Finding next-to-shortest paths in a graph

We study the problem of finding the next-to-shortest paths in a graph. A next-to-shortest $(u,v)$-path is a shortest $(u,v)$-path amongst $(u,v)$-paths with length strictly greater than the length of the shortest $(u,v)$-path. In constrast to the situation in directed graphs, where the problem has been shown to be NP-hard, providing edges of length zero are allowed, we prove the somewhat surprising result that there is a polynomial time algorithm for the undirected version of the problem

Gravitational Interactions and Fine-Structure Constant

Electromagnetic and gravitational central-field problems are studied with relativistic quantum mechanics on curved space-time backgrounds. Corrections to the transition current are identified. Analogies of the gravitational and electromagnetic spectra suggest the definition of a gravitational fine-structure constant. The electromagnetic and gravitational coupling constants enter the Einstein-Hilbert-Maxwell Lagrangian. We postulate that the variational principle holds with regard to a global dilation transformation of the space-time coordinates. The variation suggests is consistent with a functional relationship of the form alpha_QED being proportional to alpha_G^(1/2), where alpha_QED is the electrodynamic fine-structure constant, and alpha_G its gravitational analogue.Comment: 9 pages; LaTeX; Appeared in the Proceedings to the 17th Bled workshop "What Comes Beyond the Standard Models", Bled, Slovenia, July 2-28, 2014; Editors N. S. Mankoc Borstnik, H. B. Nielsen and D. Lukman; ISSN 1580-4992; book series: Bled Workshops in Physics vol. 15, no. 2, pp. 115-122 (2014

Demography of sea lamprey (Petromyzon marinus) ammocoete populations in relation to potential spawning-migration obstructions

Copyright © 2017 John Wiley & Sons, Ltd. Recent advances in the understanding of lamprey migrations have led to concerns over the impacts of obstructions on the demography of many species. This study investigated sea lamprey (Petromyzon marinus) larvae (ammocoetes) in two adjacent but contrasting rivers, both designated Special Areas of Conservation under the EC Habitats Directive (92/43/EEC), one (the River Wye) with a small number of potential migration obstructions in its upper reaches and one (the River Usk) with obstacles along its course. The geographical distributions, densities and age structures of the ammocoete populations were examined in relation to the locations of potential obstructions to the spawning migrations of anadromous adults. A minimum of three age classes was recorded as far as 200 km upstream of the mouth of the River Wye (93% of the length of the mainstem), demonstrating that adults regularly migrate to the upper reaches of the catchment (downstream of a natural waterfall). By contrast, sea lamprey ammocoetes appeared to be absent (in suitable habitat) from 20 km (17%) of the River Usk, and there was a reduction in density, prevalence and the number of age classes upstream of two putative spawning-migration obstructions. This study highlights some of the potential impacts of habitat fragmentation by obstructions on the spawning migrations of anadromous species, as inferred from ammocoete demography. When used in combination to compare contiguous reaches, ammocoete densities, prevalence and age structure may be a useful indicator of which structures are likely to be important migration obstructions, and where further studies or mitigation efforts should be focused. It is likely that passage past some obstructions is enhanced if high river levels occur during the spawning migration, but there is a need to facilitate passage during all conditions, to improve access to under-exploited spawning and nursery areas

Idealized Antenna Patterns for Use in Communication-satellite Interference Studies

Idealized antenna patterns for communication satellite interference studie

Detection of a Substantial Molecular Gas Reservoir in a brightest cluster galaxy at z = 1.7

We report the detection of CO(2-1) emission coincident with the brightest cluster galaxy (BCG) of the high-redshift galaxy cluster SpARCS1049+56, with the Redshift Search Receiver (RSR) on the Large Millimetre Telescope (LMT). We confirm a spectroscopic redshift for the gas of z = 1.7091+/-0.0004, which is consistent with the systemic redshift of the cluster galaxies of z = 1.709. The line is well-fit by a single component Gaussian with a RSR resolution-corrected FWHM of 569+/-63 km/s. We see no evidence for multiple velocity components in the gas, as might be expected from the multiple image components seen in near-infrared imaging with the Hubble Space Telescope. We measure the integrated flux of the line to be 3.6+/-0.3 Jy km/s and, using alpha_CO = 0.8 Msun (K km s^-1 pc^2)^-1 we estimate a total molecular gas mass of 1.1+/-0.1x10^11 Msun and a M_H2/M_star ~ 0.4. This is the largest gas reservoir detected in a BCG above z > 1 to date. Given the infrared-estimated star formation rate of 860+/-130 Msun/yr, this corresponds to a gas depletion timescale of ~0.1Gyr. We discuss several possible mechanisms for depositing such a large gas reservoir to the cluster center -- e.g., a cooling flow, a major galaxy-galaxy merger or the stripping of gas from several galaxies -- but conclude that these LMT data are not sufficient to differentiate between them.Comment: accepted for publication in ApJ Letter

Knowledge-based vision and simple visual machines

The vast majority of work in machine vision emphasizes the representation of perceived objects and events: it is these internal representations that incorporate the 'knowledge' in knowledge-based vision or form the 'models' in model-based vision. In this paper, we discuss simple machine vision systems developed by artificial evolution rather than traditional engineering design techniques, and note that the task of identifying internal representations within such systems is made difficult by the lack of an operational definition of representation at the causal mechanistic level. Consequently, we question the nature and indeed the existence of representations posited to be used within natural vision systems (i.e. animals). We conclude that representations argued for on a priori grounds by external observers of a particular vision system may well be illusory, and are at best place-holders for yet-to-be-identified causal mechanistic interactions. That is, applying the knowledge-based vision approach in the understanding of evolved systems (machines or animals) may well lead to theories and models that are internally consistent, computationally plausible, and entirely wrong

Numerical Simulations of Driven Relativistic MHD Turbulence

A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging neutron stars, X-ray binaries, some supernovae, and the early universe. In order to elucidate the basic properties of the relativistic magnetohydrodynamical (RMHD) turbulence present in these systems, we present results from numerical simulations of fully developed driven turbulence in a relativistically warm, weakly magnetized and mildly compressible ideal fluid. We have evolved the RMHD equations for many dynamical times on a uniform grid with 1024^3 zones using a high order Godunov code. We observe the growth of magnetic energy from a seed field through saturation at about 1% of the total fluid energy. We compute the power spectrum of velocity and density-weighted velocity and conclude that the inertial scaling is consistent with a slope of -5/3. We compute the longitudinal and transverse velocity structure functions of order p up to 11, and discuss their possible deviation from the expected scaling for non-relativistic media. We also compute the scale-dependent distortion of coherent velocity structures with respect to the local magnetic field, finding a weaker scale dependence than is expected for incompressible non-relativistic flows with a strong mean field.Comment: Accepted to Ap

Pasos Hacia La Salud: a randomized controlled trial of an internet-delivered physical activity intervention for Latinas.

BackgroundInternet access has grown markedly in Latinos during the past decade. However, there have been no Internet-based physical activity interventions designed for Latinos, despite large disparities in lifestyle-related conditions, such as obesity and diabetes, particularly in Latina women. The current study tested the efficacy of a 6-month culturally adapted, individually tailored, Spanish-language Internet-based physical activity intervention.MethodsInactive Latinas (N = 205) were randomly assigned to the Tailored Physical Activity Internet Intervention or the Wellness Contact Control Internet Group. Participants in both groups received emails on a tapered schedule over 6 months to alert them to new content on the website. The primary outcome was minutes/week of moderate to vigorous physical activity (MVPA) at 6 months as measured by the 7-Day Physical Activity Recall; activity was also measured by accelerometers. Data were collected between 2011 and 2014 and analyzed in 2015 at the University of California, San Diego.ResultsIncreases in minutes/week of MVPA were significantly greater in the Intervention Group compared to the Control Group (mean difference = 50.00, SE = 9.5, p < 0.01). Increases in objectively measured MVPA were also significantly larger in the Intervention Group (mean differences = 31.0, SE = 10.7, p < .01). The Intervention Group was also significantly more likely to meet national physical activity guidelines at 6 months (OR = 3.12, 95% CI 1.46-6.66, p < .05).ConclusionFindings from the current study suggest that this Internet-delivered individually tailored intervention successfully increased MVPA in Latinas compared to a Wellness Contact Control Internet Group.Trial registrationNCT01834287

TESS: A Relativistic Hydrodynamics Code on a Moving Voronoi Mesh

We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multi-dimensional systems of conservation laws in finite-volume form. The mesh generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluids on a dynamic Voronoi mesh. When run in Lagrangian mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical and cylindrical coordinates and is modular so that auxilliary physics solvers are readily integrated into the TESS framework and so that the TESS framework can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.Comment: ApJS, 197, 1

Electroweak Precision Constraints on the Littlest Higgs Model with T Parity

We compute the leading corrections to the properties of W and Z bosons induced at the one-loop level in the SU(5)/SO(5) Littlest Higgs model with T parity, and perform a global fit to precision electroweak data to determine the constraints on the model parameters. We find that a large part of the model parameter space is consistent with data. Values of the symmetry breaking scale as low as 500 GeV are allowed, indicating that no significant fine tuning in the Higgs potential is required. We identify a region within the allowed parameter space in which the lightest T-odd particle, the partner of the hypercharge gauge boson, has the correct relic abundance to play the role of dark matter. In addition, we find that a consistent fit to data can be obtained for large values of the Higgs mass, up to 800 GeV, due to the possibility of a partial cancellation between the contributions to the T parameter from Higgs loops and new physics.Comment: 23 pages, 9 figures. Minor correction