We consider partial orderings for stochastic processes induced by expectations of convex or increasing convex (concave or increasing concave) functionals. We prove that these orderings are implied by the analogous finite dimensional orderings.

We derive a lower bound on the differential entropy of a log-concave random variable X in terms of the p-th absolute moment of X. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds on the rate-distortion function and the channel capacity. Specifically, we study the rate-distortion function for log-concave sources and distortion measure |x− x̂|,...

BACKGROUND The temporal variation of the hemodynamic mechanical parameters during cardiac pulse wave is considered as an important atherogenic factor. Applying non-Newtonian blood molecular viscosity simulation is crucial for hemodynamic analysis. Understanding low density lipoprotein (LDL) distribution in relation to flow parameters will possibly spot the prone to atherosclerosis aorta regions...

Recent experimental and theoretical work in literature showed that several biological attachment devices are concave in shape and that such a shape enhances adhesion strength. In this paper, an analytical model is developed for the pull-off forces required to separate a rigid axisymmetric concave punch from an elastic half-space with the goal of understanding how concave shapes seen in both bio...

The estimation of a log-concave density on Rd represents a central problem in the area of nonparametric inference under shape constraints. In this paper, we study the performance of log-concave density estimators with respect to global loss functions, and adopt a minimax approach. We first show that no statistical procedure based on a sample of size n can estimate a log-concave density with res...

Background. In patients with bronchial asthma, spirometry could identify the airflow limitation of small airways by evaluating the concave shape of the maximal expiratory flow-volume (MEFV) curve. As the concave shape of the MEFV curve is not well documented, we reevaluated the importance of this curve in adult asthmatic patients. Methods. We evaluated spirometric parameters, the MEFV curve, an...

We study approaches for obtaining convex relaxations of global optimization problems containing multilinear functions. Specifically, we compare the concave and convex envelopes of these functions with the relaxations that are obtained with a standard relaxation approach, due to McCormick. The standard approach reformulates the problem to contain only bilinear terms and then relaxes each term in...

We study valid inequalities for optimizationmodels that contain both binary indicator variables and separable concave constraints. Thesemodels reduce to amixedinteger linear program (MILP) when the concave constraints are ignored, or to a nonconvex global optimization problem when the binary restrictions are ignored. In algorithms designed to solve these problems to global optimality, cutting p...

We show that the density of Z = argmax{W (t) - t2}, sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strongly log-concave or "super-Gaussian", and provide evidence in support of the conjecture.

In this work, we study continuous reformulations of zero-one concave programming problems. We introduce new concave penalty functions and we prove, using general equivalence results here derived, that the obtained continuous problems are equivalent to the original combinatorial problem.