Geometria integral i convexitat en espais de curvatura holomorfa constant

En aquest treball es tracten qüestions de la geometria integral clàssica a l'espai hiperbòlic i projectiu complex i a l'espai hermític estàndard, els anomenats espais de curvatura holomorfa constant. La geometria integral clàssica estudia, entre d'altres, l'expressió en termes geomètrics de la mesura de plans que tallen un domini convex fixat de l'espai euclidià. Aquesta expressió es dóna en termes de les integrals de curvatura mitja. Un dels resultats principals d'aquest treball expressa la mesura de plans complexos que tallen un domini fixat a l'espai hiperbòlic complex, en termes del que definim com volums intrínsecs hermítics, que generalitzen les integrals de curvatura mitja. Una altra de les preguntes que tracta la geometria integral clàssica és: donat un domini convex i l'espai de plans, com s'expressa la integral de la s-èssima integral de curvatura mitja del convex intersecció entre un pla i el convex fixat? A l'espai euclidià, a l'espai projectiu i hiperbòlic reals, aquesta integral correspon amb la s-èssima integral de curvatura mitja del convex inicial: se satisfà una propietat de reproductibitat, que no es té en els espais de curvatura holomorfa constant. En el treball donem l'expressió explícita de la integral de la curvatura mitja quan integrem sobre l'espai de plans complexos. L'expressem en termes de la integral de curvatura mitja del domini inicial i de la integral de la curvatura normal en una direcció especial: l'obtinguda en aplicar l'estructura complexa al vector normal. La motivació per estudiar els espais de curvatura holomorfa constant i, en particular, l'espai hiperbòlic complex, es troba en l'estudi del següent problema clàssic en geometria. Quin valor pren el quocient entre l'àrea i el perímetre per a successions de figures convexes del pla que creixen tendint a omplir-lo? Fins ara es coneixia el comportament d'aquest quocient en els espais de curvatura seccional negativa i que a l'espai hiperbòlic real les fites obtingudes són òptimes. Aquí provem que a l'espai hiperbòlic complex, les cotes generals no són òptimes i optimitzem la superior.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

The distribution of intestinal helminth infections in a rural village in Guatemala

Fecal egg count scores were used to investigate the distribution and abundance of intestinal helminths in the population of a rural village. Prevalences of the major helminths were 41% with Ascaris lumbricoides 60% with Trichuris trichiura and 50% with Necator americanus. All three parasites showed a highly aggregated distribution among hosts. Age/prevalence and age/intensity profiles were typical for both A. lumbricoides and T. trichiura with the highest worm burdens in the 50-10 year old children. For hookworm both prevalence and intensity curves were convex in shape with maximum infection levels in the 30-40 year old age class. Infected females had higher burdens of T. trichiura than infected males in all age classes of the population; there were no other effects of host gender. Analysis of associations between parasites within hosts revealed strong correlations between A. lumbricoides and T. lumbricoides and T. trichiura. Individuals with heavy infections of A. lumbricoides and T. trichiura showed highly significant aggregation within households. Associations between a variety of household features and heavy infections with A. lumbricoides and T. trichiura are described.

Iceberg transport technologies in spatial competition. Hotelling reborn

Transport costs in address models of differentiation are usually modeled as separable of the consumption commodity and with a parametric price. However, there are many sectors in an economy where such modeling is not satisfactory either because transportation is supplied under oligopolistic conditions or because there is a difference (loss) between the amount delivered at the point of production and the amount received at the point of consumption. This paper is a first attempt to tackle these issues proposing to study competition in spatial models using an iceberg-like transport cost technology allowing for concave and convex melting functions.

Rigid flat webs on the projective plane

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

A way to play bankruptcy problems.

The commitment among agents has always been a difficult task, especially when they have to decide how to distribute the available amount of a scarce resource among all. On the one hand, there are a multiplicity of possible ways for assigning the available amount; and, on the other hand, each agent is going to propose that distribution which provides her the highest possible award. In this paper, with the purpose of making this agreement easier, firstly we use two different sets of basic properties, called Commonly Accepted Equity Principles, to delimit what agents can propose as reasonable allocations. Secondly, we extend the results obtained by Chun (1989) and Herrero (2003), obtaining new characterizations of old and well known bankruptcy rules. Finally, using the fact that bankruptcy problems can be analyzed from awards and losses, we define a mechanism which provides a new justification of the convex combinations of bankruptcy rules. Keywords: Bankruptcy problems, Unanimous Concessions procedure, Diminishing Claims mechanism, Piniles’ rule, Constrained Egalitarian rule. JEL classification: C71, D63, D71.

Resolution of foveal detachment in dome-shaped macula after treatment by spironolactone: report of two cases and mini-review of the literature.

Dome-shaped macula (DSM) was recently described in myopic patients as a convex protrusion of the macula within a posterior pole staphyloma. The pathogenesis of DSM and the development of associated serous foveal detachment (SFD) remain unclear. The obstruction of choroidal outflow and compressive changes of choroidal capillaries have been proposed as causative factors. In this paper, we report two cases of patients with chronic SFD associated with DSM treated with oral spironolactone. After treatment, there was a complete resolution of SFD in both patients. To the best of our knowledge, this is the first report of successful treatment of SFD in DSM by a mineralocorticoid receptor antagonist.

Decomposable approximations of nuclear C*-algebras

We show that nuclear C*-algebras have a re ned version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear C*-algebra A which is closely contained in a C*-algebra B embeds into B.

A Proportional Approach to Bankruptcy Problems with a guaranteed minimum

In a distribution problem, and specfii cally in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. The Constrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that no agent receives more than her claim, a problem that can arise when using the egalitarian division. We propose an alternative modi cation, by using a convex combination of P and EA. The recursive application of this new rule finishes at the CEA rule. Our solution concept ensures a minimum amount to each agent, and distributes the remaining estate in a proportional way. Keywords: Bankruptcy problems, Proportional rule, Equal Awards, Convex combination of rules, Lorenz dominance. JEL classi fication: C71, D63, D71.

Recrystallisation rims in zircon (Valle d'Arbedo, Switzerland): an integrated cathodoluminescence, LA-ICP-MS, SHRIMP, and TEM study

Recrystallization rims are a common feature of zircon crystals that underwent metamorphism. We present a microstructural and microchemical study of partially recrystallized zircon grains collected in polymetamorphic migmatites (Valle d'Arbedo, Ticino, Switzerland). The rims are bright in cathodo-luminescence (CL), with sharp and convex contacts characterized by inward-penetrating embayments transgressing igneous zircon cores. Laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) data and transmission electron microscopy (TEM) imaging indicate that the rims are chemically and microstructurally different from the cores. The rims are strongly depleted in REE, with concentrations up to two orders of magnitude lower than in the cores, indicating a significant loss of REE during zircon recrystallization. Enrichment in non-formula elements, such as Ca, has not been observed in the rims. The microstructure of zircon cores shows a dappled intensity at and below the 100 nm scale, possibly due to radiation damage. Other defects such as pores and dislocations are absent in the core except at healed cracks. Zircon rims are mostly dapple-free, but contain nanoscale pores and strain centers, interpreted as fluid inclusions and chemical residues, respectively. Sensitive high-resolution ion microprobe (SHRIMP) U-Pb ages show that the recrystallization of the rims took place >200 Ma ago when the parent igneous zircon was not metamict. The chemical composition and the low-Ti content of the rims indicate that they form at sub-solidus temperatures (550-650 degrees C). Recrystallization rims in Valle d'Arbedo zircon are interpreted as the result of the migration of chemical reaction fronts in which fluid triggered in situ and contemporaneous interface-coupled dissolution-reprecipitation mechanisms. This study indicates that strong lattice strain resulting from the incorporation of a large amount of impurities and structural defects is not a necessary condition for zircon to recrystallize. Our observations suggest that the early formation of recrystallization rims played a major role in preserving zircon from the more recent Alpine metamorphic overprint.

Parts, places, and perspectives : a theory of spatial relations based an mereotopology and convexity

This thesis suggests to carry on the philosophical work begun in Casati's and Varzi's seminal book Parts and Places, by extending their general reflections on the basic formal structure of spatial representation beyond mereotopology and absolute location to the question of perspectives and perspective-dependent spatial relations. We show how, on the basis of a conceptual analysis of such notions as perspective and direction, a mereotopological theory with convexity can express perspectival spatial relations in a strictly qualitative framework. We start by introducing a particular mereotopological theory, AKGEMT, and argue that it constitutes an adequate core for a theory of spatial relations. Two features of AKGEMT are of particular importance: AKGEMT is an extensional mereotopology, implying that sameness of proper parts is a sufficient and necessary condition for identity, and it allows for (lower- dimensional) boundary elements in its domain of quantification. We then discuss an extension of AKGEMT, AKGEMTS, which results from the addition of a binary segment operator whose interpretation is that of a straight line segment between mereotopological points. Based on existing axiom systems in standard point-set topology, we propose an axiomatic characterisation of the segment operator and show that it is strong enough to sustain complex properties of a convexity predicate and a convex hull operator. We compare our segment-based characterisation of the convex hull to Cohn et al.'s axioms for the convex hull operator, arguing that our notion of convexity is significantly stronger. The discussion of AKGEMTS defines the background theory of spatial representation on which the developments in the second part of this thesis are built. The second part deals with perspectival spatial relations in two-dimensional space, i.e., such relations as those expressed by 'in front of, 'behind', 'to the left/right of, etc., and develops a qualitative formalism for perspectival relations within the framework of AKGEMTS. Two main claims are defended in part 2: That perspectival relations in two-dimensional space are four- place relations of the kind R(x, y, z, w), to be read as x is i?-related to y as z looks at w; and that these four-place structures can be satisfactorily expressed within the qualitative theory AKGEMTS. To defend these two claims, we start by arguing for a unified account of perspectival relations, thus rejecting the traditional distinction between 'relative' and 'intrinsic' perspectival relations. We present a formal theory of perspectival relations in the framework of AKGEMTS, deploying the idea that perspectival relations in two-dimensional space are four-place relations, having a locational and a perspectival part and show how this four-place structure leads to a unified framework of perspectival relations. Finally, we present a philosophical motivation to the idea that perspectival relations are four-place, cashing out the thesis that perspectives are vectorial properties and argue that vectorial properties are relations between spatial entities. Using Fine's notion of "qua objects" for an analysis of points of view, we show at last how our four-place approach to perspectival relations compares to more traditional understandings.

Mutational analysis of BTAF1-TBP interaction: BTAF1 can rescue DNA-binding defective TBP mutants.

The BTAF1 transcription factor interacts with TATA-binding protein (TBP) to form the B-TFIID complex, which is involved in RNA polymerase II transcription. Here, we present an extensive mapping study of TBP residues involved in BTAF1 interaction. This shows that residues in the concave, DNA-binding surface of TBP are important for BTAF1 binding. In addition, BTAF1 interacts with residues in helix 2 on the convex side of TBP as assayed in protein-protein and in DNA-binding assays. BTAF1 drastically changes the TATA-box binding specificity of TBP, as it is able to recruit DNA-binding defective TBP mutants to both TATA-containing and TATA-less DNA. Interestingly, other helix 2 interacting factors, such as TFIIA and NC2, can also stabilize mutant TBP binding to DNA. In contrast, TFIIB which interacts with a distinct surface of TBP does not display this activity. Since many proteins contact helix 2 of TBP, this provides a molecular basis for mutually exclusive TBP interactions and stresses the importance of this structural element for eukaryotic transcription.

What spatial data do we need to develop global mammal conservation strategies?

Spatial data on species distributions are available in two main forms, point locations and distribution maps (polygon ranges and grids). The first are often temporally and spatially biased, and too discontinuous, to be useful (untransformed) in spatial analyses. A variety of modelling approaches are used to transform point locations into maps. We discuss the attributes that point location data and distribution maps must satisfy in order to be useful in conservation planning. We recommend that before point location data are used to produce and/or evaluate distribution models, the dataset should be assessed under a set of criteria, including sample size, age of data, environmental/geographical coverage, independence, accuracy, time relevance and (often forgotten) representation of areas of permanent and natural presence of the species. Distribution maps must satisfy additional attributes if used for conservation analyses and strategies, including minimizing commission and omission errors, credibility of the source/assessors and availability for public screening. We review currently available databases for mammals globally and show that they are highly variable in complying with these attributes. The heterogeneity and weakness of spatial data seriously constrain their utility to global and also sub-global scale conservation analyses.