A generalization of the classical statistics \maj" and \inv" (the major index and number of inversions) on words is introduced, parame-terized by arbitrary graphs on the underlying alphabet. The question of characterizing those graphs that lead to equi-distributed \inv" and \maj" is posed and answered. R esum e: On introduit une g en eralisation des statistiques classiques que sont \maj" et \in...

The paper attempts to develop a suitable accessibility index for networks where each link has a value such that a smaller number is preferred like distance, cost, or travel time. A measure called distance sum is characterized by three independent properties: anonymity, an appropriately chosen independence axiom, and dominance preservation, which requires that a node not far to any other is at l...

This paper studies power indices based on average representations of a weighted game. If restricted to account for the lack of power of dummy voters, average representations become coherent measures of voting power, with power distributions being proportional to the distribution of weights in the average representation. This makes these indices representationcompatible, a property not fulfilled...

Recently Nikolić, Trinajstić and Randić put forward a novel modification W(G) of the Wiener number W(G), called modified Wiener index , which definition was generalized later by Gutman and the present authors. Here we study another class of modified indices defined as Wmin,λ(G)=∑(V(G) mG(u,ν) −mG(u,ν) ) and show that some of the important properties of W(G), W(G) and W(G) are also properties of...

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1 Mathematical indices, formed by combining several primary measures, can help researchers summarize, interpret and display results from plant competition experiments. This essay compiles and discusses more than 50 indices that have been used in studies of plant competition. 2 Indices allow researchers to quantify and express several attributes of plant competition, including competition intens...

One purpose of network analysis especially of social networks is to identify important actors, crucial links, subgroups, roles, network characteristics, and so on, to answer substantive questions about structures. There are three main levels of interest: the element, group, and network level. On the element level, one is interested in properties (both absolute and relative) of single actors, li...

Starting with the Thomspon sampling algorithm, recent years have seen a resurgence of interest in Bayesian algorithms for the Multi-armed Bandit (MAB) problem. These algorithms seek to exploit prior information on arm biases and while several have been shown to be regret optimal, their design has not emerged from a principled approach. In contrast, if one cared about Bayesian regret discounted ...

Distributed hash tables (DHTs) are a distributed, peer-topeer analogue of hash indices in database systems. Given a key, a DHT returns a pointer to the associated object. DHTs have also be extended to support “keyword” queries [5, 2] (object identified by multiple keys). Fundamentally, however, these approaches all return a undirected sample of the full result set. Unfortunately, most applicati...

The paper by Inal-Ince and colleagues (pag. 162-167) examines fatigue in chronic obstructive pulmonary disease (COPD) relating it to multi dimensional indices of overall disease severity, BODE and SAFE. It is the selection of these indices that will be examined in this Editorial. COPD is now considered a multi dimensional disease, in fact, quite remarkably so. A little history will remind how t...