The Journal of Mathematical Neuroscience

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Gradient estimation in dendritic reinforcement learning
The Journal of Mathematical Neuroscience - Tập 2 - Trang 1-19 - 2012
Mathieu Schiess, Robert Urbanczik, Walter Senn
We study synaptic plasticity in a complex neuronal cell model where NMDA-spikes can arise in certain dendritic zones. In the context of reinforcement learning, two kinds of plasticity rules are derived, zone reinforcement (ZR) and cell reinforcement (CR), which both optimize the expected reward by stochastic gradient ascent. For ZR, the synaptic plasticity response to the external reward signal is...... hiện toàn bộ
Editorial for Special Issue on Neurodynamics
The Journal of Mathematical Neuroscience - - 2013
Stephen Coombes, Yulia Timofeeva
Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise
The Journal of Mathematical Neuroscience - Tập 1 - Trang 1-28 - 2011
Paul C Bressloff, Yi Ming Lai
We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions ...... hiện toàn bộ
Monochromaticity of Orientation Maps in V1 Implies Minimum Variance for Hypercolumn Size
The Journal of Mathematical Neuroscience - Tập 5 - Trang 1-19 - 2015
Alexandre Afgoustidis
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: a repetitive, non-periodic, layout. This repetitive pattern is understood to be fundamental for basic non-local aspects of vision, like the perception of contours, but important questions rem...... hiện toàn bộ
The geometry of rest–spike bistability
The Journal of Mathematical Neuroscience - Tập 10 - Trang 1-18 - 2020
Giuseppe Ilario Cirillo, Rodolphe Sepulchre
Morris–Lecar model is arguably the simplest dynamical model that retains both the slow–fast geometry of excitable phase portraits and the physiological interpretation of a conductance-based model. We augment this model with one slow inward current to capture the additional property of bistability between a resting state and a spiking limit cycle for a range of input current. The resulting dynamica...... hiện toàn bộ
Inhomogeneous Sparseness Leads to Dynamic Instability During Sequence Memory Recall in a Recurrent Neural Network Model
The Journal of Mathematical Neuroscience - Tập 3 - Trang 1-23 - 2013
Daniel Medina, Christian Leibold
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 activity parameters. In this paper, we extend the classical clipped learning rule by Willshaw to networks with inhomogeneous sparseness, i.e., the number of active neurons may vary across me...... hiện toàn bộ
Frequency Preference Response to Oscillatory Inputs in Two-dimensional Neural Models: A Geometric Approach to Subthreshold Amplitude and Phase Resonance
The Journal of Mathematical Neuroscience - Tập 4 - Trang 1-41 - 2014
Horacio G Rotstein
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 for the effect of simple, but not necessarily weak, types of nonlinearities. Subthreshold resonance refers to the ability of neurons to exhibit a peak in their voltage amplitude response to osc...... hiện toàn bộ
Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience
The Journal of Mathematical Neuroscience - Tập 6 - Trang 1-92 - 2016
Peter Ashwin, Stephen Coombes, Rachel Nicks
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupl...... hiện toàn bộ
Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons
The Journal of Mathematical Neuroscience - - 2015
Sung Joon Moon, Katherine A Cook, Karthikeyan Rajendran, Ioannis G Kevrekidis, Jaime Cisternas, Carlo R Laing
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 synaptic coupling characteristic time is heterogeneous across the connections. In a network of N neurons where this heterogeneity is characterized by a prescribed random variable, the oscill...... hiện toàn bộ
Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states
The Journal of Mathematical Neuroscience - Tập 1 - Trang 1-33 - 2011
María J Cáceres, José A Carrillo, Benoît Perthame
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium...... hiện toàn bộ
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