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On a Finite-Size Neuronal Population Equation

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Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

Maria Colombo, Silja Noëmi Aline Haffter

We consider the defocusing nonlinear wave equation ❑u D jujp ⠀1u in R3 ⠂ & UOELIG;0; 1/. We prove that for any initial datum with a scaling-subcritical norm bounded by M0 the equation is globally well-posed for p D 5 C i, where i 2 .0; ...

MATHEMATICAL SCIENCE PUBL2023

Taming neuronal noise with large networks

Valentin Marc Schmutz

How does reliable computation emerge from networks of noisy neurons? While individual neurons are intrinsically noisy, the collective dynamics of populations of neurons taken as a whole can be almost deterministic, supporting the hypothesis that, in the br ...

EPFL2022

Regularization of multiplicative SDEs through additive noise

Lucio Galeati

We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure existence ...

2022

Fitting summary statistics of neural data with a differentiable spiking network simulator

Wulfram Gerstner, Johanni Michael Brea, Alireza Modirshanechi, Shuqi Wang

Fitting network models to neural activity is an important tool in neuroscience. A popular approach is to model a brain area with a probabilistic recurrent spiking network whose parameters maximize the likelihood of the recorded activity. Although this is w ...

2021

For solving tasks such as recognizing a song, answering a question, or inverting a sequence of symbols, cortical microcircuits need to integrate and manipulate information that was dispersed over time during the preceding seconds. Creating biologically rea ...

ELIFE SCIENCES PUBLICATIONS LTD2021

Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity

Wulfram Gerstner, Tilo Schwalger, Valentin Marc Schmutz

Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static s ...

2020

An efficient analytical reduction of detailed nonlinear neuron models

Felix Schürmann, Pramod Shivaji Kumbhar, Michael Emiel Gevaert, Oren Amsalem, Idan Segev, Guy Eyal

Detailed conductance-based nonlinear neuron models consisting of thousands of synapses are key for understanding of the computational properties of single neurons and large neuronal networks, and for interpreting experimental results. Simulations of these ...

2020

Recent advances in Voice Activity Detection (VAD) are driven by artificial and Recurrent Neural Networks (RNNs), however, using a VAD system in battery-operated devices requires further power efficiency. This can be achieved by neuromorphic hardware, which ...

IEEE2020

On the equation A del u plus (del u)(t) A = G

Bernard Dacorogna

Let Omega subset of R-n be an open set, A is an element of R-nxn and G : Omega -> R-nxn be given. We look for a solution u : Omega -> R-n of the equation A del u + (del u)(t) A = G We also study the associated Dirichlet problem. (C) 2020 Elsevier Ltd. All ...

PERGAMON-ELSEVIER SCIENCE LTD2020

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While most models of randomly connected neural networks assume single-neuron models with simple dynamics, neurons in the brain exhibit complex intrinsic dynamics over multiple timescales. We analyze how the dynamical properties of single neurons and recurr ...

2019