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  1. Content type: Research

    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

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  2. Content type: Research

    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

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  3. Content type: Research

    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

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  4. Content type: Research

    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

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  5. Content type: Short report

    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

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  6. Content type: Research

    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

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  7. Content type: Research

    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

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  8. Content type: Research

    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

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  9. Content type: Research

    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

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  10. Content type: Research

    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

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  11. Content type: Research

    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

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  12. Content type: Research

    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

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  13. Content type: Research

    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

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  14. Content type: Research

    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

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  15. Content type: Research

    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

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  16. Content type: Research

    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

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  17. Content type: Research

    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

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  18. Content type: Research

    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

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  19. Content type: Research

    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

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  20. Content type: Research

    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

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  21. Content type: Research

    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

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  22. Content type: Editorial

    “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

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  23. Content type: Research

    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

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  24. Content type: Research

    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

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  25. Content type: Research

    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

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  26. Content type: Research

    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

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  27. Content type: Research

    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

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  28. Content type: Research

    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

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  29. Content type: Research

    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

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  30. Content type: Research

    Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties ...

    Authors: Quentin Caudron, Simon R Donnelly, Samuel PC Brand and Yulia Timofeeva

    Citation: The Journal of Mathematical Neuroscience 2012 2:11

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  31. Content type: Research

    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

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  32. Content type: Research

    We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are repre...

    Authors: Javier Baladron, Diego Fasoli, Olivier Faugeras and Jonathan Touboul

    Citation: The Journal of Mathematical Neuroscience 2012 2:10

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  33. Content type: Research

    Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where ...

    Authors: Stephen Coombes, Helmut Schmidt and Ingo Bojak

    Citation: The Journal of Mathematical Neuroscience 2012 2:9

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  34. Content type: Research

    A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considere...

    Authors: Sid Visser, Hil GE Meijer, Michel JAM van Putten and Stephan A van Gils

    Citation: The Journal of Mathematical Neuroscience 2012 2:8

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  35. Content type: Research

    In this paper, we analyze the invasion and extinction of activity in heterogeneous neural fields. We first consider the effects of spatial heterogeneities on the propagation of an invasive activity front. In c...

    Authors: Paul C Bressloff

    Citation: The Journal of Mathematical Neuroscience 2012 2:6

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  36. Content type: Research

    We consider a coupled, heterogeneous population of relaxation oscillators used to model rhythmic oscillations in the pre-Bötzinger complex. By choosing specific values of the parameter used to describe the het...

    Authors: Carlo R Laing, Yu Zou, Ben Smith and Ioannis G Kevrekidis

    Citation: The Journal of Mathematical Neuroscience 2012 2:5

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