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  1. Research

    Neural Excitability and Singular Bifurcations

    We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define e...

    Peter De Maesschalck and Martin Wechselberger

    The Journal of Mathematical Neuroscience (JMN) 2015 5:16

    Published on: 6 August 2015

  2. Research

    The Minimal k-Core Problem for Modeling k-Assemblies

    The concept of cell assembly was introduced by Hebb and formalized mathematically by Palm in the framework of graph theory. In the study of associative memory, a cell assembly is a group of neurons that are st...

    Cynthia I. Wood and Illya V. Hicks

    The Journal of Mathematical Neuroscience (JMN) 2015 5:14

    Published on: 14 July 2015

  3. Research

    Orientation Maps in V1 and Non-Euclidean Geometry

    In the primary visual cortex, the processing of information uses the distribution of orientations in the visual input: neurons react to some orientations in the stimulus more than to others. In many species, o...

    Alexandre Afgoustidis

    The Journal of Mathematical Neuroscience (JMN) 2015 5:12

    Published on: 17 June 2015

  4. Research

    Noise-Induced Precursors of State Transitions in the Stochastic Wilson–Cowan Model

    The Wilson–Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here ...

    Ehsan Negahbani, D. Alistair Steyn-Ross, Moira L. Steyn-Ross, Marcus T. Wilson and Jamie W. Sleigh

    The Journal of Mathematical Neuroscience (JMN) 2015 5:9

    Published on: 8 April 2015

  5. Research

    Modeling Focal Epileptic Activity in the Wilson–Cowan Model with Depolarization Block

    Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity...

    Hil G. E. Meijer, Tahra L. Eissa, Bert Kiewiet, Jeremy F. Neuman, Catherine A. Schevon, Ronald G. Emerson, Robert R. Goodman, Guy M. McKhann Jr., Charles J. Marcuccilli, Andrew K. Tryba, Jack D. Cowan, Stephan A. van Gils and Wim van Drongelen

    The Journal of Mathematical Neuroscience (JMN) 2015 5:7

    Published on: 27 March 2015

  6. Research

    Path Integral Methods for Stochastic Differential Equations

    Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic...

    Carson C. Chow and Michael A. Buice

    The Journal of Mathematical Neuroscience (JMN) 2015 5:8

    Published on: 24 March 2015

  7. Research

    A Mathematical Model of a Midbrain Dopamine Neuron Identifies Two Slow Variables Likely Responsible for Bursts Evoked by SK Channel Antagonists and Terminated by Depolarization Block

    Midbrain dopamine neurons exhibit a novel type of bursting that we call “inverted square wave bursting” when exposed to Ca2+-activated small conductance (SK) K+ channel blockers in vitro. This type of bursting ha...

    Na Yu and Carmen C. Canavier

    The Journal of Mathematical Neuroscience (JMN) 2015 5:5

    Published on: 27 February 2015

  8. Research

    Shifting Spike Times or Adding and Deleting Spikes—How Different Types of Noise Shape Signal Transmission in Neural Populations

    We study a population of spiking neurons which are subject to independent noise processes and a strong common time-dependent input. We show that the response of output spikes to independent noise shapes inform...

    Sergej O Voronenko, Wilhelm Stannat and Benjamin Lindner

    The Journal of Mathematical Neuroscience 2015 5:1

    Published on: 12 January 2015

  9. Research

    Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons

    The formation of oscillating phase clusters in a network of identical Hodgkin–Huxley neurons is studied, along with their dynamic behavior. The neurons are synaptically coupled in an all-to-all manner, yet the...

    Sung Joon Moon, Katherine A Cook, Karthikeyan Rajendran, Ioannis G Kevrekidis, Jaime Cisternas and Carlo R Laing

    The Journal of Mathematical Neuroscience 2015 5:2

    Published on: 12 January 2015

  10. Short report

    Uncertainty Propagation in Nerve Impulses Through the Action Potential Mechanism

    We investigate the propagation of probabilistic uncertainty through the action potential mechanism in nerve cells. Using the Hodgkin–Huxley (H-H) model and Stochastic Collocation on Sparse Grids, we obtain an ...

    Aldemar Torres Valderrama, Jeroen Witteveen, Maria Navarro and Joke Blom

    The Journal of Mathematical Neuroscience 2015 5:3

    Published on: 12 January 2015

  11. Review

    Numerical Bifurcation Theory for High-Dimensional Neural Models

    Numerical bifurcation theory involves finding and then following certain types of solutions of differential equations as parameters are varied, and determining whether they undergo any bifurcations (qualitativ...

    Carlo R Laing

    The Journal of Mathematical Neuroscience 2014 4:13

    Published on: 25 July 2014

  12. Research

    Network Symmetry and Binocular Rivalry Experiments

    Hugh Wilson has proposed a class of models that treat higher-level decision making as a competition between patterns coded as levels of a set of attributes in an appropriately defined network (Cortical Mechani...

    Casey O Diekman and Martin Golubitsky

    The Journal of Mathematical Neuroscience 2014 4:12

    Published on: 7 May 2014

  13. Research

    Identification of Criticality in Neuronal Avalanches: II. A Theoretical and Empirical Investigation of the Driven Case

    The observation of apparent power laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of sel...

    Caroline Hartley, Timothy J Taylor, Istvan Z Kiss, Simon F Farmer and Luc Berthouze

    The Journal of Mathematical Neuroscience 2014 4:9

    Published on: 25 April 2014

  14. Research

    Cross-Correlations and Joint Gaussianity in Multivariate Level Crossing Models

    A variety of phenomena in physical and biological sciences can be mathematically understood by considering the statistical properties of level crossings of random Gaussian processes. Notably, a growing number ...

    Elena Di Bernardino, José León and Tatjana Tchumatchenko

    The Journal of Mathematical Neuroscience 2014 4:22

    Published on: 17 April 2014

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