A three dimensional signed small ball inequality

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

Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system

We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Contact melting of a three-dimensional phase change material on a flat substrate

In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement.

I. Identification and characterisation of epigenetically altered tumor supressor genes by proteomic and genomic approches / II. Studies of genes regualted by MeCP2 union to its promoter regions by proteomic and genmomic approches

DNA methylation has an important impact on normal cell physiology, thus any defects in this mechanism may be related to the development of various diseases In this project we are interested in identifying epigeneticaliy modified genes, in general controlled by processes related to the DNA methylation, by means of a new strategy combining protomic and genomic analyses. First, the two Dimensional-Difference Gel Electrophoresis (2-DIGE) protein analyses of extracts obtained from HCT-116 wt and double knockout for DNMT1 and DNMT3b (DKO) cells revealed 34 proteins overexpressed in the condition of DNMTs depletion. From five genes with higher transcript lavels in DKO cells, comparing with HCT-116 wt. oniy AKR1B1, UCHLl and VIM are melhylated in HCT-116. As expected. the DNA methvlation 1s lost in DKO cells. The rneth,vl ation of VIM and UCHLl promoters in some cancer samples has already been repaired, thus further studies has been focused on AKRlBI. AKR1B1 expression due lo DNA methyiaton of promoter region seems to occur specilfically in the colon cancer cell Iines. which was confirmed in the DNA rnethylation status and expression analyses. performed on 32 different cancer cell lines (including colon, breast, lymphoma, leukemia, neuroblastoma, glioma and lung cancer cell Iines) as well as normal colon and normal lymphocytes samples. AKRIBI expression after treatments with DNA demethvlating agent (AZA) was rescued in 5 coloncancer cell lines (including genetic regulation of the candidate gene. The methylation status of the rest of the genes identified in proteomic analysis was checked by methylation specific PCR (MSP) experiment and all appeared to be unmethylated. The similar research has been done also bv means of Mecp2-null mouse model For 14 selected candidate genes the analyses of expression leveis, methylation Status and MeCP2 interaction with promoters are currently being performed.

Esfingolipids i senyal•lització cel.lular: l'(E)-2-hexadecenal com a possible lípid bioactiu

L’esfingosina-1-fosfat (S1P) és un lípid bioactiu amb funcions crucials en la biologia cel•lular. Entre aquestes, la seva activitat mitogènica i citoprotectora són les més estudiades. L’S1P és catabolitzada intracel•lularment mitjançant l’esfingosina-1-fosfat liasa (SGPL1) per generar (E)-2-hexadecenal i fosforiletanolamina. L’objectiu d’aquest projecte és explorar si l’(E)-2-hexadecenal és realment un catabòlit innocu o bé si, pel seu caràcter acceptor de Michael, és capaç de reaccionar amb pèptids o proteïnes específics. Aquesta interacció podria traduïr-se en funcions biològiques determinades, algunes de les quals són possiblement atribuïdes a l’esfingosina-1-fosfat com a tal. Per poder explorar el potencials adductes proteïcs amb l’aldehid, s’han emprat, sobre cèl•lules HeLa que sobreexpressen SGPL1, sondes anàlegs a esfingosina i esfinganina (i els seus derivats fosforil•lats) que presenten una funció azida en la posició omega de la cadena esfingoide. Aquestes, mitjançant química click sense coure, s’han fet reaccionar amb una molècula que presenta un dibenzociclooctí unit a biotina DBCObiotina). Després d’aïllar les proteïnes així biotinilades amb una reïna d’estreptavidina, aquestes es van separar per electroforesi. Les bandes proteïques observades es van extreure del gel i es van digerir amb tripsina, per posteriorment analitzar els pèptids per MALDI-TOF, el que permetria l’identificació de proteïnes a partir de “peptide mass fingerprinting”. Lamentablement, a la fi d’aquest contracte, encara no s’ha pogut identificar cap proteïna que s’uneixi a l’aldehid alliberat per la reacció de l’esfingosina-1- fosfat liasa. No obstant, durant aquest temps s’ha millorat el mètode per detectar aquests adductes proteïcs. Per això, si la recerca continua en aquesta línia, properament es podria saber amb certesa si existeixen o no aquestes interaccions covalents entre determinades proteïnes i l’(E)-2-hexadecenal.

A bi-dimensional genome scan for prolificacy traits in pigs shows the existence of multiple epistatic QTL

Background: Prolificacy is the most important trait influencing the reproductive efficiency of pig production systems. The low heritability and sex-limited expression of prolificacy have hindered to some extent the improvement of this trait through artificial selection. Moreover, the relative contributions of additive, dominant and epistatic QTL to the genetic variance of pig prolificacy remain to be defined. In this work, we have undertaken this issue by performing one-dimensional and bi-dimensional genome scans for number of piglets born alive (NBA) and total number of piglets born (TNB) in a three generation Iberian by Meishan F2 intercross. Results: The one-dimensional genome scan for NBA and TNB revealed the existence of two genome-wide highly significant QTL located on SSC13 (P < 0.001) and SSC17 (P < 0.01) with effects on both traits. This relative paucity of significant results contrasted very strongly with the wide array of highly significant epistatic QTL that emerged in the bi-dimensional genome-wide scan analysis. As much as 18 epistatic QTL were found for NBA (four at P < 0.01 and five at P < 0.05) and TNB (three at P < 0.01 and six at P < 0.05), respectively. These epistatic QTL were distributed in multiple genomic regions, which covered 13 of the 18 pig autosomes, and they had small individual effects that ranged between 3 to 4% of the phenotypic variance. Different patterns of interactions (a × a, a × d, d × a and d × d) were found amongst the epistatic QTL pairs identified in the current work.Conclusions: The complex inheritance of prolificacy traits in pigs has been evidenced by identifying multiple additive (SSC13 and SSC17), dominant and epistatic QTL in an Iberian × Meishan F2 intercross. Our results demonstrate that a significant fraction of the phenotypic variance of swine prolificacy traits can be attributed to first-order gene-by-gene interactions emphasizing that the phenotypic effects of alleles might be strongly modulated by the genetic background where they segregate.

Proteomic analysis of peach fruit mesocarp softening and chilling injury using difference gel electrophoresis (DIGE)

Background: Peach fruit undergoes a rapid softening process that involves a number of metabolic changes. Storing fruit at low temperatures has been widely used to extend its postharvest life. However, this leads to undesired changes, such as mealiness and browning, which affect the quality of the fruit. In this study, a 2-D DIGE approach was designed to screen for differentially accumulated proteins in peach fruit during normal softening as well as under conditions that led to fruit chilling injury. Results:The analysis allowed us to identify 43 spots -representing about 18% of the total number analyzed- that show statistically significant changes. Thirty-nine of the proteins could be identified by mass spectrometry. Some of the proteins that changed during postharvest had been related to peach fruit ripening and cold stress in the past. However, we identified other proteins that had not been linked to these processes. A graphical display of the relationship between the differentially accumulated proteins was obtained using pairwise average-linkage cluster analysis and principal component analysis. Proteins such as endopolygalacturonase, catalase, NADP-dependent isocitrate dehydrogenase, pectin methylesterase and dehydrins were found to be very important for distinguishing between healthy and chill injured fruit. A categorization of the differentially accumulated proteins was performed using Gene Ontology annotation. The results showed that the 'response to stress', 'cellular homeostasis', 'metabolism of carbohydrates' and 'amino acid metabolism' biological processes were affected the most during the postharvest. Conclusions: Using a comparative proteomic approach with 2-D DIGE allowed us to identify proteins that showed stage-specific changes in their accumulation pattern. Several proteins that are related to response to stress, cellular homeostasis, cellular component organization and carbohydrate metabolism were detected as being differentially accumulated. Finally, a significant proportion of the proteins identified had not been associated with softening, cold storage or chilling injury-altered fruit before; thus, comparative proteomics has proven to be a valuable tool for understanding fruit softening and postharvest.

Two-dimensional clusters of liquid 4He

The binding energies of two-dimensional clusters (puddles) of¿4He are calculated in the framework of the diffusion Monte Carlo method. The results are well fitted by a mass formula in powers of x=N-1/2, where N is the number of particles. The analysis of the mass formula allows for the extraction of the line tension, which turns out to be 0.121 K/Å. Sizes and density profiles of the puddles are also reported.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

Some aspects of N=2 superstring

The string model with N=2 world-sheet supersymmetry is approached via ghosts, Becchi-Rouet-Stora-Tyutin cohomology, and bosonization. Some amplitudes involving massless scalars and vectors are computed at the tree level. The constraints of locality on the spectrum are analyzed. An attempt is made to "decompactify" the model into a four-dimensional theory.

Collineations of a symmetric 2-covariant tensor: Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime.

Higher-dimensional rotating charged black holes

Using the blackfold approach, we study new classes of higher-dimensional rotating black holes with electric charges and string dipoles, in theories of gravity coupled to a 2-form or 3-form field strength and to a dilaton with arbitrary coupling. The method allows to describe not only black holes with large angular momenta, but also other regimes that include charged black holes near extremality with slow rotation. We construct explicit examples of electric rotating black holes of dilatonic and non-dilatonic Einstein-Maxwell theory, with horizons of spherical and non-spherical topology. We also find new families of solutions with string dipoles, including a new class of prolate black rings. Whenever there are exact solutions that we can compare to, their properties in the appropriate regime are reproduced precisely by our solutions. The analysis of blackfolds with string charges requires the formulation of the dynamics of anisotropic fluids with conserved string-number currents, which is new, and is carried out in detail for perfect fluids. Finally, our results indicate new instabilities of near-extremal, slowly rotating charged black holes, and motivate conjectures about topological constraints on dipole hair.