Mathematical neuroscience: from neurons to circuits to systems

@article{Gutkin2003MathematicalNF,
  title={Mathematical neuroscience: from neurons to circuits to systems},
  author={Boris S. Gutkin and David J. Pinto and Bard Ermentrout},
  journal={Journal of Physiology-Paris},
  year={2003},
  volume={97},
  pages={209-219}
}
Applications of mathematics and computational techniques to our understanding of neuronal systems are provided. [...] Key Method Spatio-temporal pattern formation methods are applied to explain the patterns seen in the early stages of drug-induced visual hallucinations.Expand
A unified mathematical model of neuronal population networks
We examine systems of integro–differential equations which model activity in populations of excitatory and inhibitory neurons on spatially extended domains. First, we review previous analyticalExpand
Reproducing the Firing Properties of a Cerebellum Deep Cerebellar Nucleus with a Multi-Compartmental Morphologically Realistic Biophysical Model
TLDR
Simulations demonstrate that the inhibitory input can alter the temporal patterns in DCN and could modify sensory-tactile and other signals to interconnected motor circuits. Expand
Human Brain Networks: Spiking Neuron Models, Multistability, Synchronization, Thermodynamics, Maximum Entropy Production, and Anesthetic Cascade Mechanisms
TLDR
Lyapunov-based tests for multistability and synchronization of dynamical systems with continuously differentiable and absolutely continuous flows are established and the results are applied to excitatory and inhibitory biological neuronal networks to explain the underlying mechanism of action for anesthesia and consciousness from a multistable dynamical system perspective. Expand
Synchronization of biological neural network systems with stochastic perturbations and time delays
TLDR
A stochastic synaptic drive firing rate model for an excitatory and inhibitory cortical neuronal network in the face of system time delays is developed and sufficient conditions for global asymptotic mean-square synchronization for this model are provided. Expand
A stochastic mean field model for an excitatory and inhibitory synaptic drive cortical neuronal network
TLDR
A mean field synaptic firing rate cortical neuronal model is developed and it is demonstrated how the induction of general anesthesia can be explained using multistability; the property whereby the solutions of a dynamical system exhibit multiple attracting equilibria under asymptotically slowly changing inputs or system parameters. Expand
A stochastic mean field model for an excitatory and inhibitory synaptic drive cortical neuronal network
TLDR
A mean field synaptic firing rate cortical neuronal model is developed and it is demonstrated how the induction of general anesthesia can be explained using multistability; the property whereby the solutions of a dynamical system exhibit multiple attracting equilibria under asymptotically slowly changing inputs or system parameters. Expand
Synchronization of biological neural network systems with stochastic perturbations and time delays
TLDR
A stochastic synaptic drive firing rate model for an excitatory and inhibitory cortical neuronal network in the face of system time delays and stochastically input disturbances is developed. Expand
Dopamine and gamma band synchrony in schizophrenia – insights from computational and empirical studies
TLDR
Computational and empirical investigations indicate that dopamine can modulate cortical gamma band synchrony in an inverted‐U fashion and that the physiologic effects of dopamine on single fast‐spiking interneurons can give rise to such non‐monotonic effects at the network level. Expand
Spiking Neural Networks
TLDR
A state-of-the-art review of the development of spiking neurons and SNNs is presented, and insight into their evolution as the third generation neural networks is provided. Expand
Neurodynamics of consciousness
One of the main outstanding problems in the cognitive sciences is to understand how ongoing conscious experience is related to the workings of the brain and nervous system. Neurodynamics offers aExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 40 REFERENCES
Reliability of spike timing in neocortical neurons.
TLDR
Data suggest a low intrinsic noise level in spike generation, which could allow cortical neurons to accurately transform synaptic input into spike sequences, supporting a possible role for spike timing in the processing of cortical information by the neocortex. Expand
The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding
TLDR
It is suggested that quantities are represented as rate codes in ensembles of 50–100 neurons, which implies that single neurons perform simple algebra resembling averaging, and that more sophisticated computations arise by virtue of the anatomical convergence of novel combinations of inputs to the cortical column from external sources. Expand
A quantitative population model of whisker barrels: Re-examining the Wilson-Cowan equations
TLDR
This work employs semirigorous techniques to reduce the biologically based integrate and fire model of a rat whisker barrel to a simple set of equations, similar to the Wilson-Cowan equations, while retaining the ability for both qualitative and quantitative comparisons with the biological system. Expand
Thalamocortical response transformations in simulated whisker barrels
  • H. Kyriazi, D. Simons
  • Chemistry, Medicine
  • The Journal of neuroscience : the official journal of the Society for Neuroscience
  • 1993
TLDR
Thalamic relay neurons not only provide essential drive to the cortex but could, by changing their tonic activities, also directly regulate the tonic inhibition present in the cortex and thereby modulate cortical receptive field properties. Expand
Neural networks as spatio-temporal pattern-forming systems
Models of neural networks are developed from a biological point of view. Small networks are analysed using techniques from dynamical systems. The behaviour of spatially and temporally organizedExpand
Cortical damping: analysis of thalamocortical response transformations in rodent barrel cortex.
TLDR
It is found that strong inhibition renders the net effect of intracortical connections suppressive or damping, distinguishing it from previous amplifying models of cortical microcircuits. Expand
Dynamics of Membrane Excitability Determine Interspike Interval Variability: A Link Between Spike Generation Mechanisms and Cortical Spike Train Statistics
TLDR
The results suggest that the high CV values such as those observed in cortical spike trains are an intrinsic characteristic of type I membranes driven to firing by random inputs, in contrast to neural oscillators or neurons exhibiting type II excitability should produce regular spike trains. Expand
Spike Generating Dynamics and the Conditions for Spike-Time Precision in Cortical Neurons
TLDR
It is found that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing, and viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision. Expand
The Effects of Spike Frequency Adaptation and Negative Feedback on the Synchronization of Neural Oscillators
TLDR
It is shown through an analysis of some standard models, that the M-current adaptation alters the mechanism for repetitive firing, while the after hyperpolarization adaptation works via shunting the incoming synapses. Expand
Circuit dynamics and coding strategies in rodent somatosensory cortex.
TLDR
These findings validate the predictions of the modeling studies and demonstrate that the mechanism by which the cortex processes an afferent signal is inextricably linked with, and in fact determines, the saliency of neural codes embedded in the thalamic response. Expand
...
1
2
3
4
...