Inverse M-matrix, a new characterization

In this article we present a new characterization of inverse M-matrices, inverse row diagonally dominant M-matrices and inverse row and column diagonally dominant M-matrices, based on the positivity of certain inner products.CONICYT, project BASAL AFB17000

A pointwise spectrum and representation of operators

Artículo de publicación IS

Hadamard functions of inverse M-matricese

We prove that the class of generalized ultrametric matrices (GUM) is the largest class of bipotential matrices stable under Hadamard increasing functions. We also show that any power α ≥ 1, in the sense of Hadamard functions, of an inverse M-matrix is also inverse M-matrix. This was conjectured for α = 2 by Neumann in [Linear Algebra Appl., 285 (1998), pp. 277–290], and solved for integer α ≥ 1 by Chen in [Linear Algebra Appl., 381 (2004), pp. 53–60]. We study the class of filtered matrices, which include naturally the GUM matrices, and present some sufficient conditions for a filtered matrix to be a bipotential

THE CLASS OF INVERSE M-MATRICES ASSOCIATED TO RANDOM WALKS

Artículo de publicación ISIGiven W = M−1, with M a tridiagonal M-matrix, we show that there are two diagonal matrices D,E and two nonsingular ultrametric matrices U, V such that DWE is the Hadamard product of U and V . If M is symmetric and row diagonally dominant, we can take D = E = I. We relate this problem with potentials associated to random walks and study more closely the class of random walks that lose mass at one or two extremes

On the graphene Hamiltonian operator

We solve a second-order elliptic equation with quasi-periodic boundary conditions defined on a honeycomb lattice that represents the arrangement of carbon atoms in graphene. Our results generalize those found by Kuchment and Post (Commun Math Phys 275(3):805-826, 2007) to characterize not only the stability but also the instability intervals of the solutions. This characterization is obtained from the solutions of the energy eigenvalue problem given by the lattice Hamiltonian. We employ tools of the one-dimensional Floquet theory and specify under which conditions the one-dimensional theory is applicable to the structure of graphene. The systematic study of such stability and instability regions provides a tool to understand the propagation properties and behavior of the electrons wavefunction in a hexagonal lattice, a key problem in graphene-based technologies.PFBasal-01 (CeBiB) PFBasal-03 (CMM) Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) C13E05 Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) CONICYT FONDECYT 1140773 1180781 Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) 21110749 Spanish Government SEV-2011-008

The high cadence transient survey (HITS). Compilation and characterization of light–curve catalogs

The High Cadence Transient Survey (HiTS) aims to discover and study transient objects with characteristic timescales between hours and days, such as pulsating, eclipsing and exploding stars. This survey represents a unique laboratory to explore large etendue observations from cadences of about 0.1 days and to test new computational tools for the analysis of large data. This work follows a fully Data Science approach: from the raw data to the analysis and classification of variable sources. We compile a catalog of ∼15 million object detections and a catalog of ∼2.5 million light–curves classified by variability. The typical depth of the survey is 24.2, 24.3, 24.1 and 23.8 in u, g, r and i bands, respectively. We classified all point–like non–moving sources by first extracting features from their light–curves and then applying a Random Forest classifier. For the classification, we used a training set constructed using a combination of cross-matched catalogs, visual inspection, transfer/active learning and data augmentation. The classification model consists of several Random Forest classifiers organized in a hierarchical scheme. The classifier accuracy estimated on a test set is approximately 97%. In the unlabeled data, 3 485 sources were classified as variables, of which 1 321 were classified as periodic. Among the periodic classes we discovered with high confidence, 1 δ–scutti, 39 eclipsing binaries, 48 rotational variables and 90 RR–Lyrae and for the non–periodic classes we discovered 1 cataclysmic variables, 630 QSO, and 1 supernova candidates. The first data release can be accessed in the project archive of HiTSa