The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type I×fNI\times_{f} N

In this work we study the spectral zeta function associated with the Laplace operator acting on scalar functions defined on a warped product of manifolds of the type $I\times_{f} N$ where $I$ is an interval of the real line and $N$ is a compact, $d$-dimensional Riemannian manifold either with or without boundary. Starting from an integral representation of the spectral zeta function, we find its analytic continuation by exploiting the WKB asymptotic expansion of the eigenfunctions of the Laplace operator on $M$ for which a detailed analysis is presented. We apply the obtained results to the explicit computation of the zeta regularized functional determinant and the coefficients of the heat kernel asymptotic expansion.Comment: 29 pages, LaTe

Low-Energy Effective Action in Non-Perturbative Electrodynamics in Curved Spacetime

We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection (that we call the electromagnetic field) is constant we compute the first two coefficients of the non-perturbative asymptotic expansion of the heat kernel which are of zero and the first order in Riemannian curvature and of arbitrary order in the electromagnetic field. We apply these results to the study of the effective action in non-perturbative electrodynamics in four dimensions and derive a generalization of the Schwinger's result for the creation of scalar and spinor particles in electromagnetic field induced by the gravitational field. We discover a new infrared divergence in the imaginary part of the effective action due to the gravitational corrections, which seems to be a new physical effect.Comment: LaTeX, 42 page

Relationship between blood remifentanil concentration and stress hormone levels during pneumoperitoneum in patients undergoing laparoscopic cholecystectomy

The effect of remifentanil on stress response to surgery is unclear. However, there are not clinical studies investigating the relationship between blood remifentanil concentrations and stress hormones. Therefore, the aim of the present study was to assess the association between blood remifentanil concentrations measured after pneumoperitoneum and cortisol (CORT) or prolactin (PRL) ratio (intraoperative/preoperative value), in patients undergoing laparoscopic cholecystectom

Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension

In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By utilizing a contour integral representation of the spectral zeta function for the Laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure. Thanks to the well known relation between the zeta function and the heat kernel obtainable via Mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions. The particular case of a $d$-dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given explicitly.Comment: 26 Pages, 1 Figur

Non-Perturbative One-Loop Effective Action for Electrodynamics in Curved Spacetime

In this paper we explicitly evaluate the one-loop effective action in four dimensions for scalar and spinor fields under the influence of a strong, covariantly constant, magnetic field in curved spacetime. In the framework of zeta function regularization, we find the one-loop effective action to all orders in the magnetic field up to linear terms in the Riemannian curvature. As a particular case, we also obtain the one-loop effective action for massless scalar and spinor fields. In this setting, we found that the vacuum energy of charged spinors with small mass becomes very large due entirely by the gravitational correction.Comment: LaTeX, 23 page

Noncommutative Einstein Equations

We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a diffeomorphisms and gauge invariant action constructed by using a matrix-valued scalar curvature. Interestingly the genuine noncommutative part of the dynamical equations is described only in terms of a particular tensor density that vanishes identically in the commutative limit. A noncommutative generalization of the energy-momentum tensor for the matter field is studied as well.Comment: 17 Pages, LaTeX, reference adde

Acute Disseminated Encephalomyelitis followed by Optic Neuritis: A Rare Syndrome of Uncertain Treatment and Prognosis

Aim Acute Disseminated Encephalomyelitis followed by optic neuritis (ADEM-ON), first described in 2013, is a rare demyelinating syndrome, typical of the pediatric age. We conducted a mini review of the existing literature, focusing on clinical, laboratory, radiological, therapeutic, and prognostic aspects in order to improve the identification of new cases. Methods We searched PubMed and Cochrane Library for studies on ADEM-ON between 2013 and 2018. Results Examination of the reported cases (three case reports and eight observational studies) established the following features. Time between ADEM and ON is highly variable. Almost all patients show antimyelin oligodendrocyte glycoprotein antibody (MOG-abs) seropositivity. High-dose intravenous steroid and plasmapheresis efficacy is reported for the acute phase; oral prednisone and other maintenance drugs may be useful in avoiding relapses. The clinical history may lead to a complete recovery but also to residual deficits. Conclusion MOG-abs detection strongly supports ADEM-ON diagnosis, confirming this entity as part of MOG-abs spectrum disorder. Owing to the very small number of cases so far reported, predicting clinical evolution is very difficult

Summary of Travel Trends: 2017 National Household Travel Survey

DTFH6114F00113The 2017 National Household Travel Survey (NHTS) provides an inventory of daily travel in the US and its major Census Divisions and add-on areas. It is the only source of national-level statistics on personal travel in the US. The survey series (conducted since 1969) includes demographic data on households, people, vehicles, and detailed information on daily travel by all modes of transportation and for all purposes. NHTS survey data are collected from a sample of households and expanded to provide estimates of trips and miles of travel by travel mode, trip purpose, and other important attributes. When combined with historical data from the earlier surveys (1969, 1977, 1983, 1990, and 1995 NPTS and the 2001 NHTS, 2009 NHTS, and 2017 NHTS) these data serve as a rich source of information on the trends in travel over time. This report summarizes trends in household and personal travel patterns, including information on changes to the household-based vehicle fleet and commuting patterns. The report begins with a summary of the changes in the population, demographics, and related travel. Next, travel trends are examined at the household level, including differences between different areas of the US and by household income, for example. Next, changes in travel are summarized at the person-level, including trips by purpose and miles of travel by age and sex. Following sections detail changes in vehicle availability and usage, commute travel patterns, temporal distribution, and the travel of special populations. The 2017 NHTS was conducted with major changes in sampling strategy (an address-based sample compared to previous land-line random-digit sample) and methodology (Web-based self-reports compared to previous computer-aided interviewing). These and other critical changes are summarized here in Appendix A and in the data documentation at https://nhts.ornl.gov/. Researchers and data users are cautioned to do their best to assess how the change in methods may affect their estimates and to caution their readers about these critical changes in the data series

Small Mass Expansion of Functional Determinants on the Generalized Cone

In this paper we compute the small mass expansion for the functional determinant of a scalar Laplacian defined on the bounded, generalized cone. In the framework of zeta function regularization, we obtain an expression for the functional determinant valid in any dimension for both Dirichlet and Robin boundary conditions in terms of the spectral zeta function of the base manifold. Moreover, as a particular case, we specify the base to be a $d$-dimensional sphere and present explicit results for $d=2,3,4,5$.Comment: LaTeX, 23 page

New Developments in the Spectral Asymptotics of Quantum Gravity

A vanishing one-loop wave function of the Universe in the limit of small three-geometry is found, on imposing diffeomorphism-invariant boundary conditions on the Euclidean 4-ball in the de Donder gauge. This result suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory. All of this is made possible by a peculiar spectral cancellation on the Euclidean 4-ball, here derived and discussed.Comment: 7 pages, latex file. Paper prepared for the Conference "QFEXT05: Quantum Field Theory Under the Influence of External Conditions", Barcelona, September 5 - September 9, 2005. In the final version, the presentation has been further improved, and yet other References have been adde