Related papers: Biharmonic Distance and the Performance of Second-…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
Effective resistance is a distance between vertices of a graph that is both theoretically interesting and useful in applications. We study a variant of effective resistance called the biharmonic distance. While the effective resistance…
We consider performance deterioration of interconnected linear dynamical networks subject to exogenous stochastic disturbances. The focus of this paper is on first-order and second-order linear consensus networks. We employ the expected…
We study the performance of leader-follower noisy consensus networks, and in particular, the relationship between this performance and the locations of the leader nodes. Two types of dynamics are considered (1) noise-free leaders, in which…
Lipman et al. [ACM Transactions on Graphics 29 (3) (2010), 1--11] introduced the concept of biharmonic distance to measure the distances between pairs of points on a 3D surface. Biharmonic distance has some advantages over resistance…
The \textit{biharmonic distance} (BD) is a fundamental metric that measures the distance of two nodes in a graph. It has found applications in network coherence, machine learning, and computational graphics, among others. In spite of BD's…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
In this paper, we introduce a new method for testing the stationarity of time series, where the test statistic is obtained from measuring and maximising the difference in the second-order structure over pairs of randomly drawn intervals.…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
In this paper, we develop a novel unified methodology for performance and robustness analysis of linear dynamical networks. We introduce the notion of systemic measures for the class of first--order linear consensus networks. We classify…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
Persistence diagrams, an important summary in topological data analysis, consist of a set of ordered pairs, each with positive multiplicity. Persistence diagrams are obtained via Mobius inversion and may be compared using a one-parameter…
As bulk synchronous generators in the power grid are replaced by distributed generation interfaced through power electronics, inertia is removed from the system, prompting concerns over grid stability. Different metrics are available for…
Deriving meaningful information from observational data is often restricted by many limiting factors, the most important of which is the presence of noise. In this work, we present the use of the bicoherence function to extract information…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
Part I of this paper considered optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network…
We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…
Given an undirected graph, the resistance distance between two nodes is the resistance one would measure between these two nodes in an electrical network if edges were resistors. Summing these distances over all pairs of nodes yields the…