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Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on…
This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a combination of the negative curvature property…
We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we show that there are subsequences of radii for which the…
Reasoning about graphs evolving over time is a challenging concept in many domains, such as bioinformatics, physics, and social networks. We consider a common case in which edges can be short term interactions (e.g., messaging) or long term…
Real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links. Currently, there exists no principled mathematical theory for their dynamics -- a grand-challenge open problem. Here, we show…
A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…
Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…
We study the target control problem of asynchronous Boolean networks, to identify a set of nodes, the perturbation of which can drive the dynamics of the network from any initial state to the desired steady state (or attractor). We are…
For the basic case of $L_2$ optimal transport between two probability measures on a Euclidean space, the regularity of the coupling measure and the transport map in the tail regions of these measures is studied. For this purpose, Robert…
$\delta$-hyperbolic graphs, originally conceived by Gromov in 1987, occur often in many network applications; for fixed $\delta$, such graphs are simply called hyperbolic graphs and include non-trivial interesting classes of "non-expander"…
Many theories of physics beyond the Standard Model predict particles with non-helical trajectories in a uniform magnetic field, but standard tracking algorithms assume helical paths and so are incapable of discovering non-helical tracks.…
In autonomous driving, accurately interpreting the movements of other road users and leveraging this knowledge to forecast future trajectories is crucial. This is typically achieved through the integration of map data and tracked…
We provide the first step toward developing a hierarchical control-estimation framework to actively plan robot trajectories for anomaly detection in confined spaces. The space is represented globally using a directed region graph, where a…
We introduce a general framework for leveraging graph stream data for temporal prediction-based applications. Our proposed framework includes novel methods for learning an appropriate graph time-series representation, modeling and weighting…
We examine the problem of maximizing the reachability of a given source in temporal graphs that are given as the union of k temporal paths, i.e., every given path is a sequence of edges with strictly increasing labels that denote…
We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We present a new fully dynamic algorithm for maintaining betweenness centrality (BC) of vertices in a directed graph $G=(V,E)$ with positive edge weights. BC is a widely used parameter in the analysis of large complex networks. We achieve…
We consider weighted graphs satisfying sub-Gaussian estimate for the natural random walk. On such graphs, we study symmetric Markov chains with heavy tailed jumps. We establish a threshold behavior of such Markov chains when the index…