17,992 research outputs found
Epidemic Model with Isolation in Multilayer Networks
The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the
propagation of such airborne diseases as influenza A (H1N1). Although the SIR
model has recently been studied in a multilayer networks configuration, in
almost all the research the isolation of infected individuals is disregarded.
Hence we focus our study in an epidemic model in a two-layer network, and we
use an isolation parameter to measure the effect of isolating infected
individuals from both layers during an isolation period. We call this process
the Susceptible-Infected-Isolated-Recovered () model. The isolation
reduces the transmission of the disease because the time in which infection can
spread is reduced. In this scenario we find that the epidemic threshold
increases with the isolation period and the isolation parameter. When the
isolation period is maximum there is a threshold for the isolation parameter
above which the disease never becomes an epidemic. We also find that epidemic
models, like overestimate the theoretical risk of infection. Finally, our
model may provide a foundation for future research to study the temporal
evolution of the disease calibrating our model with real data.Comment: 18 pages, 5 figures.Accepted in Scientific Report
Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies
The Ebola virus is spreading throughout West Africa and is causing thousands
of deaths. In order to quantify the effectiveness of different strategies for
controlling the spread, we develop a mathematical model in which the
propagation of the Ebola virus through Liberia is caused by travel between
counties. For the initial months in which the Ebola virus spreads, we find that
the arrival times of the disease into the counties predicted by our model are
compatible with World Health Organization data, but we also find that reducing
mobility is insufficient to contain the epidemic because it delays the arrival
of Ebola virus in each county by only a few weeks. We study the effect of a
strategy in which safe burials are increased and effective hospitalisation
instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii)
one in mid-August---which was the actual time that strong interventions began
in Liberia. We find that if scenario (i) had been pursued the lifetime of the
epidemic would have been three months shorter and the total number of infected
individuals 80\% less than in scenario (ii). Our projection under scenario (ii)
is that the spreading will stop by mid-spring 2015
Bigger Bursts From Merging Neutron Stars
GRB 990123 may have radiated more than one solar mass equivalent in just its
gamma emissions. Though this may be within the upper limit of the binding
energy available from neutron stars in the Schwarzschild metric, it is
difficult to imagine a process with the required efficiency of conversion to
gamma rays. Neutron stars of ~10 solar mass are permitted in the Yilmaz metric.
A merger of two neutron stars of maximum mass could release approximately 10
solar mass equivalent binding energy.Comment: 5 pages, 1 figure, submitted to ApJ Letter
Epidemic model with isolation in multilayer networks
The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network and we use an isolation parameter w to measure the effect of quarantining infected individuals from both layers during an isolation period tw. We call this process the Susceptible-Infected-Isolated-Recovered (SIIR) model. Using the framework of link percolation we find that isolation increases the critical epidemic threshold of the disease because the time in which infection can spread is reduced. In this scenario we find that this threshold increases with w and tw. When the isolation period is maximum there is a critical threshold for w above which the disease never becomes an epidemic. We simulate the process and find an excellent agreement with the theoretical results.We thank the NSF (grants CMMI 1125290 and CHE-1213217) and the Keck Foundation for financial support. LGAZ and LAB wish to thank to UNMdP and FONCyT (Pict 0429/2013) for financial support. (CMMI 1125290 - NSF; CHE-1213217 - NSF; Keck Foundation; UNMdP; Pict 0429/2013 - FONCyT)Published versio
Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
A key problem in making precise perturbative QCD predictions is to set the
proper renormalization scale of the running coupling. The extended
renormalization group equations, which express the invariance of physical
observables under both the renormalization scale- and scheme-parameter
transformations, provide a convenient way for estimating the scale- and
scheme-dependence of the physical process. In this paper, we present a solution
for the scale-equation of the extended renormalization group equations at the
four-loop level. Using the principle of maximum conformality (PMC) /
Brodsky-Lepage-Mackenzie (BLM) scale-setting method, all non-conformal
terms in the perturbative expansion series can be summed into the
running coupling, and the resulting scale-fixed predictions are independent of
the renormalization scheme. Different schemes lead to different effective
PMC/BLM scales, but the final results are scheme independent. Conversely, from
the requirement of scheme independence, one not only can obtain
scheme-independent commensurate scale relations among different observables,
but also determine the scale displacements among the PMC/BLM scales which are
derived under different schemes. In principle, the PMC/BLM scales can be fixed
order-by-order, and as a useful reference, we present a systematic and
scheme-independent procedure for setting PMC/BLM scales up to NNLO. An explicit
application for determining the scale setting of up to four
loops is presented. By using the world average , we obtain the asymptotic scale for the 't Hooft associated
with the scheme, MeV, and
the asymptotic scale for the conventional scheme,
MeV.Comment: 9 pages, no figures. The formulas in the Appendix are correcte
Scaling behavior in economics: II. Modeling of company growth
In the preceding paper we presented empirical results describing the growth
of publicly-traded United States manufacturing firms within the years
1974--1993. Our results suggest that the data can be described by a scaling
approach. Here, we propose models that may lead to some insight into these
phenomena. First, we study a model in which the growth rate of a company is
affected by a tendency to retain an ``optimal'' size. That model leads to an
exponential distribution of the logarithm of the growth rate in agreement with
the empirical results. Then, we study a hierarchical tree-like model of a
company that enables us to relate the two parameters of the model to the
exponent , which describes the dependence of the standard deviation of
the distribution of growth rates on size. We find that , where defines the mean branching ratio of the hierarchical tree and
is the probability that the lower levels follow the policy of higher
levels in the hierarchy. We also study the distribution of growth rates of this
hierarchical model. We find that the distribution is consistent with the
exponential form found empirically.Comment: 19 pages LateX, RevTeX 3, 6 figures, to appear J. Phys. I France
(April 1997
Scaling behavior in economics: I. Empirical results for company growth
We address the question of the growth of firm size. To this end, we analyze
the Compustat data base comprising all publicly-traded United States
manufacturing firms within the years 1974-1993. We find that the distribution
of firm sizes remains stable for the 20 years we study, i.e., the mean value
and standard deviation remain approximately constant. We study the distribution
of sizes of the ``new'' companies in each year and find it to be well
approximated by a log-normal. We find (i) the distribution of the logarithm of
the growth rates, for a fixed growth period of one year, and for companies with
approximately the same size displays an exponential form, and (ii) the
fluctuations in the growth rates -- measured by the width of this distribution
-- scale as a power law with , . We find
that the exponent takes the same value, within the error bars, for
several measures of the size of a company. In particular, we obtain:
for sales, for number of employees,
for assets, for cost of goods sold, and
for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France
(April 1997
Universal behavior of optimal paths in weighted networks with general disorder
We study the statistics of the optimal path in both random and scale free
networks, where weights are taken from a general distribution . We
find that different types of disorder lead to the same universal behavior.
Specifically, we find that a single parameter ( for
-dimensional lattices, and for random networks)
determines the distributions of the optimal path length, including both strong
and weak disorder regimes. Here is the percolation connectivity exponent,
and depends on the percolation threshold and . For uniform,
Poisson or Gaussian the crossover from weak to strong does not occur, and only
weak disorder exists.Comment: Accepted by PR
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