Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Homologia de Lawson i descens

La meva recerca en els tres anys de gaudiment de beca s'ha centrat en l'estudi de teories semitopològiques definides a través d'espais de cicles algebraics, introduïts per Friedlander i Lawson. Hem estudiat propietats de descens d'aquestes teories i hem construït una successió espectral que calcula explícitament la cohomologia mòrfica d'una varietat tòrica. D'altra banda, estem treballant en l'estudi de propietats d'invariància homotòpica per la cohomologia mòrfica, així com en l'estructura algebraica dels grups d'homologia de Lawson.

Bases genètiques de la malformació de Chiari

La Malformació de Chiari tipus I (MCI) ha estat definida tradicionalment com la herniació de les amígdales cerebel•loses d’almenys 5mm, a través del forat mange. En general, els símptomes es posen de manifest durant la segona o tercera dècada de vida, tot i que s’han descrit casos pediàtrics. Donada la complexitat del quadre clínic, per realitzar un diagnòstic adient es requereix avaluació clínica i estudi de neuroimatge. La tècnica de preferència és la ressonància magnètica d’imatge, considerant-se actualment com a pacients de MCI aquells que presenten un descens de les amígdales superior a 3mm per sota del forat magne. L'existència de casos asimptomàtics dificulta establir una prevalença concreta, però s’ha estimat que podria estar entre 1/1000 a 1/5000 sent major en dones que en homes (2:1 aproximadament). Fins el moment, es desconeix l’etiologia de la malaltia però la hipòtesi més acceptada és que MCI és deguda al desenvolupament insuficient del mesoderm paraxial. Diferents estudis realitzats fins el moment evidencien que almenys, un subgrup de pacients amb MCI són deguts a contribució genètica: 1) casos d’agregació familiar amb afectes en tres generacions; 2) estudis de bessons 3) associació amb síndromes genètics coneguts amb herència mendeliana produïts per anomalies óssies que donen suport a la hipòtesi de la insuficiència del mesoderm com a causa de MCI. Davant l’evidència clara d’un component genètic com a principal causant de l’etiologia de MCI, l’objectiu del projecte va ser la identificació de les bases genètiques de la MCI, tant en gens responsables de les formes mendelianes com en gens responsables de les formes complexes de MCI mitjançant dues estratègies: 1-Identificació de variants genètiques de susceptibilitat en pacients amb MCI mitjançant estudis d’associació de tipus cas-control. 2-Anàlisi genètic de formes monogèniques mitjançant l’anàlisi de lligament a marcardors polimòrfics i la seqüenciació del DNA a gran escala.

Volatility smile extrapolation with an artificial neural network

I use a multi-layer feedforward perceptron, with backpropagation learning implemented via stochastic gradient descent, to extrapolate the volatility smile of Euribor derivatives over low-strikes by training the network on parametric prices.

Trajectòries d’èxit dels i les joves marroquines a Catalunya. Una anàlisi qualitativa des d’una perspectiva comparada

Les investigacions mostren que en la majoria dels països hi ha diferències significatives en el rendiment escolar entre els estudiants estrangers i els seus companys nadius. També indiquen que, tot i tenir una actitud més positiva cap a l'escola i aspiracions més elevades, els joves estrangers obtenen pitjors resultats i les seves aspiracions disminueixen amb el temps d'estada. I, especialment entre certs grups, no hi ha una millora en els seus resultats acadèmics. No obstant això, la literatura de recerca sobre migracions i educació també mostra com es distribueixen les oportunitats com les polítiques públiques -educatives - i l'estructura i cultura escolar col•laboren en la construcció de les trajectòries dels i les joves de minories. Ara bé, aquestes tendències no poden invisibilitzar les trajectòries d'èxit escolar i la creixent participació social d'una part considerable de joves (nois i noies) d'ascendència marroquina en la societat catalana. Aquest informe mostra els resultats del projecte de recerca realitzat, que analitza les condicions i possibilitats per a l'èxit acadèmic i la continuïtat educativa entre aquests joves.L'anàlisi reconstrueix els factors centrals que han permès el desenvolupament d'aquestes trajectòries i la consolidació d'aspiracions acadèmiques de llarga durada.

Avaluació de l’estructuració genètica humana a la Península Ibèrica i a d’altres regions del sudoest europeu: implicacions poblacionals i epidemiològiques

Els avenços en tècniques de genotipat de polimorfismes genètics a gran escala estan liderant una revolució en el camp de l’epidemiologia genètica i la genètica de poblacions humanes. La informació aportada per aquestes tècniques ha evidenciat l’existència d’estructuracions poblacionals que poden augmentar l’error en els estudis d’associació a escala genòmica (GWAS, genome-wide association studies). Estudis recents han demostrat la presència d’aquestes estructuracions a nivell interregional i intrarregional a Europa. El present projecte ha avaluat el grau d’estructuració genètica en poblacions de la Península Ibèrica i altres regions del sudoest europeu (Itàlia i França) per quantificar l’impacte que aquesta potencial estructuració pot tenir en el disseny d’estudis d’associació GWAS i reconstruir la història demogràfica de les poblacions de la Mediterrània. Per aconseguir aquests objectius, s’han analitzat mostres de DNA de 770 individus de 26 poblacions de la Península Ibèrica, França, Itàlia i d’altres països de la Mediterrània. Aquestes mostres van ser genotipades per 240000 SNPs utilitzant l’array 250K StyI d’Affymetrix en el marc d’aquest projecte o mitjançant altres arrays d’Affymetrix en els projectes internacionals HapMap i POPRES. S’han realitzat anàlisis estadístiques incloent anàlisis de components principals, Fst, identitat per descendència, desequilibri de lligament, barreres genètiques, etc. Aquests resultats han permés construir un marc de referència de la variabilitat en aquesta regió, avaluar el seu impacte en estudis d’associació i proposar mesures per evitar l’increment de qualsevol tipus d’error (tipus I i II) en estudis nacionals i internacionals. A més, també han permés reconstruir la història de les poblacions humanes de la Mediterrània així com analitzar les seves relacions demogràfiques. Donada la duració limitada d’aquesta acció (24 mesos, d’octubre de 2010 a setembre de 2012), els resultats d’aquest projecte es troben actualment en fase de redacció i conduiran a diverses publicacions en revistes internacionals i a la preparació de comunicacions a congressos.

Development of the femur - Implications for age and sex determination.

Growth of four variables of the femur (diapyseal length, diaphyseal length plus distal epiphysis, maximum length and vertical diameter of the head) was analyzed by polynomial regression for the purpose of evaluating its significance and capacity for age and sex determination throughout the entire life continuum. Materials included in analysis consisted of 346 specimens ranging from birth to 97 years of age from five documented osteological collections of Western European descent. Linear growth was displayed by each of the four variables. Significant sexual dimorphism was identified in two of the femoral measurements, including maximum length and vertical diameter of the head, from age 15 onward. These results indicate that the two variables may be of use in the determination of sex in sex determination from that age onward. Strong correlation coefficients were identified between femoral size and age for each of the four metric variables. These results indicate that any of the femoral measurements is likely to serve as a useful source to estimate sub-adult age in both archaeological and forensic samples.

Calibration and application of the MN2D dynamics model to the avalanches of Las Leñas (Argentina)

During the winters of 1999 and 2000 large avalanches occurred in the ski resort of Las Leñas (Los Andes, Mendoza, Argentina). On 8 September 1999 an avalanche of new, dry snow ran over a path with a 1000 m vertical drop. On 30 June and on 1 July 2000 five avalanches of similar vertical drop, which start with new snow, entrained very wet snow during their descent, and evolved into dense snow avalanches. To use the MN2D dynamics model correctly, calibration of model parameters is necessary. Also, no previous works with the use of dynamics models exist in South America. The events used to calibrate the model occurred during the winters of 1999 and 2000 and are a good sample of the kind of avalanches which can occur in this area of the Andes range. By considering the slope morphology and topography, the snow and meteorological conditions and the results of the model simulations, it was estimated that these avalanches were not extreme events with a return period greater than one hundred years. This implies that, in natural conditions, bigger, extreme avalanches could happen. In this work, the MN2D dynamics model is calibrated with two different avalanches of the same magnitude: dry and wet. The importance of the topographic data in the simulation is evaluated. It is concluded that MN2D dynamics model can be used to simulate dry extreme avalanches in Argentinean Andes but not to simulate extreme wet avalanches, which are much more sensitive to the topography.

Quasi-Nonparametric Blind Inversion of Wiener Systems

An e cient procedure for the blind inversion of a nonlinear Wiener system is proposed. We proved that the problem can be expressed as a problem of blind source separation in nonlinear mixtures, for which a solution has been recently proposed. Based on a quasi-nonparametric relative gradient descent, the proposed algorithm can perform e ciently even in the presence of hard distortions.

Association of MMP-2 polymorphisms with severe and very severe COPD: a case control study of MMPs-1, 9 and 12 in a European population.

BACKGROUND: Genetic factors play a role in chronic obstructive pulmonary disease (COPD) but are poorly understood. A number of candidate genes have been proposed on the basis of the pathogenesis of COPD. These include the matrix metalloproteinase (MMP) genes which play a role in tissue remodelling and fit in with the protease--antiprotease imbalance theory for the cause of COPD. Previous genetic studies of MMPs in COPD have had inadequate coverage of the genes, and have reported conflicting associations of both single nucleotide polymorphisms (SNPs) and SNP haplotypes, plausibly due to under-powered studies. METHODS: To address these issues we genotyped 26 SNPs, providing comprehensive coverage of reported SNP variation, in MMPs- 1, 9 and 12 from 977 COPD patients and 876 non-diseased smokers of European descent and evaluated their association with disease singly and in haplotype combinations. We used logistic regression to adjust for age, gender, centre and smoking history. RESULTS: Haplotypes of two SNPs in MMP-12 (rs652438 and rs2276109), showed an association with severe/very severe disease, corresponding to GOLD Stages III and IV. CONCLUSIONS: Those with the common A-A haplotype for these two SNPs were at greater risk of developing severe/very severe disease (p = 0.0039) while possession of the minor G variants at either SNP locus had a protective effect (adjusted odds ratio of 0.76; 95% CI 0.61 - 0.94). The A-A haplotype was also associated with significantly lower predicted FEV1 (42.62% versus 44.79%; p = 0.0129). This implicates haplotypes of MMP-12 as modifiers of disease severity.

A Gradient based algorithm for blind inversion of Wiener System using multi-variate score functions

A Wiener system is a linear time-invariant filter, followed by an invertible nonlinear distortion. Assuming that the input signal is an independent and identically distributed (iid) sequence, we propose an algorithm for estimating the input signal only by observing the output of the Wiener system. The algorithm is based on minimizing the mutual information of the output samples, by means of a steepest descent gradient approach.

Reconstructing native American migrations from whole-genome and whole-exome data.

There is great scientific and popular interest in understanding the genetic history of populations in the Americas. We wish to understand when different regions of the continent were inhabited, where settlers came from, and how current inhabitants relate genetically to earlier populations. Recent studies unraveled parts of the genetic history of the continent using genotyping arrays and uniparental markers. The 1000 Genomes Project provides a unique opportunity for improving our understanding of population genetic history by providing over a hundred sequenced low coverage genomes and exomes from Colombian (CLM), Mexican-American (MXL), and Puerto Rican (PUR) populations. Here, we explore the genomic contributions of African, European, and especially Native American ancestry to these populations. Estimated Native American ancestry is 48% in MXL, 25% in CLM, and 13% in PUR. Native American ancestry in PUR is most closely related to populations surrounding the Orinoco River basin, confirming the Southern American ancestry of the Taíno people of the Caribbean. We present new methods to estimate the allele frequencies in the Native American fraction of the populations, and model their distribution using a demographic model for three ancestral Native American populations. These ancestral populations likely split in close succession: the most likely scenario, based on a peopling of the Americas 16 thousand years ago (kya), supports that the MXL Ancestors split 12.2kya, with a subsequent split of the ancestors to CLM and PUR 11.7kya. The model also features effective populations of 62,000 in Mexico, 8,700 in Colombia, and 1,900 in Puerto Rico. Modeling Identity-by-descent (IBD) and ancestry tract length, we show that post-contact populations also differ markedly in their effective sizes and migration patterns, with Puerto Rico showing the smallest effective size and the earlier migration from Europe. Finally, we compare IBD and ancestry assignments to find evidence for relatedness among European founders to the three populations.

Weight filtration on the cohomology of complex analytic spaces

We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure. Our purely geometric proof is based on cubical descent for resolution of singularities and Poincaré-Verdier duality. Using similar techniques, we introduce the singularity filtration on the cohomology of compactificable analytic spaces. This is a new and natural analytic invariant which does not depend on the equivalence class of compactifications and is related to the weight filtration.

Classical references and their significance in The Magic Mountain by Thomas Mann

Although Thomas Mann’s novel The Magic Mountain has been the object of innumerable studies, this paper suggests that so far none of these has given truly close attention to the significance of the classical references in this novel with regard to the search for a true humanism. This is probably owing to the generally held belief that the influence of the classical tradition is relatively inconsequential in relation to the ample conjunction of philosophical ideas on which the novel is based. This article takes a differing view and, through a close analysis and comment of the explicit and implicit classical notions in the text, concludes that these ideas are also a valuable key to a greater comprehension of the ideological design of the main character, Hans Castorp, and to a certain degree they also help to continue to reflect on the most enigmatic and controversial episode of the novel: the young protagonist’s descent to the plain from the magical mountain (Zauberberg) in order to take part in the great tragedy of World War I, alien as is any war to the prevalent but ultimately futile desire that love (Liebe) should in the end prevail in the life of humans.