Waldschmidt constants for Stanley-Reisner ideals of a class of Simplicial Complexes

We study the symbolic powers of the Stanley-Reisner ideal $I_{B_n}$ of a bipyramid $B_n$ over a $n-$gon $Q_n$. Using a combinatorial approach, based on analysis of subtrees in $Q_n$ we compute the Waldschmidt constant of $I_{B_n}$.Comment: 10 pages, 2 figure

A game theoretic approach to a peer-to-peer cloud storage model

Classical cloud storage based on external data providers has been recognized to suffer from a number of drawbacks. This is due to its inherent centralized architecture which makes it vulnerable to external attacks, malware, technical failures, as well to the large premium charged for business purposes. In this paper, we propose an alternative distributed peer-to-peer cloud storage model which is based on the observation that the users themselves often have available storage capabilities to be offered in principle to other users. Our set-up is that of a network of users connected through a graph, each of them being at the same time a source of data to be stored externally and a possible storage resource. We cast the peer-to-peer storage model to a Potential Game and we propose an original decentralized algorithm which makes units interact, cooperate, and store a complete back up of their data on their connected neighbors. We present theoretical results on the algorithm as well a good number of simulations which validate our approach.Comment: 10 page

Finite-time influence systems and the Wisdom of Crowd effect

Recent contributions have studied how an influence system may affect the wisdom of crowd phenomenon. In the so-called naive learning setting, a crowd of individuals holds opinions that are statistically independent estimates of an unknown parameter; the crowd is wise when the average opinion converges to the true parameter in the limit of infinitely many individuals. Unfortunately, even starting from wise initial opinions, a crowd subject to certain influence systems may lose its wisdom. It is of great interest to characterize when an influence system preserves the crowd wisdom effect. In this paper we introduce and characterize numerous wisdom preservation properties of the basic French-DeGroot influence system model. Instead of requiring complete convergence to consensus as in the previous naive learning model by Golub and Jackson, we study finite-time executions of the French-DeGroot influence process and establish in this novel context the notion of prominent families (as a group of individuals with outsize influence). Surprisingly, finite-time wisdom preservation of the influence system is strictly distinct from its infinite-time version. We provide a comprehensive treatment of various finite-time wisdom preservation notions, counterexamples to meaningful conjectures, and a complete characterization of equal-neighbor influence systems

Distributionally robust stability of payoff allocations in stochastic coalitional games

We consider multi-agent coalitional games with uncertainty in the coalitional values. We provide a novel methodology to study the stability of the grand coalition in the case where each coalition constructs ambiguity sets for the (possibly) unknown probability distribution of the uncertainty. As a less conservative solution concept compared to worst-case approaches for coalitional stability, we consider a stochastic version of the so-called core set, i.e., the expected value core. Unfortunately, without exact knowledge of the probability distribution, the evaluation of the expected value core is an extremely challenging task. Hence, we propose the concept of distributionaly robust (DR) core. Leveraging tools from data-driven DR optimization under the Wasserstein distance, we provide finite-sample guarantees that any allocation which lies in the DR core is also stable with respect to the true probability distribution. Furthermore, we show that as the number of samples grows unbounded, the DR core converges almost surely to the true expected value core. We dedicate the last section to the computational tractability of finding an allocation in the DR core.Comment: Accepted for publication at the IEEE Conference on Decision and Control 202