Membrane equation. VCl. dv dt + V = V Na G Na + V K G K + V Cl G Cl. G total. C m. G total = G Na + G K + G Cl
|
|
|
- Domenic Davidson
- 5 years ago
- Views:
Transcription
1 Spiking neurons
2
3 Membrane equation V GNa GK GCl Cm VNa VK VCl dv dt + V = V Na G Na + V K G K + V Cl G Cl G total G total = G Na + G K + G Cl = C m G total
4 Membrane with synaptic inputs V Gleak GNa GK GCl Cm Vr VNa VK VCl dv dt + V = V r G leak + V Na G Na + V K G K + V Cl G Cl G total G total = G leak + G Na + G K + G Cl = C m G total
5 Membrane with input current V Gleak Cm Iin(t) Vr dv dt + V = V r + 1 G leak I in (t) G leak = G Na + G K + G Cl = C m G leak
6 Voltage-gated channels
7 Leaky integrate-and-fire neuron
8 Rate coding hypothesis: the signal conveyed by a neuron is in the rate of spiking. Spiking irregularity is largely due to noise and does not convey information.
9 <latexit sha1_base64="wiq25kysmvpmeyabrzs69may+ik=">aaacexicbvdns8mwhe3n15xfvy9eokoyonkkobdh6mxjbpcbazfsnn3c0rqkqtbk/wuv/itepcji1zs3/xvtrqfdfbb4ee/3sh7pixmvyrk+jdlc4tlysnm1sra+sbllbu+0zjqitjo4yphoeegsrjlpkqoy6csconbjpo2nbnk//ucepbg/v+oyuceacbpqjjsw+matuenhv04gee4dpnm+6nhnmptsk+kazsnfzyp9s2qdwhpaewixpaoknprml+nhoakjv5ghkbu2fss3rujrzehwcrjjyorhaec6mniueummk40yekgvhwar0icroff/j1iusjkopt0zijwus14u/ud1exvcuinlcaiix9ohgorbfcg8huhtqbbiy00qflt/feih0u0oxwjegj278jxpnz3amt+dv+vxrr1lsacoqa3y4aluws1ogcba4be8g1fwzjwzl8a78tedlrlfzhf8gfh5a2ainl4=</latexit> <latexit sha1_base64="wiq25kysmvpmeyabrzs69may+ik=">aaacexicbvdns8mwhe3n15xfvy9eokoyonkkobdh6mxjbpcbazfsnn3c0rqkqtbk/wuv/itepcji1zs3/xvtrqfdfbb4ee/3sh7pixmvyrk+jdlc4tlysnm1sra+sbllbu+0zjqitjo4yphoeegsrjlpkqoy6csconbjpo2nbnk//ucepbg/v+oyuceacbpqjjsw+matuenhv04gee4dpnm+6nhnmptsk+kazsnfzyp9s2qdwhpaewixpaoknprml+nhoakjv5ghkbu2fss3rujrzehwcrjjyorhaec6mniueummk40yekgvhwar0icroff/j1iusjkopt0zijwus14u/ud1exvcuinlcaiix9ohgorbfcg8huhtqbbiy00qflt/feih0u0oxwjegj278jxpnz3amt+dv+vxrr1lsacoqa3y4aluws1ogcba4be8g1fwzjwzl8a78tedlrlfzhf8gfh5a2ainl4=</latexit> <latexit sha1_base64="wiq25kysmvpmeyabrzs69may+ik=">aaacexicbvdns8mwhe3n15xfvy9eokoyonkkobdh6mxjbpcbazfsnn3c0rqkqtbk/wuv/itepcji1zs3/xvtrqfdfbb4ee/3sh7pixmvyrk+jdlc4tlysnm1sra+sbllbu+0zjqitjo4yphoeegsrjlpkqoy6csconbjpo2nbnk//ucepbg/v+oyuceacbpqjjsw+matuenhv04gee4dpnm+6nhnmptsk+kazsnfzyp9s2qdwhpaewixpaoknprml+nhoakjv5ghkbu2fss3rujrzehwcrjjyorhaec6mniueummk40yekgvhwar0icroff/j1iusjkopt0zijwus14u/ud1exvcuinlcaiix9ohgorbfcg8huhtqbbiy00qflt/feih0u0oxwjegj278jxpnz3amt+dv+vxrr1lsacoqa3y4aluws1ogcba4be8g1fwzjwzl8a78tedlrlfzhf8gfh5a2ainl4=</latexit> <latexit sha1_base64="wiq25kysmvpmeyabrzs69may+ik=">aaacexicbvdns8mwhe3n15xfvy9eokoyonkkobdh6mxjbpcbazfsnn3c0rqkqtbk/wuv/itepcji1zs3/xvtrqfdfbb4ee/3sh7pixmvyrk+jdlc4tlysnm1sra+sbllbu+0zjqitjo4yphoeegsrjlpkqoy6csconbjpo2nbnk//ucepbg/v+oyuceacbpqjjsw+matuenhv04gee4dpnm+6nhnmptsk+kazsnfzyp9s2qdwhpaewixpaoknprml+nhoakjv5ghkbu2fss3rujrzehwcrjjyorhaec6mniueummk40yekgvhwar0icroff/j1iusjkopt0zijwus14u/ud1exvcuinlcaiix9ohgorbfcg8huhtqbbiy00qflt/feih0u0oxwjegj278jxpnz3amt+dv+vxrr1lsacoqa3y4aluws1ogcba4be8g1fwzjwzl8a78tedlrlfzhf8gfh5a2ainl4=</latexit> Linear - non-linear - Poisson (LNP) model s(t) (t) P (n) = n e n! P (n) n
10 Fly H1 neuron - constant stimulus (de Ruyter et al., 1997) val histogram describing the probability density, ( ), of finding an interspike
11 Fly H1 neuron - time-varying stimulus (de Ruyter et al., 1997)
12 Spike timing can be very precise in response to time-varying signals Mainen & Sejnowski (1995)
13 Spike timing can be very precise in response to time-varying signals MT neuron response to stochastic moving dot stimuli at different levels of coherence (Newsom lab) Analysis by Bair & Koch (1996)
14
15 Neural encoding and decoding
16 Encoding and decoding are related through the joint distribution over stimulus and response h i 0-20 v av (omm/s) n av n v (omm/s) f g v av (n) n v n av (v) 0 decoding d P(v n) P(n v) e encoding v 20 P(n,v) c n 0 P(v) P(n) a v n 0 b (from Spikes)
17 s(t) sensory system stimulus (t) spike train ŝ(t) estimation algorithm estimate From Spikes, by Rieke, Warland, de Ruyter, & Bialek
18 Reconstruction kernel filter amplitude ( /s) a time (ms) Fly H1 neuron response response b Stimulus reconstruction c ŝ(t) = (t) k(t) ˆk(t) = arg min k(t) D [s(t) (t) k(t)] 2E t velocity ( /s) From Spikes, by Rieke, Warland, de Ruyter, & Bialek time (ms)
19 Strategy for estimating information rate 1. Estimate signal from spikes (t)! ŝ(t) 2. Compute noise in estimate ñ(!) = s(!) ˆ s(!) 3. Compute SNR SNR(!) = h s(!) 2 i h ñ(!) 2 i 4. Calculate lower bound to information rate from SNR R = 1 2 Z d! 2 log 2[1 + SNR(!)] Adapted from Spikes, by Rieke, Warland, de Ruyter, & Bialek
20 Coding by on- and off-cells
21 off cell on cell
22 Neural responses are half-wave rectified (action potentials are positive-only). Signals are thus combined in a push-pull fashion, similar to push-pull amplifiers. From: Neural Engineering, by Eliasmith & Anderson
23 Push-Pull decoding
24 Efficient coding model of retina (Karklin & Simoncelli 2012) Objective function: X I(X; R) j hr j i j a b ON center OFF center c
encoding and estimation bottleneck and limits to visual fidelity
Retina Light Optic Nerve photoreceptors encoding and estimation bottleneck and limits to visual fidelity interneurons ganglion cells light The Neural Coding Problem s(t) {t i } Central goals for today:
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
Information Theory. Mark van Rossum. January 24, School of Informatics, University of Edinburgh 1 / 35
1 / 35 Information Theory Mark van Rossum School of Informatics, University of Edinburgh January 24, 2018 0 Version: January 24, 2018 Why information theory 2 / 35 Understanding the neural code. Encoding
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
Synaptic Input. Linear Model of Synaptic Transmission. Professor David Heeger. September 5, 2000
Synaptic Input Professor David Heeger September 5, 2000 The purpose of this handout is to go a bit beyond the discussion in Ch. 6 of The Book of Genesis on synaptic input, and give some examples of how
1/12/2017. Computational neuroscience. Neurotechnology.
Computational neuroscience Neurotechnology https://devblogs.nvidia.com/parallelforall/deep-learning-nutshell-core-concepts/ 1 Neurotechnology http://www.lce.hut.fi/research/cogntech/neurophysiology Recording
Computational Neuroscience Summer School Neural Spike Train Analysis. An introduction to biophysical models (Part 2)
Computational Neuroscience Summer School Neural Spike Train Analysis Instructor: Mark Kramer Boston University An introduction to biophysical models (Part 2 SAMSI Short Course 2015 1 Goal: Model this,
The homogeneous Poisson process
The homogeneous Poisson process during very short time interval Δt there is a fixed probability of an event (spike) occurring independent of what happened previously if r is the rate of the Poisson process,
Model neurons!!poisson neurons!
Model neurons!!poisson neurons! Suggested reading:! Chapter 1.4 in Dayan, P. & Abbott, L., heoretical Neuroscience, MI Press, 2001.! Model neurons: Poisson neurons! Contents: Probability of a spike sequence
Exercises. Chapter 1. of τ approx that produces the most accurate estimate for this firing pattern.
1 Exercises Chapter 1 1. Generate spike sequences with a constant firing rate r 0 using a Poisson spike generator. Then, add a refractory period to the model by allowing the firing rate r(t) to depend
arxiv:cond-mat/ v2 27 Jun 1997
Entropy and Information in Neural Spike rains Steven P. Strong, 1 Roland Koberle, 1,2 Rob R. de Ruyter van Steveninck, 1 and William Bialek 1 1 NEC Research Institute, 4 Independence Way, Princeton, New
Activity Driven Adaptive Stochastic. Resonance. Gregor Wenning and Klaus Obermayer. Technical University of Berlin.
Activity Driven Adaptive Stochastic Resonance Gregor Wenning and Klaus Obermayer Department of Electrical Engineering and Computer Science Technical University of Berlin Franklinstr. 8/9, 187 Berlin fgrewe,obyg@cs.tu-berlin.de
When is an Integrate-and-fire Neuron like a Poisson Neuron?
When is an Integrate-and-fire Neuron like a Poisson Neuron? Charles F. Stevens Salk Institute MNL/S La Jolla, CA 92037 cfs@salk.edu Anthony Zador Salk Institute MNL/S La Jolla, CA 92037 zador@salk.edu
Introduction to Neural Networks U. Minn. Psy 5038 Spring, 1999 Daniel Kersten. Lecture 2a. The Neuron - overview of structure. From Anderson (1995)
Introduction to Neural Networks U. Minn. Psy 5038 Spring, 1999 Daniel Kersten Lecture 2a The Neuron - overview of structure From Anderson (1995) 2 Lect_2a_Mathematica.nb Basic Structure Information flow:
SUPPLEMENTARY INFORMATION
Spatio-temporal correlations and visual signaling in a complete neuronal population Jonathan W. Pillow 1, Jonathon Shlens 2, Liam Paninski 3, Alexander Sher 4, Alan M. Litke 4,E.J.Chichilnisky 2, Eero
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,
Efficient Spike-Coding with Multiplicative Adaptation in a Spike Response Model
ACCEPTED FOR NIPS: DRAFT VERSION Efficient Spike-Coding with Multiplicative Adaptation in a Spike Response Model Sander M. Bohte CWI, Life Sciences Amsterdam, The Netherlands S.M.Bohte@cwi.nl September
SPIKE TRIGGERED APPROACHES. Odelia Schwartz Computational Neuroscience Course 2017
SPIKE TRIGGERED APPROACHES Odelia Schwartz Computational Neuroscience Course 2017 LINEAR NONLINEAR MODELS Linear Nonlinear o Often constrain to some form of Linear, Nonlinear computations, e.g. visual
BME 5742 Biosystems Modeling and Control
BME 5742 Biosystems Modeling and Control Hodgkin-Huxley Model for Nerve Cell Action Potential Part 1 Dr. Zvi Roth (FAU) 1 References Hoppensteadt-Peskin Ch. 3 for all the mathematics. Cooper s The Cell
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
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
Visual motion processing and perceptual decision making
Visual motion processing and perceptual decision making Aziz Hurzook (ahurzook@uwaterloo.ca) Oliver Trujillo (otrujill@uwaterloo.ca) Chris Eliasmith (celiasmith@uwaterloo.ca) Centre for Theoretical Neuroscience,
Efficient coding of natural images with a population of noisy Linear-Nonlinear neurons
Efficient coding of natural images with a population of noisy Linear-Nonlinear neurons Yan Karklin and Eero P. Simoncelli NYU Overview Efficient coding is a well-known objective for the evaluation and
Biosciences in the 21st century
Biosciences in the 21st century Lecture 1: Neurons, Synapses, and Signaling Dr. Michael Burger Outline: 1. Why neuroscience? 2. The neuron 3. Action potentials 4. Synapses 5. Organization of the nervous
The Bayesian Brain. Robert Jacobs Department of Brain & Cognitive Sciences University of Rochester. May 11, 2017
The Bayesian Brain Robert Jacobs Department of Brain & Cognitive Sciences University of Rochester May 11, 2017 Bayesian Brain How do neurons represent the states of the world? How do neurons represent
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
Estimation of information-theoretic quantities
Estimation of information-theoretic quantities Liam Paninski Gatsby Computational Neuroscience Unit University College London http://www.gatsby.ucl.ac.uk/ liam liam@gatsby.ucl.ac.uk November 16, 2004 Some
Combining biophysical and statistical methods for understanding neural codes
Combining biophysical and statistical methods for understanding neural codes Liam Paninski Department of Statistics and Center for Theoretical Neuroscience Columbia University http://www.stat.columbia.edu/
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
Searching for simple models
Searching for simple models 9th Annual Pinkel Endowed Lecture Institute for Research in Cognitive Science University of Pennsylvania Friday April 7 William Bialek Joseph Henry Laboratories of Physics,
Do Neurons Process Information Efficiently?
Do Neurons Process Information Efficiently? James V Stone, University of Sheffield Claude Shannon, 1916-2001 Nothing in biology makes sense except in the light of evolution. Theodosius Dobzhansky, 1973.
Topics in Neurophysics
Topics in Neurophysics Alex Loebel, Martin Stemmler and Anderas Herz Exercise 2 Solution (1) The Hodgkin Huxley Model The goal of this exercise is to simulate the action potential according to the model
Another look at the retina as an image dithered scalar quantizer
Another look at the retina as an image dithered scalar quantizer Khaled Masmoudi, Marc Antonini, Pierre Kornprobst To cite this version: Khaled Masmoudi, Marc Antonini, Pierre Kornprobst. Another look
Phenomenological Models of Neurons!! Lecture 5!
Phenomenological Models of Neurons!! Lecture 5! 1! Some Linear Algebra First!! Notes from Eero Simoncelli 2! Vector Addition! Notes from Eero Simoncelli 3! Scalar Multiplication of a Vector! 4! Vector
Neural Encoding. Mark van Rossum. January School of Informatics, University of Edinburgh 1 / 58
1 / 58 Neural Encoding Mark van Rossum School of Informatics, University of Edinburgh January 2015 2 / 58 Overview Understanding the neural code Encoding: Prediction of neural response to a given stimulus
CHARACTERIZATION OF NONLINEAR NEURON RESPONSES
CHARACTERIZATION OF NONLINEAR NEURON RESPONSES Matt Whiteway whit8022@umd.edu Dr. Daniel A. Butts dab@umd.edu Neuroscience and Cognitive Science (NACS) Applied Mathematics and Scientific Computation (AMSC)
Adaptation in the Neural Code of the Retina
Adaptation in the Neural Code of the Retina Lens Retina Fovea Optic Nerve Optic Nerve Bottleneck Neurons Information Receptors: 108 95% Optic Nerve 106 5% After Polyak 1941 Visual Cortex ~1010 Mean Intensity
+ + ( + ) = Linear recurrent networks. Simpler, much more amenable to analytic treatment E.g. by choosing
Linear recurrent networks Simpler, much more amenable to analytic treatment E.g. by choosing + ( + ) = Firing rates can be negative Approximates dynamics around fixed point Approximation often reasonable
What do V1 neurons like about natural signals
What do V1 neurons like about natural signals Yuguo Yu Richard Romero Tai Sing Lee Center for the Neural Computer Science Computer Science Basis of Cognition Department Department Carnegie Mellon University
Dynamical mechanisms underlying contrast gain control in single neurons
PHYSICAL REVIEW E 68, 011901 2003 Dynamical mechanisms underlying contrast gain control in single neurons Yuguo Yu and Tai Sing Lee Center for the Neural Basis of Cognition, Carnegie Mellon University,
Decoding Poisson Spike Trains by Gaussian Filtering
LETTER Communicated by Paul Tiesinga Decoding Poisson Spike Trains by Gaussian Filtering Sidney R. Lehky sidney@salk.edu Computational Neuroscience Lab, Salk Institute, La Jolla, CA 92037, U.S.A. The temporal
Inferring synaptic conductances from spike trains under a biophysically inspired point process model
Inferring synaptic conductances from spike trains under a biophysically inspired point process model Kenneth W. Latimer The Institute for Neuroscience The University of Texas at Austin latimerk@utexas.edu
Voltage-clamp and Hodgkin-Huxley models
Voltage-clamp and Hodgkin-Huxley models Read: Hille, Chapters 2-5 (best Koch, Chapters 6, 8, 9 See also Hodgkin and Huxley, J. Physiol. 117:500-544 (1952. (the source Clay, J. Neurophysiol. 80:903-913
What is the neural code? Sekuler lab, Brandeis
What is the neural code? Sekuler lab, Brandeis What is the neural code? What is the neural code? Alan Litke, UCSD What is the neural code? What is the neural code? What is the neural code? Encoding: how
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
Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Model
Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Model Jonathan W. Pillow, Liam Paninski, and Eero P. Simoncelli Howard Hughes Medical Institute Center for Neural Science New York
Comparing integrate-and-fire models estimated using intracellular and extracellular data 1
Comparing integrate-and-fire models estimated using intracellular and extracellular data 1 Liam Paninski a,b,2 Jonathan Pillow b Eero Simoncelli b a Gatsby Computational Neuroscience Unit, University College
V m = the Value of the Na Battery Plus the Voltage Drop Across g Na. I Na is Isolated By Blocking I K. and g K
VoltageGated Ion Channels and the Action Potential VoltageGated Ion Channels and the Action Potential jdk3 Principles of Neural Science, chaps 8&9 The Action Potential Generation Conduction VoltageGated
Decoding Input Signals in Time Domain A Model Approach
Journal of Computational Neuroscience 6, 237 249, 24 c 24 Kluwer Academic Publishers. Manufactured in The Netherlands. Decoding Input Signals in Time Domain A Model Approach JIANFENG FENG AND DAVID BROWN
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
Mid Year Project Report: Statistical models of visual neurons
Mid Year Project Report: Statistical models of visual neurons Anna Sotnikova asotniko@math.umd.edu Project Advisor: Prof. Daniel A. Butts dab@umd.edu Department of Biology Abstract Studying visual neurons
Neuronal Dynamics: Computational Neuroscience of Single Neurons
Week 5 part 3a :Three definitions of rate code Neuronal Dynamics: Computational Neuroscience of Single Neurons Week 5 Variability and Noise: The question of the neural code Wulfram Gerstner EPFL, Lausanne,
Adaptive contrast gain control and information maximization $
Neurocomputing 65 66 (2005) 6 www.elsevier.com/locate/neucom Adaptive contrast gain control and information maximization $ Yuguo Yu a,, Tai Sing Lee b a Center for the Neural Basis of Cognition, Carnegie
Voltage-clamp and Hodgkin-Huxley models
Voltage-clamp and Hodgkin-Huxley models Read: Hille, Chapters 2-5 (best) Koch, Chapters 6, 8, 9 See also Clay, J. Neurophysiol. 80:903-913 (1998) (for a recent version of the HH squid axon model) Rothman
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
An Introductory Course in Computational Neuroscience
An Introductory Course in Computational Neuroscience Contents Series Foreword Acknowledgments Preface 1 Preliminary Material 1.1. Introduction 1.1.1 The Cell, the Circuit, and the Brain 1.1.2 Physics of
Efficient Coding. Odelia Schwartz 2017
Efficient Coding Odelia Schwartz 2017 1 Levels of modeling Descriptive (what) Mechanistic (how) Interpretive (why) 2 Levels of modeling Fitting a receptive field model to experimental data (e.g., using
Physiology Unit 2. MEMBRANE POTENTIALS and SYNAPSES
Physiology Unit 2 MEMBRANE POTENTIALS and SYNAPSES Neuron Communication Neurons are stimulated by receptors on dendrites and cell bodies (soma) Ligand gated ion channels GPCR s Neurons stimulate cells
Sean Escola. Center for Theoretical Neuroscience
Employing hidden Markov models of neural spike-trains toward the improved estimation of linear receptive fields and the decoding of multiple firing regimes Sean Escola Center for Theoretical Neuroscience
Efficient coding of natural images with a population of noisy Linear-Nonlinear neurons
To appear in: Neural Information Processing Systems (NIPS), http://nips.cc/ Granada, Spain. December 12-15, 211. Efficient coding of natural images with a population of noisy Linear-Nonlinear neurons Yan
Broadband coding with dynamic synapses
Broadband coding with dynamic synapses Benjamin Lindner Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Str. 38 1187 Dresden, Germany André Longtin Department of Physics and Center
Neural Encoding: Firing Rates and Spike Statistics
Neural Encoding: Firing Rates and Spike Statistics Dayan and Abbott (21) Chapter 1 Instructor: Yoonsuck Choe; CPSC 644 Cortical Networks Background: Dirac δ Function Dirac δ function has the following
Neural Decoding. Mark van Rossum. School of Informatics, University of Edinburgh. January 2012
Neural Decoding Mark van Rossum School of Informatics, University of Edinburgh January 2012 0 Acknowledgements: Chris Williams and slides from Gatsby Liam Paninski. Version: January 31, 2018 1 / 63 2 /
Firing Rate Distributions and Ef ciency of Information Transmission of Inferior Temporal Cortex Neurons to Natural Visual Stimuli
LETTER Communicated by Dan Ruderman Firing Rate Distributions and Ef ciency of Information Transmission of Inferior Temporal Cortex Neurons to Natural Visual Stimuli Alessandro Treves SISSA, Programme
Neural variability and Poisson statistics
Neural variability and Poisson statistics January 15, 2014 1 Introduction We are in the process of deriving the Hodgkin-Huxley model. That model describes how an action potential is generated by ion specic
Computation in a single neuron: Hodgkin and Huxley revisited
Computation in a single neuron: Hodgkin and Huxley revisited Blaise Agüera y Arcas, 1 Adrienne L. Fairhall, 2,3 and William Bialek 2,4 1 Rare Books Library, Princeton University, Princeton, New Jersey
Pacific Symposium on Biocomputing 6: (2001)
Analyzing sensory systems with the information distortion function Alexander G Dimitrov and John P Miller Center for Computational Biology Montana State University Bozeman, MT 59715-3505 falex,jpmg@nervana.montana.edu
Bayesian Computation in Recurrent Neural Circuits
Bayesian Computation in Recurrent Neural Circuits Rajesh P. N. Rao Department of Computer Science and Engineering University of Washington Seattle, WA 98195 E-mail: rao@cs.washington.edu Appeared in: Neural
AT2 Neuromodeling: Problem set #3 SPIKE TRAINS
AT2 Neuromodeling: Problem set #3 SPIKE TRAINS Younesse Kaddar PROBLEM 1: Poisson spike trains Link of the ipython notebook for the code Brain neuron emit spikes seemingly randomly: we will aim to model
Equivalent Circuit of the Membrane Connected to the Voltage Clamp. I mon. For Large Depolarizations, Both I Na and I K Are Activated
VoltageGated Ion Channels and the Action Potential jdk3 Principles of Neural Science, chaps 8&9 VoltageGated Ion Channels and the Action Potential The Action Potential Generation Conduction VoltageGated
Encoding Natural Scenes with Neural Circuits with Random Thresholds
Encoding Natural Scenes with Neural Circuits with Random Thresholds Aurel A. Lazar, Eftychios A. Pnevmatikakis and Yiyin Zhou Department of Electrical Engineering Columbia University, New York, NY 10027
Controllingthe spikingactivity in excitable membranes via poisoning
Physica A 344 (2004) 665 670 www.elsevier.com/locate/physa Controllingthe spikingactivity in excitable membranes via poisoning Gerhard Schmid, Igor Goychuk, Peter Hanggi Universitat Augsburg, Institut
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
Analyzing Neuroscience Signals using Information Theory and Complexity
12th INCF Workshop on Node Communication and Collaborative Neuroinformatics Warsaw, April 16-17, 2015 Co-Authors: Analyzing Neuroscience Signals using Information Theory and Complexity Shannon Communication
Fisher Information Quantifies Task-Specific Performance in the Blowfly Photoreceptor
Fisher Information Quantifies Task-Specific Performance in the Blowfly Photoreceptor Peng Xu and Pamela Abshire Department of Electrical and Computer Engineering and the Institute for Systems Research
Modelling stochastic neural learning
Modelling stochastic neural learning Computational Neuroscience András Telcs telcs.andras@wigner.mta.hu www.cs.bme.hu/~telcs http://pattern.wigner.mta.hu/participants/andras-telcs Compiled from lectures
Features and dimensions: Motion estimation in fly vision
Features and dimensions: Motion estimation in fly vision William Bialek a and Rob R. de Ruyter van Steveninck b a Joseph Henry Laboratories of Physics, and Lewis Sigler Institute for Integrative Genomics
Particles with opposite charges (positives and negatives) attract each other, while particles with the same charge repel each other.
III. NEUROPHYSIOLOGY A) REVIEW - 3 basic ideas that the student must remember from chemistry and physics: (i) CONCENTRATION measure of relative amounts of solutes in a solution. * Measured in units called
Spike-Frequency Adaptation: Phenomenological Model and Experimental Tests
Spike-Frequency Adaptation: Phenomenological Model and Experimental Tests J. Benda, M. Bethge, M. Hennig, K. Pawelzik & A.V.M. Herz February, 7 Abstract Spike-frequency adaptation is a common feature of
arxiv: v1 [q-bio.nc] 12 Feb 2009
![arxiv: v1 [q-bio.nc] 12 Feb 2009](/thumbs/90/103030709.jpg "arxiv: v1 [q-bio.nc] 12 Feb 2009")
arxiv:0902.2037v1 [q-bio.nc] 12 Feb 2009 Stimulus-dependent correlations in threshold-crossing spiking neurons Yoram Burak 1, Sam Lewallen 2, and Haim Sompolinsky 1,3 1 Center for Brain Science, Harvard
Bayesian probability theory and generative models
Bayesian probability theory and generative models Bruno A. Olshausen November 8, 2006 Abstract Bayesian probability theory provides a mathematical framework for peforming inference, or reasoning, using
Encoding or decoding
Encoding or decoding Decoding How well can we learn what the stimulus is by looking at the neural responses? We will discuss two approaches: devise and evaluate explicit algorithms for extracting a stimulus
CHARACTERIZATION OF NONLINEAR NEURON RESPONSES
CHARACTERIZATION OF NONLINEAR NEURON RESPONSES Matt Whiteway whit8022@umd.edu Dr. Daniel A. Butts dab@umd.edu Neuroscience and Cognitive Science (NACS) Applied Mathematics and Scientific Computation (AMSC)
Dimensionality reduction in neural models: An information-theoretic generalization of spike-triggered average and covariance analysis
Journal of Vision (2006) 6, 414 428 http://journalofvision.org/6/4/9/ 414 Dimensionality reduction in neural models: An information-theoretic generalization of spike-triggered average and covariance analysis
Dimensionality reduction in neural models: an information-theoretic generalization of spiketriggered average and covariance analysis
to appear: Journal of Vision, 26 Dimensionality reduction in neural models: an information-theoretic generalization of spiketriggered average and covariance analysis Jonathan W. Pillow 1 and Eero P. Simoncelli
Mathematical Neuroscience. Course: Dr. Conor Houghton 2010 Typeset: Cathal Ormond
Mathematical Neuroscience Course: Dr. Conor Houghton 21 Typeset: Cathal Ormond May 6, 211 Contents 1 Introduction 2 1.1 The Brain.......................................... 2 1.2 Pyramidal Neuron.....................................
Deconstructing Actual Neurons
1 Deconstructing Actual Neurons Richard Bertram Department of Mathematics and Programs in Neuroscience and Molecular Biophysics Florida State University Tallahassee, Florida 32306 Reference: The many ionic
Stochastic Oscillator Death in Globally Coupled Neural Systems
Journal of the Korean Physical Society, Vol. 52, No. 6, June 2008, pp. 19131917 Stochastic Oscillator Death in Globally Coupled Neural Systems Woochang Lim and Sang-Yoon Kim y Department of Physics, Kangwon
High-dimensional geometry of cortical population activity. Marius Pachitariu University College London
High-dimensional geometry of cortical population activity Marius Pachitariu University College London Part I: introduction to the brave new world of large-scale neuroscience Part II: large-scale data preprocessing
Statistical models for neural encoding
Statistical models for neural encoding Part 1: discrete-time models Liam Paninski Gatsby Computational Neuroscience Unit University College London http://www.gatsby.ucl.ac.uk/ liam liam@gatsby.ucl.ac.uk
Modeling and Characterization of Neural Gain Control. Odelia Schwartz. A dissertation submitted in partial fulfillment
Modeling and Characterization of Neural Gain Control by Odelia Schwartz A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Center for Neural Science
Single neuron models. L. Pezard Aix-Marseille University
Single neuron models L. Pezard Aix-Marseille University Biophysics Biological neuron Biophysics Ionic currents Passive properties Active properties Typology of models Compartmental models Differential
GENERAL ARTICLE Noisy Neurons
Noisy Neurons Hodgkin Huxley Model and Stochastic Variants Shruti Paranjape Shruti Paranjape is a fourth year student at IISER Pune, majoring in Physics. This is an article based on what she worked on
Likelihood-Based Approaches to
Likelihood-Based Approaches to 3 Modeling the Neural Code Jonathan Pillow One of the central problems in systems neuroscience is that of characterizing the functional relationship between sensory stimuli
Stochastic resonance in neuron models: Endogenous stimulation revisited
PHYSICAL REVIEW E, VOLUME 63, 031916 Stochastic resonance in neuron models: Endogenous stimulation revisited Hans E. Plesser 1,2, * and Theo Geisel 1 1 Max-Planck-Institut für Strömungsforschung and Fakultät
This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore. Title Small-signal neural models and their applications Author(s) Basu, Arindam Citation Basu, A. (01). Small-signal
THE TRANSFER AND PROPAGATION OF CORRELATED NEURONAL ACTIVITY
THE TRANSFER AND PROPAGATION OF CORRELATED NEURONAL ACTIVITY A Dissertation Presented to the Faculty of the Department of Mathematics University of Houston In Partial Fulfillment of the Requirements for
Electrophysiology of the neuron
School of Mathematical Sciences G4TNS Theoretical Neuroscience Electrophysiology of the neuron Electrophysiology is the study of ionic currents and electrical activity in cells and tissues. The work of
Channel Noise in Excitable Neuronal Membranes
Channel Noise in Excitable Neuronal Membranes Amit Manwani, Peter N. Steinmetz and Christof Koch Computation and Neural Systems Program, M-S 9-74 California Institute of Technology Pasadena, CA 95 fquixote,peter,kochg@klab.caltech.edu
!) + log(t) # n i. The last two terms on the right hand side (RHS) are clearly independent of θ and can be
Supplementary Materials General case: computing log likelihood We first describe the general case of computing the log likelihood of a sensory parameter θ that is encoded by the activity of neurons. Each