This paper studies the properties of convexity (concavity) and strategic complements (substitutes) in network formation and the implications for the structure of pairwise stable networks. First, different definitions of convexity (concavity) in own links from the literature are put into the context of diminishing marginal utility of own links. Second, it is shown that there always exists a pair...

In chance-constrained optimization problems, a solution is assumed to be feasible only with certain, sufficiently high probability. For computational and theoretical purposes, the convexity property of the resulting constraint set is treated. It is known, for example, that a suitable combination of a concavity property of the probability distribution and concavity of constraint mappings are suf...

Abstract We obtain new concavity results, up to a suitable transformation, for class of quasi-linear equations in convex domain involving the p -Laplace operator and general nonlinearity satisfying concavity-type assumptions. This provides an extension results previously known literature only torsion first eigenvalue equations. In semilinear case <m:math xmlns:m="http://www.w3.org/1998/Math/Mat...

We prove the logarithmic concavity of the Duistermaat-Heckman measure of an Hamiltonian (n− 2)-dimensional torus action for which there exists an effective commuting symplectic action of a 2-torus with symplectic orbits. Using this, we show that any symplectic (n− 2)-torus action with non-empty fixed point set which satisfies this additional 2-torus condition must be Hamiltonian.

PURPOSE To correlate parameters derived from corneal deformation resulting from non-contact tonometry integrated with an ultra-high-speed (UHS) Scheimpflug camera (Oculus Corvis ST, Scheimpflug Technology; Wetzlar, Germany) with age in normal eyes from young patients. METHODS Observational, retrospective study involving one eye randomly selected from study participants, totaling 89 healthy ey...

This paper proposes a simplex statistic for testing the joint curvature (e.g., linearity, concavity, or convexity) of a nonparametric regression function. The statistic is based on Jensen’s inequality applied to all (m+ 2)-tuples in the data having one data point in the interior of the (m+1)-dimension simplex spanned by the remaining data points (m is the dimension of the covariate vector). The...