337 research outputs found
Simple expressions for the long walk distance
The walk distances in graphs are defined as the result of appropriate
transformations of the proximity measures, where
is the weighted adjacency matrix of a connected weighted graph and is a
sufficiently small positive parameter. The walk distances are graph-geodetic,
moreover, they converge to the shortest path distance and to the so-called long
walk distance as the parameter approaches its limiting values. In this
paper, simple expressions for the long walk distance are obtained. They involve
the generalized inverse, minors, and inverses of submatrices of the symmetric
irreducible singular M-matrix where is the Perron
root of Comment: 7 pages. Accepted for publication in Linear Algebra and Its
Application
Enough is not enough: Medical studentsâ knowledge of early warning signs of childhood cancer
Background. The reported incidence of childhood cancer in upper-middle-income South Africa (SA) is much lower than in high-income countries, partly due to under-diagnosis and under-reporting. Documented survival rates are disturbingly low, prompting an analysis of potential factors that may be responsible.Objectives. To determine final-year medical studentsâ level of knowledge of early warning signs of childhood cancer and whether a correlation existed between test scores and participantsâ age, gender and previous exposure to a person with cancer.Methods. A two-part questionnaire based on the Saint Siluan mnemonic, testing both recall and recognition of early warning signs of childhood cancer, was administered. The Mann-Whitney-Wilcoxon test was used to assess differences in continuous and count variables between demographic data, experience and responses, and Fisherâs exact test and Spearmanâs rank correlation coefficient were used to determine correlations between demographic data, previous contact with persons with cancer and test scores. A novel equality ratio was calculated to compare the recall and recognition sections and allowed analysis of recall v. recognition.Results. The 84 participants recalled a median of six signs each (interquartile range 4 - 7) and correctly recognised a median of 70% in the recognition section, considered a pass mark. There was no correlation between participantsâ age, gender, previous contact with a person with cancer and recognition scores. Students with previous exposure to a person with cancer had higher scores in the recall section, but this did not achieve statistical significance. Students were able to recognise more signs of haematological malignancies than central nervous system (CNS) malignancies.Conclusion. The study demonstrated a marked inconsistency between recall and recognition of signs of childhood cancer, with signs of CNS malignancies being least recognised. However, the majority of students could recognise enough early warning signs to meet the university pass standard. Although this study demonstrated acceptable recognition of early warning signs of childhood cancer at one university, we suggest that long-term recall in medical practitioners is poor, as reflected in the low age-standardised ratios of childhood cancer in SA. We recommend increased ongoing exposure to paediatric oncology in medical school and improved awareness programmes to increase early referrals
First- and second-order phase transitions in a driven lattice gas with nearest-neighbor exclusion
A lattice gas with infinite repulsion between particles separated by
lattice spacing, and nearest-neighbor hopping dynamics, is subject to a drive
favoring movement along one axis of the square lattice. The equilibrium (zero
drive) transition to a phase with sublattice ordering, known to be continuous,
shifts to lower density, and becomes discontinuous for large bias. In the
ordered nonequilibrium steady state, both the particle and order-parameter
densities are nonuniform, with a large fraction of the particles occupying a
jammed strip oriented along the drive. The relaxation exhibits features
reminiscent of models of granular and glassy materials.Comment: 8 pages, 5 figures; results due to bad random number generator
corrected; significantly revised conclusion
Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions
We address the thermodynamics (equilibrium density profiles, phase diagram,
instability analysis...) and the collapse of a self-gravitating gas of Brownian
particles in D dimensions, in both canonical and microcanonical ensembles. In
the canonical ensemble, we derive the analytic form of the density scaling
profile which decays as f(x)=x^{-\alpha}, with alpha=2. In the microcanonical
ensemble, we show that f decays as f(x)=x^{-\alpha_{max}}, where \alpha_{max}
is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in
the limit of large D. Finally, we solve the problem in D=2, which displays
rather rich and peculiar features
Structure Factors and Their Distributions in Driven Two-Species Models
We study spatial correlations and structure factors in a three-state
stochastic lattice gas, consisting of holes and two oppositely ``charged''
species of particles, subject to an ``electric'' field at zero total charge.
The dynamics consists of two nearest-neighbor exchange processes, occuring on
different times scales, namely, particle-hole and particle-particle exchanges.
Using both, Langevin equations and Monte Carlo simulations, we study the
steady-state structure factors and correlation functions in the disordered
phase, where density profiles are homogeneous. In contrast to equilibrium
systems, the average structure factors here show a discontinuity singularity at
the origin. The associated spatial correlation functions exhibit intricate
crossovers between exponential decays and power laws of different kinds. The
full probability distributions of the structure factors are universal
asymmetric exponential distributions.Comment: RevTex, 18 pages, 4 postscript figures included, mistaken half-empty
page correcte
Affine Gravity, Palatini Formalism and Charges
Affine gravity and the Palatini formalism contribute both to produce a simple
and unique formula for calculating charges at spatial and null infinity for
Lovelock type Lagrangians whose variational derivatives do not depend on
second-order derivatives of the field components. The method is based on the
covariant generalization due to Julia and Silva of the Regge-Teitelboim
procedure that was used to define properly the mass in the classical
formulation of Einstein's theory of gravity. Numerous applications reproduce
standard results obtained by other secure but mostly specialized methods. As a
novel application we calculate the Bondi energy loss in five dimensional
gravity, based on the asymptotic solution given by Tanabe, Tanahashi and
Shiromizu, and obtain, as expected, the same result. We also give the
superpotential for Einstein-Gauss-Bonnet gravity and find the superpotential
for Lovelock theories of gravity when the number of dimensions tends to
infinity with maximally symmetrical boundaries. The paper is written in
standard component formalism.Comment: The work is dedicated to Joshua Goldberg from whom I learned and got
interested in conservation laws in General Relativity (J.K
Charged BTZ-like Black Holes in Higher Dimensions
Motivated by many worthwhile paper about (2 + 1)-dimensional BTZ black holes,
we generalize them to to (n + 1)-dimensional solutions, so called BTZ-like
solutions. We show that the electric field of BTZ-like solutions is the same as
(2 + 1)-dimensional BTZ black holes, and also their lapse functions are
approximately the same, too. By these similarities, it is also interesting to
investigate the geometric and thermodynamics properties of the BTZ-like
solutions. We find that, depending on the metric parameters, the BTZ-like
solutions may be interpreted as black hole solutions with inner (Cauchy) and
outer (event) horizons, an extreme black hole or naked singularity. Then, we
calculate thermodynamics quantities and conserved quantities, and show that
they satisfy the first law of thermodynamics. Finally, we perform a stability
analysis in the canonical ensemble and show that the BTZ-like solutions are
stable in the whole phase space.Comment: 5 pages, two column format, one figur
Understanding Galaxy Formation and Evolution
The old dream of integrating into one the study of micro and macrocosmos is
now a reality. Cosmology, astrophysics, and particle physics intersect in a
scenario (but still not a theory) of cosmic structure formation and evolution
called Lambda Cold Dark Matter (LCDM) model. This scenario emerged mainly to
explain the origin of galaxies. In these lecture notes, I first present a
review of the main galaxy properties, highlighting the questions that any
theory of galaxy formation should explain. Then, the cosmological framework and
the main aspects of primordial perturbation generation and evolution are
pedagogically detached. Next, I focus on the ``dark side'' of galaxy formation,
presenting a review on LCDM halo assembling and properties, and on the main
candidates for non-baryonic dark matter. It is shown how the nature of
elemental particles can influence on the features of galaxies and their
systems. Finally, the complex processes of baryon dissipation inside the
non-linearly evolving CDM halos, formation of disks and spheroids, and
transformation of gas into stars are briefly described, remarking on the
possibility of a few driving factors and parameters able to explain the main
body of galaxy properties. A summary and a discussion of some of the issues and
open problems of the LCDM paradigm are given in the final part of these notes.Comment: 50 pages, 10 low-resolution figures (for normal-resolution, DOWNLOAD
THE PAPER (PDF, 1.9 Mb) FROM http://www.astroscu.unam.mx/~avila/avila.pdf).
Lectures given at the IV Mexican School of Astrophysics, July 18-25, 2005
(submitted to the Editors on March 15, 2006
Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
The mathematical theory of gravitational lensing has revealed many generic
and global properties. Beginning with multiple imaging, we review
Morse-theoretic image counting formulas and lower bound results, and
complex-algebraic upper bounds in the case of single and multiple lens planes.
We discuss recent advances in the mathematics of stochastic lensing, discussing
a general formula for the global expected number of minimum lensed images as
well as asymptotic formulas for the probability densities of the microlensing
random time delay functions, random lensing maps, and random shear, and an
asymptotic expression for the global expected number of micro-minima. Multiple
imaging in optical geometry and a spacetime setting are treated. We review
global magnification relation results for model-dependent scenarios and cover
recent developments on universal local magnification relations for higher order
caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of
General Relativity and Gravitatio
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