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A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak $L^\infty$-solutions are renormalized. But then, if the noise is nondegenerate, uniqueness…
We consider motion of an overdamped Brownian particle subject to stochastic resetting in one dimension. In contrast to the usual setting where the particle is instantaneously reset to a preferred location (say, the origin), here we consider…
We derive the effective hamiltonian for a charge-Josephson qubit in a circuit with no use of phenomenological arguments, showing how energy renormalizations induced by the environment appear with no need of phenomenological counterterms.…
Convolutional neural networks (CNNs), one of the key architectures of deep learning models, have achieved superior performance on many machine learning tasks such as image classification, video recognition, and power systems. Despite their…
We determine the small signal gain and noise response of an amplifier based on the nonlinear response of a quantum nanomechanical resonator. The resonator is biased in the nonlinear regime by a strong harmonic bias force and we determine…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…
The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular,…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
Transport of a Brownian particle moving along the axis of a three-dimensional asymmetric periodic tube is investigated in the presence of asymmetric unbiased forces. The reduction of the coordinates may involve not only the appearance of…
Having a priori knowledge of the force acting on a noisy system it is possible to solve the issue relative to the interpretation of multiplicative noise terms (aka Ito-Stratonovich dilemma). We experimentally show that for a Brownian…
Corrupting the input and hidden layers of deep neural networks (DNNs) with multiplicative noise, often drawn from the Bernoulli distribution (or 'dropout'), provides regularization that has significantly contributed to deep learning's…
Model-free reconstruction of the bifurcation diagrams of Chua's circuits by the technique of parameter-aware reservoir computing is investigated. We demonstrate that: (1) reservoir computer can be utilized as a noise filter to recover the…
In recent literature there has been a lot of interest in the phenomena of noise induced transport in the absence of an average bias occurring in spatially periodic systems far from equilibrium. One of the main motivations in this area is to…
Transport of Brownian particles interacting with each other via the Morse potential is investigated in the presence of an ac driving force applied locally at one end of the chain. By using numerical simulations, we find that the system can…
The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced…
We study an inverse problem for the time-dependent Maxwell system in an inhomogeneous and anisotropic medium. The objective is to recover the initial electric field $\mathbf{E}_0$ in a bounded domain $\Omega \subset \mathbb{R}^3$, using…
A system of periodically coupled nonlinear phase oscillators submitted to both additive and multiplicative white noises has been recently shown to exhibit ratchetlike transport, negative zero-bias conductance, and anomalous hysteresis.…
Based on analytical and numerical calculations we study the dynamics of an overdamped colloidal particle moving in two dimensions under time-delayed, non-linear feedback control. Specifically, the particle is subject to a force derived from…
Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with…
We present a noise deconvolution technique for obtaining noiseless expectation values of noisy observables at the output of multiqubit quantum channels. For any number of qubits or in the presence of correlations, our protocol applies to…