Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex optimization. We show how an interior method can be used to efficiently compute the proximal operator of a quadratic-support function under different metrics. When th...

We present an integer linear formulation that uses the so-called “distance variables” to solve the quadratic assignment problem (QAP). The model involves O(n) variables. Valid equalities and inequalities are additionally proposed. We further improved the model by using metric properties as well as an algebraic characterization of the Manhattan distance matrices that Mittelman and Peng [28] rece...

Cardiac catheterization procedure produces ventriculograms which have very low contrast in the apical, anterior and inferior zones of the left ventricle (LV). Pixel-based classi ers operating on these images produce boundaries which have systematic positional and orientation bias and have a mean error of about 10.5 mm. Using the LV convex information, comprising of the apex and the aortic valve...

In the real world, it is common that different experts have different opinions on the same problem due to their different experience. How to come up with a consistent decision becomes a critical issue. As an example, patient similarity assessment is an important task in the context of patient cohort identification for comparative effectiveness studies and clinical decision support applications....

In the present work we approximate an ultrarelativistic jet by a homogeneous beam of null matter with finite width. Then, we study the influence of this beam over the spacetime metric in the framework of higher-derivative gravity. We find an exact shock wave solution of the quadratic gravity field equations and compare it with the solution to Einstein’s gravity. We show that the effect of highe...

Recently the Master Constraint Programme (MCP) for Loop Quantum Gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single Master constraint. The MCP is designed to overcome the complications associated with the non – Lie – algebra structure of the Dirac algebra of Hamiltonian constraints and was successfully tested in various field theory models. For t...

The moduli space of quadratic differentials is not compact: when some loop on a Riemann surface M becomes short in the flat metric defined by a quadratic differential q, the corresponding point (M, q) of the moduli space tends to a “cusp”. We describe typical degenerations, thus describing “generic cusps of moduli space”. The part of the boundary of the moduli space which does not arise from “g...

A family of variable metric methods for convex constrained optimization was introduced recently by Birgin, Mart́ınez and Raydan. One of the members of this family is the Inexact Spectral Projected Gradient (ISPG) method for minimization with convex constraints. At each iteration of these methods a strictly convex quadratic function with convex constraints must be (inexactly) minimized. In the ca...

and Applied Analysis 3 Theorem 1.3 see 26–28 . Let X, d be a complete generalized metric space and let J : X → X be a strictly contractive mapping with Lipschitz constant L < 1. Then for each given element x ∈ X, either d ( Jx, J 1x ) ∞ 1.7 for all nonnegative integers n or there exists a positive integer n0 such that 1 d Jx, J 1x < ∞, for all n ≥ n0; 2 the sequence {Jnx} converges to a fixed p...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...