We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a basic random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a great variety of distributions observed in nature, which can hardly be described by the conventional methods. As a simple example, we explicitly derive the...

Let red and blue points be distributed on R according to two independent Poisson processes R and B and let each red (blue) point independently be equipped with a random number of half-edges according to a probability distribution ν (μ). We consider translation-invariant bipartite random graphs with vertex classes defined by the point sets of R and B, respectively, generated by a scheme based on...

We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies or political organizations, in which decisions are made by a voting process. Previous studies assume that agent weights (corresponding to the size of a caucus or a political party) are fixed; we analyze new domains in which the w...

This paper studies an incentive structure for cooperation and its stability in peer-assisted services when there exists multiple content providers, using a coalition game theoretic approach. We first consider a generalized coalition structure consisting of multiple providers with many assisting peers, where peers assist providers to reduce the operational cost in content distribution. To distri...

Over the last two decades, optical frequency combs (OFCs) have enabled some of most accurate measurements in physics. Distributing light from OFCs via fibers could make these high-accuracy measurement tools available more widely, a few dedicated metrology laboratories to other and industry. However, performance distributed is strongly limited by impairments standard single mode fiber (SMF), not...