@ugent.be Ghent University, Electronics and Information

More information

Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components

Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components John Z. Sun Massachusetts Institute of Technology September 21, 2011 Outline Automata Theory Error in Automata Controlling

More information

Synaptic dynamics. John D. Murray. Synaptic currents. Simple model of the synaptic gating variable. First-order kinetics

Synaptic dynamics. John D. Murray. Synaptic currents. Simple model of the synaptic gating variable. First-order kinetics Synaptic dynamics John D. Murray A dynamical model for synaptic gating variables is presented. We use this to study the saturation of synaptic gating at high firing rate. Shunting inhibition and the voltage

More information

Introduction Biologically Motivated Crude Model Backpropagation

Introduction Biologically Motivated Crude Model Backpropagation Introduction Biologically Motivated Crude Model Backpropagation 1 McCulloch-Pitts Neurons In 1943 Warren S. McCulloch, a neuroscientist, and Walter Pitts, a logician, published A logical calculus of the

More information

Comparison of receptive fields to polar and Cartesian stimuli computed with two kinds of models

Comparison of receptive fields to polar and Cartesian stimuli computed with two kinds of models Supplemental Material Comparison of receptive fields to polar and Cartesian stimuli computed with two kinds of models Motivation The purpose of this analysis is to verify that context dependent changes

More information

Exploring a Simple Discrete Model of Neuronal Networks

Exploring a Simple Discrete Model of Neuronal Networks Exploring a Simple Discrete Model of Neuronal Networks Winfried Just Ohio University Joint work with David Terman, Sungwoo Ahn,and Xueying Wang August 6, 2010 An ODE Model of Neuronal Networks by Terman

More information

Neural Networks. Fundamentals of Neural Networks : Architectures, Algorithms and Applications. L, Fausett, 1994

Neural Networks. Fundamentals of Neural Networks : Architectures, Algorithms and Applications. L, Fausett, 1994 Neural Networks Neural Networks Fundamentals of Neural Networks : Architectures, Algorithms and Applications. L, Fausett, 1994 An Introduction to Neural Networks (nd Ed). Morton, IM, 1995 Neural Networks

More information

Problems of neural field dynamics in two dimensions

Problems of neural field dynamics in two dimensions Problems of neural field dynamics in two dimensions Hecke Schrobsdorff hecke@chaos.gwdg.de MPI für Strömungsforschung Göttingen neural field dynamics p.1 Neural Fields? In 1977 Amari founded the theory

More information

Introduction to Neural Networks

Introduction to Neural Networks Introduction to Neural Networks What are (Artificial) Neural Networks? Models of the brain and nervous system Highly parallel Process information much more like the brain than a serial computer Learning

More information

Artifical Neural Networks

Artifical Neural Networks Neural Networks Artifical Neural Networks Neural Networks Biological Neural Networks.................................. Artificial Neural Networks................................... 3 ANN Structure...........................................

More information

IN THIS turorial paper we exploit the relationship between

IN THIS turorial paper we exploit the relationship between 508 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 10, NO. 3, MAY 1999 Weakly Pulse-Coupled Oscillators, FM Interactions, Synchronization, Oscillatory Associative Memory Eugene M. Izhikevich Abstract We study

More information

Dendritic cable with active spines: a modelling study in the spike-diffuse-spike framework

Dendritic cable with active spines: a modelling study in the spike-diffuse-spike framework Dendritic cable with active spines: a modelling study in the spike-diffuse-spike framework Yulia Timofeeva a, Gabriel Lord a and Stephen Coombes b a Department of Mathematics, Heriot-Watt University, Edinburgh,

More information

Synfire Waves in Small Balanced Networks

Synfire Waves in Small Balanced Networks Synfire Waves in Small Balanced Networks Yuval Aviel 1,3, David Horn 2 and Moshe Abeles 1 1 Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem, Israel. 2 School of Physics and

More information

Discrete and Indiscrete Models of Biological Networks

Discrete and Indiscrete Models of Biological Networks Discrete and Indiscrete Models of Biological Networks Winfried Just Ohio University November 17, 2010 Who are we? What are we doing here? Who are we? What are we doing here? A population of interacting

More information

Neural networks. Chapter 19, Sections 1 5 1

Neural networks. Chapter 19, Sections 1 5 1 Neural networks Chapter 19, Sections 1 5 Chapter 19, Sections 1 5 1 Outline Brains Neural networks Perceptrons Multilayer perceptrons Applications of neural networks Chapter 19, Sections 1 5 2 Brains 10

More information

Neuromorphic Sensing and Control of Autonomous Micro-Aerial Vehicles

Neuromorphic Sensing and Control of Autonomous Micro-Aerial Vehicles Neuromorphic Sensing and Control of Autonomous Micro-Aerial Vehicles Commercialization Fellowship Technical Presentation Taylor Clawson Ithaca, NY June 12, 2018 About Me: Taylor Clawson 3 rd year PhD student

More information

Synchrony and Desynchrony in Integrate-and-Fire Oscillators

Synchrony and Desynchrony in Integrate-and-Fire Oscillators LETTER Communicated by David Terman Synchrony and Desynchrony in Integrate-and-Fire Oscillators Shannon R. Campbell Department of Physics, The Ohio State University, Columbus, Ohio 43210, U.S.A. DeLiang

More information

Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops

Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops Math. Model. Nat. Phenom. Vol. 5, No. 2, 2010, pp. 67-99 DOI: 10.1051/mmnp/20105203 Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops J. Ma 1 and J. Wu 2 1 Department of

More information

Predicting Synchrony in Heterogeneous Pulse Coupled Oscillators

Predicting Synchrony in Heterogeneous Pulse Coupled Oscillators Predicting Synchrony in Heterogeneous Pulse Coupled Oscillators Sachin S. Talathi 1, Dong-Uk Hwang 1, Abraham Miliotis 1, Paul R. Carney 1, and William L. Ditto 1 1 J Crayton Pruitt Department of Biomedical

More information

Linear Algebra for Time Series of Spikes

Linear Algebra for Time Series of Spikes Linear Algebra for Time Series of Spikes Andrew Carnell and Daniel Richardson University of Bath - Department of Computer Science Bath - UK Abstract. The set of time series of spikes is expanded into a

More information

Neural Networks: Basics. Darrell Whitley Colorado State University

Neural Networks: Basics. Darrell Whitley Colorado State University Neural Networks: Basics Darrell Whitley Colorado State University In the Beginning: The Perceptron X1 W W 1,1 1,2 X2 W W 2,1 2,2 W source, destination In the Beginning: The Perceptron The Perceptron Learning

More information

Lecture 16: Introduction to Neural Networks

Lecture 16: Introduction to Neural Networks Lecture 16: Introduction to Neural Networs Instructor: Aditya Bhasara Scribe: Philippe David CS 5966/6966: Theory of Machine Learning March 20 th, 2017 Abstract In this lecture, we consider Bacpropagation,

More information

Nonlinear systems, chaos and control in Engineering

Nonlinear systems, chaos and control in Engineering Nonlinear systems, chaos and control in Engineering Module 1 block 3 One-dimensional nonlinear systems Cristina Masoller Cristina.masoller@upc.edu http://www.fisica.edu.uy/~cris/ Schedule Flows on the

More information

Neural networks. Chapter 20. Chapter 20 1

Neural networks. Chapter 20. Chapter 20 1 Neural networks Chapter 20 Chapter 20 1 Outline Brains Neural networks Perceptrons Multilayer networks Applications of neural networks Chapter 20 2 Brains 10 11 neurons of > 20 types, 10 14 synapses, 1ms

More information

Locust Olfaction. Synchronous Oscillations in Excitatory and Inhibitory Groups of Spiking Neurons. David C. Sterratt

Locust Olfaction. Synchronous Oscillations in Excitatory and Inhibitory Groups of Spiking Neurons. David C. Sterratt Locust Olfaction Synchronous Oscillations in Excitatory and Inhibitory Groups of Spiking Neurons David C. Sterratt Institute for Adaptive and Neural Computation, Division of Informatics, University of

More information

Neurophysiology of a VLSI spiking neural network: LANN21

Neurophysiology of a VLSI spiking neural network: LANN21 Neurophysiology of a VLSI spiking neural network: LANN21 Stefano Fusi INFN, Sezione Roma I Università di Roma La Sapienza Pza Aldo Moro 2, I-185, Roma fusi@jupiter.roma1.infn.it Paolo Del Giudice Physics

More information

CONTINUOUS TIME CORRELATION ANALYSIS TECHNIQUES FOR SPIKE TRAINS

CONTINUOUS TIME CORRELATION ANALYSIS TECHNIQUES FOR SPIKE TRAINS CONTINUOUS TIME CORRELATION ANALYSIS TECHNIQUES FOR SPIKE TRAINS By IL PARK A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE

More information

Artificial neural networks

Artificial neural networks Artificial neural networks Chapter 8, Section 7 Artificial Intelligence, spring 203, Peter Ljunglöf; based on AIMA Slides c Stuart Russel and Peter Norvig, 2004 Chapter 8, Section 7 Outline Brains Neural

More information

Lecture IV: LTI models of physical systems

Lecture IV: LTI models of physical systems BME 171: Signals and Systems Duke University September 5, 2008 This lecture Plan for the lecture: 1 Interconnections of linear systems 2 Differential equation models of LTI systems 3 eview of linear circuit

More information

Single Neuron Dynamics for Retaining and Destroying Network Information?

Single Neuron Dynamics for Retaining and Destroying Network Information? Single Neuron Dynamics for Retaining and Destroying Network Information? Michael Monteforte, Tatjana Tchumatchenko, Wei Wei & F. Wolf Bernstein Center for Computational Neuroscience and Faculty of Physics

More information

Neural networks. Chapter 20, Section 5 1

Neural networks. Chapter 20, Section 5 1 Neural networks Chapter 20, Section 5 Chapter 20, Section 5 Outline Brains Neural networks Perceptrons Multilayer perceptrons Applications of neural networks Chapter 20, Section 5 2 Brains 0 neurons of

More information

Supplementary information for:

Supplementary information for: Supplementary information for: Synaptic polarity of the interneuron circuit controlling C. elegans locomotion Franciszek Rakowski a, Jagan Srinivasan b, Paul W. Sternberg b, and Jan Karbowski c,d a Interdisciplinary

More information

Neural Networks. Chapter 18, Section 7. TB Artificial Intelligence. Slides from AIMA 1/ 21

Neural Networks. Chapter 18, Section 7. TB Artificial Intelligence. Slides from AIMA   1/ 21 Neural Networks Chapter 8, Section 7 TB Artificial Intelligence Slides from AIMA http://aima.cs.berkeley.edu / 2 Outline Brains Neural networks Perceptrons Multilayer perceptrons Applications of neural

More information

Neural Networks 1 Synchronization in Spiking Neural Networks

Neural Networks 1 Synchronization in Spiking Neural Networks CS 790R Seminar Modeling & Simulation Neural Networks 1 Synchronization in Spiking Neural Networks René Doursat Department of Computer Science & Engineering University of Nevada, Reno Spring 2006 Synchronization

More information

Systems Biology: A Personal View IX. Landscapes. Sitabhra Sinha IMSc Chennai

Systems Biology: A Personal View IX. Landscapes. Sitabhra Sinha IMSc Chennai Systems Biology: A Personal View IX. Landscapes Sitabhra Sinha IMSc Chennai Fitness Landscapes Sewall Wright pioneered the description of how genotype or phenotypic fitness are related in terms of a fitness

More information

Event-driven simulations of nonlinear integrate-and-fire neurons

Event-driven simulations of nonlinear integrate-and-fire neurons Event-driven simulations of nonlinear integrate-and-fire neurons A. Tonnelier, H. Belmabrouk, D. Martinez Cortex Project, LORIA, Campus Scientifique, B.P. 239, 54 56 Vandoeuvre-lès-Nancy, France Abstract

More information

Evolving multi-segment super-lamprey CPG s for increased swimming control

Evolving multi-segment super-lamprey CPG s for increased swimming control Evolving multi-segment super-lamprey CPG s for increased swimming control Leena N. Patel 1 and Alan Murray 1 and John Hallam 2 1- School of Engineering and Electronics, The University of Edinburgh, Kings

More information

W (x) W (x) (b) (a) 1 N

W (x) W (x) (b) (a) 1 N Delay Adaptation in the Nervous System Christian W. Eurich a, Klaus Pawelzik a, Udo Ernst b, Andreas Thiel a, Jack D. Cowan c and John G. Milton d a Institut fur Theoretische Physik, Universitat Bremen,

More information

arxiv: v1 [q-bio.nc] 13 Feb 2018

arxiv: v1 [q-bio.nc] 13 Feb 2018 Gain control with A-type potassium current: I A as a switch between divisive and subtractive inhibition Joshua H Goldwyn 1*, Bradley R Slabe 2, Joseph B Travers 3, David Terman 2 arxiv:182.4794v1 [q-bio.nc]

More information

Neural Coding: Integrate-and-Fire Models of Single and Multi-Neuron Responses

Neural Coding: Integrate-and-Fire Models of Single and Multi-Neuron Responses Neural Coding: Integrate-and-Fire Models of Single and Multi-Neuron Responses Jonathan Pillow HHMI and NYU http://www.cns.nyu.edu/~pillow Oct 5, Course lecture: Computational Modeling of Neuronal Systems

More information

How do synapses transform inputs?

How do synapses transform inputs? Neurons to networks How do synapses transform inputs? Excitatory synapse Input spike! Neurotransmitter release binds to/opens Na channels Change in synaptic conductance! Na+ influx E.g. AMA synapse! Depolarization

More information

neural networks Balázs B Ujfalussy 17 october, 2016 idegrendszeri modellezés 2016 október 17.

neural networks Balázs B Ujfalussy 17 october, 2016 idegrendszeri modellezés 2016 október 17. neural networks Balázs B Ujfalussy 17 october, 2016 Hierarchy of the nervous system behaviour idegrendszeri modellezés 1m CNS 10 cm systems 1 cm maps 1 mm networks 100 μm neurons 1 μm synapses 10 nm molecules

More information

High-conductance states in a mean-eld cortical network model

High-conductance states in a mean-eld cortical network model Neurocomputing 58 60 (2004) 935 940 www.elsevier.com/locate/neucom High-conductance states in a mean-eld cortical network model Alexander Lerchner a;, Mandana Ahmadi b, John Hertz b a Oersted-DTU, Technical

More information

Dendritic computation

Dendritic computation Dendritic computation Dendrites as computational elements: Passive contributions to computation Active contributions to computation Examples Geometry matters: the isopotential cell Injecting current I

More information

Computing with inter-spike interval codes in networks ofintegrate and fire neurons

Computing with inter-spike interval codes in networks ofintegrate and fire neurons Neurocomputing 65 66 (2005) 415 420 www.elsevier.com/locate/neucom Computing with inter-spike interval codes in networks ofintegrate and fire neurons Dileep George a,b,, Friedrich T. Sommer b a Department

More information

Scalable Inference for Neuronal Connectivity from Calcium Imaging

Scalable Inference for Neuronal Connectivity from Calcium Imaging Scalable Inference for Neuronal Connectivity from Calcium Imaging Alyson K. Fletcher Sundeep Rangan Abstract Fluorescent calcium imaging provides a potentially powerful tool for inferring connectivity

More information

The Application of Extreme Learning Machine based on Gaussian Kernel in Image Classification

The Application of Extreme Learning Machine based on Gaussian Kernel in Image Classification he Application of Extreme Learning Machine based on Gaussian Kernel in Image Classification Weijie LI, Yi LIN Postgraduate student in College of Survey and Geo-Informatics, tongji university Email: 1633289@tongji.edu.cn

More information

SpikeAnts, a spiking neuron network modelling the emergence of organization in a complex system

SpikeAnts, a spiking neuron network modelling the emergence of organization in a complex system SpikeAnts, a spiking neuron network modelling the emergence of organization in a complex system Sylvain Chevallier TAO, INRIA-Saclay Univ. Paris-Sud F-9145 Orsay, France sylchev@lri.fr Hélène Paugam-Moisy

More information

COMS 4771 Introduction to Machine Learning. Nakul Verma

COMS 4771 Introduction to Machine Learning. Nakul Verma COMS 4771 Introduction to Machine Learning Nakul Verma Announcements HW1 due next lecture Project details are available decide on the group and topic by Thursday Last time Generative vs. Discriminative

More information

The NEURON simulation environment Networks and more. Michael Rudolph

The NEURON simulation environment Networks and more. Michael Rudolph The NEURON simulation environment Networks and more Michael Rudolph Advanced Course in Computational Neuroscience Obidos, Portugal, 2004 References web: http://www.neuron.yale.edu/ http://neuron.duke.edu/

More information

Neuronal Dynamics: Computational Neuroscience of Single Neurons

Neuronal Dynamics: Computational Neuroscience of Single Neurons Week 4 part 5: Nonlinear Integrate-and-Fire Model 4.1 From Hodgkin-Huxley to 2D Neuronal Dynamics: Computational Neuroscience of Single Neurons Week 4 Recing detail: Two-dimensional neuron models Wulfram

More information

At the Edge of Chaos: Real-time Computations and Self-Organized Criticality in Recurrent Neural Networks

At the Edge of Chaos: Real-time Computations and Self-Organized Criticality in Recurrent Neural Networks At the Edge of Chaos: Real-time Computations and Self-Organized Criticality in Recurrent Neural Networks Thomas Natschläger Software Competence Center Hagenberg A-4232 Hagenberg, Austria Thomas.Natschlaeger@scch.at

More information