Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...

•Accessibility by non-experts: researchers in the social sciences should be able to use the system to share and explore data with no involvement from experts in data privacy, computer science, or statistics. •Generality: the system should be applicable and effective on a wide variety of heterogeneous datasets hosted in a repository such as the Harvard Dataverse. •Workflow-compatibility: the sys...

We present a series of results we obtained recently about the intersection numbers of tautological classes on moduli spaces of curves, including a simple formula of the n-point functions for Witten's tau classes, an effective recursion formula to compute higher Weil-Petersson volumes, several new recursion formulae of intersection numbers and our proof of a conjecture of Itzykson and Zuber conc...

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

Oblivious Transfer (OT) is a fundamental primitive in cryptography, supporting protocols such as Multi-Party Computation and Private Set Intersection (PSI), that are used applications like contact discovery, remote diagnosis tracing. Due to its nature, it utterly important execution secure even if arbitrarily composed with other instances of the same, or protocols. This property can be guarante...

This article presents a research focused on the Virtual Battlespace 2 scenarios development for private security industry (PSI) purposes. In the first part, the VBS2 scenario creation options are described. In the second part, a description of the scenario representing the most common workload of employees of PSI can be found. In the last part, the process of developing this scenario in 2D and ...

let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in th...