A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation.

Abstract:

:Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between bursting and non-bursting states, mean-field descriptions of macroscopic bursting behavior are a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons and examine whether states of collective bursting behavior can arise from short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. Analyzing the mean-field model via bifurcation analysis, we find that bursting behavior emerges for both types of short-term adaptation. This bursting behavior can coexist with steady-state behavior, providing a bistable regime that allows for transient switches between synchronized and nonsynchronized states of population dynamics. For all of these findings, we demonstrate a close correspondence between the spiking neural network and the mean-field model. Although the mean-field model has been derived under the assumptions of an infinite population size and all-to-all coupling inside the population, we show that this correspondence holds even for small, sparsely coupled networks. In summary, we provide mechanistic descriptions of phase transitions between bursting and steady-state population dynamics, which play important roles in both healthy neural communication and neurological disorders.

journal_name

Neural Comput

journal_title

Neural computation

authors

Gast R,Schmidt H,Knösche TR

doi

10.1162/neco_a_01300

subject

Has Abstract

pub_date

2020-09-01 00:00:00

pages

1615-1634

issue

9

eissn

0899-7667

issn

1530-888X

journal_volume

32

pub_type

杂志文章
  • On the Convergence of the LMS Algorithm with Adaptive Learning Rate for Linear Feedforward Networks.

    abstract::We consider the problem of training a linear feedforward neural network by using a gradient descent-like LMS learning algorithm. The objective is to find a weight matrix for the network, by repeatedly presenting to it a finite set of examples, so that the sum of the squares of the errors is minimized. Kohonen showed t...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.1991.3.2.226

    authors: Luo ZQ

    更新日期:1991-07-01 00:00:00

  • Constraint on the number of synaptic inputs to a visual cortical neuron controls receptive field formation.

    abstract::To date, Hebbian learning combined with some form of constraint on synaptic inputs has been demonstrated to describe well the development of neural networks. The previous models revealed mathematically the importance of synaptic constraints to reproduce orientation selectivity in the visual cortical neurons, but biolo...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.04-08-752

    authors: Tanaka S,Miyashita M

    更新日期:2009-09-01 00:00:00

  • Incremental active learning for optimal generalization.

    abstract::The problem of designing input signals for optimal generalization is called active learning. In this article, we give a two-stage sampling scheme for reducing both the bias and variance, and based on this scheme, we propose two active learning methods. One is the multipoint search method applicable to arbitrary models...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976600300014773

    authors: Sugiyama M,Ogawa H

    更新日期:2000-12-01 00:00:00

  • Derivatives of logarithmic stationary distributions for policy gradient reinforcement learning.

    abstract::Most conventional policy gradient reinforcement learning (PGRL) algorithms neglect (or do not explicitly make use of) a term in the average reward gradient with respect to the policy parameter. That term involves the derivative of the stationary state distribution that corresponds to the sensitivity of its distributio...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.12-08-922

    authors: Morimura T,Uchibe E,Yoshimoto J,Peters J,Doya K

    更新日期:2010-02-01 00:00:00

  • The dynamics of discrete-time computation, with application to recurrent neural networks and finite state machine extraction.

    abstract::Recurrent neural networks (RNNs) can learn to perform finite state computations. It is shown that an RNN performing a finite state computation must organize its state space to mimic the states in the minimal deterministic finite state machine that can perform that computation, and a precise description of the attracto...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.1996.8.6.1135

    authors: Casey M

    更新日期:1996-08-15 00:00:00

  • Abstract stimulus-specific adaptation models.

    abstract::Many neurons that initially respond to a stimulus stop responding if the stimulus is presented repeatedly but recover their response if a different stimulus is presented. This phenomenon is referred to as stimulus-specific adaptation (SSA). SSA has been investigated extensively using oddball experiments, which measure...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00077

    authors: Mill R,Coath M,Wennekers T,Denham SL

    更新日期:2011-02-01 00:00:00

  • A Novel Reconstruction Framework for Time-Encoded Signals with Integrate-and-Fire Neurons.

    abstract::Integrate-and-fire neurons are time encoding machines that convert the amplitude of an analog signal into a nonuniform, strictly increasing sequence of spike times. Under certain conditions, the encoded signals can be reconstructed from the nonuniform spike time sequences using a time decoding machine. Time encoding a...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00764

    authors: Florescu D,Coca D

    更新日期:2015-09-01 00:00:00

  • Simultaneous rate-synchrony codes in populations of spiking neurons.

    abstract::Firing rates and synchronous firing are often simultaneously relevant signals, and they independently or cooperatively represent external sensory inputs, cognitive events, and environmental situations such as body position. However, how rates and synchrony comodulate and which aspects of inputs are effectively encoded...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976606774841521

    authors: Masuda N

    更新日期:2006-01-01 00:00:00

  • Mirror symmetric topographic maps can arise from activity-dependent synaptic changes.

    abstract::Multiple adjacent, roughly mirror-image topographic maps are commonly observed in the sensory neocortex of many species. The cortical regions occupied by these maps are generally believed to be determined initially by genetically controlled chemical markers during development, with thalamocortical afferent activity su...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/0899766053491904

    authors: Schulz R,Reggia JA

    更新日期:2005-05-01 00:00:00

  • Design of charge-balanced time-optimal stimuli for spiking neuron oscillators.

    abstract::In this letter, we investigate the fundamental limits on how the interspike time of a neuron oscillator can be perturbed by the application of a bounded external control input (a current stimulus) with zero net electric charge accumulation. We use phase models to study the dynamics of neurons and derive charge-balance...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00643

    authors: Dasanayake IS,Li JS

    更新日期:2014-10-01 00:00:00

  • ASIC Implementation of a Nonlinear Dynamical Model for Hippocampal Prosthesis.

    abstract::A hippocampal prosthesis is a very large scale integration (VLSI) biochip that needs to be implanted in the biological brain to solve a cognitive dysfunction. In this letter, we propose a novel low-complexity, small-area, and low-power programmable hippocampal neural network application-specific integrated circuit (AS...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco_a_01107

    authors: Qiao Z,Han Y,Han X,Xu H,Li WXY,Song D,Berger TW,Cheung RCC

    更新日期:2018-09-01 00:00:00

  • A causal perspective on the analysis of signal and noise correlations and their role in population coding.

    abstract::The role of correlations between neuronal responses is crucial to understanding the neural code. A framework used to study this role comprises a breakdown of the mutual information between stimuli and responses into terms that aim to account for different coding modalities and the distinction between different notions...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00588

    authors: Chicharro D

    更新日期:2014-06-01 00:00:00

  • Spiking neural P systems with weights.

    abstract::A variant of spiking neural P systems with positive or negative weights on synapses is introduced, where the rules of a neuron fire when the potential of that neuron equals a given value. The involved values-weights, firing thresholds, potential consumed by each rule-can be real (computable) numbers, rational numbers,...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00022

    authors: Wang J,Hoogeboom HJ,Pan L,Păun G,Pérez-Jiménez MJ

    更新日期:2010-10-01 00:00:00

  • Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell.

    abstract::To understand the interspike interval (ISI) variability displayed by visual cortical neurons (Softky & Koch, 1993), it is critical to examine the dynamics of their neuronal integration, as well as the variability in their synaptic input current. Most previous models have focused on the latter factor. We match a simple...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.1997.9.5.971

    authors: Troyer TW,Miller KD

    更新日期:1997-07-01 00:00:00

  • Optimal sequential detection of stimuli from multiunit recordings taken in densely populated brain regions.

    abstract::We address the problem of detecting the presence of a recurring stimulus by monitoring the voltage on a multiunit electrode located in a brain region densely populated by stimulus reactive neurons. Published experimental results suggest that under these conditions, when a stimulus is present, the measurements are gaus...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00257

    authors: Nossenson N,Messer H

    更新日期:2012-04-01 00:00:00

  • Pattern generation by two coupled time-discrete neural networks with synaptic depression.

    abstract::Numerous animal behaviors, such as locomotion in vertebrates, are produced by rhythmic contractions that alternate between two muscle groups. The neuronal networks generating such alternate rhythmic activity are generally thought to rely on pacemaker cells or well-designed circuits consisting of inhibitory and excitat...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976698300017449

    authors: Senn W,Wannier T,Kleinle J,Lüscher HR,Müller L,Streit J,Wyler K

    更新日期:1998-07-01 00:00:00

  • Representation sharpening can explain perceptual priming.

    abstract::Perceiving and identifying an object is improved by prior exposure to the object. This perceptual priming phenomenon is accompanied by reduced neural activity. But whether suppression of neuronal activity with priming is responsible for the improvement in perception is unclear. To address this problem, we developed a ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.04-09-999

    authors: Moldakarimov S,Bazhenov M,Sejnowski TJ

    更新日期:2010-05-01 00:00:00

  • A Reservoir Computing Model of Reward-Modulated Motor Learning and Automaticity.

    abstract::Reservoir computing is a biologically inspired class of learning algorithms in which the intrinsic dynamics of a recurrent neural network are mined to produce target time series. Most existing reservoir computing algorithms rely on fully supervised learning rules, which require access to an exact copy of the target re...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco_a_01198

    authors: Pyle R,Rosenbaum R

    更新日期:2019-07-01 00:00:00

  • Propagating distributions up directed acyclic graphs.

    abstract::In a previous article, we considered game trees as graphical models. Adopting an evaluation function that returned a probability distribution over values likely to be taken at a given position, we described how to build a model of uncertainty and use it for utility-directed growth of the search tree and for deciding o...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976699300016881

    authors: Baum EB,Smith WD

    更新日期:1999-01-01 00:00:00

  • A neurocomputational model for cocaine addiction.

    abstract::Based on the dopamine hypotheses of cocaine addiction and the assumption of decrement of brain reward system sensitivity after long-term drug exposure, we propose a computational model for cocaine addiction. Utilizing average reward temporal difference reinforcement learning, we incorporate the elevation of basal rewa...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.10-08-882

    authors: Dezfouli A,Piray P,Keramati MM,Ekhtiari H,Lucas C,Mokri A

    更新日期:2009-10-01 00:00:00

  • Making the error-controlling algorithm of observable operator models constructive.

    abstract::Observable operator models (OOMs) are a class of models for stochastic processes that properly subsumes the class that can be modeled by finite-dimensional hidden Markov models (HMMs). One of the main advantages of OOMs over HMMs is that they admit asymptotically correct learning algorithms. A series of learning algor...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.10-08-878

    authors: Zhao MJ,Jaeger H,Thon M

    更新日期:2009-12-01 00:00:00

  • Kernels for longitudinal data with variable sequence length and sampling intervals.

    abstract::We develop several kernel methods for classification of longitudinal data and apply them to detect cognitive decline in the elderly. We first develop mixed-effects models, a type of hierarchical empirical Bayes generative models, for the time series. After demonstrating their utility in likelihood ratio classifiers (a...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00164

    authors: Lu Z,Leen TK,Kaye J

    更新日期:2011-09-01 00:00:00

  • On the emergence of rules in neural networks.

    abstract::A simple associationist neural network learns to factor abstract rules (i.e., grammars) from sequences of arbitrary input symbols by inventing abstract representations that accommodate unseen symbol sets as well as unseen but similar grammars. The neural network is shown to have the ability to transfer grammatical kno...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976602320264079

    authors: Hanson SJ,Negishi M

    更新日期:2002-09-01 00:00:00

  • Discrete states of synaptic strength in a stochastic model of spike-timing-dependent plasticity.

    abstract::A stochastic model of spike-timing-dependent plasticity (STDP) postulates that single synapses presented with a single spike pair exhibit all-or-none quantal jumps in synaptic strength. The amplitudes of the jumps are independent of spiking timing, but their probabilities do depend on spiking timing. By making the amp...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.07-08-814

    authors: Elliott T

    更新日期:2010-01-01 00:00:00

  • Bayesian model assessment and comparison using cross-validation predictive densities.

    abstract::In this work, we discuss practical methods for the assessment, comparison, and selection of complex hierarchical Bayesian models. A natural way to assess the goodness of the model is to estimate its future predictive capability by estimating expected utilities. Instead of just making a point estimate, it is important ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/08997660260293292

    authors: Vehtari A,Lampinen J

    更新日期:2002-10-01 00:00:00

  • Fast recursive filters for simulating nonlinear dynamic systems.

    abstract::A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters and static nonlinearities. The parameters of these filters and nonlinearities ma...

    journal_title:Neural computation

    pub_type: 信件

    doi:10.1162/neco.2008.04-07-506

    authors: van Hateren JH

    更新日期:2008-07-01 00:00:00

  • Are loss functions all the same?

    abstract::In this letter, we investigate the impact of choosing different loss functions from the viewpoint of statistical learning theory. We introduce a convexity assumption, which is met by all loss functions commonly used in the literature, and study how the bound on the estimation error changes with the loss. We also deriv...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976604773135104

    authors: Rosasco L,De Vito E,Caponnetto A,Piana M,Verri A

    更新日期:2004-05-01 00:00:00

  • Distributed control of uncertain systems using superpositions of linear operators.

    abstract::Control in the natural environment is difficult in part because of uncertainty in the effect of actions. Uncertainty can be due to added motor or sensory noise, unmodeled dynamics, or quantization of sensory feedback. Biological systems are faced with further difficulties, since control must be performed by networks o...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00151

    authors: Sanger TD

    更新日期:2011-08-01 00:00:00

  • Piecewise-linear neural networks and their relationship to rule extraction from data.

    abstract::This article addresses the topic of extracting logical rules from data by means of artificial neural networks. The approach based on piecewise linear neural networks is revisited, which has already been used for the extraction of Boolean rules in the past, and it is shown that this approach can be important also for t...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2006.18.11.2813

    authors: Holena M

    更新日期:2006-11-01 00:00:00

  • A bio-inspired, computational model suggests velocity gradients of optic flow locally encode ordinal depth at surface borders and globally they encode self-motion.

    abstract::Visual navigation requires the estimation of self-motion as well as the segmentation of objects from the background. We suggest a definition of local velocity gradients to compute types of self-motion, segment objects, and compute local properties of optical flow fields, such as divergence, curl, and shear. Such veloc...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00479

    authors: Raudies F,Ringbauer S,Neumann H

    更新日期:2013-09-01 00:00:00