Eikonal Approximation to 5D Wave Equations as Geodesic Motion in a Curved 4D Spacetime

We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the symplectic structure of the corresponding mechanics. We then apply an analogous method to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics to demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. Finally we discuss the case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg-Schr\"odinger equation. This construction provides a model for an underlying quantum mechanical structure for classical dynamical motion along geodesics on a pseudo-Riemannian manifold. The locally symplectic structure which emerges is that of Stueckelberg's covariant mechanics on this manifold.Comment: TeX file. 17 pages. Rewritten for clarit

Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities

The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force) was previously calculated for the perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to {\it quantum} fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections which we refer to as Bogoliubov corrections. The leading order term is identified as the Casimir energy of a massless scalar field moving with wave velocity equal to the speed of sound in the BEC. We then obtain the leading order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary lengths and obtain the finite-size correction to the parallel plate scenario.Comment: 12 pages; no figures; v.2: version accepted for publication in JSTAT v.3: references adde

G-CORE a core for future graph query languages

We report on a community effort between industry and academia to shape the future of graph query languages. We argue that existing graph database management systems should consider supporting a query language with two key characteristics. First, it should be composable, meaning, that graphs are the input and the output of queries. Second, the graph query language should treat paths as first-class citizens. Our result is G-CORE, a powerful graph query language design that fulfills these goals, and strikes a careful balance between path query expressivity and evaluation complexity

The labor market effects of technology shocks

We analyze the effects of neutral and investment-specific technology shocks on hours worked and unemployment. We characterize the response of unemployment in terms of job separation and job finding rates. We find that job separation rates mainly account for the impact response of unemployment while job finding rates for movements along its adjustment path. Neutral shocks increase unemployment and explain a substantial portion of unemployment and output volatilityinvestment-specific shocks expand employment and hours worked and mostly contribute to hours worked volatility. We show that this evidence is consistent with the view that neutral technological progress prompts Schumpeterian creative destruction, while investment specific technological progress has standard neoclassical feature

Credit Supply: Identifying Balance-Sheet Channels with Loan Applications and Granted Loans

To identify credit availability we analyze the extensive and intensive margins of lending with loan applications and all loans granted in Spain. We find that during the period analyzed both worse economic and tighter monetary conditions reduce loan granting, especially to firms or from banks with lower capital or liquidity ratios. Moreover, responding to applications for the same loan, weak banks are less likely to grant the loan. Our results suggest that firms cannot offset the resultant credit restriction by turning to other banks. Importantly the bank-lending channel is notably stronger when we account for unobserved time-varying firm heterogeneity in loan demand and quality

Wage inequality, segregation by skill and the price of capital in an assignment model

Some pieces of empirical evidence suggest that in the U.S., over the last few decades, (i) wage inequality between-plants has risen much more than wage inequality within-plants and (ii) there has been an increase in the segregation of workers by skill into separate plants. This paper presents a frictionless assignment model in which these two features can be explained simultaneously as the result of the decline in the relative price of capital. Additional implications of the model regarding the skill premium and the dispersion in labor productivity across plants are also consistent with the empirical evidence. [resumen de autor

Cardiovascular disease, chronic kidney disease, and diabetes mortality burden of cardiometabolic risk factors from 1980 to 2010: A comparative risk assessment

Background: High blood pressure, blood glucose, serum cholesterol, and BMI are risk factors for cardiovascular diseases and some of these factors also increase the risk of chronic kidney disease and diabetes. We estimated mortality from cardiovascular diseases, chronic kidney disease, and diabetes that was attributable to these four cardiometabolic risk factors for all countries and regions from 1980 to 2010. Methods: We used data for exposure to risk factors by country, age group, and sex from pooled analyses of population-based health surveys. We obtained relative risks for the effects of risk factors on cause-specific mortality from meta-analyses of large prospective studies. We calculated the population attributable fractions for each risk factor alone, and for the combination of all risk factors, accounting for multicausality and for mediation of the effects of BMI by the other three risks. We calculated attributable deaths by multiplying the cause-specific population attributable fractions by the number of disease-specific deaths. We obtained cause-specific mortality from the Global Burden of Diseases, Injuries, and Risk Factors 2010 Study. We propagated the uncertainties of all the inputs to the final estimates. Findings: In 2010, high blood pressure was the leading risk factor for deaths due to cardiovascular diseases, chronic kidney disease, and diabetes in every region, causing more than 40% of worldwide deaths from these diseases; high BMI and glucose were each responsible for about 15% of deaths, and high cholesterol for more than 10%. After accounting for multicausality, 63% (10·8 million deaths, 95% CI 10·1-11·5) of deaths from these diseases in 2010 were attributable to the combined effect of these four metabolic risk factors, compared with 67% (7·1 million deaths, 6·6-7·6) in 1980. The mortality burden of high BMI and glucose nearly doubled from 1980 to 2010. At the country level, age-standardised death rates from these diseases attributable to the combined effects of these four risk factors surpassed 925 deaths per 100 000 for men in Belarus, Kazakhstan, and Mongolia, but were less than 130 deaths per 100 000 for women and less than 200 for men in some high-income countries including Australia, Canada, France, Japan, the Netherlands, Singapore, South Korea, and Spain. Interpretation: The salient features of the cardiometabolic disease and risk factor epidemic at the beginning of the 21st century are high blood pressure and an increasing effect of obesity and diabetes. The mortality burden of cardiometabolic risk factors has shifted from high-income to low-income and middle-income countries. Lowering cardiometabolic risks through dietary, behavioural, and pharmacological interventions should be a part of the global response to non-communicable diseases. Funding: UK Medical Research Council, US National Institutes of Health. © 2014 Elsevier Ltd