Improving prediction performance of stellar parameters using functional models

This paper investigates the problem of prediction of stellar parameters, based on the star's electromagnetic spectrum. The knowledge of these parameters permits to infer on the evolutionary state of the star. From a statistical point of view, the spectra of different stars can be represented as functional data. Therefore, a two-step procedure decomposing the spectra in a functional basis combined with a regression method of prediction is proposed. We also use a bootstrap methodology to build prediction intervals for the stellar parameters. A practical application is also provided to illustrate the numerical performance of our approach

Spectra of weighted rooted graphs having prescribed subgraphs at some levels

Let B be a weighted generalized Bethe tree of k levels (k > 1) in which nj is the number of vertices at the level k-j+1 (1 ≤ j ≤ k). Let Δ \subset {1, 2,., k-1} and F={Gj:j \in Δ}, where Gj is a prescribed weighted graph on each set of children of B at the level k-j+1. In this paper, the eigenvalues of a block symmetric tridiagonal matrix of order n1+n2 +...+nk are characterized as the eigenvalues of symmetric tridiagonal matrices of order j, 1≤j≤k, easily constructed from the degrees of the vertices, the weights of the edges, and the eigenvalues of the matrices associated to the family of graphs F. These results are applied to characterize the eigenvalues of the Laplacian matrix, including their multiplicities, of the graph β(F) obtained from β and all the graphs in F={Gj:j \in Δ}; and also of the signless Laplacian and adjacency matrices whenever the graphs of the family F are regular.CIDMAFCTFEDER/POCI 2010PTDC/MAT/112276/2009Fondecyt - IC Project 11090211Fondecyt Regular 110007

Copies of a rooted weighted graph attached to an arbitrary weighted graph and applications

The spectrum of the Laplacian, signless Laplacian and adjacency matrices of the family of the weighted graphs R{H}, obtained from a connected weighted graph R on r vertices and r copies of a modified Bethe tree H by identifying the root of the i-th copy of H with the i-th vertex of R, is determined

Information mobility in complex networks

The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals. The mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix. The fractional time at which a network diffuses 50% of the information contained in its nodes (1/ k50 ) is also introduced. We then show that the scale-free random networks display better spread of information than the non scale-free ones. We study 38 real-world networks and analyze their performance in spreading information from their nodes. We find that some real-world networks perform even better than the scale-free networks with the same average degree and we point out some of the structural parameters that make this possible

Compton Scattering by the Proton using a Large-Acceptance Arrangement

Compton scattering by the proton has been measured using the tagged-photon facility at MAMI (Mainz) and the large-acceptance arrangement LARA. The new data are interpreted in terms of dispersion theory based on the SAID-SM99K parameterization of photo-meson amplitudes. It is found that two-pion exchange in the t-channel is needed for a description of the data in the second resonance region. The data are well represented if this channel is modeled by a single pole with mass parameter m(sigma)=600 MeV. The asymptotic part of the spin dependent amplitude is found to be well represented by pi-0-exchange in the t-channel. A backward spin-polarizability of gamma(pi)=(-37.1+-0.6(stat+syst)+-3.0(model))x10^{-4}fm^4 has been determined from data of the first resonance region below 455 MeV. This value is in a good agreement with predictions of dispersion relations and chiral pertubation theory. From a subset of data between 280 and 360 MeV the resonance pion-photoproduction amplitudes were evaluated leading to a E2/M1 multipole ratio of the p-to-Delta radiative transition of EMR(340 MeV)=(-1.7+-0.4(stat+syst)+-0.2(model))%. It was found that this number is dependent on the parameterization of photo-meson amplitudes. With the MAID2K parameterization an E2/M1 multipole ratio of EMR(340 MeV)=(-2.0+-0.4(stat+syst)+-0.2(model))% is obtained

Radiating and non-radiating sources in elasticity

In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.Comment: 17 page

Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation