Geodesics on Lie groups: Euler equations and totally geodesic subgroup

The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler-Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given. The setting works both in the classical nite dimensional case, and in the category of in nite dimensional Fr echet Lie groups, in which di eomorphism groups are included. Using the framework we give new examples of both nite and in nite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving di eomorphisms is totally geodesic. The paper also gives a general framework for the representation of Euler-Arnold equations in arbitrary choice of dual pairing

Matter-screened Casimir force and Casimir-Polder force in planar structures

Using a recently developed theory of the Casimir force (Raabe C and Welsch D-G 2005 Phys. Rev. A 71 013814), we calculate the force that acts on a plate in front of a planar wall and the force that acts on the plate in the case where the plate is part of matter that fills the space in front of the wall. We show that in the limit of a dielectric plate whose permittivity is close to unity, the force obtained in the former case reduces to the ordinary, i.e., unscreened Casimir-Polder force acting on isolated atoms. In the latter case, the theory yields the Casimir-Polder force that is screened by the surrounding matter.Comment: 11 pages, 1 figure -- published online at J. Opt. B on Nov 16 200

Gestational and lactational exposure of rats to xenoestrogens results in reduced testicular size and sperm production

EHP is a publication of the U.S. government. Publication of EHP lies in the public domain and is therefore without copyright. Research articles from EHP may be used freely; however, articles from the News section of EHP may contain photographs or figures copyrighted by other commercial organizations and individuals that may not be used without obtaining prior approval from both the EHP editors and the holder of the copyright. Use of any materials published in EHP should be acknowledged (for example, "Reproduced with permission from Environmental Health Perspectives") and a reference provided for the article from which the material was reproduced.This study assessed whether exposure of male rats to two estrogenic, environmental chemicals, 4-octylphenol (OP) and butyl benzyl phthalate (BBP) during gestation or during the first 21 days of postnatal life, affected testicular size or spermatogenesis in adulthood (90-95 days of age). Chemicals were administered via the drinking water or concentrations of 10-1000 micrograms/l (OP) or 1000 micrograms/l (BBP), diethylstilbestrol (DES; 100 micrograms/l) and an octylphenol polyethoxylate (OPP; 1000 micrograms/l), which is a weak estrogen or nonestrogenic in vitro, were administered as presumptive positive and negative controls, respectively. Controls received the vehicle (ethanol) in tap water. In study 1, rats were treated from days 1-22 after births in studies 2 and 3, the mothers were treated for approximately 8-9 weeks, spanning a 2-week period before mating throughout gestation and 22 days after giving birth. With the exception of DES, treatment generally had no major adverse effect or body weight: in most instances, treated animals were heavier than controls at day 22 and at days 90-95. Exposure to OP, OPP, or BBP at a concentration of 1000 micrograms/1 resulted in a small (5-13%) but significant (p < 0.01 or p < 0.0001) reduction in mean testicular size in studies 2 and 3, an effect that was still evident when testicular weight was expressed relative to body, weight or kidney weight. The effect of OPP is attributed to its metabolism in vivo to OP. DES exposure caused similar reductions in testicular size but also caused reductions in body weight, kidney weight, and litter size. Ventral prostate weight was reduced significantly in DES-treated rats and to minor extent in OP-treated rats. Comparable but more minor effects of treatment with DES or OP on testicular size were observed in study 1. None of the treatments had any adverse effect on testicular morphology or on the cross-sectional area of the lumen or seminiferous epithelium at stages VII-VIII of the spermatogenic cycle, but DES, OP, and BBP caused reductions of 10-21% (p < 0.05 to p < 0.001) in daily sperm production. Humans are exposed to phthalates, such as BBP, and to alkylphenol polyethoxylates, such as OP, but to what extent is unknown. More detailed studies are warranted to assess the possible risk to the development of the human testis from exposure to these and other environmental estrogens

COVID-19 infection and death rates: the need to incorporate causal explanations for the data and avoid bias in testing

COVID-19 testing strategies are primarily driven by medical need - focusing on people already hospitalized with significant symptoms or on people most at risk. However, such testing is highly biased because it fails to identify the extent to which COVID-19 is present in people with mild or no symptoms. If we wish to understand the true rate of COVID-19 infection and death, we need to take full account of the causal explanations for the resulting data to avoid highly misleading conclusions about infection and death rates. We describe how causal (Bayesian network) models can provide such explanations and the need to combine these with more random testing in order to achieve reliable data and predictions for the both policy makers and the public

One-loop effective potential in M4 x T2 with and without 't Hooft flux

We review the basic notions of compactification in the presence of a background flux. In extra-dimentional models with more than five dimensions, Scherk and Schwarz boundary conditions have to satisfy 't Hooft consistency conditions. Different vacuum configurations can be obtained, depending whether trivial or non-trivial 't Hooft flux is considered. The presence of the "magnetic" background flux provide, in addition, a mechanism for producing four-dimensional chiral fermions. Particularizing to the six-dimensional case, we calculate the one-loop effective potential for a U(N) gauge theory on M4 x T2. We firstly review the well known results of the trivial 't Hooft flux case, where one-loop contributions produce the usual Hosotani dynamical symmetry breaking. Finally we applied our result for describing, for the first time, the one-loop contributions in the non-trivial 't Hooft flux case

Nonequilibrium Atom-Dielectric Forces Mediated by a Quantum Field

In this paper we give a first principles microphysics derivation of the nonequilibrium forces between an atom, treated as a three dimensional harmonic oscillator, and a bulk dielectric medium modeled as a continuous lattice of oscillators coupled to a reservoir. We assume no direct interaction between the atom and the medium but there exist mutual influences transmitted via a common electromagnetic field. By employing concepts and techniques of open quantum systems we introduce coarse-graining to the physical variables - the medium, the quantum field and the atom's internal degrees of freedom, in that order - to extract their averaged effects from the lowest tier progressively to the top tier. The first tier of coarse-graining provides the averaged effect of the medium upon the field, quantified by a complex permittivity (in the frequency domain) describing the response of the dielectric to the field in addition to its back action on the field through a stochastic forcing term. The last tier of coarse- graining over the atom's internal degrees of freedom results in an equation of motion for the atom's center of mass from which we can derive the force on the atom. Our nonequilibrium formulation provides a fully dynamical description of the atom's motion including back action effects from all other relevant variables concerned. In the long-time limit we recover the known results for the atom-dielectric force when the combined system is in equilibrium or in a nonequilibrium stationary state.Comment: 24 pages, 2 figure

Quantum corrections from a path integral over reparametrizations

We study the path integral over reparametrizations that has been proposed as an ansatz for the Wilson loops in the large-$N$ QCD and reproduces the area law in the classical limit of large loops. We show that a semiclassical expansion for a rectangular loop captures the L\"uscher term associated with $d=26$ dimensions and propose a modification of the ansatz which reproduces the L\"uscher term in other dimensions, which is observed in lattice QCD. We repeat the calculation for an outstretched ellipse advocating the emergence of an analog of the L\"uscher term and verify this result by a direct computation of the determinant of the Laplace operator and the conformal anomaly

Inferring the Origin Locations of Tweets with Quantitative Confidence

Social Internet content plays an increasingly critical role in many domains, including public health, disaster management, and politics. However, its utility is limited by missing geographic information; for example, fewer than 1.6% of Twitter messages (tweets) contain a geotag. We propose a scalable, content-based approach to estimate the location of tweets using a novel yet simple variant of gaussian mixture models. Further, because real-world applications depend on quantified uncertainty for such estimates, we propose novel metrics of accuracy, precision, and calibration, and we evaluate our approach accordingly. Experiments on 13 million global, comprehensively multi-lingual tweets show that our approach yields reliable, well-calibrated results competitive with previous computationally intensive methods. We also show that a relatively small number of training data are required for good estimates (roughly 30,000 tweets) and models are quite time-invariant (effective on tweets many weeks newer than the training set). Finally, we show that toponyms and languages with small geographic footprint provide the most useful location signals.Comment: 14 pages, 6 figures. Version 2: Move mathematics to appendix, 2 new references, various other presentation improvements. Version 3: Various presentation improvements, accepted at ACM CSCW 201

Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the symplectic structure in the case $\epsilon=0$. In the case $0<\epsilon\ll 1$ the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order

Enhanced dispersion interaction in confined geometry

The dispersion interaction between two point-like particles confined in a dielectric slab between two plates of another dielectric medium is studied within a continuum (Lifshitz) theory. The retarded (Casimir-Polder) interaction at large inter-particle distances is found to be strongly enhanced as the mismatch between the dielectric permittivities of the two media is increased. The large-distance interaction is multiplied due to confinement by a factor of $(33\gamma^{5/2}+13\gamma^{-3/2})/46$ at zero temperature, and by $(5\gamma^2+\gamma^{-2})/6$ at finite temperature, \gamma=\ein(0)/\eout(0) being the ratio between the static dielectric permittivities of the inner and outer media. This confinement-induced amplification of the dispersion interaction can reach several orders of magnitude.Comment: 4 page