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We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…

Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanism for point processes. Here, we are interested in their domains of attraction and…

Learning stochastic models of dynamical systems from observed data is of interest in many scientific fields. Here, we propose a new method for this task within the family of dynamical variational autoencoders. The proposed double projection…

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…

This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…

Nowadays distributed computing approach has become very popular due to several advantages over the centralized computing approach as it also offers high performance computing at a very low cost. Each router implements some queuing mechanism…

Buoyancy-driven exchange flows arise in the natural and built environment wherever bodies of fluids at different densities are connected by a narrow constriction. In this paper we study these flows in the laboratory using the canonical…

We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore,…

This paper analyzes a (1, $\lambda$)-Evolution Strategy, a randomized comparison-based adaptive search algorithm, optimizing a linear function with a linear constraint. The algorithm uses resampling to handle the constraint. Two cases are…

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound…

Stokes flow, discussed by G.G. Stokes in 1851, describes many microscopic biological flow phenomena, including cilia-driven transport and flagellar motility; the need to quantify and understand these flows has motivated decades of…

In this article we show that the phase-ordering scaling state for binary fluids is not necessarily unique and that local correlations in the initial conditions can be responsible for selecting the scaling state. We describe a new scaling…

Constant step-size Stochastic Gradient Descent exhibits two phases: a transient phase during which iterates make fast progress towards the optimum, followed by a stationary phase during which iterates oscillate around the optimal point. In…

We set up the scaling theory for stably stratified turbulent fluids. For a system having infinite extent in the horizontal directions, but with a finite width in the vertical direction, this theory predicts that the inertial range can…

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a…

Longitudinal oscillations of bunched beams in synchrotrons have been analyzed by accelerator physicists for decades, and a closed theory is well-known [1]. The first modes of oscillation are the coherent dipole mode, quadrupole mode, and…

We revisit the well-known problem of multiscaling in substances passively advected by homogeneous and isotropic turbulent flows or passive scalar turbulence. To that end we propose a two-parameter continuum hydrodynamic model for an…

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…

This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…

Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…