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  1. 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:

  2. 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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  3. 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

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  4. 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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  5. 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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  6. 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

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  7. 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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  8. 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

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  9. 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

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  10. 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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  11. 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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  12. 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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  13. 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

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  14. 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

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  15. 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

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  16. 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:

  17. 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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  18. 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:

  19. 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:

  20. 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:

  21. 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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  22. 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:

  23. 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:

  24. 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:

  25. 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:

  26. 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:

  27. 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

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  28. 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:

  29. “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:

  30. The spread of activity in neural populations is a well-known phenomenon. To understand the propagation speed and the stability of stationary fronts in neural populations, the present work considers a neural fi...

    Authors: Axel Hutt and Linghai Zhang

    Citation: The Journal of Mathematical Neuroscience 2013 3:9

    Content type: Research

    Published on:

  31. Theoretical models of associative memory generally assume most of their parameters to be homogeneous across the network. Conversely, biological neural networks exhibit high variability of structural as well as...

    Authors: Daniel Medina and Christian Leibold

    Citation: The Journal of Mathematical Neuroscience 2013 3:8

    Content type: Research

    Published on:

  32. Binocular rivalry is the alternation in visual perception that can occur when the two eyes are presented with different images. Wilson proposed a class of neuronal network models that generalize rivalry to mul...

    Authors: Casey O Diekman, Martin Golubitsky and Yunjiao Wang

    Citation: The Journal of Mathematical Neuroscience 2013 3:6

    Content type: Research

    Published on:

  33. In this paper, we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate ...

    Authors: Timothy J Taylor, Caroline Hartley, Péter L Simon, Istvan Z Kiss and Luc Berthouze

    Citation: The Journal of Mathematical Neuroscience 2013 3:5

    Content type: Research

    Published on:

  34. Mathematical neuroendocrinology is a branch of mathematical neurosciences that is specifically interested in endocrine neurons, which have the uncommon ability of secreting neurohormones into the blood. One of...

    Authors: Maciej Krupa, Alexandre Vidal and Frédérique Clément

    Citation: The Journal of Mathematical Neuroscience 2013 3:4

    Content type: Research

    Published on:

  35. Although spike trains are the principal channel of communication between neurons, a single stimulus will elicit different spike trains from trial to trial. This variability, in both spike timings and spike num...

    Authors: Hannah Julienne and Conor Houghton

    Citation: The Journal of Mathematical Neuroscience 2013 3:3

    Content type: Research

    Published on:

  36. Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to wea...

    Authors: Kyle CA Wedgwood, Kevin K Lin, Ruediger Thul and Stephen Coombes

    Citation: The Journal of Mathematical Neuroscience 2013 3:2

    Content type: Research

    Published on:

  37. We analytically investigate the stability of splay states in the networks of N globally pulse-coupled phase-like models of neurons. We develop a perturbative technique which allows determining the Floquet exponen...

    Authors: Simona Olmi, Antonio Politi and Alessandro Torcini

    Citation: The Journal of Mathematical Neuroscience 2012 2:12

    Content type: Research

    Published on:

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