Analytical formula for the Uehling potential

The closed analytical expression for the Uehling potential is derived. The Uehling potential describes the lowest-order correction on vacuum polarisation in atomic and muon-atomic systems. We also derive the analytical formula for the interaction potential between two electrically charged point particles which includes correction to the vacuum polarisation, but has correct asymptotic behaviour at larger $r$. Our three-term analytical formula for the Uehling potential opens a new avenue in the study of the vacuum polarisation in light atomic systems.Comment: arXiv admin note: substantial text overlap with arXiv:1103.204

Vacuum polarization calculations for hydrogenlike and alkalilike ions

Complete vacuum polarization calculations incorporating finite nuclear size are presented for hydrogenic ions with principal quantum numbers n=1-5. Lithiumlike, sodiumlike, and copperlike ions are also treated starting with Kohn-Sham potentials, and including first-order screening corrections. In both cases dominant Uehling terms are calculated with high accuracy, and smaller Wichmann- Kroll terms are obtained using numerical electron Green's functions.Comment: 23 pages, 1 figur

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur

Consistent histories of systems and measurements in spacetime

Traditional interpretations of quantum theory in terms of wave function collapse are particularly unappealing when considering the universe as a whole, where there is no clean separation between classical observer and quantum system and where the description is inherently relativistic. As an alternative, the consistent histories approach provides an attractive "no collapse" interpretation of quantum physics. Consistent histories can also be linked to path-integral formulations that may be readily generalized to the relativistic case. A previous paper described how, in such a relativistic spacetime path formalism, the quantum history of the universe could be considered to be an eignestate of the measurements made within it. However, two important topics were not addressed in detail there: a model of measurement processes in the context of quantum histories in spacetime and a justification for why the probabilities for each possible cosmological eigenstate should follow Born's rule. The present paper addresses these topics by showing how Zurek's concepts of einselection and envariance can be applied in the context of relativistic spacetime and quantum histories. The result is a model of systems and subsystems within the universe and their interaction with each other and their environment.Comment: RevTeX 4; 37 pages; v2 is a revision in response to reviewer comments, connecting the discussion in the paper more closely to consistent history concepts; v3 has minor editorial corrections; accepted for publication in Foundations of Physics; v4 has a couple minor typographical correction

Precise calculation of parity nonconservation in cesium and test of the standard model

We have calculated the 6s-7s parity nonconserving (PNC) E1 transition amplitude, E_{PNC}, in cesium. We have used an improved all-order technique in the calculation of the correlations and have included all significant contributions to E_{PNC}. Our final value E_{PNC} = 0.904 (1 +/- 0.5 %) \times 10^{-11}iea_{B}(-Q_{W}/N) has half the uncertainty claimed in old calculations used for the interpretation of Cs PNC experiments. The resulting nuclear weak charge Q_{W} for Cs deviates by about 2 standard deviations from the value predicted by the standard model.Comment: 24 pages, 8 figure

Entropic Corrections to Coulomb's Law

Two well-known quantum corrections to the area law have been introduced in the literatures, namely, logarithmic and power-law corrections. Logarithmic corrections, arises from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, while, power-law correction appears in dealing with the entanglement of quantum fields in and out the horizon. Inspired by Verlinde's argument on the entropic force, and assuming the quantum corrected relation for the entropy, we propose the entropic origin for the Coulomb's law in this note. Also we investigate the Uehling potential as a radiative correction to Coulomb potential in 1-loop order and show that for some value of distance the entropic corrections of the Coulomb's law is compatible with the vacuum-polarization correction in QED. So, we derive modified Coulomb's law as well as the entropy corrected Poisson's equation which governing the evolution of the scalar potential $\phi$. Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.Comment: 17 pages, 5 figures, accepted in IJT

Diatreta Cups, Light in Roman Dining Spaces

Cage cups or Diatreta are ancient Roman glass vessels produced by creating a thick blown blank of glass that, once cooled down, is taken to a glass cutter or diatretarii. The latter would cut and carve away most of the glass leaving a transparent vessel inside and an open-work decoration separated through thin posts of glass. The work is very delicate and exclusive, produced within limited space in time with no record of similar vessels until the late 1800 (Donald B. Harden & Toynbee 1959, p.181). Many of these glass objects have good-will inscriptions or decorations that express the importance of drinking. As for their provenance, most –when found in context- have been found in pagan burials. Nevertheless some fragments have been found in Christian environments or with Christian motifs like the Szekszárd cup. The location of these finds is mostly in the Rhine area –northern Empire, when Milan was one of its capitals (Aquaro 2004)- but the actual extent of finds expand throughout the 4th century extent of the Roman Empire. Considering their typological analysis there are basically two types, beaker and bowl. Beakers are considered drinking vessels as they either display a legend or a mythological reference to drink or wine. Whereas a general consensus agrees that open bowl-form cups were hanging lamps (Whitehouse 1988, p.28) since the 1986 find of a diatreta bowl with copper alloy hanging attachments. It is clear these were luxury objects to be used in special occasions and spaces. The aim of this paper is to understand the space were socialisation and drinking took place and the importance of luxurious objects to adorn, display and use. The paper will also put forward the idea that the beaker shaped diatreta vessels, usually considered for drinking, could have been lamps that encouraged drinking and good will to the guests. This paper is structured to first consider an introduction to late luxury Roman glass and then analysing the typological shape of all, or most of the diatreta currently known; secondly, through assessment by the means of comparison, analyse the writings or decorations the vessels were endowed with. Thirdly, by describing and understanding the people and the space were these vessels would have been used, emphasise the beauty of illuminating such spaces with these vessels. According to Herodotus in his historical investigation –5th century-, dress habits and food regime are elements of extreme importance to understand a people (Caporusso et al. 2011, p.12). This idea is not only valid for Herodotus’ time but it is something anthropology uses time and again to explain different aspects in people’s way of life. Through food and its environment, the dining space, this paper will aim to put the cage cups into a social context in order to give emphasis to the hypothesis of light versus wine

Association of genetic variation with systolic and diastolic blood pressure among African Americans: the Candidate Gene Association Resource study

The prevalence of hypertension in African Americans (AAs) is higher than in other US groups; yet, few have performed genome-wide association studies (GWASs) in AA. Among people of European descent, GWASs have identified genetic variants at 13 loci that are associated with blood pressure. It is unknown if these variants confer susceptibility in people of African ancestry. Here, we examined genome-wide and candidate gene associations with systolic blood pressure (SBP) and diastolic blood pressure (DBP) using the Candidate Gene Association Resource (CARe) consortium consisting of 8591 AAs. Genotypes included genome-wide single-nucleotide polymorphism (SNP) data utilizing the Affymetrix 6.0 array with imputation to 2.5 million HapMap SNPs and candidate gene SNP data utilizing a 50K cardiovascular gene-centric array (ITMAT-Broad-CARe [IBC] array). For Affymetrix data, the strongest signal for DBP was rs10474346 (P= 3.6 × 10−8) located near GPR98 and ARRDC3. For SBP, the strongest signal was rs2258119 in C21orf91 (P= 4.7 × 10−8). The top IBC association for SBP was rs2012318 (P= 6.4 × 10−6) near SLC25A42 and for DBP was rs2523586 (P= 1.3 × 10−6) near HLA-B. None of the top variants replicated in additional AA (n = 11 882) or European-American (n = 69 899) cohorts. We replicated previously reported European-American blood pressure SNPs in our AA samples (SH2B3, P= 0.009; TBX3-TBX5, P= 0.03; and CSK-ULK3, P= 0.0004). These genetic loci represent the best evidence of genetic influences on SBP and DBP in AAs to date. More broadly, this work supports that notion that blood pressure among AAs is a trait with genetic underpinnings but also with significant complexit

Association of genetic variation with systolic and diastolic blood pressure among African Americans: the Candidate Gene Association Resource study.

The prevalence of hypertension in African Americans (AAs) is higher than in other US groups; yet, few have performed genome-wide association studies (GWASs) in AA. Among people of European descent, GWASs have identified genetic variants at 13 loci that are associated with blood pressure. It is unknown if these variants confer susceptibility in people of African ancestry. Here, we examined genome-wide and candidate gene associations with systolic blood pressure (SBP) and diastolic blood pressure (DBP) using the Candidate Gene Association Resource (CARe) consortium consisting of 8591 AAs. Genotypes included genome-wide single-nucleotide polymorphism (SNP) data utilizing the Affymetrix 6.0 array with imputation to 2.5 million HapMap SNPs and candidate gene SNP data utilizing a 50K cardiovascular gene-centric array (ITMAT-Broad-CARe [IBC] array). For Affymetrix data, the strongest signal for DBP was rs10474346 (P= 3.6 × 10(-8)) located near GPR98 and ARRDC3. For SBP, the strongest signal was rs2258119 in C21orf91 (P= 4.7 × 10(-8)). The top IBC association for SBP was rs2012318 (P= 6.4 × 10(-6)) near SLC25A42 and for DBP was rs2523586 (P= 1.3 × 10(-6)) near HLA-B. None of the top variants replicated in additional AA (n = 11 882) or European-American (n = 69 899) cohorts. We replicated previously reported European-American blood pressure SNPs in our AA samples (SH2B3, P= 0.009; TBX3-TBX5, P= 0.03; and CSK-ULK3, P= 0.0004). These genetic loci represent the best evidence of genetic influences on SBP and DBP in AAs to date. More broadly, this work supports that notion that blood pressure among AAs is a trait with genetic underpinnings but also with significant complexity

Mendelian randomization and mediation analysis of leukocyte telomere length and risk of lung and head and neck cancers

Background: Evidence from observational studies of telomere length (TL) has been conflicting regarding its direction of association with cancer risk. We investigated the causal relevance of TL for lung and head and neck cancers using Mendelian Randomization (MR) and mediation analyses. Methods: We developed a novel genetic instrument for TL in chromosome 5p15.33, using variants identified through deep-sequencing, that were genotyped in 2051 cancer-free subjects. Next, we conducted an MR analysis of lung (16 396 cases, 13 013 controls) and head and neck cancer (4415 cases, 5013 controls) using eight genetic instruments for TL. Lastly, the 5p15.33 instrument and distinct 5p15.33 lung cancer risk loci were evaluated using two-sample mediation analysis, to quantify their direct and indirect, telomere-mediated, effects. Results: The multi-allelic 5p15.33 instrument explained 1.49-2.00% of TL variation in our data (p = 2.6 × 10-9). The MR analysis estimated that a 1000 base-pair increase in TL increases risk of lung cancer [odds ratio (OR) = 1.41, 95% confidence interval (CI): 1.20-1.65] and lung adenocarcinoma (OR = 1.92, 95% CI: 1.51-2.22), but not squamous lung carcinoma (OR = 1.04, 95% CI: 0.83-1.29) or head and neck cancers (OR = 0.90, 95% CI: 0.70-1.05). Mediation analysis of the 5p15.33 instrument indicated an absence of direct effects on lung cancer risk (OR = 1.00, 95% CI: 0.95-1.04). Analysis of distinct 5p15.33 susceptibility variants estimated that TL mediates up to 40% of the observed associations with lung cancer risk. Conclusions: Our findings support a causal role for long telomeres in lung cancer aetiology, particularly for adenocarcinoma, and demonstrate that telomere maintenance partially mediates the lung cancer susceptibility conferred by 5p15.33 loci