Related papers: Recursive approach for non-Markovian time-convolut…
Consider a sequence $(\eta^N(t) :t\ge 0)$ of continuous-time, irreducible Markov chains evolving on a fixed finite set $E$, indexed by a parameter $N$. Denote by $R_N(\eta,\xi)$ the jump rates of the Markov chain $\eta^N_t$, and assume that…
We present a new numerical scheme to treat the non-linear evolution of cosmological power spectra. Governing equations for matter power spectra have been previously derived by a non-perturbative technique with closure approximation.…
We present a closed-form solution for n-th term of a general three-term recurrence relation with arbitrary given n-dependent coefficients. The derivation and corresponding proof are based on two approaches, which we develop and describe in…
Recent advances in learning dynamical systems from data have shown significant promise. However, many existing methods assume access to the full state of the system -- an assumption that is rarely satisfied in practice, where systems are…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatio-temporal systems including fluid turbulence is supported by non-chaotic, exactly recurring time-periodic solutions of the…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…
The ubiquitous effects of the environment on quantum-mechanical systems generally cause temporally correlated fluctuations. This particularly holds for systems of interest for quantum computation where such effects lead to correlated…
The dynamic regressor extension and mixing procedure is employed to redesign a conventional adaptive observer algorithm for affine systems. A reduced-order observer is designed without the construction of the state transition matrix. The…
We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…
This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…
This study proposes an approach to describing personality dynamics through mathematical modelling of introversion, extroversion, and ambiversion processes. Introversion is interpreted as a recursive process characterized by deep…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
Dissipative phase transitions in quantum systems have been largely studied under the so-called Markovian approximation, where the environments to which the systems are coupled are memoryless. Here, we present a generalization of the…
This paper investigates a recursive formulation of auto-regressive multi-fidelity Gaussian process regression in the challenging setting of noisy and non-nested high- and low-fidelity data. We propose a decoupled optimization strategy based…
The aim of this survey is to present the main important techniques and tools from variational analysis used for first and second order dynamical systems of implicit type for solving monotone inclusions and non-smooth optimization problems.…
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
The time evolution of Markovian open quantum systems is governed by Lindblad master equations, whose solution can be formally written as the Lindbladian exponential acting on the initial density matrix. By expanding this Lindbladian…