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Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience [PDF]

Journal of Mathematical Neuroscience, 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.
Peter Ashwin, Rachel Nicks, Stephen Coombes   +2 more
exaly   +8 more sources

Mathematical Foundations of Neuroscience [PDF]

Interdisciplinary Applied Mathematics, 2010
The Hodgkin-Huxley Equations.- Dendrites.- Dynamics.- The Variety of Channels.- Bursting Oscillations.- Propagating Action Potentials.- Synaptic Channels.- Neural Oscillators: Weak Coupling.- Neuronal Networks: Fast/Slow Analysis.- Noise.- Firing Rate Models.- Spatially Distributed Networks.
Bard Ermentrout, David H Terman
exaly   +2 more sources

Systems Neuroscience of Mathematical Cognition and Learning

, 2018
International audienceIn this chapter, we take a systems neuroscience approach and review neurocognitive systems involved in mathematical cognition and learning, highlighting functional brain circuits that support these processes and sources of ...
Teresa Iuculano, Vinod Menon
exaly   +2 more sources

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Canonical models for mathematical neuroscience

Proceedings of International Conference on Neural Networks (ICNN'97), 2002
A major drawback to most mathematical models in neuroscience is that they are either far away from reality or the results depend on the specific model. A promising alternative approach takes advantage of the fact that many complicated systems behave similarly when they operate near critical regimes, such as bifurcations.
Frank C. Hoppensteadt, Eugene M. Izhikevich   +1 more
openaire   +1 more source

Neurosciences mathématiques / Mathematical neuroscience

L’annuaire du Collège de France, 2018
Responsable : Jonathan Touboul Publications del Molino L.C.G., Pakdaman K., Touboul J. et Wainrib G., « The real ginibre ensemble with real eigenvalues », Journal of Statistical Physics, vol. 163, n° 2, 2016, p. 303-323, DOI : 10.1007/s10955-016-1485-0. Freret-Hodara B., Cui Y., Griveau A., Vigier L., Arai Y., Touboul J.
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Role of Mathematics in Neuroscience

Journal of Applied Science and Education (JASE), 2023
With the growing role and application of mathematics in almost every field it is no doubt that it plays an experimental and crucial role in an advancing field of neuroscience which is still under constant research. The aim of the report is two fundamental points: to show how mathematical models that enlighten a few pieces of neuroscience can be built ...
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Mathematical modeling and the neuroscience of metaphor

SPIE Proceedings, 2008
We look at a characterization of metaphor from cognitive linguistics, extracting the salient features of metaphorical processing. We examine the neurobiology of dendrites, specifically spike timing-dependent plasticity (STDP), and the modulation of backpropagating action potentials (bAPs), to generate a neuropil-centric model of cortical processing ...
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Some Joys and Trials of Mathematical Neuroscience

Journal of Nonlinear Science, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

NEUROSCIENCE AND MATHEMATICAL EDUCATION

Journal of Interdisciplinary Debates
This article explored how neuroscience knowledge can enrich pedagogical practice in teaching Mathematics, especially in the final years of Elementary School. The research problem investigated how neuroscience contributes to understanding brain development, students and to formulating effective pedagogical strategies.
Emanuel Adeilton de O. Andrade, Isaías Pessoa da Silva, Maria Aldeni de O. Andrade, Francisco De Assis de O. Andrade   +3 more
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Mathematical Modeling in Neuroscience

2020
Mathematical modeling has been and will continue to be central to the understanding of the emerging function of the nervous system. From the firing of action potentials – with their all-or-none characteristic – to the rich dynamical repertoire of neural networks, the equations and numerical models that describe them are a key part of our understanding ...
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