Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

This paper shows that certain quotients of entire functions are characteristic functions. Under some conditions, we provide expressions for the densities of such characteristic functions which turn out to be generalized Dirichlet series which in turn can be expressed as an infinite linear combination of exponential or Laplace densities. We apply these results to several examples.

Weighted norm inequalities for Fourier transforms of radial functions

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

On the number of higher order Delaunay triangulations

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

Notch1 functions as a tumor suppressor in mouse skin.

Notch proteins are important in binary cell-fate decisions and inhibiting differentiation in many developmental systems, and aberrant Notch signaling is associated with tumorigenesis. The role of Notch signaling in mammalian skin is less well characterized and is mainly based on in vitro studies, which suggest that Notch signaling induces differentiation in mammalian skin. Conventional gene targeting is not applicable to establishing the role of Notch receptors or ligands in the skin because Notch1-/- embryos die during gestation. Therefore, we used a tissue-specific inducible gene-targeting approach to study the physiological role of the Notch1 receptor in the mouse epidermis and the corneal epithelium of adult mice. Unexpectedly, ablation of Notch1 results in epidermal and corneal hyperplasia followed by the development of skin tumors and facilitated chemical-induced skin carcinogenesis. Notch1 deficiency in skin and in primary keratinocytes results in increased and sustained expression of Gli2, causing the development of basal-cell carcinoma-like tumors. Furthermore, Notch1 inactivation in the epidermis results in derepressed beta-catenin signaling in cells that should normally undergo differentiation. Enhanced beta-catenin signaling can be reversed by re-introduction of a dominant active form of the Notch1 receptor. This leads to a reduction in the signaling-competent pool of beta-catenin, indicating that Notch1 can inhibit beta-catenin-mediated signaling. Our results indicate that Notch1 functions as a tumor-suppressor gene in mammalian skin.

Dynamical modeling and analysis of large cellular regulatory networks.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

Peroxisome proliferator-activated receptors: insight into multiple cellular functions.

Peroxisome proliferator-activated receptors, PPARs, (NR1C) are nuclear hormone receptors implicated in energy homeostasis. Upon activation, these ligand-inducible transcription factors stimulate gene expression by binding to the promoter of target genes. The different structural domains of PPARs are presented in terms of activation mechanisms, namely ligand binding, phosphorylation, and cofactor interaction. The specificity of ligands, such as fatty acids, eicosanoids, fibrates and thiazolidinediones (TZD), is described for each of the three PPAR isotypes, alpha (NR1C1), beta (NR1C2) and gamma (NR1C3), so as the differential tissue distribution of these isotypes. Finally, general and specific functions of the PPAR isotypes are discussed, namely their implication in the control of inflammatory responses, cell proliferation and differentiation, the roles of PPARalpha in fatty acid catabolism and of PPARgamma in adipogenesis.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

The contribution of aging to the understanding of the dimensionality of executive functions.

It has been reported in the literature that executive functions may be fractioned into updating, shifting, and inhibition. The present study aimed to explore whether these executive sub-components can be identified in a more age-heterogeneous sample and see if they are prone to an age-related decline. We tested the performances of 81 individuals aged from 18 to 88 years old in each executive sub-component, working memory, fluid intelligence and processing speed. Correlation analysis revealed only a slight positive relationship between the two updating measures. A linear decrement with age was observed only for two complex executive tests. Tasks indexing working memory, processing speed and fluid intelligence showed a stronger linear decline with age than executive tasks. In conclusion, our results did not replicate the executive structure known from the literature, and revealed that decrement in executive function is not an unavoidable concomitant of aging but rather concerns specific executive tasks.

Agent based simulation to optimise emergency departments

Nowadays, many of the health care systems are large and complex environments and quite dynamic, specifically Emergency Departments, EDs. It is opened and working 24 hours per day throughout the year with limited resources, whereas it is overcrowded. Thus, is mandatory to simulate EDs to improve qualitatively and quantitatively their performance. This improvement can be achieved modelling and simulating EDs using Agent-Based Model, ABM and optimising many different staff scenarios. This work optimises the staff configuration of an ED. In order to do optimisation, objective functions to minimise or maximise have to be set. One of those objective functions is to find the best or optimum staff configuration that minimise patient waiting time. The staff configuration comprises: doctors, triage nurses, and admissions, the amount and sort of them. Staff configuration is a combinatorial problem, that can take a lot of time to be solved. HPC is used to run the experiments, and encouraging results were obtained. However, even with the basic ED used in this work the search space is very large, thus, when the problem size increases, it is going to need more resources of processing in order to obtain results in an acceptable time.

Les TIC a l'ensenyament de la modelització matemàtica en Ciències Econòmiques i en Ciències Experimentals

Aquest projecte proposa materials didàctics per a un nou plantejament de les assignatures de Matemàtiques dels primers cursos de Ciències Empresarials i d'Enginyeria Tècnica, més acord amb el procés de convergència europea, basat en la realització de projectes que anomenem “Tallers de Modelització Matemàtica” (TMM) en els quals: (1) Els alumnes parteixen de situacions i problemes reals per als quals han de construir per sí mateixos els models matemàtics més adients i, a partir de la manipulació adequada d’aquests models, poden obtenir la informació necessària per donar-los resposta. (2) El treball de construcció, experimentació i avaluació dels models es realitza amb el suport de la calculadora simbòlica Wiris i del full de càlcul Excel com a instruments “normalitzats” del treball matemàtic d’estudiants i professors. (3) S’adapten els programes de les assignatures de matemàtiques de primer curs per tal de poder-les associar a un petit nombre de Tallers que parteixen de situacions adaptades a cada titulació. L’assignatura de Matemàtiques per a les Ciències Empresarials s’articula entorn de dos tallers independents: “Matrius de transició” pel que fa a l’àlgebra lineal i “Previsió de vendes” per a la modelització funcional en una variable. L’assignatura de Matemàtiques per a l’Enginyeria s’articula entorn d’un únic taller, “Models de poblacions”, que abasta la majoria de continguts del curs: successions i models funcionals en una variable, àlgebra lineal i equacions diferencials. Un conjunt d’exercicis interactius basats en la calculadora simbòlica WIRIS (Wiris-player) serveix de suport per al treball tècnic imprescindible per al desenvolupament de les dues assignatures. L’experimentació d’aquests tallers durant 2 cursos consecutius (2006/07 i 2007/08) en dues universitats catalanes (URL i UAB) ha posat en evidència tant els innegables avantatges del nou dispositiu docent per a l’aprenentatge dels estudiants, així com les restriccions institucionals que actualment dificulten la seva gestió i difusió.

Social insect genomes exhibit dramatic evolution in gene composition and regulation while preserving regulatory features linked to sociality.

Genomes of eusocial insects code for dramatic examples of phenotypic plasticity and social organization. We compared the genomes of seven ants, the honeybee, and various solitary insects to examine whether eusocial lineages share distinct features of genomic organization. Each ant lineage contains ∼4000 novel genes, but only 64 of these genes are conserved among all seven ants. Many gene families have been expanded in ants, notably those involved in chemical communication (e.g., desaturases and odorant receptors). Alignment of the ant genomes revealed reduced purifying selection compared with Drosophila without significantly reduced synteny. Correspondingly, ant genomes exhibit dramatic divergence of noncoding regulatory elements; however, extant conserved regions are enriched for novel noncoding RNAs and transcription factor-binding sites. Comparison of orthologous gene promoters between eusocial and solitary species revealed significant regulatory evolution in both cis (e.g., Creb) and trans (e.g., fork head) for nearly 2000 genes, many of which exhibit phenotypic plasticity. Our results emphasize that genomic changes can occur remarkably fast in ants, because two recently diverged leaf-cutter ant species exhibit faster accumulation of species-specific genes and greater divergence in regulatory elements compared with other ants or Drosophila. Thus, while the "socio-genomes" of ants and the honeybee are broadly characterized by a pervasive pattern of divergence in gene composition and regulation, they preserve lineage-specific regulatory features linked to eusociality. We propose that changes in gene regulation played a key role in the origins of insect eusociality, whereas changes in gene composition were more relevant for lineage-specific eusocial adaptations.

Superatomic Boolean algebras constructed from strongly unbounded functions

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

Welfare Maximizing Contest Success Functions when the Planner Cannot Commit

We analyze how a contest organizer chooses optimally the winner when the contestants' efforts are already exerted and commitment to the use of a given contest success function is not possible. We de…ne the notion of rationalizability in mixed-strategies to capture such a situation. Our approach allows to derive different contest success functions depending on the aims and attitudes of the decider. We derive contest success functions which are closely related to commonly used functions providing new support for them. By taking into account social welfare considerations our approach bridges the contest literature and the recent literature on political economy. Keywords: Endogenous Contests, Contest Success Function, Mixed-Strategies. JEL Classi…cation: C72 (Noncooperative Games), D72 (Economic Models of Political Processes: Rent-Seeking, Elections), D74 (Conflict; Conflict Resolution; Alliances)

Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results

We define different concepts of group strategy-proofness for social choice functions. We discuss the connections between the defined concepts under different assumptions on their domains of definition. We characterize the social choice functions that satisfy each one of them and whose ranges consist of two alternatives, in terms of two types of basic properties.