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Probabilistic solutions of high order partial differential equations

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Supersymmetries in nonequilibrium Langevin dynamics

Elisabeth Agoritsas

Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It has been known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). Th ...

2021

Normalized Gaussian path integrals

Giulio Corazza

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...

AMER PHYSICAL SOC2020

An Ultra Low-Noise Micropower PPG Sensor

Antonino Caizzone

Nowadays, efficient and remote health monitoring is becoming increasingly important, given both the ageing of population and the combined action of an increase in obesity level and cardiovascular diseases. The healthcare industry is becoming more reliant o ...

EPFL2020

Increasing risk: Dynamic mean-preserving spreads

Max-Olivier Hongler

We extend the celebrated Rothschild and Stiglitz (1970) definition of Mean-Preserving Spreads to a dynamic framework. We adapt the original integral conditions to transition probability densities, and give sufficient conditions for their satisfaction. We t ...

2020

Fokker-Planck-Poisson kinetics: Multi-phase flow beyond equilibrium

Mohsen Sadr

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighboring phases, yet their closure far from the continuum needs to be modeled. Along the hierarchy of kinetic ...

2020

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

Max-Olivier Hongler, Roger Filliger

We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial dif ...

Springer2019

Noise-induced desynchronization and stochastic escape from equilibrium in complex networks

Robin Delabays

Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. If these terms are large enough, the ...

2019

UniXGrad: A Universal, Adaptive Algorithm with Optimal Guarantees for Constrained Optimization

Volkan Cevher, Ali Kavis

We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth problems with eit ...

2019

UniXGrad: A Universal, Adaptive Algorithm with Optimal Guarantees for Constrained Optimization

Volkan Cevher, Ali Kavis

We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, simultaneously achieves the optimal rates for smooth/non-smooth problems with either det ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Noise Analysis For Environmental Loading Effect On Gps Position Time Series

Jean-Philippe Lucien Montillet, Feng Zhou

This paper focusses on the impact of environment mass loading on GPS time-series of position changes and noise characteristic. We make use of position time series of 206 GPS station ranging from 2001 to 2013 globally distributed. Firstly, we investigate th ...

Institute of Rock Structure and Mechanics, AS CR2017