Abstract. It was shown in [7, 9] that harmonic numbers satisfy certain reciprocity relations, which are in particular useful for the analysis of the quickselect algorithm. The aim of this work is to show that a reciprocity relation from [7, 9] can be generalized to finite variants of multiple zeta values, involving a finite variant of the shuffle identity for multiple zeta values. We present th...

If reciprocity principles are invoked in seismic data processing algorithms, one has to make sure that those processes maintain reciprocity. I outline briefly the derivation of reciprocity principles for elastic wave equations and show that discretized or approximated wave equations can lose symmetry properties and thus reciprocities. This effect is important if one is concernd about true-ampli...

How can cooperation persist in the face of a temptation to 'cheat'? Several recent papers have suggested that the answer may lie in indirect reciprocity. Altruistic individuals may benefit by eliciting altruism from observers, rather than (as in direct reciprocity) from the recipient of the aid they provide. Here, we point out that indirect reciprocity need not always favour cooperation; by con...

Many mechanisms for the emergence and maintenance of altruistic behavior in social dilemma situations have been proposed. Indirect reciprocity is one such mechanism, where other-regarding actions of a player are eventually rewarded by other players with whom the original player has not interacted. The upstream reciprocity (also called generalized indirect reciprocity) is a type of indirect reci...

e description of the reciprocity phenomenon is more tricky than it is supposed in grammatical handbooks: It must cover both the issues of lexicon and of syntax and of their interplay as well. e lexical counterpart of the English expression each other is not the central (core) means for denoting reciprocity in some Slavonic languages, esp. in Czech. e troublemaking Czech reflexive se/siplays ...

The answer to questions like this can be found with the quadratic reciprocity law in F[T ]. It has a strong resemblance to the quadratic reciprocity law in Z. We restrict to F with odd characteristic because when F has characteristic 2 every element of F[T ]/(π) is a square, so our basic question is silly in characteritic 2. (There is a good analogue of quadratic reciprocity in characteristic 2...

We extend the concept of manifold with boundary to weight and boundary weight functions. With the new concept, we obtained the double reciprocity laws for simplicial complexes, cubical complexes, and lattice polyhedra with weight functions. For a polyhedral manifold with boundary, if the weight function has the constant value 1, then the boundary weight function has the constant value 1 on the ...

The evolution of cooperation among nonrelatives has been explained by direct, indirect, and strong reciprocity. Animals should base the decision to help others on expected future help, which they may judge from past behavior of their partner. Although many examples of cooperative behavior exist in nature where reciprocity may be involved, experimental evidence for strategies predicted by direct...

Background Social networking services (SNSs) are widely used as communicative tools for a variety of purposes. SNSs rely on the users' individual activities associated with some cost and effort, and thus it is not known why users voluntarily continue to participate in SNSs. Because the structures of SNSs are similar to that of the public goods (PG) game, some studies have focused on why volunta...

Reciprocity plays a key role maintaining cooperation in society. However, little is known about the neural process that underpins human reciprocity during social interactions. Our neuroimaging study manipulated partner identity (computer, human) and strategy (random, tit-for-tat) in repeated prisoner's dilemma games and investigated the neural correlate of reciprocal interaction with humans. Re...