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 Mathematics , 2012, Abstract: Recently heterogeneous base station structure has been adopted in cellular systems to enhance system throughput and coverage. In this paper, the uplink coverage probability for the heterogeneous cellular systems is analyzed and derived in closed-form. The randomness on the locations and number of mobile users is taken into account in the analysis. Based on the analytical results, the impacts of various system parameters on the uplink performance are investigated in detail. The correctness of the analytical results is also verified by simulation results. These analytical results can thus serve as a guidance for system design without the need of time consuming simulations.
 PLOS ONE , 2011, DOI: 10.1371/journal.pone.0021385 Abstract: This study investigates the genetic diversity, population structure and demographic history of the afrotropical butterfly Bicyclus anynana using mitochondrial DNA (mtDNA). Samples from six wild populations covering most of the species range from Uganda to South Africa were compared for the cytochrome c oxidase subunit gene (COI). Molecular diversity indices show overall high mtDNA diversity for the populations, but low nucleotide divergence between haplotypes. Our results indicate relatively little geographic population structure among the southern populations, especially given the extensive distributional range and an expectation of limited gene flow between populations. We implemented neutrality tests to assess signatures of recent historical demographic events. Tajima's D test and Fu's FS test both suggested recent population growth for the populations. The results were only significant for the southernmost populations when applying Tajima's D, but Fu's FS indicated significant deviations from neutrality for all populations except the one closest to the equator. Based on our own findings and those from pollen and vegetation studies, we hypothesize that the species range of B. anynana was reduced to equatorial refugia during the last glacial period, and that the species expanded southwards during the past 10.000 years. These results provide crucial background information for studies of phenotypic and molecular adaptation in wild populations of B. anynana.
 Quantitative Biology , 2010, DOI: 10.1103/PhysRevE.81.056108 Abstract: Up to now, the effects of having heterogeneous networks of contacts have been studied mostly for diseases which are not persistent in time, i.e., for diseases where the infectious period can be considered very small compared to the lifetime of an individual. Moreover, all these previous results have been obtained for closed populations, where the number of individuals does not change during the whole duration of the epidemics. Here, we go one step further and analyze, both analytically and numerically, a radically different kind of diseases: those that are persistent and can last for an individual's lifetime. To be more specific, we particularize to the case of Tuberculosis' (TB) infection dynamics, where the infection remains latent for a period of time before showing up and spreading to other individuals. We introduce an epidemiological model for TB-like persistent infections taking into account the heterogeneity inherent to the population structure. This sort of dynamics introduces new analytical and numerical challenges that we are able to sort out. Our results show that also for persistent diseases the epidemic threshold depends on the ratio of the first two moments of the degree distribution so that it goes to zero in a class of scale-free networks when the system approaches the thermodynamic limit.
 Quantitative Biology , 2013, DOI: 10.1371/journal.pcbi.1003567 Abstract: Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place. In particular, averaging payoffs garnered through game interactions rather than accumulating the payoffs can altogether remove the cooperative advantage of heterogeneous graphs while such a difference does not affect the outcome on homogeneous structures. In addition, the rate at which game interactions occur can alter the evolutionary outcome. Less interactions allow heterogeneous graphs to support more cooperation than homogeneous graphs, while higher rates of interactions make homogeneous and heterogeneous graphs virtually indistinguishable in their ability to support cooperation. Most importantly, we show that common measures of evolutionary advantage used in homogeneous populations, such as a comparison of the fixation probability of a rare mutant to that of the resident type, are no longer valid in heterogeneous populations. Heterogeneity causes a bias in where mutations occur in the population which affects the mutant's fixation probability. We derive the appropriate measures for heterogeneous populations that account for this bias.
 Computer Science , 2012, Abstract: We study the critical properties of a model of information spreading based on the SIS epidemic model. Spreading rates decay with time, as ruled by two parameters, $\epsilon$ and $l$, that can be either constant or randomly distributed in the population. The spreading dynamics is developed on top of Erd\"os-Renyi networks. We present the mean-field analytical solution of the model in its simplest formulation, and Monte Carlo simulations are performed for the more heterogeneous cases. The outcomes show that the system undergoes a nonequilibrium phase transition whose critical point depends on the parameters $\epsilon$ and $l$. In addition, we conclude that the more heterogeneous the population, the more favored the information spreading over the network.
 BMC Evolutionary Biology , 2010, DOI: 10.1186/1471-2148-10-382 Abstract: Species ranges are never fixed, but remain in continual flux in response to demographic, genetic, ecological and environmental variation. Colonization occurs at the range margin when populations spill over into new sites, typically followed by population extinction as environmental and other forces prevent persistence in these new habitats. As the climate has warmed, this turn-over has resulted in expansions that appear more permanent. Consistent northward range shifts have been documented for several vertebrate and invertebrate species in the northern hemisphere, but particularly Lepidoptera, whose historical distributions are usually well-known [1,2]. But what do colonizers look like in these new populations - are they just a sample of the main population or do they differ phenotypically or genotypically? How do these new populations adapt to the novel environmental conditions they encounter and is change likely to persist over longer time scales?Joji Otaki and co-workers [1] have charted recent range expansion in the beautifully named pale grass blue butterfly (Zizeeria maha). From 1990-2000, this species progressively marched more than 100 km up the west coast of Japan, towards the top of Honshu island - known in precise detail thanks to assiduous collecting of amateur Japanese lepidopterists. Similar northward movements are known in several other Japanese butterflies [1]. Temperature records suggest increasing summer temperatures facilitated the northward range shift.Accompanying this colonisation, the pale grass blue has undergone an outbreak of wing pattern diversification. Three novel ventral wing patterns are recognizable with either inner spot elongation, outer spot elongation or reduction of both inner and outer spots (Figure 1). Novel phenotypes occurred at high frequencies in the new environments (10-15%), but were hardly ever seen across the main species range. These individuals showed no other obvious phenotypic changes, and the response was not simil
 Physics , 2010, DOI: 10.1016/j.aop.2010.06.006 Abstract: We derive the generalization of Wigner's causality bounds and Bethe's integral formula for the effective range parameter to arbitrary dimension and arbitrary angular momentum. We also discuss the impact of these constraints on the separation of low- and high-momentum scales and universality in low-energy scattering. Some of our results were summarized earlier in a letter publication. In this work, we present full derivations and several detailed examples.
 Thomas D. Cohen Physics , 1999, Abstract: In this talk the $Q$ counting scheme to implement effective field theory is discussed. It is pointed out that there are two small mass scales in the problem $m_\pi$ and $1/a$ with $1/a \ll m_\pi$. It is argued that while the expansion based on $1/a$ being small compared to the underlying short distance scales works well, the chiral expansion may not. The coefficients of the effective range expansion are sensitive to the chiral physics and are very poorly described in $Q$ counting at lowest nontrivial order. A shape function'' is introduced which again is sensitive to pionic physics and insensitive to fitting procedures. It is also poorly described in $Q$ counting.
 Quantitative Biology , 2014, DOI: 10.1103/PhysRevLett.113.108102 Abstract: Phenotypic heterogeneity is a strategy commonly used by bacteria to rapidly adapt to changing environmental conditions. Here, we study the interplay between phenotypic heterogeneity and genetic diversity in spatially extended populations. By analyzing the spatio-temporal dynamics, we show that the level of mobility and the type of competition qualitatively influence the persistence of phenotypic heterogeneity. While direct competition generally promotes persistence of phenotypic heterogeneity, specialization dominates in models with indirect competition irrespective of the degree of mobility.
 Physics , 2015, Abstract: The phenomenon of radicalization is investigated within an heterogeneous population composed of a core subpopulation, sharing a way of life locally rooted, and a recently immigrated subpopulation of different origins with ways of life which can be partly in conflict with the local one. While core agents are embedded in the country prominent culture and identity, they are not likely to modify their way of life, which make them naturally inflexible about it. On the opposite, the new comers can either decide to live peacefully with the core people adapting their way of life, or to keep strictly on their way and oppose the core population, leading eventually to criminal activities. To study the corresponding dynamics of radicalization we introduce a 3-state agent model with a proportion of inflexible agents and a proportion of flexible ones, which can be either peaceful or opponent. Assuming agents interact via weighted pairs within a Lotka-Volterra like Ordinary Differential Equation framework, the problem is analytically solved exactly. Results shed a new light on the instrumental role core agents can play through individual activeness towards peaceful agents to either curb or inflate radicalization. Some hints are outlined at new possible public policies towards social integration.
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