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A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be…
A sampling procedure to compute exactly the rate of activated processes arising in systems at equilibrium or nonequilibrium steady state is presented. The procedure is a generalization of the method in [A. Warmflash, P. Bhimalapuram, and A.…
For systems in nonequilibrium steady states, a novel modulated Gaussian probability distribution is derived to incorporate a new phenomenon of biased current fluctuations, discovered by recent laboratory experiments and confirmed by…
Diffusive motion in an externally driven potential is considered. It is shown that the distribution of work required to drive the system from an initial equilibrium state to another is Gaussian for slow but finite driving. Our result is…
We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
Scalar diffraction calculations such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, X-rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Gaussian Process State Space Models (GP-SSM) are a data-driven stochastic model class suitable to represent nonlinear dynamics. They have become increasingly popular in non-parametric modeling approaches since they provide not only a…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics…
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
A simple expression for the non-equilibrium distribution function in ultra-fast transient processes is proposed. Postulating its dependence on temporal derivatives of the equilibrium integrals of motion, non-equilibrium analogues of the…
This paper deals with the problem of robust output regulation of systems governed by nonlinear contraction semigroups. After adding an integral action to the system, we design a feedback law based on the so-called forwarding approach. For…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate…
Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…
We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…