Global existence and exponential decay for hyperbolic dissipative relativistic fluid theories

We consider dissipative relativistic fluid theories on a fixed flat, compact, globally hyperbolic, Lorentzian manifold. We prove that for all initial data in a small enough neighborhood of the equilibrium states (in an appropriate Sobolev norm), the solutions evolve smoothly in time forever and decay exponentially to some, in general undetermined, equilibrium state. To prove this, three conditions are imposed on these theories. The first condition requires the system of equations to be symmetric hyperbolic, a fundamental requisite to have a well posed and physically consistent initial value formulation. The second condition is a generic consequence of the entropy law, and is imposed on the non principal part of the equations. The third condition is imposed on the principal part of the equations and it implies that the dissipation affects all the fields of the theory. With these requirements we prove that all the eigenvalues of the symbol associated to the system of equations of the fluid theory have strictly negative real parts, which in fact, is an alternative characterization for the theory to be totally dissipative. Once this result has been obtained, a straight forward application of a general stability theorem due to Kreiss, Ortiz, and Reula, implies the results above mentioned.Comment: 10 pages, Late

The Initial-Boundary Value Problem in General Relativity

In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.Comment: 11 pages, 2 figures. Contribution to a special volume for Mario Castagnino's seventy fifth birthda

A causal statistical family of dissipative divergence type fluids

In this paper we investigate some properties, including causality, of a particular class of relativistic dissipative fluid theories of divergence type. This set is defined as those theories coming from a statistical description of matter, in the sense that the three tensor fields appearing in the theory can be expressed as the three first momenta of a suitable distribution function. In this set of theories the causality condition for the resulting system of hyperbolic partial differential equations is very simple and allow to identify a subclass of manifestly causal theories, which are so for all states outside equilibrium for which the theory preserves this statistical interpretation condition. This subclass includes the usual equilibrium distributions, namely Boltzmann, Bose or Fermi distributions, according to the statistics used, suitably generalized outside equilibrium. Therefore this gives a simple proof that they are causal in a neighborhood of equilibrium. We also find a bigger set of dissipative divergence type theories which are only pseudo-statistical, in the sense that the third rank tensor of the fluid theory has the symmetry and trace properties of a third momentum of an statistical distribution, but the energy-momentum tensor, while having the form of a second momentum distribution, it is so for a different distribution function. This set also contains a subclass (including the one already mentioned) of manifestly causal theories.Comment: LaTex, documentstyle{article

Book free 33-Uniform Hypergraphs

A $k$-book in a hypergraph consists of $k$ Berge triangles sharing a common edge. In this paper we prove that the number of the hyperedges in a $k$-book-free 3-uniform hypergraph on $n$ vertices is at most $\frac{n^2}{8}(1+o(1))$

Strongly hyperbolic second order Einstein's evolution equations

BSSN-type evolution equations are discussed. The name refers to the Baumgarte, Shapiro, Shibata, and Nakamura version of the Einstein evolution equations, without introducing the conformal-traceless decomposition but keeping the three connection functions and including a densitized lapse. It is proved that a pseudo-differential first order reduction of these equations is strongly hyperbolic. In the same way, densitized Arnowitt-Deser-Misner evolution equations are found to be weakly hyperbolic. In both cases, the positive densitized lapse function and the spacelike shift vector are arbitrary given fields. This first order pseudodifferential reduction adds no extra equations to the system and so no extra constraints.Comment: LaTeX, 16 pages, uses revtex4. Referee corections and new appendix added. English grammar improved; typos correcte

Differentiating the Visual Aesthetics of the Sublime and the Beautiful: Selective Effects of Stimulus Size, Height, and Color on Sublimity and Beauty Ratings in Photographs

Despite the philosophical literature concerning the sublime and the beautiful, dating back to Burke (1759/2008), there is still limited empirical evidence regarding the visual aesthetics of sublimity and beauty. The present article asks whether the manner in which photographs are presented can alter the perception of the sublimity and beauty ratings of these photographs. In a set of studies, it is reported that the increase of presentation size increases sublimity more than beauty (Study 1) and that this is mainly driven by the effects of visual angle (Study 3). While increasing presentation height affects both sublimity and beauty positively and in similar degrees (Study 1), the presence of color (vs. black and white [monochrome]) is predominantly related to judgments of beauty (Study 2). Brightness and contrast levels affected neither sublimity nor beauty (Study 3). An important methodological point is that all inferential statistics use linear mixed models, which treat both participants and stimuli as random effects. In addition, each participant receives different random subsets of stimuli, increasing the size of the stimulus set. Overall, the analyses incorporate 233 photographs and 245 participants in total, which allows the generalizability of findings. Sublimity and beauty respond differentially to different presentational cues, which demonstrates the importance of simultaneously considering sublimity and beauty in empirical studies on aesthetic judgments

Selective Deletion of PTEN in Dopamine Neurons Leads to Trophic Effects and Adaptation of Striatal Medium Spiny Projecting Neurons

The widespread distribution of the tumor suppressor PTEN in the nervous system suggests a role in a broad range of brain functions. PTEN negatively regulates the signaling pathways initiated by protein kinase B (Akt) thereby regulating signals for growth, proliferation and cell survival. Pten deletion in the mouse brain has revealed its role in controlling cell size and number. In this study, we used Cre-loxP technology to specifically inactivate Pten in dopamine (DA) neurons (Pten KO mice). The resulting mutant mice showed neuronal hypertrophy, and an increased number of dopaminergic neurons and fibers in the ventral mesencephalon. Interestingly, quantitative microdialysis studies in Pten KO mice revealed no alterations in basal DA extracellular levels or evoked DA release in the dorsal striatum, despite a significant increase in total DA tissue levels. Striatal dopamine receptor D1 (DRD1) and prodynorphin (PDyn) mRNA levels were significantly elevated in KO animals, suggesting an enhancement in neuronal activity associated with the striatonigral projection pathway, while dopamine receptor D2 (DRD2) and preproenkephalin (PPE) mRNA levels remained unchanged. In addition, PTEN inactivation protected DA neurons and significantly enhanced DA-dependent behavioral functions in KO mice after a progressive 6OHDA lesion. These results provide further evidence about the role of PTEN in the brain and suggest that manipulation of the PTEN/Akt signaling pathway during development may alter the basal state of dopaminergic neurotransmission and could provide a therapeutic strategy for the treatment of Parkinson's disease, and other neurodegenerative disorders

Strategy for the management of diabetic macular edema: the European Vitreo-Retinal Society macular edema study

Objective. To compare the efficacy of different therapies in the treatment of diabetic macular edema (DME). Design. Nonrandomized, multicenter clinical study. Participants. 86 retina specialists from 29 countries provided clinical information on 2,603 patients with macular edema including 870 patients with DME. Methods. Reported data included the type and number of treatment(s) performed, the pre-and posttreatment visual acuities, and other clinical findings.The results were analyzed by the French INSEE (National Institute of Statistics and Economic Studies). Main Outcome Measures. Mean change of visual acuity and mean number of treatments performed. Results.The change in visual acuity over time in response to each treatment was plotted in second order polynomial regression trend lines. Intravitreal triamcinolone monotherapy resulted in some improvement in vision. Treatmentwith threshold or subthreshold grid laser also resulted in minimal vision gain. Anti-VEGF therapy resulted in more significant visual improvement. Treatment with pars plana vitrectomy and internal limiting membrane (ILM) peeling alone resulted in an improvement in vision greater than that observed with anti-VEGF injection alone. In our DME study, treatment with vitrectomy and ILM peeling alone resulted in the better visual improvement compared to other therapies

Factors influencing terrestriality in primates of the Americas and Madagascar

Among mammals, the order Primates is exceptional in having a high taxonomic richness in which the taxa are arboreal, semiterrestrial, or terrestrial. Although habitual terrestriality is pervasive among the apes and African and Asian monkeys (catarrhines), it is largely absent among monkeys of the Americas (platyrrhines), as well as galagos, lemurs, and lorises (strepsirrhines), which are mostly arboreal. Numerous ecological drivers and species-specific factors are suggested to set the conditions for an evolutionary shift from arboreality to terrestriality, and current environmental conditions may provide analogous scenarios to those transitional periods. Therefore, we investigated predominantly arboreal, diurnal primate genera from the Americas and Madagascar that lack fully terrestrial taxa, to determine whether ecological drivers (habitat canopy cover, predation risk, maximum temperature, precipitation, primate species richness, human population density, and distance to roads) or species-specific traits (bodymass, group size, and degree of frugivory) associate with increased terrestriality. We collated 150,961 observation hours across 2,227 months from 47 species at 20 sites in Madagascar and 48 sites in the Americas. Multiple factors were associated with ground use in these otherwise arboreal species, including increased temperature, a decrease in canopy cover, a dietary shift away from frugivory, and larger group size. These factors mostly explain intraspecific differences in terrestriality. As humanity modifies habitats and causes climate change, our results suggest that species already inhabiting hot, sparsely canopied sites, and exhibiting more generalized diets, are more likely to shift toward greater ground use