Related papers: Parametrizations of degenerate density matrices
This paper studies the numerical approximation of evolution equations by nonlinear parametrizations $u(t)=\Phi(\param(t))$ with time-dependent parameters $\param(t)$, which are to be determined in the computation. The motivation comes from…
Let $M=(m_{ij})$ be a symmetric matrix of order $n$ whose elements lie in an arbitrary field $\mathbb{F}$, and let $G$ be the graph with vertex set $\{1,\ldots,n\}$ such that distinct vertices $i$ and $j$ are adjacent if and only if $m_{ij}…
One introduces a class of projective parameterizations that resemble generalized de Jonqui\`eres maps. Any such parametrization defines a birational map $\mathfrak{F}$ of $\pp^n$ onto a hypersurface $V(F)\subset \pp^{n+1}$ with a strong…
A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…
We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise $\ell_1$ regularization to the free energy of the quantum system. Based on the…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
In this paper we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of optimality of such decompositions. For some classes of positive…
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
We construct model-independent parametrizations of the individual QCD form factors relevant to Lambda_b --> Lambda_c l nu decays. These results follow from dispersion relations and analyticity, and incorporate an improvement in the…
Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…
We consider the problem of enumerating hypermatrices of format $2 \times (k + 1) \times k$ over a finite field that have nonzero hyperdeterminant and whose nonzero entries are restricted to a plane partition. We conjecture an attractive…
A Lie-Yamaguti algebra is a non-associative algebraic structure that generalizes both Lie algebras and Lie triple systems. We first consider the factorization problem for Lie-Yamaguti algebras that essentially related to the bicrossed…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
Automated per-instance algorithm selection and configuration have shown promising performances for a number of classic optimization problems, including satisfiability, AI planning, and TSP. The techniques often rely on a set of features…
We suggest that the extended Lee-Friedrichs model could be directly used as a practical parametrization method for the experimental analysis of resonance structures. This parametrization incorporates the constraints of relativistic phase…
For a given discrete decomposable graphical model, we identify several alternative parametrizations, and construct the corresponding reference priors for suitable groupings of the parameters. Specifically, assuming that the cliques of the…
We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix…
Due to considerable recent interest in the use of density matrices for a wide variety of purposes, including quantum computation, we present a general method for their parameterizations in terms of Euler angles. We assert that this is of…
In this paper we consider the problem of deformation quantization of the algebra of polynomial functions on coadjoint orbits of semisimple lie groups. The deformation of an orbit is realized by taking the quotient of the universal…