Related papers: The weighted horizontal linear complementarity pro…
A symmetric matrix $A$ is completely positive (CP) if there exists an entrywise nonnegative matrix $V$ such that $A = V V ^T$. In this paper, we study the CP-matrix approximation problem of projecting a matrix onto the intersection of a set…
Real and virtual corrections in NNLO QCD require multi-dimensional integrals with overlapping singularities. We first review ideas and methods which have been proposed for performing such computations. We then present a new method for the…
We study connections between the problem of the existence of positive solutions for certain nonlinear equations and weighted norm inequalities. In particular, we obtain explicit criteria for the solvability of the Dirichlet problem…
We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph…
Jordan geometries are defined as spaces equipped with point reflections depending on triples of points, exchanging two of the points and fixing the third. In a similar way, symmetric spaces have been defined by Loos (Symmetric Spaces I,…
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…
In this paper we study polynomials $(P_n)$ which are hermitian orthogonal on two arcs of the unit circle with respect to weight functions which have square root singularities at the end points of the arcs, an arbitrary nonvanishing…
Although a unique solution is guaranteed in the Linear complementarity problem (LCP) when the matrix $\mathbf{M}$ is positive definite, practical applications often involve cases where $\mathbf{M}$ is only positive semi-definite, leading to…
A banded matrix is a real square matrix where nonzero entries appear around the main diagonal. In this article, we consider linear complementarity properties of (variants) of banded matrices. Focusing on triangular matrices and the newly…
In this paper, we consider the second-order cone tensor eigenvalue complementarity problem (SOCTEiCP) and present three different reformulations to the model under consideration. Specifically, for the general SOCTEiCP, we first show its…
We study a general class of quasilinear elliptic equations with nonstandard growth to prove the existence of a very weak solution to such a problem. A key ingredient in the proof is a priori global weighted gradient estimate of a very weak…
While studying some properties of linear operators in a Euclidean Jordan algebra, Gowda, Sznajder and Tao have introduced generalized lattice operations based on the projection onto the cone of squares. In two recent papers of the authors…
Given an input graph and weights on its vertices, the maximum co-2-plex problem is to find a subset of vertices maximizing the sum of their weights and inducing a graph of degree at most 1. In this article, we analyze polyhedral aspects of…
We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…
This dissertation represents work on three different subjects relating to quantum gravity and the AdS/CFT correspondence. First, we review a holographic computation of the one-loop corrections to the Weyl anomaly on Ricci flat backgrounds…
We construct a weighted version of polyhedral products and compute its cohomology in special cases. This is applied to resolve Steenrod's cohomology realization problem in a case related to products of spheres.
We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights $w$ having finitely many zeros and singularities (i.e., points where $w$ becomes infinite) on an interval and not too ``rapidly…
The Euclidean algorithm in algebra is applied to a class of gravitational lenses for which the lens equation consists of any set of coupled polynomial equations in the image position. In general, this algorithm allows us to reduce an…
In this paper we argue for a close connection between the non-existence of global symmetries in quantum gravity and a unitary resolution of the black hole information problem. In particular we show how the essential ingredients of recent…
In this paper, we study the linear complementarity problems on the monotone extended second order cones. We demonstrate that the linear complementarity problem on the monotone extended second order cone can be converted into a mixed…