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Research
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...
The Journal of Mathematical Neuroscience (JMN) 2015 5:12
Published on: 17 June 2015
Research
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...
The Journal of Mathematical Neuroscience (JMN) 2015 5:11
Published on: 30 May 2015
Research
In the primary visual cortex of many mammals, the processing of sensory information involves recognizing stimuli orientations. The repartition of preferred orientations of neurons in some areas is remarkable: ...
The Journal of Mathematical Neuroscience (JMN) 2015 5:10
Published on: 8 April 2015
Research
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 ...
The Journal of Mathematical Neuroscience (JMN) 2015 5:9
Published on: 8 April 2015
Research
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...
The Journal of Mathematical Neuroscience (JMN) 2015 5:7
Published on: 27 March 2015
Research
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...
The Journal of Mathematical Neuroscience (JMN) 2015 5:8
Published on: 24 March 2015
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...
The Journal of Mathematical Neuroscience (JMN) 2015 5:6
Published on: 15 March 2015
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...
The Journal of Mathematical Neuroscience (JMN) 2015 5:5
Published on: 27 February 2015
Research
We consider applications of path-integral methods to the analysis of a stochastic hybrid model representing a network of synaptically coupled spiking neuronal populations. The state of each local population is...
The Journal of Mathematical Neuroscience (JMN) 2015 5:4
Published on: 27 February 2015
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 ...
The Journal of Mathematical Neuroscience 2015 5:3
Published on: 12 January 2015
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...
The Journal of Mathematical Neuroscience 2015 5:2
Published on: 12 January 2015
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...
The Journal of Mathematical Neuroscience 2015 5:1
Published on: 12 January 2015
Review
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...
The Journal of Mathematical Neuroscience 2014 4:13
Published on: 25 July 2014
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...
The Journal of Mathematical Neuroscience 2014 4:14
Published on: 24 July 2014
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...
The Journal of Mathematical Neuroscience 2014 4:11
Published on: 8 May 2014
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...
The Journal of Mathematical Neuroscience 2014 4:12
Published on: 7 May 2014
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...
The Journal of Mathematical Neuroscience 2014 4:8
Published on: 29 April 2014
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...
The Journal of Mathematical Neuroscience 2014 4:9
Published on: 25 April 2014
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...
The Journal of Mathematical Neuroscience 2014 4:10
Published on: 25 April 2014
Editorial
The Journal of Mathematical Neuroscience 2014 4:7
Published on: 17 April 2014
Research
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 ...
The Journal of Mathematical Neuroscience 2014 4:22
Published on: 17 April 2014
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...
The Journal of Mathematical Neuroscience 2014 4:2
Published on: 17 April 2014
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 ...
The Journal of Mathematical Neuroscience 2014 4:4
Published on: 17 April 2014
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...
The Journal of Mathematical Neuroscience 2014 4:6
Published on: 17 April 2014
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....
The Journal of Mathematical Neuroscience 2014 4:1
Published on: 17 April 2014
