This work exploits the resemblance between content-based image retrieval and image analysis with respect to the design of image descriptors and their effectiveness. In this context, two shape descriptors are proposed: contour saliences and segment saliences. Contour saliences revisits its original definition, where the location of concave points was a problem, and provides a robust approach to ...

We propose solution methods for previouslyunsolved constrained MDPs in which actions can continuously modify the transition probabilities within some acceptable sets. While many methods have been proposed to solve regular MDPs with large state sets, there are few practical approaches for solving constrained MDPs with large action sets. In particular, we show that the continuous action sets can ...

The theory of second-order epi-derivatives of extended-real-valued functions is applied to convex functions on lR and shown to be closely tied to proto-differentiation of the corresponding subgradient multifunctions, as well as to second-order epi-differentiation of conjugate functions. An extension is then made to saddle functions, which by definition are convex in one argument and concave in ...

Convex analysis” is developed for functions defined on integer lattice points. We investigate the class of functions which enjoy a variant of Steinitz’s exchange property. It includes linear functions on matroids, valuations on matroids (in the sense of Dress and Wenzel), and separable concave functions on the integral base polytope of submodular systems. It is shown that a function ω has the S...

The paper studies local convexity properties of parts of digital boundaries. An online and linear-time algorithm is introduced for the decomposition of a digital boundary into convex and concave parts. In addition, other data are computed in the same time without any extra cost: the hull of each convex or concave part as well as the Bezout points of each edge of those hulls. The proposed algori...

The minimum concave cost network flow problem (MCCNFP) is NP-hard, but efficient polynomial-time algorithms exist for some special cases such as the uncapacitated lot-sizing problem and many of its variants. We study the MCCNFP over a grid network with a general nonnegative separable concave cost function. We show that this problem is polynomially solvable when all sources are in the first eche...

Machine learning models are known to memorize the unique properties of individual data points in a training set. This memorization capability can be exploited by several types attacks infer information about data, most notably, membership inference attacks. In this paper, we propose an approach based on leakage for guaranteeing privacy. Specifically, use conditional form notion maximal quantify...

In this paper we will solve a generalization of the problem “Touring a Sequence of Polygons” where polygons can be concave and a weight is considered when visiting them. The main idea to solve the problem is triangulation of the polygons and adding some Steiner on the edges. We will also use a modified version of BUSHWHACK algorithm to find the shortest path among Steiner points. The running ti...

We consider Nash–Cournot oligopolistic market equilibrium models with concave cost functions. Concavity implies, in general, that a local equilibrium point is not necessarily a global one. We give conditions for existence of global equilibrium points. We then propose an algorithm for finding a global equilibrium point or for detecting that the problem is unsolvable. Numerical experiments on som...

The notions of union-soft semigroups, union-soft l-ideals, and union-soft r-ideals are introduced, and related properties are investigated. Characterizations of a union-soft semigroup, a union-soft l-ideal, and a union-soft r-ideal are provided. The concepts of union-soft products and union-soft semiprime soft sets are introduced, and their properties related to union-soft l-ideals and union-so...