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We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for…

We present theory and algorithms for the computation of probability-weighted "keep-out" sets to assure probabilistically safe navigation in the presence of multiple rigid body obstacles with stochastic dynamics. Our forward stochastic…

This paper considers stochastic-constrained stochastic optimization where the stochastic constraint is to satisfy that the expectation of a random function is below a certain threshold. In particular, we study the setting where data samples…

Global strategies to contain a pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission rate between individuals. Despite such measures, essential institutions, including hospitals,…

Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…

Mathematical models represent one of the fundamental ways of studying nature. In special, epidemic models have shown to be particularly useful in the understanding of the course of diseases and in the planning effective control policies. A…

We study and develop the stochastic Markov reward model (sMRM), which extends the Markov chain where transition time/reward as modelled as random variables. Techniques are presented to enable computing first-passage time distributions (or…

In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…

In this paper we propose several novel distributed gradient-based temporal difference algorithms for multi-agent off-policy learning of linear approximation of the value function in Markov decision processes with strict information…

Reinforcement learning is an emerging approaches to facilitate multi-stage sequential decision-making problems. This paper studies a real-time multi-stage stochastic power dispatch considering multivariate uncertainties. Current researches…

Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…

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…

In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…

We compute the transition probability between two learning tasks, and show that it decomposes into two factors. The first depends on the geometry of the loss landscape of a model trained on each task, independent of any particular model…

We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…

We consider the problem of steering a system with unknown, stochastic dynamics to satisfy a rich, temporally layered task given as a signal temporal logic formula. We represent the system as a Markov decision process in which the states are…

In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…

In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…