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.

An alternative plate tectonic model for the Palaeozoic-Early Mesozoic Palaeotethyan evolution of Southeast Asia (northern Thailand-Myanmar)

An alternative model for the geodynamic evolution of Southeast Asia is proposed and inserted in a modern plate tectonic model. The reconstruction methodology is based on dynamic plate boundaries, constrained by data such as spreading rates and subduction velocities; in this way it differs from classical continental drift models proposed so far. The different interpretations about the location of the Palaeotethys suture in Thailand are revised, the Tertiary Mae Yuam fault is seen as the emplacement of the suture. East of the suture we identify an Indochina derived terrane for which we keep the name Shan-Thai, formerly used to identify the Cimmerian block present in Southeast Asia, now called Sibumasu. This nomenclatural choice was made on the basis of the geographic location of the terrane (Eastern Shan States in Burma and Central Thailand) and in order not to introduce new confusing terminology. The closure of the Eastern Palaeotethys is related to a southward subduction of the ocean, that triggered the Eastern Neotethys to open as a back-arc, due to the presence of Late Carboniferous-Early Permian arc magmatism in Mergui (Burma) and in the Lhasa block (South Tibet), and to the absence of arc magmatism of the same age East of the suture. In order to explain the presence of Carboniferous-Early Permian and Permo-Triassic volcanic arcs in Cambodia, Upper Triassic magmatism in Eastern Vietnam and Lower Permian-Middle Permian arc volcanites in Western Sumatra, we introduce the Orang Laut terranes concept. These terranes were detached from Indochina and South China during back-arc opening of the Poko-Song Ma system, due to the westward subduction of the Palaeopacific. This also explains the location of the Cathaysian West Sumatra block to the West of the Cimmerian Sibumasu block.

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.

Enriched basaltic andesites from mid-crustal fractional crystallization, recharge, and assimilation (Pilavo Volcano, Western Cordillera of Ecuador)

The origin of andesite is an important issue in petrology because andesite is the main eruptive product at convergent margins, corresponds to the average crustal composition and is often associated with major Cu-Au mineralization. In this study we present petrographic, mineralogical, geochemical and isotopic data for basaltic andesites of the latest Pleistocene Pilavo volcano, one of the most frontal volcanoes of the Ecuadorian Quaternary arc, situated upon thick (30-50 km) mafic crust composed of accreted Cretaceous oceanic plateau rocks and overlying mafic to intermediate Late Cretaceous-Late Tertiary magmatic arcs. The Pilavo rocks are basaltic andesites (54-57 center dot 5 wt % SiO(2)) with a tholeiitic affinity as opposed to the typical calc-alkaline high-silica andesites and dacites (SiO(2) 59-66 wt %) of other frontal arc volcanoes of Ecuador (e.g. Pichincha, Pululahua). They have much higher incompatible element contents (e.g. Sr 650-1350 ppm, Ba 650-1800 ppm, Zr 100-225 ppm, Th 5-25 ppm, La 15-65 ppm) and Th/La ratios (0 center dot 28-0 center dot 36) than Pichincha and Pululahua, and more primitive Sr ((87)Sr/(86)Sr similar to 0 center dot 7038-0 center dot 7039) and Nd (epsilon(Nd) similar to +5 center dot 5 to +6 center dot 1) isotopic signatures. Pilavo andesites have geochemical affinities with modern and recent high-MgO andesites (e.g. low-silica adakites, Setouchi sanukites) and, especially, with Archean sanukitoids, for both of which incompatible element enrichments are believed to result from interactions of slab melts with peridotitic mantle. Petrographic, mineral chemistry, bulk-rock geochemical and isotopic data indicate that the Pilavo magmatic rocks have evolved through three main stages: (1) generation of a basaltic magma in the mantle wedge region by flux melting induced by slab-derived fluids (aqueous, supercritical or melts); (2) high-pressure differentiation of the basaltic melt (at the mantle-crust boundary or at lower crustal levels) through sustained fractionation of olivine and clinopyroxene, leading to hydrous, high-alumina basaltic andesite melts with a tholeiitic affinity, enriched in incompatible elements and strongly impoverished in Ni and Cr; (3) establishment of one or more mid-crustal magma storage reservoirs in which the magmas evolved through dominant amphibole and clinopyroxene (but no plagioclase) fractionation accompanied by assimilation of the modified plutonic roots of the arc and recharge by incoming batches of more primitive magma from depth. The latter process has resulted in strongly increasing incompatible element concentrations in the Pilavo basaltic andesites, coupled with slightly increasing crustal isotopic signatures and a shift towards a more calc-alkaline affinity. Our data show that, although ultimately originating from the slab, incompatible element abundances in arc andesites with primitive isotopic signatures can be significantly enhanced by intra-crustal processes within a thick juvenile mafic crust, thus providing an additional process for the generation of enriched andesites.

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.