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Via molecular dynamics simulations we have studied kinetics of vapor-"solid" phase transition in an active matter model in which self-propulsion is introduced via the well-known Vicsek rule. The overall density of the particles is chosen in…
Guidance is a cornerstone of modern diffusion models, playing a pivotal role in conditional generation and enhancing the quality of unconditional samples. However, current approaches to guidance scheduling--determining the appropriate…
This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…
This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
The space of density matrices is embedded in a Euclidean space to deduce the dynamical equation satisfied by the state of an open quantum system. The Euclidean norm is used to obtain an explicit expression for the speed of the evolution of…
We study the ergodic behaviour of a discrete-time process $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $t\to\infty$.…
We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
An emerging and challenging area in mathematical control theory called Ensemble Control encompasses a class of problems that involves the guidance of an uncountably infinite collection of structurally identical dynamical systems, which are…
This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
The lack of superposition of different position states or the emergence of classicality in macroscopic systems have been a puzzle for decades. Classicality exists in every measuring apparatus, and is the key for understanding what can be…
This work addresses the exact characterization of the covariance dynamics related to linear discrete-time systems subject to both additive and parametric stochastic uncertainties that are potentially unbounded. Using this characterization,…
This work develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II to have a wider stability range…
This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…
The dynamics of open quantum systems is formulated in a minimally extended state space comprising the degrees of freedom of a system of interest and a finite set of non-unitary, pure-state reservoir modes. This formal structure, derived…
In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…