For the functional A[ f ] = ∑k=1 ak f (zk) , we give necessary and sufficient conditions over the real numbers zk , such that, the inequality A[ f ] 0 , holds for some classes of convex functions. Then, we deduce an inequality related to Alzer’s inequality and a weighted majorization inequality.

We present a generic method for considering incomplete but gradually expandable sociological data in agent-based modeling based on the classic model of cultural dissemination by Axelrod. Our method extension was inspired by research on the diffusion of citizen photovoltaic initiatives, i.e. by initiatives in which citizens collectively invest in photovoltaic plants and share the profits. Owing ...

We consider a different L-Minkowski combination of compact sets in R than the one introduced by Firey and we prove an L-BrunnMinkowski inequality, p ∈ [0, 1], for a general class of measures called convex measures that includes log-concave measures, under unconditional assumptions. As a consequence, we derive concavity properties of the function t 7→ μ(t 1 pA), p ∈ (0, 1], for unconditional con...

We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on Rn, with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly conve...

A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering conditional probabilities that two randomly chosen vertices are adjacent given that they have r common neighbours. We denote such probabilities cl(r) and call r ...

Social chemosignaling is a part of human behavior, but how chemosignals transfer from one individual to another is unknown. In turn, humans greet each other with handshakes, but the functional antecedents of this behavior remain unclear. To ask whether handshakes are used to sample conspecific social chemosignals, we covertly filmed 271 subjects within a structured greeting event either with or...

A social welfare function entitled ‘ordinal Nash’ is proposed. It is based on risk preferences and assumes a common, worst social tate (origin) for all individuals. The crucial axiom in the characterization of the function is a weak version of independence of rrelevant alternatives. This axiom considers relative risk positions with respect to the origin. Thus, the resulting social preference ak...

Cognitive and social deficits lie at the core of many neuropsychiatric diseases and are among the many behavioral symptoms not amenable to pharmacological intervention. Despite significant advances in identifying genes potentially involved in the pathogenesis of complex psychiatric conditions such as autism and schizophrenia, knowledge of the physiological functions that are affected (and are t...

We consider the social preference ordering in a society where each individual’s preference domain is restricted to a subset of the whole set of alternatives. We show that the social welfare function satisfying unrestricted domain property, independence of irrelevant alternatives and weak Pareto optimality is always dictatorial when at least one individual is entitled to express his/her preferen...