Low codimensional intrinsic regular submanifolds in the Heisenberg group H^n

The thesis mainly concerns the study of intrinsically regular submanifolds of low codimension in the Heisenberg group H^n, called H-regular surfaces of low codimension, from the point of view of geometric measure theory. We consider an H-regular surface of H^n of codimension k, with k between 1 and n, parametrized by a uniformly intrinsically differentiable map acting between two homogeneous complementary subgroups of H^n, with target subgroup horizontal of dimension k. In particular the considered submanifold is the intrinsic graph of the parametrization. We extend various results of Ambrosio, Serra Cassano and Vittone, available for the case when k = 1. We prove that the uniform intrinsic differentiability of the parametrizing map is equivalent to the existence and continuity of its intrinsic differential, to the local existence of a suitable approximating family of Euclidean regular maps, and, when the domain and the codomain of the map are orthogonal, to the existence and continuity of suitably defined intrinsic partial derivatives of the function. Successively, we present a series of area formulas, proved in collaboration with V. Magnani. They allow to compute the (2n+2−k)-dimensional spherical Hausdorff measure and the (2n+2−k)-dimensional centered Hausdorff measure of the parametrized H-regular surface, with respect to any homogeneous distance fixed on H^n. Furthermore, we focus on (G,M)-regular sets of G, where G and M are two arbitrary Carnot groups. Suitable implicit function theorems ensure the local existence of an intrinsic parametrization of such a set, at any of its points. We prove that it is uniformly intrinsically differentiable. Finally, we prove a coarea-type inequality for a continuously Pansu differentiable function acting between two Carnot groups endowed with homogeneous distances. We assume that the level sets of the function are uniformly lower Ahlfors regular and that the Pansu differential is everywhere surjective.

Ferromagnetism, paramagnetism, and a Curie-Weiss metal in an electron-doped Hubbard model on a triangular lattice

Motivated by the unconventional properties and rich phase diagram of NaxCoO2 we consider the electronic and magnetic properties of a two-dimensional Hubbard model on an isotropic triangular lattice doped with electrons away from half-filling. Dynamical mean-field theory (DMFT) calculations predict that for negative intersite hopping amplitudes (t < 0) and an on-site Coulomb repulsion, U, comparable to the bandwidth, the system displays properties typical of a weakly correlated metal. In contrast, for t > 0 a large enhancement of the effective mass, itinerant ferromagnetism, and a metallic phase with a Curie-Weiss magnetic susceptibility are found in a broad electron doping range. The different behavior encountered is a consequence of the larger noninteracting density of states (DOS) at the Fermi level for t > 0 than for t < 0, which effectively enhances the mass and the scattering amplitude of the quasiparticles. The shape of the DOS is crucial for the occurrence of ferromagnetism as for t > 0 the energy cost of polarizing the system is much smaller than for t < 0. Our observation of Nagaoka ferromagnetism is consistent with the A-type antiferromagnetism (i.e., ferromagnetic layers stacked antiferromagnetically) observed in neutron scattering experiments on NaxCoO2. The transport and magnetic properties measured in NaxCoO2 are consistent with DMFT predictions of a metal close to the Mott insulator and we discuss the role of Na ordering in driving the system towards the Mott transition. We propose that the Curie-Weiss metal phase observed in NaxCoO2 is a consequence of the crossover from a bad metal with incoherent quasiparticles at temperatures T > T-* and Fermi liquid behavior with enhanced parameters below T-*, where T-* is a low energy coherence scale induced by strong local Coulomb electron correlations. Our analysis also shows that the one band Hubbard model on a triangular lattice is not enough to describe the unusual properties of NaxCoO2 and is used to identify the simplest relevant model that captures the essential physics in NaxCoO2. We propose a model which allows for the Na ordering phenomena observed in the system which, we propose, drives the system close to the Mott insulating phase even at large dopings.

Effects of Optimal Medical Treatment With or Without Coronary Revascularization on Angina and Subsequent Revascularizations in Patients With Type 2 Diabetes Mellitus and Stable Ischemic Heart Disease

Background-In the Bypass Angioplasty Revascularization Investigation 2 Diabetes (BARI 2D) trial, an initial strategy of coronary revascularization and optimal medical treatment (REV) compared with an initial optimal medical treatment with the option of subsequent revascularization (MED) did not reduce all-cause mortality or the composite of cardiovascular death, myocardial infarction, and stroke in patients with type 2 diabetes mellitus and stable ischemic heart disease. In the same population, we tested whether the REV strategy was superior to the MED strategy in preventing worsening and new angina and subsequent coronary revascularizations. Methods and Results-Among the 2364 men and women (mean age, 62.4 years) with type 2 diabetes mellitus, documented coronary artery disease, and myocardial ischemia, 1191 were randomized to the MED and 1173 to the REV strategy preselected in the percutaneous coronary intervention (796) and coronary artery bypass graft (377) strata. Compared with the MED strategy, the REV strategy at the 3-year follow-up had a lower rate of worsening angina (8% versus 13%; P < 0.001), new angina (37% versus 51%; P = 0.001), and subsequent coronary revascularizations (18% versus 33%; P < 0.001) and a higher rate of angina-free status (66% versus 58%; P = 0.003). The coronary artery bypass graft stratum patients were at higher risk than those in the percutaneous coronary intervention stratum, and had the greatest benefits from REV. Conclusions-In these patients, the REV strategy reduced the occurrence of worsening angina, new angina, and subsequent coronary revascularizations more than the MED strategy. The symptomatic benefits were observed particularly for high-risk patients.

Which Inequality? The Inequality of Endowments Versus the Inequality of Rewards

Society often allocates valuable resources - such as prestigious positions, salaries, or marriage partners - via tournament-like institutions. In such situations, inequality affects incentives to compete and hence has a direct effect on equilibrium choices and hence material outcomes. We introduce a new distinction between inequality in initial endowments (e.g. ability, inherited wealth) and inequality of what one can obtain as rewards (e.g. prestigious positions, money). We show that these two types of inequality have opposing effects on equilibrium behavior and wellbeing. Greater inequality of rewards tends to hurt most people — both the middle class and the poor, — who are forced into greater effort. In contrast, greater inequality of endowments tends to benefit the middle class. Thus, which type of inequality is considered hugely affects the correctness of our intuitions about the implications of inequality.

Novel loci for adiponectin levels and their influence on type 2 diabetes and metabolic traits: a multi-ethnic meta-analysis of 45,891 individuals.

Circulating levels of adiponectin, a hormone produced predominantly by adipocytes, are highly heritable and are inversely associated with type 2 diabetes mellitus (T2D) and other metabolic traits. We conducted a meta-analysis of genome-wide association studies in 39,883 individuals of European ancestry to identify genes associated with metabolic disease. We identified 8 novel loci associated with adiponectin levels and confirmed 2 previously reported loci (P = 4.5×10(-8)-1.2×10(-43)). Using a novel method to combine data across ethnicities (N = 4,232 African Americans, N = 1,776 Asians, and N = 29,347 Europeans), we identified two additional novel loci. Expression analyses of 436 human adipocyte samples revealed that mRNA levels of 18 genes at candidate regions were associated with adiponectin concentrations after accounting for multiple testing (p<3×10(-4)). We next developed a multi-SNP genotypic risk score to test the association of adiponectin decreasing risk alleles on metabolic traits and diseases using consortia-level meta-analytic data. This risk score was associated with increased risk of T2D (p = 4.3×10(-3), n = 22,044), increased triglycerides (p = 2.6×10(-14), n = 93,440), increased waist-to-hip ratio (p = 1.8×10(-5), n = 77,167), increased glucose two hours post oral glucose tolerance testing (p = 4.4×10(-3), n = 15,234), increased fasting insulin (p = 0.015, n = 48,238), but with lower in HDL-cholesterol concentrations (p = 4.5×10(-13), n = 96,748) and decreased BMI (p = 1.4×10(-4), n = 121,335). These findings identify novel genetic determinants of adiponectin levels, which, taken together, influence risk of T2D and markers of insulin resistance.

A genome-wide association search for type 2 diabetes genes in African Americans.

African Americans are disproportionately affected by type 2 diabetes (T2DM) yet few studies have examined T2DM using genome-wide association approaches in this ethnicity. The aim of this study was to identify genes associated with T2DM in the African American population. We performed a Genome Wide Association Study (GWAS) using the Affymetrix 6.0 array in 965 African-American cases with T2DM and end-stage renal disease (T2DM-ESRD) and 1029 population-based controls. The most significant SNPs (n = 550 independent loci) were genotyped in a replication cohort and 122 SNPs (n = 98 independent loci) were further tested through genotyping three additional validation cohorts followed by meta-analysis in all five cohorts totaling 3,132 cases and 3,317 controls. Twelve SNPs had evidence of association in the GWAS (P<0.0071), were directionally consistent in the Replication cohort and were associated with T2DM in subjects without nephropathy (P<0.05). Meta-analysis in all cases and controls revealed a single SNP reaching genome-wide significance (P<2.5×10(-8)). SNP rs7560163 (P = 7.0×10(-9), OR (95% CI) = 0.75 (0.67-0.84)) is located intergenically between RND3 and RBM43. Four additional loci (rs7542900, rs4659485, rs2722769 and rs7107217) were associated with T2DM (P<0.05) and reached more nominal levels of significance (P<2.5×10(-5)) in the overall analysis and may represent novel loci that contribute to T2DM. We have identified novel T2DM-susceptibility variants in the African-American population. Notably, T2DM risk was associated with the major allele and implies an interesting genetic architecture in this population. These results suggest that multiple loci underlie T2DM susceptibility in the African-American population and that these loci are distinct from those identified in other ethnic populations.

Wage inequality and unemployment with overeducation

A skill-biased change in technology can account at once for the changes observed in a number of important variables of the US labour market between 1970 and 1990. These include the increasing inequality in wages, both between and within education groups, and the increase in unemployment at all levels of education. In contrast, in previous literature this type of technology shock cannot account for all of these changes. The paper uses a matching model with a segmented labour market, an imperfect correlation between individual ability and education, and a fixed cost of setting up a job. The endogenous increase in overeducation is key to understand the response of unemployment to the technology shock.

Review of the type material of three species of Polietina Schnabl & Dziedzicki (Diptera, Muscidae)

The type material of three species of Polietina Schnabl & Dziedzicki, 1911 was examined. Polietina flavidicincta (Stein, 1904) is redescribed and a lectotype is designated; P. stellata (Couri, 1982) is considered junior synonym of P. flavithorax (Stein, 1904), and for the latter a lectotype is designated. The neotype previously designated is considered invalid.

Wage inequality in a frictional labor market

Wage inequality in the United States has grown substantially in thepast two decades. Standard supply-demand analysis in the empiricsof inequality (e.g.Katz and Murphy (1992)) indicates that we mayattribute some of this trend to an outward shift in the demand forhigh skilled labor. In this paper we examine a simple static channelin which the wage premium for skill may grow -increased firm entry.We consider a model of wage dispersion where there are two types ofworkers and homogeneous firms must set wages and preferences forwhat type of worker they would like to hire. We find that both thewage differential and the demand for high skill workers can increasewith the proportion of high skill workers -these high skill workerstherefore 'create' their own demand without exogenous factors. Inaddition, within group wage inequality can increase in step with thebetween group wage inequality. Simulations of the model are providedin order to compare the findings with empirical results.

Certain problems concerning polynomials and transcendental entire functions of exponential type

Soit $\displaystyle P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ un polynôme de degré $n$ et $\displaystyle M:=\sup_{|z|=1}|P(z)|.$ Sans aucne restriction suplémentaire, on sait que $|P'(z)|\leq Mn$ pour $|z|\leq 1$ (inégalité de Bernstein). Si nous supposons maintenant que les zéros du polynôme $P$ sont à l'extérieur du cercle $|z|=k,$ quelle amélioration peut-on apporter à l'inégalité de Bernstein? Il est déjà connu [{\bf \ref{Mal1}}] que dans le cas où $k\geq 1$ on a $$(*) \qquad |P'(z)|\leq \frac{n}{1+k}M \qquad (|z|\leq 1),$$ qu'en est-il pour le cas où $k < 1$? Quelle est l'inégalité analogue à $(*)$ pour une fonction entière de type exponentiel $\tau ?$ D'autre part, si on suppose que $P$ a tous ses zéros dans $|z|\geq k \, \, (k\geq 1),$ quelle est l'estimation de $|P'(z)|$ sur le cercle unité, en terme des quatre premiers termes de son développement en série entière autour de l'origine. Cette thèse constitue une contribution à la théorie analytique des polynômes à la lumière de ces questions.

Social Inequality and Social Policy outside the OECD

Almost all Latin American countries are still marked by extreme forms of social inequality – and to an extent, this seems to be the case regardless of national differences in the economic development model or the strength of democracy and the welfare state. Recent research highlights the fact that the heterogeneous labour markets in the region are a key source of inequality. At the same time, there is a strengthening of ‘exclusive’ social policy, which is located at the fault lines of the labour market and is constantly (re-)producing market-mediated disparities. In the last three decades, this type of social policy has even enjoyed democratic legitimacy. These dynamics challenge many of the assumptions guiding social policy and democratic theory, which often attempt to account for the specificities of the region by highlighting the purported flaws of certain policies. We suggest taking a different perspective: social policy in Latin American should not be grasped as a deficient or flawed type of social policy, but as a very successful relation of political domination. ‘Relational social analysis’ locates social policy in the ‘tension zone’ constituted by the requirements of economic reproduction, demands for democratic legitimacy and the relative autonomy of the state. From this vantage point, we will make the relation of domination in question accessible for empirical research. It seems particularly useful for this purpose to examine the recent shifts in the Latin American labour markets, which have undergone numerous reforms. We will examine which mechanisms, institutions and constellations of actors block or activate the potentials of redistribution inherent in such processes of political reform. This will enable us to explore the socio-political field of forces that has been perpetuating the social inequalities in Latin America for generations.

Digital Inequality

Unpicking and understanding if and how the web is linked to inequality means: Recognising that the access divide is not over, Thinking beyond hardware, Thinking beyond demographic variables, Developing a conceptual and theoretical toolkit, Beyond technological determinism, Co-constitution, Intersectionality, Technical capital

Inequality of opportunity in educational achievement in Latin America: evidence from PISA 2006-2009

We assess inequality of opportunity in educational achievement in six Latin American countries, employing two waves of PISA data (2006 and 2009). By means of a non-parametric approach using a decomposable inequality index, GE(0), we rank countries according to their degree of inequality of opportunity. We work with alternative characterizations of types: school type (public or private), gender, parental education, and combinations of those variables. We calculate incremental contributions of each set of circumstances to inequality. We provide rankings of countries based on unconditional inequalities (using conventional indices) and on conditional inequalities (EOp indices), and the two sets of rankings do not always coincide. Inequality of opportunities range from less than 1% to up to 27%, with substantial heterogeneity according to the year, the country, the subject and the specificication of circumstances. Robustness checks based on bootstrap and the use of an alternative index confirm most of the initial results.

Inequality, intergenerational mobility and redistributive policies under endogenous information

This paper presents a dynamic model to study how different levels of information about the root determinants of wealth (luck versus effort) can impact inequality and intergenerational mobility through societal beliefs, individual choices and redistributive policies. To my knowledge, the model presented is the first dynamicmodel in which skills are stochastic and both beliefs and voted redistribution are determined endogenously. The model is able to explain a number of empirical facts. Large empirical evidence shows that the difference in the political support for redistribution appears to reflect differences in the social perceptions regarding the determinants of individual wealth and the underlying sources of income inequality. Moreover the beliefs about the determinants of wealth impact individual choices of effort and therefore the beliefs about the determinants of wealth impact inequality and mobility both through choices of effort and redistributive policies. The model generates multiple equilibria (US versus Europe-type) which may account for the observed features not only in terms of societal beliefs and redistribution but also in terms of perceived versus real mobility and inequality.

Coordination, inclusiveness and wage inequality between median and bottom income workers

What explains cross-national variation in wage inequality? Research in comparative political economy stresses the importance of the welfare state and wage coordination in reducing not only disposable income inequality but also gross earnings inequality. However, the cross-national variation in gross earnings inequality between median and low income workers is at odds with this conventional wisdom: the German coordinated market economy is now more unequal in this type of inequality than the UK, a liberal market economy. To solve this puzzle, I argue that non-inclusive coordination benefits median but not bottom income workers and is as a result associated with higher – rather than lower - wage inequality. I find support for this argument using a large N quantitative analysis of wage inequality in a panel of Western European countries. Results are robust to the inclusion of numerous controls, country fixed effects, and also hold with a sample of OECD countries. Taken together these findings force us to reconsider the relationship between coordination and wage inequality at the bottom of the income distribution.