2,946 research outputs found
Behavior of different numerical schemes for population genetic drift problems
In this paper, we focus on numerical methods for the genetic drift problems,
which is governed by a degenerated convection-dominated parabolic equation. Due
to the degeneration and convection, Dirac singularities will always be
developed at boundary points as time evolves. In order to find a \emph{complete
solution} which should keep the conservation of total probability and
expectation, three different schemes based on finite volume methods are used to
solve the equation numerically: one is a upwind scheme, the other two are
different central schemes. We observed that all the methods are stable and can
keep the total probability, but have totally different long-time behaviors
concerning with the conservation of expectation. We prove that any extra
infinitesimal diffusion leads to a same artificial steady state. So upwind
scheme does not work due to its intrinsic numerical viscosity. We find one of
the central schemes introduces a numerical viscosity term too, which is beyond
the common understanding in the convection-diffusion community. Careful
analysis is presented to prove that the other central scheme does work. Our
study shows that the numerical methods should be carefully chosen and any
method with intrinsic numerical viscosity must be avoided.Comment: 17 pages, 8 figure
Cascading failures in coupled networks with both inner-dependency and inter-dependency links
We study the percolation in coupled networks with both inner-dependency and
inter-dependency links, where the inner- and inter-dependency links represent
the dependencies between nodes in the same or different networks, respectively.
We find that when most of dependency links are inner- or inter-ones, the
coupled networks system is fragile and makes a discontinuous percolation
transition. However, when the numbers of two types of dependency links are
close to each other, the system is robust and makes a continuous percolation
transition. This indicates that the high density of dependency links could not
always lead to a discontinuous percolation transition as the previous studies.
More interestingly, although the robustness of the system can be optimized by
adjusting the ratio of the two types of dependency links, there exists a
critical average degree of the networks for coupled random networks, below
which the crossover of the two types of percolation transitions disappears, and
the system will always demonstrate a discontinuous percolation transition. We
also develop an approach to analyze this model, which is agreement with the
simulation results well.Comment: 9 pages, 4 figure
Effects of heritability on evolutionary cooperation in spatial prisoner’s dilemma games
AbstractWe study the effects of heritability on the evolution of the spatial prisoner’s dilemma game. In our model, the fitness of each player is composed of the instantaneous payoff from the interactions and the inherited fitness from the last generation. Based on extensive simulations, we find that the density of cooperators is enhanced by increasing the heritability of players over a wide range of the model parameter. The mean fitness of cooperators and defectors are also studied for understanding our results
Effects of aromatizable and nonaromatizable androgens on the sex inversion of red-spotted grouper (Epinephelus akaara)
The effects of aromatizable 17α-methyltestosterone (MT) and non-aromatizable 17α-methyldihydrotestosterone (MDHT) on sex inversion in red-spotted grouper, Epinephelus akaara, were investigated. Fish were implanted with MT, MDHT and MT+AI (aromatase inhibitor, AI) respectively for one month. The results showed that the three treated groups turned into transitional stage with intersex gonads, which contained atretic oocytes and spermatogenic germ cells at all stages of spermatogenesis. The controls did not change sex. The gonads of more than half MT-implanted fish were in early transitional stages of sex inversion, whereas those of more than half MDHT and MT+AI-implanted fish were in late transitional stages of sex inversion. No difference in serum estradiol-17β (E2) levels between the controls and the treated groups were observed, whereas 11-ketotestosterone (11-KT) and testosterone (T) levels increased in all treated groups. Significantly lower gonadosomatic index (GSI) and gonadal aromatase activity were observed in the treated groups, which were in accordance with the lower mRNA expression of P450aromA. However, P450aromB mRNA expression increased in the MT group, while it did not change in the MDHT group. These results suggest that the sex inversion of red-spotted grouper by MT and MDHT implantation might be due to the suppression of P450aromA gene expression, and resulting in both the decrease of the ovarian estrogen –secretion, as well as the increase in the 11-KT levels. Furthermore, the main reason for MT being less effective than MDHT might be due to partial aromatization of MT to estrogen
Information filtering based on transferring similarity
In this Brief Report, we propose a new index of user similarity, namely the
transferring similarity, which involves all high-order similarities between
users. Accordingly, we design a modified collaborative filtering algorithm,
which provides remarkably higher accurate predictions than the standard
collaborative filtering. More interestingly, we find that the algorithmic
performance will approach its optimal value when the parameter, contained in
the definition of transferring similarity, gets close to its critical value,
before which the series expansion of transferring similarity is convergent and
after which it is divergent. Our study is complementary to the one reported in
[E. A. Leicht, P. Holme, and M. E. J. Newman, Phys. Rev. E {\bf 73} 026120
(2006)], and is relevant to the missing link prediction problem.Comment: 4 pages, 4 figure
Depth penetration and scope extension of failures in the cascading of multilayer networks
Real-world complex systems always interact with each other, which causes
these systems to collapse in an avalanche or cascading manner in the case of
random failures or malicious attacks. The robustness of multilayer networks has
attracted great interest, where the modeling and theoretical studies of which
always rely on the concept of multilayer networks and percolation methods. A
straightforward and tacit assumption is that the interdependence across network
layers is strong, which means that a node will fail entirely with the removal
of all links if one of its interdependent neighbours fails. However, this
oversimplification cannot describe the general form of interactions across the
network layers in a real-world multilayer system. In this paper, we reveal the
nature of the avalanche disintegration of general multilayer networks with
arbitrary interdependency strength across network layers. Specifically, we
identify that the avalanche process of the whole system can essentially be
decomposed into two microscopic cascading dynamics in terms of the propagation
direction of the failures: depth penetration and scope extension. In the
process of depth penetration, the failures propagate from layer to layer, where
the greater the number of failed nodes is, the greater the destructive power
that will emerge in an interdependency group. In the process of scope
extension, failures propagate with the removal of connections in each network
layer. Under the synergy of the two processes, we find that the percolation
transition of the system can be discontinuous or continuous with changes in the
interdependency strength across network layers, which means that sudden
system-wide collapse can be avoided by controlling the interdependency strength
across network layers
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