Related papers: Intermittency as metastability: a predictive appro…
We consider a random walk with catastrophes which was introduced to model population biology. It is known that this Markov chain gets eventually absorbed at $0$ for all parameter values. Recently, it has been shown that this chain exhibits…
We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
By introducing extrinsic noise as well as intrinsic uncertainty into a network with stochastic events, this paper studies the dynamics of the resulting Markov random network and characterizes a novel phenomenon of intermittent…
In general terms, intermittency is the property for which time evolving systems alternate among two or more different regimes. Predicting the instance when the regime switch will occur is extremely challenging, often practically impossible.…
We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this…
We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two…
We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic…
We investigate the uniform stability properties of discrete-time linear switched systems subject to arbitrary switching, focusing on the "marginally unstable" regime in which the system is not Lyapunov stable but in which trajectories…
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events…
We introduce the concept of a Markov influence system (MIS) and analyze its dynamics. An MIS models a random walk in a graph whose edges and transition probabilities change endogenously as a function of the current distribution. This…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…
Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…
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…
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…
Suppose an online platform wants to compare a treatment and control policy, e.g., two different matching algorithms in a ridesharing system, or two different inventory management algorithms in an online retail site. Standard randomized…
We present a case study applying learning-based distributionally robust model predictive control to highway motion planning under stochastic uncertainty of the lane change behavior of surrounding road users. The dynamics of road users are…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total…