Fox, Gromov, Lafforgue, Naor, and Pach proved a regularity lemma for semi-algebraic kuniform hypergraphs of bounded complexity, showing that for each ǫ > 0 the vertex set can be equitably partitioned into a bounded number of parts (in terms of ǫ and the complexity) so that all but an ǫ-fraction of the k-tuples of parts are homogeneous. We prove that the number of parts can be taken to be polyno...

A secret key generation algorithm from UWB channel measurements is proposed. The security of the technique is based on the reciprocity and spatial correlation properties of UWB radio channel measurements. The channel reciprocity property allows two communicating radio receivers to measure the state of their common radio channel to a high degree of agreement. The spatial correlation property of ...

Based on the variational formulation of linear thermodynamics as developed previously by the writer, thermomechanical reciprocity relations are discussed which lead to new methods of analysis of thermal stresses. These reciprocity relations are quite different from the usual ones derived from the analogy of thermal loading with a combination of surface and body-force distribution. The results a...

Reciprocity is a second-order correlation that has been recently detected in all real directed networks and shown to have a crucial effect on the dynamical processes taking place on them. However, no current theoretical model generates networks with this nontrivial property. Here we propose a grand-canonical class of models reproducing the observed patterns of reciprocity by regarding single an...

This article is devoted to the (one-dimensional) logarithmic functional with argument being one-dimensional cycle in the group (C∗)2. This functional generalizes usual logarithm, that can be viewed as zero-dimensional logarithmic functional. Logarithmic functional inherits multiplicative property of the logarithm. It generalizes the functional introduced by Beilinson for topological proof of th...

In this paper, we study the graph polynomial that records spanning rooted forests fG of a given graph. This polynomial has a remarkable reciprocity property. We give a new bijective proof for this theorem which has Prüfer coding as a special case.

We investigate the concept of mindreading in a trust–reciprocity experiment. Our results show that the Trustees send back more, the stronger the Trustors’ property rights are. But instead of strategically relying on this reciprocal behavior, Trustors tend to unilaterally implement a fair outcome.  2000 Elsevier Science S.A. All rights reserved.

On March 3, 1998, the centenary of Emil Artin was celebrated at the Universiteit van Amsterdam. This paper is based on the two morning lectures, enti-tled`Artin reciprocity and quadratic reciprocity' and`Class eld theory in practice', which were delivered by the authors. It provides an elementary introduction to Artin reciprocity and illustrates its practical use by establishing a recently obse...

We consider game-theoretic rationales for minimal cooperativity, in particular responses to questions or requests for help with false answers. Lying enables preservation of property and face for both speaker and hearer and constitutes a Pareto-optimal outcome. Rationales for this behavior include expectations of reciprocity, other-regarding, and maintenance of face.

It has been a challenge to understand the formation and roles of social groups or natural communities in the evolution of species, societies and real world networks. Here, we propose the hypothesis that homophyly/kinship is the intrinsic mechanism of natural communities, introduce the notion of the affinity exponent and propose the homophyly/kinship model of networks. We demonstrate that the ne...