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  1. 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

    Published on:

  2. 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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  3. 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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  4. 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

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  5. 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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  6. 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

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  7. 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

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  8. 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

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  9. 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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  10. 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:

  11. 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

    Published on:

  12. 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

    Published on:

  13. 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:

  14. 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

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  15. 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:

  16. 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:

  17. 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

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  18. 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

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  19. 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

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  20. 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:

  21. 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:

  22. 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...

    Authors: Casey O Diekman and Martin Golubitsky

    Citation: The Journal of Mathematical Neuroscience 2014 4:12

    Content type: Research

    Published on:

  23. We study the effects of synaptic plasticity on the determination of firing period and relative phases in a network of two oscillatory neurons coupled with reciprocal inhibition. We combine the phase response c...

    Authors: Zeynep Akcay, Amitabha Bose and Farzan Nadim

    Citation: The Journal of Mathematical Neuroscience 2014 4:8

    Content type: Research

    Published on:

  24. The most basic functional role commonly ascribed to synchrony in the brain is that of amplifying excitatory neuronal signals. The reasoning is straightforward: When positive charge is injected into a leaky tar...

    Authors: Christoph Börgers, Jie Li and Nancy Kopell

    Citation: The Journal of Mathematical Neuroscience 2014 4:10

    Content type: Research

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  25. 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...

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

    Citation: The Journal of Mathematical Neuroscience 2014 4:9

    Content type: Research

    Published on:

  26. Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Galán recently introduced a novel stochast...

    Authors: Deena R Schmidt and Peter J Thomas

    Citation: The Journal of Mathematical Neuroscience 2014 4:6

    Content type: Research

    Published on:

  27. We propose a theoretical motivation to quantify actual physiological features, such as the shape index distributions measured by Jones and Palmer in cats and by Ringach in macaque monkeys. We will adopt the un...

    Authors: D Barbieri, G Citti and A Sarti

    Citation: The Journal of Mathematical Neuroscience 2014 4:5

    Content type: Research

    Published on:

  28. Analysis of sinusoidal noisy leaky integrate-and-fire models and comparison with experimental data are important to understand the neural code and neural synchronization and rhythms. In this paper, we propose ...

    Authors: Alexandre Iolov, Susanne Ditlevsen and André Longtin

    Citation: The Journal of Mathematical Neuroscience 2014 4:4

    Content type: Research

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  29. When dealing with classical spike train analysis, the practitioner often performs goodness-of-fit tests to test whether the observed process is a Poisson process, for instance, or if it obeys another type of p...

    Authors: Patricia Reynaud-Bouret, Vincent Rivoirard, Franck Grammont and Christine Tuleau-Malot

    Citation: The Journal of Mathematical Neuroscience 2014 4:3

    Content type: Research

    Published on:

  30. Population density models that are used to describe the evolution of neural populations in a phase space are closely related to the single neuron model that describes the individual trajectories of the neurons...

    Authors: Grégory Dumont, Jacques Henry and Carmen Oana Tarniceriu

    Citation: The Journal of Mathematical Neuroscience 2014 4:2

    Content type: Research

    Published on:

  31. We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape....

    Authors: Christian Kuehn and Martin G Riedler

    Citation: The Journal of Mathematical Neuroscience 2014 4:1

    Content type: Research

    Published on:

  32. In this paper, we study the dynamics of a quadratic integrate-and-fire neuron, spiking in the gamma (30–100 Hz) range, coupled to a delta/theta frequency (1–8 Hz) neural oscillator. Using analytical and semian...

    Authors: Lorenzo Fontolan, Maciej Krupa, Alexandre Hyafil and Boris Gutkin

    Citation: The Journal of Mathematical Neuroscience 2013 3:16

    Content type: Research

    Published on:

  33. Oscillations in the basal ganglia are an active area of research and have been shown to relate to the hypokinetic motor symptoms of Parkinson’s disease. We study oscillations in a multi-channel mean field mode...

    Authors: Robert Merrison-Hort, Nada Yousif, Felix Njap, Ulrich G Hofmann, Oleksandr Burylko and Roman Borisyuk

    Citation: The Journal of Mathematical Neuroscience 2013 3:14

    Content type: Research

    Published on:

  34. The phase response curve (PRC) is a powerful tool to study the effect of a perturbation on the phase of an oscillator, assuming that all the dynamics can be explained by the phase variable. However, factors li...

    Authors: Oriol Castejón, Antoni Guillamon and Gemma Huguet

    Citation: The Journal of Mathematical Neuroscience 2013 3:13

    Content type: Research

    Published on:

  35. We investigate firing threshold manifolds in a mathematical model of an excitable neuron. The model analyzed investigates the phenomenon of post-inhibitory rebound spiking due to propofol anesthesia and is ada...

    Authors: John Mitry, Michelle McCarthy, Nancy Kopell and Martin Wechselberger

    Citation: The Journal of Mathematical Neuroscience 2013 3:12

    Content type: Research

    Published on:

  36. “Neurodynamics” is an interdisciplinary area of mathematics where dynamical systems theory (deterministic and stochastic) is the primary tool for elucidating the fundamental mechanisms responsible for the beha...

    Authors: Stephen Coombes and Yulia Timofeeva

    Citation: The Journal of Mathematical Neuroscience 2013 3:10

    Content type: Editorial

    Published on:

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