Kirchhoff Index As a Measure of Edge Centrality in Weighted Networks: Nearly Linear Time Algorithms

Most previous work of centralities focuses on metrics of vertex importance and methods for identifying powerful vertices, while related work for edges is much lesser, especially for weighted networks, due to the computational challenge. In this paper, we propose to use the well-known Kirchhoff index as the measure of edge centrality in weighted networks, called $\theta$-Kirchhoff edge centrality. The Kirchhoff index of a network is defined as the sum of effective resistances over all vertex pairs. The centrality of an edge $e$ is reflected in the increase of Kirchhoff index of the network when the edge $e$ is partially deactivated, characterized by a parameter $\theta$. We define two equivalent measures for $\theta$-Kirchhoff edge centrality. Both are global metrics and have a better discriminating power than commonly used measures, based on local or partial structural information of networks, e.g. edge betweenness and spanning edge centrality. Despite the strong advantages of Kirchhoff index as a centrality measure and its wide applications, computing the exact value of Kirchhoff edge centrality for each edge in a graph is computationally demanding. To solve this problem, for each of the $\theta$-Kirchhoff edge centrality metrics, we present an efficient algorithm to compute its $\epsilon$-approximation for all the $m$ edges in nearly linear time in $m$. The proposed $\theta$-Kirchhoff edge centrality is the first global metric of edge importance that can be provably approximated in nearly-linear time. Moreover, according to the $\theta$-Kirchhoff edge centrality, we present a $\theta$-Kirchhoff vertex centrality measure, as well as a fast algorithm that can compute $\epsilon$-approximate Kirchhoff vertex centrality for all the $n$ vertices in nearly linear time in $m$

Plasma-wave generation in a dynamic spacetime

We propose a new electromagnetic-emission mechanism in magnetized, force-free plasma, which is driven by the evolution of the underlying dynamic spacetime. In particular, the emission power and angular distribution of the emitted fast-magnetosonic and Alfv\'en waves are separately determined. Previous numerical simulations of binary black hole mergers occurring within magnetized plasma have recorded copious amounts of electromagnetic radiation that, in addition to collimated jets, include an unexplained, isotropic component which becomes dominant close to merger. This raises the possibility of multimessenger gravitational-wave and electromagnetic observations on binary black hole systems. The mechanism proposed here provides a candidate analytical characterization of the numerical results, and when combined with previously understood mechanisms such as the Blandford-Znajek process and kinetic-motion-driven radiation, allows us to construct a classification of different electromagnetic radiation components seen in the inspiral stage of compact-binary coalescences.Comment: 7 pages, 1 figure, published versio

Max-plus fundamental solution semigroups for a class of difference Riccati equations

Recently, a max-plus dual space fundamental solution semigroup for a class of difference Riccati equation (DRE) has been developed. This fundamental solution semigroup is represented in terms of the kernel of a specific max-plus linear operator that plays the role of the dynamic programming evolution operator in a max-plus dual space. In order to fully understand connections between this dual space fundamental solution semigroup and evolution of the value function of the underlying optimal control problem, a new max-plus primal space fundamental solution semigroup for the same class of difference Riccati equations is presented. Connections and commutation results between this new primal space fundamental solution semigroup and the recently developed dual space fundamental solution semigroup are established.Comment: 17 pages, 3 figure

Bubbles and Experience: An Experiment with a Steady Inflow of New Traders

We revisit the effect of traders' experience on price bubbles by introducing either one-third or two-thirds steady inflow of new traders in the repeated experimental asset markets. We find that bubbles are not significantly abated by the third repetition of the market with the inflow of new traders. The relative importance of experience to the formation of bubbles depends on the proportion of new traders in the market. Our findings identify a market environment where increased experience is not sufficient to eliminate price bubbles.Bubbles; Asset Markets; Experience; Inflow of Traders

Challenges Facing East Asian Immigrant Children in Sexual Abuse Cases

Immigrants from East Asia make up 14.21% of the total number of immigrants in Canada. These families face many challenges as they acculturate to North America but, sadly, some of these children may be at risk for sexual abuse. In this position paper, we outline the ways in which East Asian children are at a particular disadvantage when considering prosecution of those who perpetrate abuse compared to Western non-immigrant children. We focus specifically on two areas of concern: 1) Cultural differences that can impact the disclosure of sexual abuse; and, 2) Language differences which reduce the chances that perpetrators will be prosecuted for sexual abuse. The consequences for East Asian immigrant youth who allege (or are suspected) that they are victims of abuse are serious. East Asian children face an uphill battle to see justice in sexual abuse cases. Thus, a significant portion of immigrant children will not see their abusers punished and, worse, the knowledge that prosecution is unlikely makes East Asian immigrant children a targeted population for those who abuse