Topological reversibility and causality in feed-forward networks

Systems whose organization displays causal asymmetry constraints, from evolutionary trees to river basins or transport networks, can be often described in terms of directed paths (causal flows) on a discrete state space. Such a set of paths defines a feed-forward, acyclic network. A key problem associated with these systems involves characterizing their intrinsic degree of path reversibility: given an end node in the graph, what is the uncertainty of recovering the process backwards until the origin? Here we propose a novel concept, \textit{topological reversibility}, which rigorously weigths such uncertainty in path dependency quantified as the minimum amount of information required to successfully revert a causal path. Within the proposed framework we also analytically characterize limit cases for both topologically reversible and maximally entropic structures. The relevance of these measures within the context of evolutionary dynamics is highlighted.Comment: 9 pages, 3 figure

Distributed Robust Set-Invariance for Interconnected Linear Systems

We introduce a class of distributed control policies for networks of discrete-time linear systems with polytopic additive disturbances. The objective is to restrict the network-level state and controls to user-specified polyhedral sets for all times. This problem arises in many safety-critical applications. We consider two problems. First, given a communication graph characterizing the structure of the information flow in the network, we find the optimal distributed control policy by solving a single linear program. Second, we find the sparsest communication graph required for the existence of a distributed invariance-inducing control policy. Illustrative examples, including one on platooning, are presented.Comment: 8 Pages. Submitted to American Control Conference (ACC), 201

Ultra-Reliable Low-Latency Vehicular Networks: Taming the Age of Information Tail

While the notion of age of information (AoI) has recently emerged as an important concept for analyzing ultra-reliable low-latency communications (URLLC), the majority of the existing works have focused on the average AoI measure. However, an average AoI based design falls short in properly characterizing the performance of URLLC systems as it cannot account for extreme events that occur with very low probabilities. In contrast, in this paper, the main objective is to go beyond the traditional notion of average AoI by characterizing and optimizing a URLLC system while capturing the AoI tail distribution. In particular, the problem of vehicles' power minimization while ensuring stringent latency and reliability constraints in terms of probabilistic AoI is studied. To this end, a novel and efficient mapping between both AoI and queue length distributions is proposed. Subsequently, extreme value theory (EVT) and Lyapunov optimization techniques are adopted to formulate and solve the problem. Simulation results shows a nearly two-fold improvement in terms of shortening the tail of the AoI distribution compared to a baseline whose design is based on the maximum queue length among vehicles, when the number of vehicular user equipment (VUE) pairs is 80. The results also show that this performance gain increases significantly as the number of VUE pairs increases.Comment: Accepted in IEEE GLOBECOM 2018 with 7 pages, 6 figure

Rate-Distortion Function of the Stochastic Block Model

The stochastic block model (SBM) is extensively used to model networks in which users belong to certain communities. In recent years, the study of information-theoretic compression of such networks has gained attention, with works primarily focusing on lossless compression. In this work, we address the lossy compression of SBM graphs by characterizing the rate-distortion function under a Hamming distortion constraint. Specifically, we derive the conditional rate-distortion function of the SBM with community membership as side information. We approach this problem as the classical Wyner-Ziv lossy problem by minimising mutual information of the graph and its reconstruction conditioned on community labels. Lastly, we also derive the rate-distortion function of the Erd\H{o}s-R\'enyi (ER) random graph model.Comment: 9 pages, 1 figure, Accepted for presentation at Asilomar Conference on Signals, Systems, and Computers, 202