We study the convexity of mutual information along the evolution of the heat equation. We prove that if the initial distribution is log-concave, then mutual information is always a convex function of time. We also prove that if the initial distribution is either bounded, or has finite fourth moment and Fisher information, then mutual information is eventually convex, i.e., convex for all large ...

Carroll and Kimball (1996) show that the consumption function for an agent with time-separable, isoelastic preferences is concave in the presence of income uncertainty. In this paper I show that concavity breaks down if we abandon time-separability. Namely, if an agent maximizing an isoelastic recursive utility has preferences for early resolution of uncertainty, there always exists a distribut...

The stable allocation model is a many-to-many matching model in which each pair’s partnership is represented by a nonnegative integer. This paper establishes a link between two different formulations of this model; the choice function model studied thoroughly by Alkan and Gale and the discrete-concave (M♮-concave) value function model introduced by Eguchi, Fujishige and Tamura. We show that the...

This paper addresses the issue of endogenizing the equilibrium solution when a private –domestic or foreign –…rm competes in the quantities with a public, welfare maximizing …rm. Theoretical literature on mixed oligopolies provides results and policy implications that crucially rely on the notion of equilibrium assumed, either sequential or simultaneous. In the framework of the endogenous timin...

For divisor methods of apportionment with concave up or concave down rounding functions, we prove explicit formulas for the threshold values—the lower and upper bounds for the percentage of population that are necessary and sufficient for a state to receive a particular number of seats. Among the rounding functions with fixed concavity are those based on power means, which include the methods o...

This paper surveys the work of the qualitativespatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and show how a rich language can be built up from surprisingly few primitives. This language can distingui...

Many statistical characteristics y = f(x1, . . . , xn) are continuous, symmetric, and either concave or convex; examples include population variance

In this paper, we introduce a more general approach to the fuzzification of fuzzy concavity. More specifically, degree L , M -fuzzy concavity is introduced and characterized as generalization id="M2"> -concave structure id="M3"> conca...