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With the rise of generative models, there is a growing interest in unifying all tasks within a generative framework. Anomaly detection methods also fall into this scope and utilize diffusion models to generate or reconstruct normal samples…
We investigate how non-Markovian mechanical dissipation affects exceptional points in linearized optomechanical systems with red-sideband drive. For a chosen non-Ohmic mechanical bath, we derive analytical conditions for the…
Fickian yet non-Gaussian diffusion is a ubiquitous phenomenon observed in various biological and soft matter systems. This anomalous dynamics is typically attributed to heterogeneous environments inducing spatiotemporal variations in the…
Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian…
Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…
Stochastic thermodynamics and the associated fluctuation relations provide the means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Motivated by multiple applications in social networks, nervous systems, and financial risk analysis, we consider the problem of learning the underlying (directed) influence graph or causal graph of a high-dimensional multivariate…
Non-Markovian dynamics go beyond the Markovian approximation by capturing memory effects and information backflow in open quantum systems, which are crucial for describing realistic physical processes. In this work, we study the exact…
The transition from reversible microdynamics to irreversible transport can be studied very efficiently with the help of the so-called projection method. We give a concise introduction to that method, illustrate its power by using it to…
A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
We study a fundamental instability mechanism in nonlinear, nonlocal dynamical systems arising from the interaction of long-range memory and stochastic regime switching. The dynamics are governed by network-coupled, operator-valued Volterra…
In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…
Using recently proposed measures for non-Markovianity [H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. {\bf 103}, 210401 (2009)], we study the dynamics of a qubit coupled to a spin environment via an energy-exchange mechanism. We…
We study the non-Markovian effects on the dynamics of entanglement in an exactly-solvable model that involves two independent oscillators each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional…
Here, we introduce a stochastic partial differential equation (SPDE) formulation driven by temporally correlated noise to describe light propagation beyond the standard Markov approximation. By representing the squared refractive index…
In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…
Monte Carlo (MC) simulations of transport in random porous networks indicate that for high variances of the log-normal permeability distribution, the transport of a passive tracer is non-Fickian. Here we model this non-Fickian dispersion in…
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…