Sizes of linear descriptions in combinatorial optimization

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Univ., Dissertation, 2015

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Regional income inequalities in Europe: an updated measurement and some decomposition results

In this paper well-known summary inequality indexes are used to explore interregional income inequalities in Europe. In particular, we mainly employ Theils’population-weighted index because of its appealing properties. Two decomposition analysis are applied. First, regional inequalities are decomposed by regional subgroups (countries). Second, intertemporal inequality changes are separated into income and population changes. The main results can be summarized as follows. First, data confirm a reduction in crossregional inequality during 1982-97. Second, this reduction is basically due to real convergence among countries. Third, currently the greater part of European interregional disparities is within-country by nature, which introduce an important challenge for the European policy. Fourth, inequality changes are due mainly to income variations, population changes playing a minor role.

Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

"Vegeu el resum a l'inici del document del fitxer adjunt."

Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

Determinació de la ubicació estructural dels ions Yb3+ i Nb3+ en Yb:RTP, Nb:RTP i (Nb,Yb):RTP

Estudi elaborat a partir d’una estada al Stony Brook University al juliol del 2006. El RbTiOPO4 (RTP) monocristal•lí és un material d' òptica no lineal molt rellevant i utilitzat en la tecnologia làser actual, químicament molt estable i amb unes propietats físiques molt destacades, entre elles destaquen els alts coeficients electro-òptics i l'alt llindar de dany òptic que presenta. En els últims anys s’està utilitzant tecnològicament en aplicacions d'òptica no lineal en general i electro-òptiques en particular. En alguns casos ja ha substituït, millorant prestacions, a materials tals com el KTP o el LNB(1). Dopant RTP amb ions lantànids (Ln3+) (2-4), el material es converteix en un material làser auto-doblador de freqüència, combinant les seves propietats no lineals amb les de matriu làser. El RTP genera radiació de segon harmònic (SHG) a partir d’un feix fonamental amb longituds d’ona inferiors a 990 nm, que és el límit que presenta el KTP.La determinació de la ubicació estructural i l’estudi de l'entorn local del ions actius làser és de fonamental importància per a la correcta interpretació de les propietats espectroscòpiques d’aquest material. Mesures de difracció de neutrons sobre mostra de pols cristal•lí mostren que els ions Nb5+ i Ln3+ només substitueixin posicions de Ti4+ (8-9). Estudis molt recents d'EPR (electron paramagnetic resonance) semblen indicar que quan la concentració d'ió Ln3+ es baixa, aquest ió presenta la tendència a substituir l'ió alcalí present a l'estructura (10).Després dels resultats obtinguts en el present treball a partir de la tècnica EXAFS a la instal•lació sincrotò del Brookhaven National Laboratory/State University of New York (Stony Brook) es pot concloure definitivament que els ions Nb s’ubiquen en la posició Ti (1) i que els ions Yb3+ es distribueixen paritariament en les dues posicions del Ti (1 i 2). Aquests resultats aporten una valuosa informació per a la correcta interpretació dels espectres, tant d’absorció com d’emissió, del material i per la avaluació dels paràmetres del seu comportament durant l'acció làser.

Norm inequalities in multidimensional Lorentz spaces

In this paper we obtain necessary and sufficient conditions for double trigonometric series to belong to generalized Lorentz spaces, not symmetric in general. Estimates for the norms are given in terms of coefficients.

Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Chronic murine myocarditis due to Trypanosoma cruzi: an ultrastructural study and immunochemical characterization of cardiac interstitial matrix

In an attempt to define the mouse-model for chronic Chagas' disease, a serological, histopathological and ultrastructural study as well as immunotyping of myocardium collagenic matrix were performed on Swiss mice, chronically infected with Trypanosoma cruzi strains: 21 SF and mambaí (Type II); PMN and Bolivia (Type III), spontaneously surviving after 154 to 468 days of infection. Haemagglutination and indirect immunofluorescence tests showed high titres of specific antibodies. The ultrastructural study disclosed the cellular constitution of the inflammatory infiltrate showing the predominance of monocytes, macrophages with intense phagocytic activity, fibroblasts, myofibroblasts and abundant collagen matrix suggesting the association of the inflammatory process with fibrogenesis in chronic chagasic cardiomyopathy. Artertolar and blood capillary alterations together with dissociation of cardiac cells from the capillary wall by edema and inflammation were related to ultrastructural lesions of myocardial cells. Rupture of parasitized cardiac myocells contribute to intensify the inflammatory process in focal areas. Collagen immunotyping showed the predominance of Types III and IV collagen. Collagen degradation and phagocytosis were present suggesting a reversibility of the fibrous process. The mouse model seems to be valuable in the study of the pathogenetic mechanisms in Chagas cardiomyopathy, providing that T. cruzi strains of low virulence and high pathogenecity are used.

Effects of selection and drift on G matrix evolution in a heterogeneous environment: a multivariate Qst-Fst Test with the freshwater snail Galba truncatula.

Unraveling the effect of selection vs. drift on the evolution of quantitative traits is commonly achieved by one of two methods. Either one contrasts population differentiation estimates for genetic markers and quantitative traits (the Q(st)-F(st) contrast) or multivariate methods are used to study the covariance between sets of traits. In particular, many studies have focused on the genetic variance-covariance matrix (the G matrix). However, both drift and selection can cause changes in G. To understand their joint effects, we recently combined the two methods into a single test (accompanying article by Martin et al.), which we apply here to a network of 16 natural populations of the freshwater snail Galba truncatula. Using this new neutrality test, extended to hierarchical population structures, we studied the multivariate equivalent of the Q(st)-F(st) contrast for several life-history traits of G. truncatula. We found strong evidence of selection acting on multivariate phenotypes. Selection was homogeneous among populations within each habitat and heterogeneous between habitats. We found that the G matrices were relatively stable within each habitat, with proportionality between the among-populations (D) and the within-populations (G) covariance matrices. The effect of habitat heterogeneity is to break this proportionality because of selection for habitat-dependent optima. Individual-based simulations mimicking our empirical system confirmed that these patterns are expected under the selective regime inferred. We show that homogenizing selection can mimic some effect of drift on the G matrix (G and D almost proportional), but that incorporating information from molecular markers (multivariate Q(st)-F(st)) allows disentangling the two effects.

A public-key cryptosystem based on second order linear sequences

Based on Lucas functions, an improved version of the Diffie-Hellman distribution key scheme and to the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Cell-matrix interactions in Schistosomal portal fibrosis: a dynamic event

In recent years, one of the most significant progress in the understanding of liver diseases was the demonstration that liver fibrosis is a dynamic process resulting from a balance between synthesis and degradation of several matrix components, collagen in particular. Thus, fibrosis has been found to be a very early event during liver diseases, be it of toxic, viral or parasitic origin, and to be spontaneously reversible, either partially or totally. In liver fibrosis cell matrix interactions are dependent on the existence of the many factors (sometimes acting in combination) which produce the same events at the cellular and molecular levels. These events are: (i) the recruitment of fiber-producing cells, (ii) their proliferation, (iii) the secretion of matrix constituents of the extracellular matrix, and (iv) the remodeling and degradation of the newly formed matrix. All these events represent, at least in principle, a target for a therapeutic intervention aimed at influencing the experimentally induced hepatic fibrosis. In this context, hepatosplenic schistosomiasis is of particular interest, being an immune cell-mediated granulomatous disease and a model of liver fibrosis allowing extensive studies in human and animals as well as providing original in vitro models.

Performance of matrix-assisted laser desorption ionization-time of flight mass spectrometry for identification of bacterial strains routinely isolated in a clinical microbiology laboratory.

Matrix-assisted laser desorption ionization-time of flight mass spectrometry (MALDI-TOF MS) has recently been introduced in diagnostic microbiology laboratories for the identification of bacterial and yeast strains isolated from clinical samples. In the present study, we prospectively compared MALDI-TOF MS to the conventional phenotypic method for the identification of routine isolates. Colonies were analyzed by MALDI-TOF MS either by direct deposition on the target plate or after a formic acid-acetonitrile extraction step if no valid result was initially obtained. Among 1,371 isolates identified by conventional methods, 1,278 (93.2%) were putatively identified to the species level by MALDI-TOF MS and 73 (5.3%) were identified to the genus level, but no reliable identification was obtained for 20 (1.5%). Among the 1,278 isolates identified to the species level by MALDI-TOF MS, 63 (4.9%) discordant results were initially identified. Most discordant results (42/63) were due to systematic database-related taxonomical differences, 14 were explained by poor discrimination of the MALDI-TOF MS spectra obtained, and 7 were due to errors in the initial conventional identification. An extraction step was required to obtain a valid MALDI-TOF MS identification for 25.6% of the 1,278 valid isolates. In conclusion, our results show that MALDI-TOF MS is a fast and reliable technique which has the potential to replace conventional phenotypic identification for most bacterial strains routinely isolated in clinical microbiology laboratories.