THE COMPACT SUPPORT PROPERTY FOR SOLUTIONS TO THE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH COLORED NOISE

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In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term. Large devi ...

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Ion transport through biological and solid-state nanochannels is known to be a highly noisy process. The power spectrum of current fluctuations is empirically known to scale like the inverse of frequency, following the long-standing yet poorly understood H ...

Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The cons ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

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Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...

A space-time adaptive algorithm is presented to solve the incompressible Navier-Stokes equations. Time discretization is performed with the BDF2 method while continuous, piecewise linear anisotropic finite elements are used for the space discretization. Th ...

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Collaborative learning algorithms, such as distributed SGD (or D-SGD), are prone to faulty machines that may deviate from their prescribed algorithm because of software or hardware bugs, poisoned data or malicious behaviors. While many solutions have been ...

THE COMPACT SUPPORT PROPERTY FOR SOLUTIONS TO THE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH COLORED NOISE

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LDP and CLT for SPDEs with transport noise

Low-Rank Tensor Methods for High-Dimensional Problems

Multi-agent Learning with Privacy Guarantees

Disentangling 1/f noise from confined ion dynamics

Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Functional data analysis with rough sample paths?

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Distributionally Robust Linear Quadratic Control

Stochastic particle transport by deep-water irregular breaking waves

Enhanced Leaching of Zinc Ferrite by the Formation of a Solid Solution With Magnetite in Hydrochloric Acid Solution

On a Finite-Size Neuronal Population Equation

An adaptive space-time algorithm for the incompressible Navier-Stokes equations

Machine Learning Methods for Robust Uncertainty Quantification and Controller Approximation

Universal and adaptive methods for robust stochastic optimization

Potential scientific synergies in weak lensing studies between the CSST and Euclid space probes

Robust Collaborative Learning with Linear Gradient Overhead