Rule of sum

About: Rule of sum is a research topic. Over the lifetime, 239 publications have been published within this topic receiving 2380 citations.

Resistance-Distance Sum Rules*

Abstract: The chemical potential for a novel intrinsic graph metric, the resistance distance, is briefly recalled, and then a number of » sum rules« for this metric are established. »Global« and » local « types of sum rules are identified. The sums in the » global « sum rules are graph invariants, and the sum rules provide inter-relations amongst different invariants, some involving the resistance distance while others do not. Illustrative applications to more » regular « graphs are made.

Generalized scoring rules and the frequency of coalitional manipulability

Abstract: We introduce a class of voting rules called generalized scoring rules. Under such a rule, each vote generates a vector of k scores, and the outcome of the voting rule is based only on the sum of these vectors---more specifically, only on the order (in terms of score) of the sum's components. This class is extremely general: we do not know of any commonly studied rule that is not a generalized scoring rule.We then study the coalitional manipulation problem for generalized scoring rules. We prove that under certain natural assumptions, if the number of manipulators is O(np) (for any p 1/2) and o(n), then the probability that a random profile is manipulable (to any possible winner under the voting rule) is 1--O(e--Ω(n2p--1)). We also show that common voting rules satisfy these conditions (for the uniform distribution). These results generalize earlier results by Procaccia and Rosenschein as well as even earlier results on the probability of an election being tied.

Exact Spectral Function Sum Rules

Abstract: A general procedure for extracting exact spectral-function sum rules is presented. The short-distance behavior of products of vector and axial-vector currents is related to the convergence (or superconvergence) of the original first and second spectral sum rules together with a third sum rule involving only the spin-0 spectral function. The operator-product expansion is then applied to determine all (and only) those linear combinations of current propagators for which the short-distance behavior is sufficiently soft to yield superconvergent sum rules for the corresponding combinations of spectral functions. Our method is applied to determine the complete set of sum rules for a theory defined by a global chiral SU(4)\ifmmode\times\else\texttimes\fi{}SU(4) symmetry, broken (a) explicitly by hadron (quark) masses and (b) by dynamical symmetry breaking to any subgroup containing the symmetry group of the mass matrix. Our derivation is strictly true only for asymptotically free theories, but the results are expected to apply for a range of other theories. The method is easily extended to deal with current propagators involving scalar and pseudoscalar densities (not necessarily divergences of vector or axial-vector currents)---the relevant sum rules in the context of the SU(4)\ifmmode\times\else\texttimes\fi{}SU(4) model are derived. Finally, we compare our approach and results to those of several recent studies of the spectral-function sum rules. An appendix presents a proof that Wilson functions exhibit the full symmetries of any theory, whether or not these are spontaneously broken.