Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

Work motivation and pro-social behavior in the delivery of public services : theoretical and empirical insights

This Ph.D. dissertation seeks to study the work motivation of employees in the delivery of public services. The questioning on work motivation in public services in not new but it becomes central for governments which are now facing unprecedented public debts. The objective of this research is twofold : First, we want to see if the work motivation of employees in public services is a continuum (intrinsic and extrinsic motivations cannot coexist) or a bi-dimensional construct (intrinsic and extrinsic motivations coexist simultaneously). The research in public administration literature has focused on the concept of public service motivation, and considered motivation to be uni-dimensional (Perry and Hondeghem 2008). However, no study has yet tackled both types of motivation, the intrinsic and extrinsic ones, in the same time. This dissertation proposes, in Part I, a theoretical assessment and an empirical test of a global work motivational structure, by using a self-constructed Swiss dataset with employees from three public services, the education sector, the security sector and the public administrative services sector. Our findings suggest that work motivation in public services in not uni-dimensional but bi-dimensional, the intrinsic and extrinsic motivations coexist simultaneously and can be positively correlated (Amabile et al. 1994). Our findings show that intrinsic motivation is as important as extrinsic motivation, thus, the assumption that employees in public services are less attracted by extrinsic rewards is not confirmed for this sample. Other important finding concerns the public service motivation concept, which, as theoretically predicted, represents the major motivational dimension of employees in the delivery of public services. Second, the theory of public service motivation makes the assumption that employees in public services engage in activities that go beyond their self-interest, but never uses this construct as a determinant for their pro-social behavior. In the same time, several studies (Gregg et al. 2011 and Georgellis et al. 2011) bring evidence about the pro-social behavior of employees in public services. However, they do not identify which type of motivation is at the origin of this behavior, they only make the assumption of an intrinsically motivated behavior. We analyze the pro-social behavior of employees in public services and use the public service motivation as determinant of their pro-social behavior. We add other determinants highlighted by the theory of pro-social behavior (Bénabou and Tirole 2006), by Le Grand (2003) and by fit theories (Besley and Ghatak 2005). We test these determinants on Part II and identify for each sector of activity the positive or the negative impact on pro-social behavior of Swiss employees. Contrary to expectations, we find, for this sample, that both intrinsic and extrinsic factors have a positive impact on pro-social behavior, no crowding-out effect is identified in this sample. We confirm the hypothesis of Le Grand (2003) about the positive impact of the opportunity cost on pro-social behavior. Our results suggest a mix of action-oriented altruism and out-put oriented altruism of employees in public services. These results are relevant when designing incentives schemes for employees in the delivery of public services.

Parental post-traumatic reactions after premature birth: implications for sleeping and eating problems in the infant.

BACKGROUND: Progress in perinatal medicine has made it possible to increase the survival of very or extremely low birthweight infants. Developmental outcomes of surviving preterm infants have been analysed at the paediatric, neurological, cognitive, and behavioural levels, and a series of perinatal and environmental risk factors have been identified. The threat to the child's survival and invasive medical procedures can be very traumatic for the parents. Few empirical reports have considered post-traumatic stress reactions of the parents as a possible variable affecting a child's outcome. Some studies have described sleeping and eating problems as related to prematurity; these problems are especially critical for the parents. OBJECTIVE: To examine the effects of post-traumatic reactions of the parents on sleeping and eating problems of the children. DESIGN: Fifty families with a premature infant (25-33 gestation weeks) and a control group of 25 families with a full term infant participated in the study. Perinatal risks were evaluated during the hospital stay. Mothers and fathers were interviewed when their children were 18 months old about the child's problems and filled in a perinatal post-traumatic stress disorder questionnaire (PPQ). RESULTS: The severity of the perinatal risks only partly predicts a child's problems. Independently of the perinatal risks, the intensity of the post-traumatic reactions of the parents is an important predictor of these problems. CONCLUSIONS: These findings suggest that the parental response to premature birth mediates the risks of later adverse outcomes. Preventive intervention should be promoted.

The determinants of social spending in Spain (1880-1960): Is Lindert right?

[spa] El principal objetivo de este artículo se centra en analizar los orígenes del Estado de Bienestar en España a partir del marco teórico elaborado por Peter Lindert. Con este fin, se ofrece un análisis econométrico de los factores que determinaron la evolución del gasto social público en este país entre 1880 y 1960. Utilizando nueva evidencia cuantitativa, se construyó un panel de datos por quinquenios con el porcentaje de gasto social respecto al PIB desagregado en tres partidas: sanidad, seguridad social y beneficencia. El análisis permite insertar el caso español en el debate internacional y los resultados revelan interesantes singularidades de este país.

Convergent genetic architecture underlies social organization in ants.

Complex adaptive polymorphisms are common in nature, but what mechanisms maintain the underlying favorable allelic combinations [1-4]? The convergent evolution of polymorphic social organization in two independent ant species provides a great opportunity to investigate how genomes evolved under parallel selection. Here, we demonstrate that a large, nonrecombining "social chromosome" is associated with social organization in the Alpine silver ant, Formica selysi. This social chromosome shares architectural characteristics with that of the fire ant Solenopsis invicta [2], but the two show no detectable similarity in gene content. The discovery of convergence at two levels-the phenotype and the genetic architecture associated with alternative social forms-points at general genetic mechanisms underlying transitions in social organization. More broadly, our findings are consistent with recent theoretical studies suggesting that suppression of recombination plays a key role in facilitating coordinated shifts in coadapted traits [5, 6].

Soziale Unterschiede in der vor- und nachgeburtlichen Sterblichkeit: Schweiz 1979-1985. [Social differences in the prenatal and postnatal mortality: Switzerland 1979-1985].

The influence of social factors on birthweight and fetal and infant mortality was investigated in the Swiss birth cohort from 1979-85 (N = 519,933). The proportion of newborns with low-birthweight (less than 2500 g) was higher in lower social classes. Stillbirth-rate, neonatal and postneonatal mortality were higher in lower social classes, too. When controlling for birthweight, the increase in mortality in the lower social classes became somewhat less striking. Marked social differences in perinatal mortality were found in the newborns with normal weight, whereas almost no difference could be detected in the low-birthweight-group.

Current status of a model system: the gene Gp-9 and its association with social organization in fire ants.

The Gp-9 gene in fire ants represents an important model system for studying the evolution of social organization in insects as well as a rich source of information relevant to other major evolutionary topics. An important feature of this system is that polymorphism in social organization is completely associated with allelic variation at Gp-9, such that single-queen colonies (monogyne form) include only inhabitants bearing B-like alleles while multiple-queen colonies (polygyne form) additionally include inhabitants bearing b-like alleles. A recent study of this system by Leal and Ishida (2008) made two major claims, the validity and significance of which we examine here. After reviewing existing literature, analyzing the methods and results of Leal and Ishida (2008), and generating new data from one of their study sites, we conclude that their claim that polygyny can occur in Solenopsis invicta in the U.S.A. in the absence of expression of the b-like allele Gp-9(b) is unfounded. Moreover, we argue that available information on insect OBPs (the family of proteins to which GP-9 belongs), on the evolutionary/population genetics of Gp-9, and on pheromonal/behavioral control of fire ant colony queen number fails to support their view that GP-9 plays no role in the chemosensory-mediated communication that underpins regulation of social organization. Our analyses lead us to conclude that there are no new reasons to question the existing consensus view of the Gp-9 system outlined in Gotzek and Ross (2007).

Computational problems in perfect phylogeny haplotyping: typing without calling the allele.

A haplotype is an m-long binary vector. The XOR-genotype of two haplotypes is the m-vector of their coordinate-wise XOR. We study the following problem: Given a set of XOR-genotypes, reconstruct their haplotypes so that the set of resulting haplotypes can be mapped onto a perfect phylogeny (PP) tree. The question is motivated by studying population evolution in human genetics, and is a variant of the perfect phylogeny haplotyping problem that has received intensive attention recently. Unlike the latter problem, in which the input is "full" genotypes, here we assume less informative input, and so may be more economical to obtain experimentally. Building on ideas of Gusfield, we show how to solve the problem in polynomial time, by a reduction to the graph realization problem. The actual haplotypes are not uniquely determined by that tree they map onto, and the tree itself may or may not be unique. We show that tree uniqueness implies uniquely determined haplotypes, up to inherent degrees of freedom, and give a sufficient condition for the uniqueness. To actually determine the haplotypes given the tree, additional information is necessary. We show that two or three full genotypes suffice to reconstruct all the haplotypes, and present a linear algorithm for identifying those genotypes.

Genetic regulation of colony social organization in fire ants: an integrative overview

Expression of colony social organization in fire ants appears to be under the control of a single Mendelian factor of large effect. Variation in colony queen number in Solenopsis invicta and its relatives is associated with allelic variation at the gene Gp-9, but not with variation at other unlinked genes; workers regulate queen identity and number on the basis of Gp-9 genotypic compatibility. Nongeneticfactors, such as prior social experience, queen reproductive status, and local environment, have negligible effects on queen number which illustrates the nearly complete penetrance of Gp-9. As predicted, queen number can be manipulated experimentally by altering worker Gp-9 genotype frequencies. The Gp-9 allele lineage associated with polygyny in South American fire? ants has been retained across multiple speciation events, which may signal the action of balancing selection to maintain social polymorphism in these species. Moreover positive selection is implicated in driving the molecular evolution of Gp-9 in association with the origin of polygyny. The identity of the product of Gp-9 as an odorant-binding protein suggests plausible scenarios for its direct involvement in the regulation of queen number via a role in chemical communication. While these and other lines of evidence show that Gp-9 represents a legitimate candidate gene of major effect, studies aimed at determining (i) the biochemical pathways in which GP-9 functions; (ii) the phenotypic effects of molecular variation at Gp-9 and other pathway genes; and (iii) the potential involvement of genes in linkage disequilibrium with Gp-9 are needed to elucidate the genetic architecture underlying social organization in fire ants. Information that reveals the links between molecular variation, individual phenotype, and colony-level behaviors, combined with behavioral models that incorporate details of the chemical communication involved in regulating queen number will yield a novel integrated view of the evolutionary changes underlying a key social adaptation.