19,692 research outputs found
Analytical Solution of the Voter Model on Disordered Networks
We present a mathematical description of the voter model dynamics on
heterogeneous networks. When the average degree of the graph is
the system reaches complete order exponentially fast. For , a finite
system falls, before it fully orders, in a quasistationary state in which the
average density of active links (links between opposite-state nodes) in
surviving runs is constant and equal to , while an
infinite large system stays ad infinitum in a partially ordered stationary
active state. The mean life time of the quasistationary state is proportional
to the mean time to reach the fully ordered state , which scales as , where is the number of nodes of the
network, and is the second moment of the degree distribution. We find
good agreement between these analytical results and numerical simulations on
random networks with various degree distributions.Comment: 20 pages, 8 figure
Burnout Assessment Tool (BAT): Validity evidence from Brazil and Portugal
The Burnout Assessment Tool (BAT) is gaining increased attention as a sound and innovative instrument in its conceptualization of burnout. BAT has been adapted by several countries, revealing promising validity evidence. This paper aims to present the psychometric properties of the Brazilian and Portuguese versions of the BAT in both the 23-item and 12-item versions. BAT’s validity evidence based on the internal structure (dimensionality, reliability, and measurement invariance) and validity evidence based on the relations to other variables are the focus of research. A cross-sectional study was conducted with two non-probabilistic convenience samples from two countries (N = 3103) one from Brazil (nBrazil = 2217) and one from Portugal (nPortugal = 886). BAT’s original structure was confirmed, and it achieved measurement invariance across countries. Using both classic test theory and item response theory as frameworks, the BAT presented good validity evidence based on the internal structure. Furthermore, the BAT showed good convergent evidence (i.e., work engagement, co-worker support, role clarity, work overload, and negative change). In conclusion, the psychometric properties of the BAT make this freely available instrument a promising way to measure and compare burnout levels of Portuguese and Brazilian workers.info:eu-repo/semantics/publishedVersio
Preferential attachment in the protein network evolution
The Saccharomyces cerevisiae protein-protein interaction map, as well as many
natural and man-made networks, shares the scale-free topology. The preferential
attachment model was suggested as a generic network evolution model that yields
this universal topology. However, it is not clear that the model assumptions
hold for the protein interaction network. Using a cross genome comparison we
show that (a) the older a protein, the better connected it is, and (b) The
number of interactions a protein gains during its evolution is proportional to
its connectivity. Therefore, preferential attachment governs the protein
network evolution. The evolutionary mechanism leading to such preference and
some implications are discussed.Comment: Minor changes per referees requests; to appear in PR
Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit
In the present work we study numerically quasi-equatorial lensing by the
charged, stationary, axially-symmetric Kerr-Sen dilaton-axion black hole in the
strong deflection limit. In this approximation we compute the magnification and
the positions of the relativistic images. The most outstanding effect is that
the Kerr-Sen black hole caustics drift away from the optical axis and shift in
clockwise direction with respect to the Kerr caustics. The intersections of the
critical curves on the equatorial plane as a function of the black hole angular
momentum are found, and it is shown that they decrease with the increase of the
parameter . All of the lensing quantities are compared to particular
cases as Schwarzschild, Kerr and Gibbons-Maeda black holes.Comment: 31 pages, 17 figures; V2 references added, some typos corrected, V3
references added, language corrections, V4 table added, minor technical
correction
Gravitational Lensing by Rotating Naked Singularities
We model massive compact objects in galactic nuclei as stationary,
axially-symmetric naked singularities in the Einstein-massless scalar field
theory and study the resulting gravitational lensing. In the weak deflection
limit we study analytically the position of the two weak field images, the
corresponding signed and absolute magnifications as well as the centroid up to
post-Newtonian order. We show that there are a static post-Newtonian
corrections to the signed magnification and their sum as well as to the
critical curves, which are function of the scalar charge. The shift of the
critical curves as a function of the lens angular momentum is found, and it is
shown that they decrease slightingly for the weakly naked and vastly for the
strongly naked singularities with the increase of the scalar charge. The
point-like caustics drift away from the optical axis and do not depend on the
scalar charge. In the strong deflection limit approximation we compute
numerically the position of the relativistic images and their separability for
weakly naked singularities. All of the lensing quantities are compared to
particular cases as Schwarzschild and Kerr black holes as well as
Janis--Newman--Winicour naked singularities.Comment: 35 pages, 30 figure
Coevolution of Glauber-like Ising dynamics on typical networks
We consider coevolution of site status and link structures from two different
initial networks: a one dimensional Ising chain and a scale free network. The
dynamics is governed by a preassigned stability parameter , and a rewiring
factor , that determines whether the Ising spin at the chosen site flips
or whether the node gets rewired to another node in the system. This dynamics
has also been studied with Ising spins distributed randomly among nodes which
lie on a network with preferential attachment. We have observed the steady
state average stability and magnetisation for both kinds of systems to have an
idea about the effect of initial network topology. Although the average
stability shows almost similar behaviour, the magnetisation depends on the
initial condition we start from. Apart from the local dynamics, the global
effect on the dynamics has also been studied. These parameters show interesting
variations for different values of and , which helps in determining
the steady-state condition for a given substrate.Comment: 8 pages, 10 figure
Lack of consensus in social systems
We propose an exactly solvable model for the dynamics of voters in a
two-party system. The opinion formation process is modeled on a random network
of agents. The dynamical nature of interpersonal relations is also reflected in
the model, as the connections in the network evolve with the dynamics of the
voters. In the infinite time limit, an exact solution predicts the emergence of
consensus, for arbitrary initial conditions. However, before consensus is
reached, two different metastable states can persist for exponentially long
times. One state reflects a perfect balancing of opinions, the other reflects a
completely static situation. An estimate of the associated lifetimes suggests
that lack of consensus is typical for large systems.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let
Analytical theory for the initial mass function: CO clumps and prestellar cores
We derive an analytical theory of the prestellar core initial mass function
based on an extension of the Press-Schechter statistical formalism. With the
same formalism, we also obtain the mass spectrum for the non self-gravitating
clumps produced in supersonic flows. The mass spectrum of the self-gravitating
cores reproduces very well the observed initial mass function and identifies
the different mechanisms responsible for its behaviour. The theory predicts
that the shape of the IMF results from two competing contributions, namely a
power-law at large scales and an exponential cut-off (lognormal form) centered
around the characteristic mass for gravitational collapse. The cut-off exists
already in the case of pure thermal collapse, provided that the underlying
density field has a lognormal distribution. Whereas pure thermal collapse
produces a power-law tail steeper than the Salpeter value, dN/dlog M\propto
M^{-x}, with x=1.35, this latter is recovered exactly for the (3D) value of the
spectral index of the velocity power spectrum, n\simeq 3.8, found in
observations and in numerical simulations of isothermal supersonic turbulence.
Indeed, the theory predicts that x=(n+1)/(2n-4) for self-gravitating structures
and x=2-n'/3 for non self-gravitating structures, where n' is the power
spectrum index of log(rho). We show that, whereas supersonic turbulence
promotes the formation of both massive stars and brown dwarfs, it has an
overall negative impact on star formation, decreasing the star formation
efficiency. This theory provides a novel theoretical foundation to understand
the origin of the IMF and to infer its behaviour in different environments. It
also provides a complementary approach and useful guidance to numerical
simulations exploring star formation, while making testable predictions.Comment: To appear in Ap
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