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Many biological, social, and communication systems can be modeled by ``searchers'' moving through a complex network. For example, intracellular cargo is transported on tubular networks, news and rumors spread through online social networks,…
Graphons, as limit objects of dense graph sequences, play a central role in the statistical analysis of network data. However, existing graphon estimation methods often struggle with scalability to large networks and resolution-independent…
Robust control and maintenance of the grid relies on accurate data. Both PMUs and state estimators are prone to false data injection attacks. Thus, it is crucial to have a mechanism for fast and accurate detection of an agent maliciously…
We study the evolution of a general class of stochastic processes (containing, e.g. SIS and SIR models) on large random networks, focusing on a particular general class of random graph models. To approximate the expected dynamics of these…
The Method of Successive Approximations (MSA) is a fixed-point iterative method used to solve stochastic optimal control problems. It is an indirect method based on the conditions derived from the Stochastic Maximum Principle (SMP), an…
Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…
Stochastic optimization is a vital field in the realm of mathematical optimization, finding applications in diverse areas ranging from operations research to machine learning. In this paper, we introduce a novel first-order optimization…
Interval Markov chains extend classical Markov chains with the possibility to describe transition probabilities using intervals, rather than exact values. While the standard formulation of interval Markov chains features closed intervals,…
We consider an elementary model for self-organised criticality, the activated random walk on the complete graph. We introduce a discrete time Markov chain as follows. At each time step, we add an active particle at a random vertex and let…
To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order…
In this paper we introduce a class of Markov models, termed best-effort networks, designed to capture performance indices such as mean transfer times in data networks with best-effort service. We introduce the so-called min bandwidth…
A new approach for optimal estimation of Markov chains with sparse transition matrices is presented.
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
In high performance systems it is sometimes hard to build very large graphs that are efficient both with respect to memory and compute. This paper proposes a data structure called Markov-chain-priority-queue (MCPrioQ), which is a lock-free…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…
Adding edges between layers of interconnected networks is an important way to optimize the spreading dynamics. While previous studies mostly focus on the case of adding a single edge, the theoretical optimal strategy for adding multiple…
We establish non-asymptotic error bounds for the classical Maximal Likelihood Estimation of the transition matrix of a given Markov chain. Meanwhile, in the reversible case, we propose a new reversibility-preserving online Symmetric…