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
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...
Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise
The Journal of Mathematical Neuroscience - Tập 1 - Trang 1-28 - 2011
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 ...
Monochromaticity of Orientation Maps in V1 Implies Minimum Variance for Hypercolumn Size
The Journal of Mathematical Neuroscience - Tập 5 - Trang 1-19 - 2015
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...
The geometry of rest–spike bistability
The Journal of Mathematical Neuroscience - Tập 10 - Trang 1-18 - 2020
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...
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
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...
The dynamics underlying pseudo-plateau bursting in a pituitary cell model
The Journal of Mathematical Neuroscience - Tập 1 - Trang 1-23 - 2011
Pituitary cells of the anterior pituitary gland secrete hormones in response to
patterns of electrical activity. Several types of pituitary cells produce short
bursts of electrical activity which are more effective than single spikes in
evoking hormone release. These bursts, called pseudo-plateau bursts, are unlike
bursts studied mathematically in neurons (plateau bursting) and the standard
fast-s...
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
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...
Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience
The Journal of Mathematical Neuroscience - Tập 6 - Trang 1-92 - 2016
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...
Efficient calculation of heterogeneous non-equilibrium statistics in coupled firing-rate models
The Journal of Mathematical Neuroscience - Tập 9 - Trang 1-11 - 2019
Understanding nervous system function requires careful study of transient
(non-equilibrium) neural response to rapidly changing, noisy input from the
outside world. Such neural response results from dynamic interactions among
multiple, heterogeneous brain regions. Realistic modeling of these large
networks requires enormous computational resources, especially when
high-dimensional parameter spaces...
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