We examine theoretical properties of value of information (VOI) in the selection problem, and identify cases of submodularity and supermodularity. We use these properties to compute approximately optimal measurement batch policies, implemented on a “wine selection problem” example.

We show that the rearrangement algorithm introduced in Puccetti and Rüschendorf (2012a) to compute distributional bounds can be used also to compute sharp lower and upper bounds on the expected value of a supermodular function of d random variables having fixed marginal distributions. Compared to the analytical methods existing in the literature the algorithm is widely applicable, more easily o...

We investigate the problem of maximizing sum submodular and supermodular functions under a fairness constraint. This function is non-submodular in general. For an offline model, we introduce two approximation algorithms: A greedy algorithm threshold algorithm. streaming propose one-pass also analyze ratios these algorithms, which all depend on total curvature function. The computable polynomial...

This article proposes a unified class of generalized location-scale mixture multivariate elliptical distributions and studies integral stochastic orderings random vectors following such distributions. Given vector Z, independent X Y, the scale parameter this is mixed with function α(Z) its skew another β(Z). Sufficient (and necessary) conditions are established for stochastically comparing diff...

A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical nonnegative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system, which are then extended to arbitrary valuations on ...

Given a simple bipartite graph G and an integer t ≥ 2, we derive a formula for the maximum number of edges in a subgraph H of G so that H contains no node of degree larger than t and H contains no complete bipartite graph Kt,t as a subgraph. In the special case t = 2 this fomula was proved earlier by Z. Király [6], sharpening a result of D. Hartvigsen [4]. For any integer t ≥ 2, we also determi...

Throughout, let p be a positive integer and let be the set of permutations over {1; : : : ; p}. A real-valued function over subsets of {1; : : : ; p}, with (∅)=0, de7nes a mapping of into R where ∈ is mapped into the vector whose kth coordinate ( )k is the augmented -value obtained from adding k to the coordinates that precede it, according to the ranking induced by . The permutation polytope c...

We show that local potential maximizer ([15]) with constant weights is stochastically stable in the log-linear dynamics provided that the payoff function or the associated local potential function is supermodular. We illustrate and discuss, through a series of examples, the use of our main results as well as other concepts closely related to local potential maximizer: weighted potential maximiz...