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  1. We consider finite and infinite all-to-all coupled networks of identical theta neurons. Two types of synaptic interactions are investigated: instantaneous and delayed (via first-order synaptic processing). Ext...

    Authors: Carlo R. Laing

    Citation: The Journal of Mathematical Neuroscience 2018 8:4

    Content type: Research

    Published on:

  2. Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with conside...

    Authors: Jehan Alswaihli, Roland Potthast, Ingo Bojak, Douglas Saddy and Axel Hutt

    Citation: The Journal of Mathematical Neuroscience 2018 8:3

    Content type: Research

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  3. We investigate the sparse functional identification of complex cells and the decoding of spatio-temporal visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm is formulated as a ...

    Authors: Aurel A. Lazar, Nikul H. Ukani and Yiyin Zhou

    Citation: The Journal of Mathematical Neuroscience 2018 8:2

    Content type: Research

    Published on:

  4. The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically coupled McCulloch–Pitts binary neurons interact to perform emergent computation. Alt...

    Authors: Christopher J. Hillar and Ngoc M. Tran

    Citation: The Journal of Mathematical Neuroscience 2018 8:1

    Content type: Research

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  5. We present a simple rate-reduced neuron model that captures a wide range of complex, biologically plausible, and physiologically relevant spiking behavior. This includes spike-frequency adaptation, postinhibit...

    Authors: Koen Dijkstra, Yuri A. Kuznetsov, Michel J. A. M. van Putten and Stephan A. van Gils

    Citation: The Journal of Mathematical Neuroscience 2017 7:13

    Content type: Research

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  6. Continuum neural field equations model the large-scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded a...

    Authors: Aytül Gökçe, Daniele Avitabile and Stephen Coombes

    Citation: The Journal of Mathematical Neuroscience 2017 7:12

    Content type: Research

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  7. We examine a family of random firing-rate neural networks in which we enforce the neurobiological constraint of Dale’s Law—each neuron makes either excitatory or inhibitory connections onto its post-synaptic t...

    Authors: Andrea K. Barreiro, J. Nathan Kutz and Eli Shlizerman

    Citation: The Journal of Mathematical Neuroscience 2017 7:10

    Content type: Research

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  8. Neural mass models provide a useful framework for modelling mesoscopic neural dynamics and in this article we consider the Jansen and Rit neural mass model (JR-NMM). We formulate a stochastic version of it whi...

    Authors: Markus Ableidinger, Evelyn Buckwar and Harald Hinterleitner

    Citation: The Journal of Mathematical Neuroscience 2017 7:8

    Content type: Research

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  9. Bursting is a phenomenon found in a variety of physical and biological systems. For example, in neuroscience, bursting is believed to play a key role in the way information is transferred in the nervous system...

    Authors: Maria Luisa Saggio, Andreas Spiegler, Christophe Bernard and Viktor K. Jirsa

    Citation: The Journal of Mathematical Neuroscience 2017 7:7

    Content type: Research

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  10. Point neuron models with a Heaviside firing rate function can be ill-posed. That is, the initial-condition-to-solution map might become discontinuous in finite time. If a Lipschitz continuous but steep firing rat...

    Authors: Bjørn Fredrik Nielsen

    Citation: The Journal of Mathematical Neuroscience 2017 7:6

    Content type: Research

    Published on:

  11. Low frequency firing is modeled by Type 1 neurons with a SNIC, but, because of the vertical slope of the square-root-like fI curve, low f only occurs over a narrow range of I. When an adaptive current is added, ...

    Authors: Arthur S. Sherman and Joon Ha

    Citation: The Journal of Mathematical Neuroscience 2017 7:4

    Content type: Research

    Published on:

  12. The Bienenstock–Cooper–Munro (BCM) learning rule provides a simple setup for synaptic modification that combines a Hebbian product rule with a homeostatic mechanism that keeps the weights bounded. The homeosta...

    Authors: Lawrence C. Udeigwe, Paul W. Munro and G. Bard Ermentrout

    Citation: The Journal of Mathematical Neuroscience 2017 7:2

    Content type: Research

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  13. Recent experimental evidence on the clustering of glutamate and GABA transporters on astrocytic processes surrounding synaptic terminals pose the question of the functional relevance of the astrocytes in the r...

    Authors: Aurélie Garnier, Alexandre Vidal and Habib Benali

    Citation: The Journal of Mathematical Neuroscience 2016 6:10

    Content type: Research

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  14. Presented here is a model of neural tissue in a conductive medium stimulated by externally injected currents. The tissue is described as a conductively isotropic bidomain, i.e. comprised of intra and extracell...

    Authors: Benjamin L. Schwartz, Munish Chauhan and Rosalind J. Sadleir

    Citation: The Journal of Mathematical Neuroscience 2016 6:9

    Content type: Research

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  15. We show that point-neuron models with a Heaviside firing rate function can be ill posed. More specifically, the initial-condition-to-solution map might become discontinuous in finite time. Consequently, if finite...

    Authors: Bjørn Fredrik Nielsen and John Wyller

    Citation: The Journal of Mathematical Neuroscience 2016 6:7

    Content type: Research

    Published on:

  16. Sensory input to the lamprey central pattern generator (CPG) for locomotion is known to have a significant role in modulating lamprey swimming. Lamprey CPGs are known to have the ability to entrain to a bendin...

    Authors: Nicole Massarelli, Geoffrey Clapp, Kathleen Hoffman and Tim Kiemel

    Citation: The Journal of Mathematical Neuroscience 2016 6:6

    Content type: Research

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  17. Jack Cowan’s remarkable career has spanned, and molded, the development of neuroscience as a quantitative and mathematical discipline combining deep theoretical contributions, rigorous mathematical work and gr...

    Authors: Paul C. Bressloff, Bard Ermentrout, Olivier Faugeras and Peter J. Thomas

    Citation: The Journal of Mathematical Neuroscience 2016 6:4

    Content type: Editorial

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  18. The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the class...

    Authors: Rüdiger Thul, Stephen Coombes and Carlo R. Laing

    Citation: The Journal of Mathematical Neuroscience 2016 6:3

    Content type: Research

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  19. In 1972–1973 Wilson and Cowan introduced a mathematical model of the population dynamics of synaptically coupled excitatory and inhibitory neurons in the neocortex. The model dealt only with the mean numbers o...

    Authors: Jack D. Cowan, Jeremy Neuman and Wim van Drongelen

    Citation: The Journal of Mathematical Neuroscience 2016 6:1

    Content type: Research

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  20. With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus ...

    Authors: Saing Paul Hou, Wassim M. Haddad, Nader Meskin and James M. Bailey

    Citation: The Journal of Mathematical Neuroscience (JMN) 2015 5:20

    Content type: Research

    Published on:

  21. In this note, we clarify the well-posedness of the limit equations to the mean-field N-neuron models proposed in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos...

    Authors: Mireille Bossy, Olivier Faugeras and Denis Talay

    Citation: The Journal of Mathematical Neuroscience (JMN) 2015 5:19

    Content type: Short report

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  22. In a previous work (Dafilis et al. in Chaos 23(2):023111, 2013), evidence was presented for four-dimensional chaos in Liley’s mesoscopic model of the electroencephalogram. The study was limited to one paramete...

    Authors: Mathew P. Dafilis, Federico Frascoli, Peter J. Cadusch and David T. J. Liley

    Citation: The Journal of Mathematical Neuroscience (JMN) 2015 5:18

    Content type: Short report

    Published on:

  23. 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...

    Authors: Peter De Maesschalck and Martin Wechselberger

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

    Content type: Research

    Published on:

  24. 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...

    Authors: Cynthia I. Wood and Illya V. Hicks

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

    Content type: Research

    Published on:

  25. Simple-spike synchrony between Purkinje cells projecting to a common neuron in the deep cerebellar nucleus is emerging as an important factor in the encoding of output information from cerebellar cortex. A phe...

    Authors: Sergio Verduzco-Flores

    Citation: The Journal of Mathematical Neuroscience (JMN) 2015 5:13

    Content type: Research

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  26. 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...

    Authors: Alexandre Afgoustidis

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

    Content type: Research

    Published on:

  27. This paper challenges and extends earlier seminal work. We consider the problem of describing mathematically the spontaneous activity of V1 by combining several important experimental observations including (1...

    Authors: Romain Veltz, Pascal Chossat and Olivier Faugeras

    Citation: The Journal of Mathematical Neuroscience (JMN) 2015 5:11

    Content type: Research

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  28. 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 ...

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

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

    Content type: Research

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  29. 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...

    Authors: 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

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

    Content type: Research

    Published on:

  30. 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...

    Authors: Carson C. Chow and Michael A. Buice

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

    Content type: Research

    Published on:

  31. We introduce a new formalism for evaluating analytically the cross-correlation structure of a finite-size firing-rate network with recurrent connections. The analysis performs a first-order perturbative expans...

    Authors: Diego Fasoli, Olivier Faugeras and Stefano Panzeri

    Citation: The Journal of Mathematical Neuroscience (JMN) 2015 5:6

    Content type: Research

    Published on:

  32. 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...

    Authors: Na Yu and Carmen C. Canavier

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

    Content type: Research

    Published on:

  33. 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 ...

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

    Citation: The Journal of Mathematical Neuroscience 2015 5:3

    Content type: Short report

    Published on:

  34. 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...

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

    Citation: The Journal of Mathematical Neuroscience 2015 5:2

    Content type: Research

    Published on:

  35. 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...

    Authors: Sergej O Voronenko, Wilhelm Stannat and Benjamin Lindner

    Citation: The Journal of Mathematical Neuroscience 2015 5:1

    Content type: Research

    Published on:

  36. Motivated by a model for neural networks with adaptation and fatigue, we study a conservative fragmentation equation that describes the density probability of neurons with an elapsed time s after its last dischar...

    Authors: Khashayar Pakdaman, Benoît Perthame and Delphine Salort

    Citation: The Journal of Mathematical Neuroscience 2014 4:14

    Content type: Research

    Published on:

  37. We investigate the dynamic mechanisms of generation of subthreshold and phase resonance in two-dimensional linear and linearized biophysical (conductance-based) models, and we extend our analysis to account fo...

    Authors: Horacio G Rotstein

    Citation: The Journal of Mathematical Neuroscience 2014 4:11

    Content type: Research

    Published on:

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