George M. Napolitano

Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: scalar case

Recent work in the literature had evaluated the energy-momentum tensor of a Casimir apparatus in a weak gravitational field, for an electromagnetic field subject to perfect conductor boundary conditions on parallel plates. The Casimir apparatus was then predicted to experience a tiny push in the upward direction, and the regularized energy-momentum tensor was evaluated to first order in the gravitational acceleration. This analysis made it desirable to assess what happens in a simpler case. For this purpose, the present paper studies a free, real massless scalar field subject to homogeneous Dirichlet conditions on the parallel plates. Working again to first order in the constant gravity acceleration, the resulting regularized and renormalized energy-momentum tensor is found to be covariantly conserved, while the trace anomaly vanishes if the massless scalar field is conformally coupled to gravity. Conformal coupling also ensures a finite Casimir energy and finite values of the pressure upon parallel plates. (Less)

Energy-momentum tensor for a scalar Casimir apparatus in a weak gravitational field: Neumann conditions

We consider a Casimir apparatus consisting of two perfectly conducting parallel plates, subject to the weak gravitational field of the Earth. The aim of this paper is the calculation of the energy-momentum tensor of this system for a free, real massless scalar field satisfying Neumann boundary conditions on the plates. The small gravity acceleration (considered here as not varying between the two plates) allows us to perform all calculations to first order in this parameter. Some interesting results are found: a correction, depending on the gravity acceleration, to the well-known Casimir energy and pressure on the plates. Moreover, this scheme predicts a tiny force in the upwards direction acting on the apparatus. These results are supported by two consistency checks: the covariant conservation of the energy-momentum tensor and the vanishing of its regularized trace, when the scalar field is conformally coupled to gravity.

The Ising Model on the Random Planar Causal Triangulation: Bounds on the Critical Line and Magnetization Properties

We investigate a Gibbs (annealed) probability measure defined on Ising spin configurations on causal triangulations of the plane. We study the region where such measure can be defined and provide bounds on the boundary of this region (critical line). We prove that for any finite random triangulation the magnetization of the central spin is sensitive to the boundary conditions. Furthermore, we show that in the infinite volume limit, the magnetization of the central spin vanishes for values of the temperature high enough.

Impact of HPV vaccination on outcome of cervical cytology screening in Denmark-A register-based cohort study: Impact of HPV vaccination in Denmark

4vHPV vaccination has been tested in randomized controlled trials under almost ideal conditions, and studies of real‐life use have compared outcome between vaccinated and unvaccinated women from the same birth cohort and mostly before screening age. Here we present the first—to our knowledge—evaluation of the impact of the 4vHPV vaccination in real life without selection bias in the reported data. The study has been carried out by comparing the results after first cervical screening between an HPV‐vaccinated and an unvaccinated birth cohort, consisting of women born in Denmark in 1993 and 1983, respectively. Cytology data covering an 8‐year period, from the age of 15 (age of HPV‐vaccination) to age 23 (age of invitation to first cervical screening), were retrieved from the Danish National Pathology Register. Abnormal cytology, defined as atypical squamous cell of undetermined significance and worse (ASCUS+) was detected in 9.4% of women born in 1993 as compared with 9.0% of women born in 1983; RR = 1.04 (95% CI 0.96–1.12), p = .29. Detection of high‐grade squamous intraepithelial lesion (HSIL) was statistically significantly lower in the 1993 than in the 1983 cohort, RR = 0.6 (95% CI 0.5–0.7), p < .0001, while the opposite pattern was seen for ASCUS RR = 1.4 (95% CI 1.2–1.6), p < .0001. The decrease in HSIL means that more women can be spared referral for colposcopy and biopsy. The increase of ASCUS could be explained by transition from conventional to liquid‐based cytology, but this observation requires further monitoring.

Overdiagnosis in breast cancer screening

The purpose of breast cancer screening is to reduce breast cancer mortality. In order to achieve this purpose, an X-ray search—a mammography examination—is made of the breast tissue of healthy women to detect potential cancers that have not given rise to symptoms. With early detection, a woman with breast cancer can be offered a more efficient treatment than it would otherwise had been possible. If screening works, women with screen-detected breast cancer will have a better prognosis than women diagnosed with symptoms of breast cancer.

Screening mammography: benefit of double reading by breast density

PurposeThe currently recommended double reading of all screening mammography examinations is an economic burden for screening programs. The sensitivity of screening is higher for women with low breast density than for women with high density. One may therefore ask whether single reading could replace double reading at least for women with low density. We addressed this question using data from a screening program where the radiologists coded their readings independently.MethodsData include all screening mammography examinations in the Capital Region of Denmark from 1 November 2012 to 31 December 2013. Outcome of screening was assessed by linkage to the Danish Pathology Register. We calculated sensitivity, specificity, number of interval cancers, and false positive-tests per 1000 screened women by both single reader and consensus BI-RADS density code.ResultsIn total 54,808 women were included. The overall sensitivity of double reading was 72%, specificity was 97.6%, 3 women per 1000 screened experienced an interval cancer, and 24 a false-positive test. Across all BI-RADS density codes, single reading consistently decreased sensitivity as compared with consensus reading. The same was true for specificity, apart from results across BI-RADS density codes set by reader 2.ConclusionsSingle reading decreased sensitivity as compared with double reading across all BI-RADS density codes. This included results based on consensus BI-RADS density codes. This means that replacement of double with single reading would have negative consequences for the screened women, even if density could be assessed automatically calibrated to the usual consensus level.

Critical line of the Ising model on 2-dimensional CDT and its dual

In this paper we study the annealed coupling of an Ising model with 2-dimensional causal dynamical triangulation model. After a short review of previous results, we prove the existence of the so-called critical line and derive its analytical properties and asymptotics. In addition, relations between the model and its dual are investigated.

Geometry and physics of pseudodifferential operators on manifolds

A review is made of the basic tools used in mathematics to define acalculus for pseudodifferential operators on Riemannian manifolds endowed with aconnection: existence theorem for the function that generalizes the phase; analogueof Taylor’s theorem; torsion and curvature terms in the symbolic calculus; the twokinds of derivative acting on smooth sections of the cotangent bundle of the Riemannianmanifold; the concept of symbol as an equivalence class. Physical motivationsand applications are then outlined, with emphasis on Green functions of quantumfield theory and Parker’s evaluation of Hawking radiation.

Structure of a randomly grown 2-d network.

We introduce a growing random network on a plane as a model of a growing neuronal network. The properties of the structure of the induced graph are derived. We compare our results with available data. In particular, it is shown that depending on the parameters of the model the system undergoes in time different phases of the structure. We conclude with a possible explanation of some empirical data on the connections between neurons.