Related papers: The Choi-Cholesky algorithm for completely positiv…

We initiate and study the theory of ``real decomposable maps" between real operator systems. Formally, this is new even in the complex case, which hitherto has restricted itself to the case where the systems are complex C*-algebras. We…

By the Choi matrix criteria it is easy to determine if a specific linear matrix map is completely positive, but to establish whether a linear matrix map is positive is much less straightforward. In this paper we consider classes of linear…

This paper develops and analyzes a new algorithm for QR decomposition with column pivoting (QRCP) of rectangular matrices with many more rows than columns. The algorithm carefully combines methods from randomized numerical linear algebra to…

In this paper, we develop a framework for designing arbitrary high order low-rank schemes for the Lindblad equation with time-dependent Hamiltonians. Our approach is based on nested Picard iterative integrators (NPI) and results in schemes…

In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship…

The question of when zeros (i.e., sparsity) in a positive definite matrix $A$ are preserved in its Cholesky decomposition, and vice versa, was addressed by Paulsen et al. in the Journal of Functional Analysis (85, pp151-178). In particular,…

Anar A. Dosiev in [Local operator spaces, unbounded operators and multinormed $C^*$-algebras, J. Funct. Anal. 255 (2008), 1724-1760], obtained a Stinespring's theorem for local completely positive maps (in short: local CP-maps) on locally…

Two algorithms are presented for "compiling" influence diagrams into a set of simple decision rules. These decision rules define simple-to-execute, complete, consistent, and near-optimal decision procedures. These compilation algorithms can…

This work introduces and systematically studies a new convex cone of PCOP (pairwise copositive). We establish that this cone is dual to the cone of PCP (pairwise completely positive) and, critically, provides a complete characterization for…

Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…

We prove that the PPT$^2$ conjecture holds for linear maps between matrix algebras which are covariant under the action of the diagonal unitary group. Many salient examples, like the Choi-type maps, depolarizing maps, dephasing maps,…

Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…

We expand upon work from many hands on the decomposition of nuclear maps. Such maps can be characterized by their ability to be approximately written as the composition of maps to and from matrices. Under certain conditions (such as…

We outline a new approach to the characterization as well as to the classification of positive maps. This approach is based on the facial structures of the set of states and of the cone of positive maps. In particular, the equivalence…

A method to predict the emergence of different kinds of ordered collective behaviors in systems of globally coupled chaotic maps is proposed. The method is based on the analogy between globally coupled maps and a map subjected to an…

We derive simple and unified closed-form expressions for projections with respect to fidelity (equivalently, the Bures and purified distances) onto several sets of interest. These include projections of bipartite positive semidefinite (PSD)…

Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…

The problem of finding completely positive matrices with equal cp-rank and rank is considered. We give some easy-to-check sufficient conditions on the entries of a doubly nonnegative matrix for it to be completely positive with equal…

Convergence is a crucial issue in iterative algorithms. Damping is commonly employed to ensure the convergence of iterative algorithms. The conventional ways of damping are scalar-wise, and either heuristic or empirical. Recently, an…

An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a…