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On a Finite-Size Neuronal Population Equation

Publications associées (44)

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Statistical models of effective connectivity in neural microcircuits

Joao Emanuel Felipe Gerhard

To appreciate how neural circuits in the brain control behaviors, we must identify how the neurons comprising the circuit are connected. Neuronal connectivity is difficult to determine experimentally, whereas neuronal activity can often be readily measured ...

EPFL2014

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The growing number of large-scale neuronal network models has created a need for standards and guidelines to ease model sharing and facilitate the replication of results across different simulators. To foster community efforts towards such standards, the I ...

2011

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Multiple measures have been developed to quantify the similarity between two spike trains. These measures have been used for the quantification of the mismatch between neuron models and experiments as well as for the classification of neuronal responses in ...

Massachusetts Institute of Technology Press2011

Sequences of events in noise-driven excitable systems with slow variables often show serial correlations among their intervals of events. Here, we employ a master equation for generalized non-renewal processes to calculate the interval and count statistics ...

2011

Goodness-of-fit tests for neural population models: the multivariate time-rescaling theorem

Joao Emanuel Felipe Gerhard

Statistical models of neural activity are at the core of the field of modern computational neuroscience. The activity of single neurons has been modeled to successfully explain dependencies of neural dynamics to its own spiking history, to external stimuli ...

2010

Statistical tests for neural population models - The multivariate time rescaling theorem

Joao Emanuel Felipe Gerhard

The coordinated, collective spiking activity of neuronal populations encodes and processes information. One approach towards understanding such population based computation is to fit statistical models to simultaneously recorded spike trains and use these ...

2010

We describe in this article two recent results [11], [12], obtained by the author jointly with W. Schlag and D. Tataru, about singular solutions for the critical wave maps equation, as well as the critical focussing semilinear wave equation. Specifically, ...

2010

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In this paper a detailed mathematical procedure is described to evaluate modal scattering parameters conventionally defined in planar multilayered structures excited by wave ports. Combined Field Integral Equation technique is implemented and solved using ...

2009

The non-linear stochastic wave equation in high dimensions

Daniel Conus

The main topic of this thesis is the study of the non-linear stochastic wave equation in spatial dimension greater than 3 driven by spatially homogeneous Gaussian noise that is white in time. We are interested in questions of existence and uniqueness of so ...

EPFL2008

Simple Neuron Models and Adaptation

Skander Mensi

Predicting activity of single neuron is an important part of the computational neuroscience and a great challenge. Several mathematical models exist, from the simple (one compartment and few parameters, like the SRM or the IF-type models), to the more comp ...

2008