Solvability of subprincipal type operators

In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order $k \ge 2$ at a nonradial involutive manifold $\Sigma_2$. We shall assume that the operator is of subprincipal type, which means that the $k$:th inhomogeneous blowup at $\Sigma_2$ of the refined principal symbol is of principal type with Hamilton vector field parallel to the base $\Sigma_2$, but transversal to the symplectic leaves of $\Sigma_2$ at the characteristics. When $k = \infty$ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of $\Sigma_2$, and does not satisfying the Nirenberg-Treves condition (${\Psi}$). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that $P$ is not solvable.Comment: Changed the formulation of Theorem 2.15, added an assuption. Corrected errors and clarified the arguments. Added reference

Callous-Unemotional Traits Moderate Anticipated Guilt and Wrongness Judgments to Everyday Moral Transgressions in Adolescents.

Callous-unemotional (CU) traits observed during childhood and adolescence are thought to be precursors of psychopathic traits in adulthood. Adults with high levels of psychopathic traits typically present antisocial behavior. Such behavior can be indicative of atypical moral processing. Evidence suggests that moral dysfunction in these individuals may stem from a disruption of affective components of moral processing rather than from an inability to compute moral judgments per se. No study to date has tested if the dissociation between affective and cognitive dimensions of moral processing linked to psychopathic traits in adulthood is also linked to CU traits during development. Here, 47 typically developing adolescents with varying levels of CU traits completed a novel, animated cartoon task depicting everyday moral transgressions and indicated how they would feel in such situations and how morally wrong the situations were. Adolescents with higher CU traits reported reduced anticipated guilt and wrongness appraisals of the transgressions. However, our key finding was a significant interaction between CU traits and anticipated guilt in predicting wrongness judgments. The strength of the association between anticipated guilt and wrongness judgement was significantly weaker for those with higher levels of CU traits. This evidence extends our knowledge on the cognitive-affective processing deficits that may underlie moral dysfunction in youth who are at heightened risk for antisocial behavior and psychopathy in adulthood. Future longitudinal research is required to elucidate whether there is an increased dissociation between different components of moral processing from adolescence to adulthood for those with high psychopathic traits

A de Sitter Hoedown

Rotating black holes in de Sitter space are known to have interesting limits where the temperatures of the black hole and cosmological horizon are equal. We give a complete description of the thermal phase structure of all allowed rotating black hole configurations. Only one configuration, the rotating Nariai limit, has the black hole and cosmological horizons both in thermal and rotational equilibrium, in that both the temperatures and angular velocities of the two horizons coincide. The thermal evolution of the spacetime is shown to lead to the pure de Sitter spacetime, which is the most entropic configuration. We then provide a comprehensive study of the wave equation for a massless scalar in the rotating Nariai geometry. The absorption cross section at the black hole horizon is computed and a condition is found for when the scattering becomes superradiant. The boundary-to-boundary correlators at finite temperature are computed at future infinity. The quasinormal modes are obtained in explicit form. Finally, we obtain an expression for the expectation value of the number of particles produced at future infinity starting from a vacuum state with no incoming particles at past infinity. Some of our results are used to provide further evidence for a recent holographic proposal between the rotating Nariai geometry and a two-dimensional conformal field theory.Comment: 35 + 1 pages, 9 figures; v3: typos correcte

The Eyes Have It: Sex and Sexual Orientation Differences in Pupil Dilation Patterns

Recent research suggests profound sex and sexual orientation differences in sexual response. These results, however, are based on measures of genital arousal, which have potential limitations such as volunteer bias and differential measures for the sexes. The present study introduces a measure less affected by these limitations. We assessed the pupil dilation of 325 men and women of various sexual orientations to male and female erotic stimuli. Results supported hypotheses. In general, self-reported sexual orientation corresponded with pupil dilation to men and women. Among men, substantial dilation to both sexes was most common in bisexual-identified men. In contrast, among women, substantial dilation to both sexes was most common in heterosexual-identified women. Possible reasons for these differences are discussed. Because the measure of pupil dilation is less invasive than previous measures of sexual response, it allows for studying diverse age and cultural populations, usually not included in sexuality research

Associação do reflexo vermelho em recém-nascidos com variáveis neonatais

Objetivou-se investigar o resultado do teste do reflexo vermelho, conhecido como teste do olhinho, e associar as impressões do reflexo com variáveis neonatais. Este é um estudo descritivo, quantitativo, realizado com 190 recém-nascidos de uma maternidade pública, dos quais 187 apresentaram resultado não alterado e três suspeitos. Observaram-se diferentes nuances de coloração do reflexo: em 50 (26,3%) a coloração do reflexo apresentou-se vermelha; 34 (17,9%) laranja-avermelhado; 92 (48,4%) alaranjado; 11 (5,8%) amarelo claro e três (1,6%) com manchas esbranquiçadas. Encontraram-se associações estatisticamente significantes entre o instrumento gradiente de cores e variáveis neonatais: peso (p=0,03), idade gestacional (p=0,019) e oxigenoterapia (p=0,024). Enfermeiros capacitados para prática e avaliação desse teste podem se tornar profissionais em potencial para a prevenção da cegueira infantil.The aim of this study was to investigate the results of the red reflex test and to associate these results with neonatal variables. This descriptive study was conducted with 190 newborns in a public maternity hospital. A total of 187 infants presented no alteration and three presented suspect results. Different shades of reflex color were observed: 50 (26.3%) presented red; 34 (17.9%) orange-red, 92 (48.4%) orange, 11 (5.8%) light yellow and three (1.6%) milky white spots. Statistically significant associations between the color gradient instrument and neonatal variables were found: weight (p=0.03), gestational age (p=0.019) and oxygen therapy (p=0.024). Nurses trained to practice and evaluate this test may become professionals in the potential for the prevention of childhood blindness.Se objetivó investigar el resultado de la prueba del reflejo rojo, conocido como prueba del ojito, y asociar las impresiones del reflejo con variables neonatales. Se trata de un estudio descriptivo, cuantitativo, realizado con 190 recién nacidos de una maternidad pública; de los cuales 187 presentaron resultados no alterados y tres sospechosos. Se observaron diferentes matices de coloración del reflejo: en 50 (26,3%) se presentó rojo; 34 (17,9%) naranja rojizo; 92 (48,4%) anaranjado; 11 (5,8%) amarillo claro y tres (1,6%) con manchas blanquecinas. Se encontraron asociaciones estadísticamente significativas entre el instrumento gradiente de colores y las variables neonatales: peso (p=0,03), edad de gestación (p=0,019) y oxigenoterapia (p=0,024). Enfermeros capacitados para la práctica y evaluación de esa prueba pueden tornarse profesionales en potencial para la prevención de la ceguera infantil

Non-extremal Black Hole Microstates: Fuzzballs of Fire or Fuzzballs of Fuzz ?

We construct the first family of microstate geometries of near-extremal black holes, by placing metastable supertubes inside certain scaling supersymmetric smooth microstate geometries. These fuzzballs differ from the classical black hole solution macroscopically at the horizon scale, and for certain probes the fluctuations between various fuzzballs will be visible as thermal noise far away from the horizon. We discuss whether these fuzzballs appear to infalling observers as fuzzballs of fuzz or as fuzzballs of fire. The existence of these solutions suggests that the singularity of non-extremal black holes is resolved all the way to the outer horizon and this "backwards in time" singularity resolution can shed light on the resolution of spacelike cosmological singularities.Comment: 34 pages, 10 figure

Linearized stability analysis of gravastars in noncommutative geometry

In this work, we find exact gravastar solutions in the context of noncommutative geometry, and explore their physical properties and characteristics. The energy density of these geometries is a smeared and particle-like gravitational source, where the mass is diffused throughout a region of linear dimension $\sqrt{(\alpha)}$ due to the intrinsic uncertainty encoded in the coordinate commutator. These solutions are then matched to an exterior Schwarzschild spacetime. We further explore the dynamical stability of the transition layer of these gravastars, for the specific case of $\beta=M^2/\alpha<1.9$, where M is the black hole mass, to linearized spherically symmetric radial perturbations about static equilibrium solutions. It is found that large stability regions exist and, in particular, located sufficiently close to where the event horizon is expected to form.Comment: 6 pages, 3 figure

Dynamical Boson Stars

The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called {\em geons}, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name {\em boson stars}. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.Comment: 79 pages, 25 figures, invited review for Living Reviews in Relativity; major revision in 201