Related papers: Efficient recognition of totally nonnegative matri…
The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable (the resultant is a polynomial in the…
Computing $p \rightarrow q$ norm for matrices is a classical problem in computational mathematics and power iteration is a well-known method for computing $p \rightarrow q $ norm for a matrix with nonnegative entries. Here we define an…
The observation of neutrinoless double beta decay will have important consequences. First it will signal that lepton number is not conserved and the neutrinos are Majorana particles. Second, it represents our best hope for determining the…
We perform a systematic and complete analysis of texture zeros in the lepton mass matrices and identify all viable and maximally restrictive cases of pairs (M_\ell, M_D) and (M_\ell, M_L), where M_\ell, M_D and M_L are the charged-lepton,…
We will consider completely positive maps defined on tensor products of von Neumann algebras and taking values in the algebra of bounded operators on a Hilbert space and particularly certain convex subsets of the set of such maps. We show…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
We show that precision measurement of (1) sum of neutrino masses by cosmological observation and (2) lifetime of neutrinoless double beta decay in ton-scale experiments, with supplementary use of (3) effective mass measured in single beta…
In this paper, we prove that any collocation matrix of Bessel polynomials at positive points is strictly totally positive, that is, all its minors are positive. Moreover, an accurate method to construct the bidiagonal factorization of these…
We exhibit a lower-triangular matrix of polynomials $T(a,c,d,e,f,g)$ in six indeterminates that appears empirically to be coefficientwise totally positive, and which includes as a special case the Eulerian triangle. We prove the…
This article derives lower bounds on the supremal (strict) p-negative type of finite metric spaces using purely elementary techniques. The bounds depend only on the cardinality and the (scaled) diameter of the underlying finite metric…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
In view of recent measurements of the mixing angle \theta_{13} a possibility to determine the difference of two CP Majorana phases of the neutrino mixing matrix from the study of neutrinoless double-beta decay is investigated. We show that…
There have been some effective tools for solving (constant/parametric) semi-algebraic systems in Maple's library RegularChains since Maple 13. By using the functions of the library, e.g., RealRootClassfication, one can prove and discover…
A new method of analysing positive bistochastic maps on the algebra of complex matrices $M_{3}$ has been proposed. By identifying the set of such maps with a convex set of linear operators on $\mathbb{R}^{8}$, one can employ techniques from…
In this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space $M_\Sigma$ with singular stratum $\beta M$ (a closed manifold of positive codimension) and associated link equal to…
Recently the evidence of the neutrinoless double $\beta$ ($0\nu \beta\beta$) decay has been announced. This means that neutrinos are Majorana particles and their mass hierarchy is forced to certain patterns in the diagonal basis of charged…
Assuming that the neutrino mass matrix is diagonalized by the tribimaximal mixing matrix, we explore the textures for the charged lepton mass matrix that render an $U_{PMNS}$ lepton mixing matrix consistent with data. In particular we are…
Motivated by satisfiability of constraints with function symbols, we consider numerical inequalities on non-negative integers. The constraints we consider are a conjunction of a linear system Ax = b and a conjunction of (non-)convex…
Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for…
A real symmetric matrix $A$ is said to be completely positive if it can be written as $BB^t$ for some (not necessarily square) nonnegative matrix $B$. A simple graph $G$ is called a completely positive graph if every doubly nonnegative…