Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Stellar turbulence and mode physics

An overview of selected topical problems on modelling oscillation properties in solar-like stars is presented. High-quality oscillation data from both space-borne intensity observations and ground-based spectroscopic measurements provide first tests of the still-ill-understood, superficial layers in distant stars. Emphasis will be given to modelling the pulsation dynamics of the stellar surface layers, the stochastic excitation processes and the associated dynamics of the turbulent fluxes of heat and momentum.Comment: Proc. HELAS Workshop on 'Synergies between solar and stellar modelling', eds M. Marconi, D. Cardini, M. P. Di Mauro, Astrophys. Space Sci., in the pres

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group

We study Sobolev-type metrics of fractional order $s\geq0$ on the group \Diff_c(M) of compactly supported diffeomorphisms of a manifold $M$. We show that for the important special case $M=S^1$ the geodesic distance on \Diff_c(S^1) vanishes if and only if $s\leq\frac12$. For other manifolds we obtain a partial characterization: the geodesic distance on \Diff_c(M) vanishes for $M=\R\times N, s<\frac12$ and for $M=S^1\times N, s\leq\frac12$, with $N$ being a compact Riemannian manifold. On the other hand the geodesic distance on \Diff_c(M) is positive for $\dim(M)=1, s>\frac12$ and $\dim(M)\geq2, s\geq1$. For $M=\R^n$ we discuss the geodesic equations for these metrics. For $n=1$ we obtain some well known PDEs of hydrodynamics: Burgers' equation for $s=0$, the modified Constantin-Lax-Majda equation for $s=\frac 12$ and the Camassa-Holm equation for $s=1$.Comment: 16 pages. Final versio

The area-to-mass ratio and fractal dimension of marine flocs

publisher: Elsevier articletitle: The area-to-mass ratio and fractal dimension of marine flocs journaltitle: Estuarine, Coastal and Shelf Science articlelink: http://dx.doi.org/10.1016/j.ecss.2017.03.026 content_type: article copyright: © 2017 The Authors. Published by Elsevier Ltd

Carbon fiber masculinity: Disability and surfaces of homosociality

In this paper I am concerned with instances in which carbon fiber extends performances of masculinity that are attached to particular kinds of hegemonic male bodies. In examining carbon fiber as a prosthetic form of masculinity, I advance three main arguments. Firstly, carbon fiber can be a site of the supersession of disability that is affected through masculinized technology. Disability can be ‘overcome’ through carbon fiber. Disability is often culturally coded as feminine (Pedersen, 2001; Meeuf, 2009; Garland-Thompson 1997). Building on this cultural construction of disability as feminine, in and as a technology of masculine homosociality (Sedgwick, 1985), carbon fiber reproduced disability as feminine when carbon fiber prosthetic lower legs allowed Oscar Pistorius to compete in the non-disabled Olympic games. Secondly, I argue that carbon fiber can be a homosocial surface; that is, carbon fiber becomes both a surface extension of the self and a third party mediator in homosocial relationships, a surface that facilitates intimacy between men in ways that devalue femininity in both male and female bodies. I examine surfaces as material extensions of subjectivity, and carbon fiber surfaces as vectors of the cultural economies of masculine competition to which I refer. Thirdly, the case of Oscar Pistorius is exemplary of the masculinization of carbon fire, and the associated binding of a psychic attitude of misogyny and power to a form of violent and competitive masculine subjectivity. In this article I explore the affects, economies and surfaces of what I call ‘carbon fiber masculinity’ and discusses Pistorius’ use of carbon fiber, homosociality and misogyny as forms of protest masculinity through which he unconsciously attempted to recuperate his gendered identity from emasculating discourses of disability

A putative causal relationship between genetically determined female body shape and posttraumatic stress disorder

Background: The nature and underlying mechanisms of the observed increased vulnerability to posttraumatic stress disorder (PTSD) in women are unclear. Methods: We investigated the genetic overlap of PTSD with anthropometric traits and reproductive behaviors and functions in women. The analysis was conducted using female-specific summary statistics from large genome-wide association studies (GWAS) and a cohort of 3577 European American women (966 PTSD cases and 2611 trauma-exposed controls). We applied a high-resolution polygenic score approach and Mendelian randomization analysis to investigate genetic correlations and causal relationships. Results: We observed an inverse association of PTSD with genetically determined anthropometric traits related to body shape, independent of body mass index (BMI). The top association was related to BMI-adjusted waist circumference (WCadj; R = -0.079, P &lt; 0.001, Q = 0.011). We estimated a relative decrease of 64.6% (95% confidence interval = 27.5-82.7) in the risk of PTSD per 1-SD increase in WCadj. MR-Egger regression intercept analysis showed no evidence of pleiotropic effects in this association (Ppleiotropy = 0.979). We also observed associations of genetically determined WCadj with age at first sexual intercourse and number of sexual partners (P = 0.013 and P &lt; 0.001, respectively). Conclusions: There is a putative causal relationship between genetically determined female body shape and PTSD, which could be mediated by evolutionary mechanisms involved in human sexual behaviors

Epigenome-wide association of PTSD from heterogeneous cohorts with a common multi-site analysis pipeline

Compelling evidence suggests that epigenetic mechanisms such as DNA methylation play a role in stress regulation and in the etiologic basis of stress related disorders such as Post traumatic Stress Disorder (PTSD). Here we describe the purpose and methods of an international consortium that was developed to study the role of epigenetics in PTSD. Inspired by the approach used in the Psychiatric Genomics Consortium, we brought together investigators representing seven cohorts with a collective sample size of N = 1147 that included detailed information on trauma exposure, PTSD symptoms, and genome-wide DNA methylation data. The objective of this consortium is to increase the analytical sample size by pooling data and combining expertise so that DNA methylation patterns associated with PTSD can be identified. Several quality control and analytical pipelines were evaluated for their control of genomic inflation and technical artifacts with a joint analysis procedure established to derive comparable data over the cohorts for meta-analysis. We propose methods to deal with ancestry population stratification and type I error inflation and discuss the advantages and disadvantages of applying robust error estimates. To evaluate our pipeline, we report results from an epigenome-wide association study (EWAS) of age, which is a well-characterized phenotype with known epigenetic associations. Overall, while EWAS are highly complex and subject to similar challenges as genome-wide association studies (GWAS), we demonstrate that an epigenetic meta-analysis with a relatively modest sample size can be well-powered to identify epigenetic associations. Our pipeline can be used as a framework for consortium efforts for EWAS

Apêndices e fossetas pré-auriculares : existe alguma correlação destes achados com défict auditivo ou malformações renais em nossa população?

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Conditioned fear and extinction learning performance and its association with psychiatric symptoms in active duty Marines

BACKGROUND: Posttraumatic Stress Disorder (PTSD) is a major public health concern, especially given the recent wars in Iraq and Afghanistan. Nevertheless, despite a sharp increase in the incidence of psychiatric disorders in returning veterans, empirically based prevention strategies are still lacking. To develop effective prevention and treatment strategies, it is necessary to understand the underlying biological mechanisms contributing to PTSD and other trauma related symptoms. METHODS: The “Marine Resiliency Study II” (MRS-II; October 2011–October 2013) Neurocognition project is an investigation of neurocognitive performance in Marines about to be deployed to Afghanistan. As part of this investigation, 1195 Marines and Navy corpsmen underwent a fear conditioning and extinction paradigm and psychiatric symptom assessment prior to deployment. The current study assesses (1) the effectiveness of the fear potentiated startle paradigm in producing fear learning and extinction and (2) the association of performance in the paradigm with baseline psychiatric symptom classes (healthy: n = 923, PTSD symptoms: n = 42, anxiety symptoms: n = 37, and depression symptoms: n = 12). RESULTS: Results suggest that the task was effective in producing differential fear learning and fear extinction in this cohort. Further, distinct patterns emerged differentiating the PTSD and anxiety symptom classes from both healthy and depression classes. During fear acquisition, the PTSD symptom group was the only group to show deficient discrimination between the conditioned stimulus (CS+) and safety cue (CS−), exhibiting larger startle responses during the safety cue compared to the healthy group. During extinction learning, the PTSD symptom group showed significantly less reduction in their CS+ responding over time compared to the healthy group, as well as reduced extinction of self-reported anxiety to the CS+ by the end of the extinction session. Conversely, the anxiety symptom group showed normal safety signal discrimination and extinction of conditioned fear, but exhibited increased baseline startle reactivity and potentiated startle to CS+, as well as higher self-reported anxiety to both cues. The depression symptom group showed similar physiological and self-report measures as the healthy group. DISCUSSION: These data are consistent with the idea that safety signal discrimination is a relatively specific marker of PTSD symptoms compared to general anxiety and depression symptoms. Further research is needed to determine if deficits in fear inhibition vs. exaggerated fear responding are separate biological “domains” across anxiety disorders that may predict differential biological mechanisms and possibly treatment needs. Future longitudinal analyses will examine whether poor learning of safety signals provides a marker of vulnerability to develop PTSD or is specific to symptom state

Energy loss due to defect formation from 206Pb recoils in SuperCDMS germanium detectors

The Super Cryogenic Dark Matter Search experiment at the Soudan Underground Laboratory studied energy loss associated with defect formation in germanium crystals at mK temperatures using in situ 210Pb sources. We examine the spectrum of 206Pb nuclear recoils near its expected 103 keV endpoint energy and determine an energy loss of (6:08 ± 0:18)%, which we attribute to defect formation. From this result and using TRIM simulations, we extract the first experimentally determined average displacement threshold energy of 19.7+0.6−0.5 eV for germanium. This has implications for the analysis thresholds of future germanium-based dark matter searches