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.

Eimeria curvata n. sp.(Apicomplexa: Eimeriidae) in Columbina talpacoti and Scardafella squammata (Aves: Columbidae) from Brazil

Eimeria curvata is a new coccidian described in the doves Columbina talpacoti and Scardafella squammata from western of the State of São Paulo, Brazil. The oocysts are ovoid to ellipsoid, 18.3 (17-19) µm x 15.5 (15-17) µm, with a shape index of 1.2 (1.1-1.3). The wall is colorless, smooth and double-layered. A polar granule is present, but there is no micropyle or oocyst residuum. The sporocysts are elongate, 12.3 (11.5-13) µm x 5.8 (5.5-6) µm with a curved anterior portion and a smooth, thin, single-layered wall. The Stieda body is protuberant and nipple-like; there is no substieda body. The sporozoites lie head-to-tail in the sporocyst and contain a large refractile body at the extremities. The sporocyst residuum contains small granules uniformly distributed in the middle of the sporocyst. The prevalence of E. curvata n. sp. was 17.4% and 12.8% in C. talpacoti and S. squammata, respectively.

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.

Strategies to promote translational research within the European Organisation for Research and Treatment of Cancer (EORTC) Head and Neck Cancer Group: a report from the Translational Research Subcommittee.

Head and neck squamous cell cancer (HNSCC) is the sixth leading cause of cancer-related deaths worldwide. These tumors are commonly diagnosed at advanced stages and mortality rates remain high. Even cured patients suffer the consequences of aggressive treatment that includes surgery, chemotherapy, and radiotherapy. In the past, in clinical trials, HNSCC was considered as a single disease entity. Advances in molecular biology with the development of genomic and proteomic approaches have demonstrated distinct prognostic HNSCC patient subsets beyond those defined by traditional clinical-pathological factors such as tumor subsite and stage [Cho W (ed). An Omics Perspective on Cancer Research. New York/Berlin: Springer 2010]. Validation of these biomarkers in large prospective clinical trials is required before their clinical implementation. To promote this research, the European Organisation for Research and Treatment of Cancer (EORTC) Head and Neck Cancer Program will develop the following strategies-(i) biobanking: prospective tissue collection from uniformly treated patients in the setting of clinical trials; (ii) a group of physicians, physician-scientists, and EORTC Headquarters staff devoted to patient-oriented head and neck cancer research; (iii) a collaboration between the basic scientists of the Translational Research Division interested in head and neck cancer research and the physicians of the Head and Neck Cancer Group; and (iv) funding through the EORTC Grant Program and the Network Core Institutions Consortium. In the present report, we summarize our strategic plans to promote head and neck cancer research within the EORTC framework.

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.

Characterization of metabolites in infiltrating gliomas using ex vivo &supl;H high-resolution magic angle spinning spectroscopy.

Gliomas are routinely graded according to histopathological criteria established by the World Health Organization. Although this classification can be used to understand some of the variance in the clinical outcome of patients, there is still substantial heterogeneity within and between lesions of the same grade. This study evaluated image-guided tissue samples acquired from a large cohort of patients presenting with either new or recurrent gliomas of grades II-IV using ex vivo proton high-resolution magic angle spinning spectroscopy. The quantification of metabolite levels revealed several discrete profiles associated with primary glioma subtypes, as well as secondary subtypes that had undergone transformation to a higher grade at the time of recurrence. Statistical modeling further demonstrated that these metabolomic profiles could be differentially classified with respect to pathological grading and inter-grade conversions. Importantly, the myo-inositol to total choline index allowed for a separation of recurrent low-grade gliomas on different pathological trajectories, the heightened ratio of phosphocholine to glycerophosphocholine uniformly characterized several forms of glioblastoma multiforme, and the onco-metabolite D-2-hydroxyglutarate was shown to help distinguish secondary from primary grade IV glioma, as well as grade II and III from grade IV glioma. These data provide evidence that metabolite levels are of interest in the assessment of both intra-grade and intra-lesional malignancy. Such information could be used to enhance the diagnostic specificity of in vivo spectroscopy and to aid in the selection of the most appropriate therapy for individual patients.

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.

A system to evaluate the accuracy of a visual mosaicking methodology

When underwater vehicles navigate close to the ocean floor, computer vision techniques can be applied to obtain motion estimates. A complete system to create visual mosaics of the seabed is described in this paper. Unfortunately, the accuracy of the constructed mosaic is difficult to evaluate. The use of a laboratory setup to obtain an accurate error measurement is proposed. The system consists on a robot arm carrying a downward looking camera. A pattern formed by a white background and a matrix of black dots uniformly distributed along the surveyed scene is used to find the exact image registration parameters. When the robot executes a trajectory (simulating the motion of a submersible), an image sequence is acquired by the camera. The estimated motion computed from the encoders of the robot is refined by detecting, to subpixel accuracy, the black dots of the image sequence, and computing the 2D projective transform which relates two consecutive images. The pattern is then substituted by a poster of the sea floor and the trajectory is executed again, acquiring the image sequence used to test the accuracy of the mosaicking system

Medical image registration based on random line sampling

One of the key aspects in 3D-image registration is the computation of the joint intensity histogram. We propose a new approach to compute this histogram using uniformly distributed random lines to sample stochastically the overlapping volume between two 3D-images. The intensity values are captured from the lines at evenly spaced positions, taking an initial random offset different for each line. This method provides us with an accurate, robust and fast mutual information-based registration. The interpolation effects are drastically reduced, due to the stochastic nature of the line generation, and the alignment process is also accelerated. The results obtained show a better performance of the introduced method than the classic computation of the joint histogram

Shape complexity based on mutual information

Shape complexity has recently received attention from different fields, such as computer vision and psychology. In this paper, integral geometry and information theory tools are applied to quantify the shape complexity from two different perspectives: from the inside of the object, we evaluate its degree of structure or correlation between its surfaces (inner complexity), and from the outside, we compute its degree of interaction with the circumscribing sphere (outer complexity). Our shape complexity measures are based on the following two facts: uniformly distributed global lines crossing an object define a continuous information channel and the continuous mutual information of this channel is independent of the object discretisation and invariant to translations, rotations, and changes of scale. The measures introduced in this paper can be potentially used as shape descriptors for object recognition, image retrieval, object localisation, tumour analysis, and protein docking, among others

Expression and localization of PPARs in the rat ovary during follicular development and the periovulatory period.

PPARs are a family of nuclear hormone receptors involved in various processes that could influence ovarian function. We investigated the cellular localization and expression of PPARs during follicular development in ovarian tissue collected from rats 0, 6, 12, 24, and 48 h post-PMSG. A second group of animals received human CG (hCG) 48 h post-PMSG. Their ovaries were removed 0, 4, 8, 12, and 24 h post-hCG to study the periovulatory period. mRNAs corresponding to the PPAR isotypes (alpha, delta, and gamma) were localized by in situ hybridization. Changes in the levels of mRNA for the PPARs were determined by ribonuclease protection assays. PPAR gamma mRNA was localized primarily to granulosa cells, and levels of expression did not change during follicular development. Four hours post-hCG, levels of mRNA for PPAR gamma decreased (P < 0.05) but not uniformly in all follicles. At 24 h post-hCG, levels of PPAR gamma mRNA were reduced 64%, but some follicles maintained high expression. In contrast, mRNAs for PPAR alpha and delta were located primarily in theca and stroma, and their levels did not change during the intervals studied. To investigate the physiologic significance of PPAR gamma in the ovary, granulosa cells from PMSG-primed rats were cultured for 48 h with prostaglandin J(2) (PGJ(2)) and ciglitazone, PPAR gamma activators. Both compounds increased progesterone and E2 secretion (P < 0.05). These data suggest that PPAR gamma is involved in follicular development, has a negative influence on the luteinization of granulosa cells, and/or regulates the periovulatory shift in steroid production. The more general and steady expression of PPARs alpha and delta indicate that they may play a role in basal ovarian function.