Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2n) and compute the fractional hypertree-width of H in time O(1.734601n.m).1

Deux extensions de Théorèmes de Hamburger (portant sur l'équation fonctionnelle de la fonction dzêta)

We propose two types of extensions to Hamburger’s theorems on the Dirichlet series with functional equation like the one of the Riemann zeta function, under weaker hypotheses. This builds upon the dictionary betweeen the moderate meromorphic functions with functional equation and the tempered distributions with extended S-support condition.

Desenvolupament de codis numèrics per a la resolució de fluxos turbulents en ordinadors paral·lels emprant discretitzacions tipus symmetry-preserving

Projecte de recerca elaborat a partir d’una estada a la University of Groningen, Holanda, entre 2007 i 2009. La simulació directa de la turbulència (DNS) és una eina clau dins de la mecànica de fluids computacional. Per una banda permet conèixer millor la física de la turbulència i per l'altra els resultats obtinguts són claus per el desenvolupament dels models de turbulència. No obstant, el DNS no és una tècnica vàlida per a la gran majoria d'aplicacions industrials degut al elevats costos computacionals. Per tant, és necessari cert grau de modelització de la turbulència. En aquest context, s'han introduïts importants millores basades en la modelització del terme convectiu (no lineal) emprant symmetry-preserving regularizations. En tracta de modificar adequadament el terme convectiu a fi de reduir la producció d'escales més i més petites (vortex-stretching) tot mantenint tots els invariants de les equacions originals. Fins ara, aquest models s'han emprat amb èxit per nombres de Rayleigh (Ra) relativament elevats. En aquest punt, disposar de resultats DNS per a configuracions més complexes i nombres de Ra més elevats és clau. En aquest contexte, s'han dut a terme simulacions DNS en el supercomputador MareNostrum d'una Differentially Heated Cavity amb Ra=1e11 i Pr=0.71 durant el primer any dels dos que consta el projecte. A més a més, s'ha adaptat el codi a fi de poder simular el fluxe al voltant d'un cub sobre una pared amb Re=10000. Aquestes simulacions DNS són les més grans fetes fins ara per aquestes configuracions i la seva correcta modelització és un gran repte degut la complexitat dels fluxes. Aquestes noves simulacions DNS estan aportant nous coneixements a la física de la turbulència i aportant resultats indispensables per al progrés de les modelitzacións tipus symmetry-preserving regularization.

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces.

Impact of normalization on miRNA microarray expression profiling.

Profiling miRNA levels in cells with miRNA microarrays is becoming a widely used technique. Although normalization methods for mRNA gene expression arrays are well established, miRNA array normalization has so far not been investigated in detail. In this study we investigate the impact of normalization on data generated with the Agilent miRNA array platform. We have developed a method to select nonchanging miRNAs (invariants) and use them to compute linear regression normalization coefficients or variance stabilizing normalization (VSN) parameters. We compared the invariants normalization to normalization by scaling, quantile, and VSN with default parameters as well as to no normalization using samples with strong differential expression of miRNAs (heart-brain comparison) and samples where only a few miRNAs are affected (by p53 overexpression in squamous carcinoma cells versus control). All normalization methods performed better than no normalization. Normalization procedures based on the set of invariants and quantile were the most robust over all experimental conditions tested. Our method of invariant selection and normalization is not limited to Agilent miRNA arrays and can be applied to other data sets including those from one color miRNA microarray platforms, focused gene expression arrays, and gene expression analysis using quantitative PCR.

Refacció d'Ontologies : creació d'un plugin per a Protégé

El projecte centra els seus esforços en la darrera activitat: el refactoring d'ontologies. En concret, les expressades en OWL, el llenguatge per a ontologies pensat pel W3C. El resultat final del projecte ha estat la implementació en Java d'un plugin per a Protégé que permet l'execució d'operacions de refactoring sobre ontologies OWL. Part principal del plugin és un framework que ofereix el marc d'execució per a les operacions implementades i permet incorporar noves operacions sense haver-lo de modificar.

Parametrization of spectral surfaces of a class of periodic 5-diagonal matrices

The main result of this work is a parametric description of the spectral surfaces of a class of periodic 5-diagonal matrices, related to the strong moment problem. This class is a self-adjoint twin of the class of CMV matrices. Jointly they form the simplest possible classes of 5-diagonal matrices.

Holomorphic maps between moduli spaces

We prove that every non-constant holomorphic map&em&M&/em&&sub&g,p&/sub&→ &em&M&/em&&sub& g',p'&/sub& between moduli spaces of Riemann surfaces is a forgetful map, provided that g ≥ 6 and g' ≤ 2g-2.

A Derivada de um Integral

O cálculo do valor da derivada de um integral ocorre com certa frequência na vida profissional de físicos, químicos, engenheiros, economistas ou biólogos. É frequente, contudo, surgir alguma dificuldade no decurso da sua aprendizagem. Este texto, assente na doutrina essencial e desenvolvido através de um conjunto vasto de exemplos significativos, visa, precisamente, ajudar os estudantes universitários de cursos de licenciatura diversos a ultrapassar os obstáculos referidos, assim conseguindo dominar um tema que é tão simples quão importante.

Natural classification of knots

The principal objective of the knot theory is to provide a simple way of classifying and ordering all the knot types. Here, we propose a natural classification of knots based on their intrinsic position in the knot space that is defined by the set of knots to which a given knot can be converted by individual intersegmental passages. In addition, we characterize various knots using a set of simple quantum numbers that can be determined upon inspection of minimal crossing diagram of a knot. These numbers include: crossing number; average three-dimensional writhe; number of topological domains; and the average relaxation value

High-pressure ultrasonic study of vibrational anharmonicity in bcc Cu-Al-Be alloys

To quantify the vibrational anharmonicity of the long-wavelength acoustic modes of bcc Cu74.1Al23.1Be2.8 near its martensitic transition temperature Ms (261 K), the hydrostatic pressure derivatives (¿CIJ/¿P)P=0 of the elastic stiffness moduli have been measured. The Grüneisen parameters at 268 K (just above Ms), especially of longitudinal modes, which become smaller than those of the shear modes, are quite different from those at 295 K: the anharmonicity changes markedly in the vicinity of the transition. Similar trends are noted for Cu66.5Al12.7Zn20.8. Experimental data near Ms are used to estimate cubic invariants in the strain order parameters in a Landau formalism.

Issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity

Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants of the motion. Time-dependent invariants arise through the choice of an intrinsic time, or equivalently through the imposition of time-dependent gauge fixation conditions. One example of such a time-dependent gauge fixing is the Komar-Bergmann use of Weyl curvature scalars in general relativity. An analogous gauge fixing is also imposed for the relativistic free particle and the resulting complete set time-dependent invariants for this exactly solvable model are displayed. In contrast with the free particle case, we show that gauge invariants that are simultaneously constants of motion cannot exist in general relativity. They vary with intrinsic time.

Proposed gravitational wave observatory based on solid elastic spheres

Spherical gravitational wave (GW) detectors offer a wealth of so far unexplored possibilities to detect gravitational radiation. We find that a sphere can be used as a powerful testbed for any metric theory of gravity, not only general relativity as considered so far, by making use of a deconvolution procedure for all the electric components of the Riemann tensor. We also find that the spheres cross section is large at two frequencies, and advantageous at higher frequencies in the sense that a single antenna constitutes a real xylophone in its own. Proposed GW networks will greatly benefit from this. The main features of a two large sphere observatory are reported.

Cosmic strings and Einstein-Rosen soliton waves

We consider all generalized soliton solutions of the Einstein-Rosen form in the cylindrical context. They are Petrov type-I solutions which describe solitonlike waves interacting with a line source placed on the symmetry axis. Some of the solutions develop a curvature singularity on the axis which is typical of massive line sources, whereas others just have the conical singularity revealing the presence of a static cosmic string. The analysis is based on the asymptotic behavior of the Riemann and metric tensors, the deficit angle, and a C-velocity associated to Thornes C-energy. The C-energy is found to be radiated along the null directions.