Let B be a Borel set in E with volume V (B) = ∞. It is shown that almost all lattices L in E contain infinitely many pairwise disjoint d-tuples, that is sets of d linearly independent points in B. A consequence of this result is the following: let S be a star body in E with V (S) = ∞. Then for almost all lattices L in E the successive minima λ1(S,L), . . . , λd(S,L) of S with respect to L are 0...

Abstract This paper introduces and studies a class of evolutionary dynamics—pairwise interact-and-imitate dynamics (PIID)—in which agents are matched in pairs, engage symmetric game, imitate the opponent with probability that depends on difference their payoffs. We provide condition underlying named supremacy, show population state all play supreme strategy is globally asymptotically stable. ex...

Abstract Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has pivotal in the development of modern decision-making methods. The evaluation is very often done linguistically. Several scales proposed to translate linguistic into quantitative evaluation. In this paper, we perform an experiment investigate, under our methodological choices,...

We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of points. This is in contrast to previous works that obtain these parameters through the minimization of the reconstruction error of individual points. The prop...

This paper adopts mechanism design to investigate the coexistence of …at money and higherreturn assets. We consider an economy with pairwise meetings where …at money and riskfree capital compete as means of payment, as in Lagos and Rocheteau (2008). The trading mechanism in pairwise meetings is chosen among all individually rational, renegotiation-proof mechanisms to maximize society’s welfare....