On a Finite-Size Neuronal Population Equation

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Numerous tasks in robotics and character animation involve solving combinations of inverse kinematics and motion planning problems that require the precise design of pose sequences to achieve desired motion objectives. Accounting for the complex interplay ...

The International Tokamak Physics Activity (ITPA) has developed a comprehensive overview of the results of its coordinated R&D activities in fusion physics and diagnostics implemented during the past two decades with the aim of developing an improved physi ...

The Industrial Internet of Things (IIoT) is reshaping manufacturing, industrial processes, and infrastructure management. By fostering new levels of automation, efficiency, and predictive maintenance, IIoT is transforming traditional industries into intell ...

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

In computational neuroscience, multicompartment models are among the most biophysically realistic representations of single neurons. Constructing such models usually involves the use of the patch-clamp technique to record somatic voltage signals under diff ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Proprioception tells the brain the state of the body based on distributed sensors in the body. However, the principles that govern proprioceptive processing from those distributed sensors are poorly understood. Here, we employ a task-driven neural network ...

In humans and animals, surprise is a physiological reaction to an unexpected event, but how surprise can be linked to plausible models of neuronal activity is an open problem. We propose a self-supervised spiking neural network model where a surprise signa ...

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

Neural decoding of the visual system is a subject of research interest, both to understand how the visual system works and to be able to use this knowledge in areas, such as computer vision or brain-computer interfaces. Spike-based decoding is often used, ...

In this thesis we will present two results on global existence for nonlinear dispersive equations with data at or below the scaling regularity. In chapter 1 we take a probabilistic perspective to study the energy-critical nonlinear Schrödinger equation in ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Subcortical brain structures such as the basal ganglia or the thalamus are involved in regulating motor and cognitive behavior. However, their contribution to perceptual consciousness is still unclear, due to the inherent difficulties of recording subcorti ...

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

Proprioception tells the brain the state of the body based on distributed sensory neurons. Yet, the principles that govern proprioceptive processing are poorly understood. Here, we employ a task -driven modeling approach to investigate the neural code of p ...

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

Over the course of a lifetime, the human brain acquires an astonishing amount of semantic knowledge and autobiographical memories, often with an imprinting strong enough to allow detailed information to be recalled many years after the initial learning exp ...

On a Finite-Size Neuronal Population Equation

Chattez avec Graph Search

Inverse Geometric Locomotion

Introduction and Overview: Chapter 1 of the Special Issue: on the Path to Tokamak Burning Plasma Operation

Physics-Enhanced Graph Neural Networks for Soft Sensing in Industrial Internet of Things

Generalization of Scaled Deep ResNets in the Mean-Field Regime

A multi-modal fitting approach to construct single-neuron models with patch clamp and high-density microelectrode arrays

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Task-driven neural network models predict neural dynamics of proprioception: Neural network model weights

Fast adaptation to rule switching using neuronal surprise

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Anomalous dissipation and other non-smooth phenomena in fluids

Predicting Visual Stimuli From Cortical Response Recorded With Wide-Field Imaging in a Mouse

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Subcortical correlates of consciousness with human single neuron recordings

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Task-driven neural network models predict neural dynamics of proprioception

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

From low-rank retractions to dynamical low-rank approximation and back

Stochastic particle transport by deep-water irregular breaking waves

A theory of memory consolidation and synaptic pruning in cortical circuits