Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions

We consider the $d=1$ nonlinear Fokker-Planck-like equation with fractional derivatives $\frac{\partial}{\partial t}P(x,t)=D \frac{\partial^{\gamma}}{\partial x^{\gamma}}[P(x,t) ]^{\nu}$. Exact time-dependent solutions are found for $\nu = \frac{2-\gamma}{1+ \gamma}$ ($-\infty<\gamma \leq 2$). By considering the long-distance {\it asymptotic} behavior of these solutions, a connection is established, namely $q=\frac{\gamma+3}{\gamma+1}$ ($0<\gamma \le 2$), with the solutions optimizing the nonextensive entropy characterized by index $q$ . Interestingly enough, this relation coincides with the one already known for L\'evy-like superdiffusion (i.e., $\nu=1$ and $0<\gamma \le 2$). Finally, for $(\gamma,\nu)=(2, 0)$ we obtain $q=5/3$ which differs from the value $q=2$ corresponding to the $\gamma=2$ solutions available in the literature ($\nu<1$ porous medium equation), thus exhibiting nonuniform convergence.Comment: 3 figure

Reaction-diffusion systems and nonlinear waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.Comment: LaTeX, 16 pages, corrected typo

Enhancement of Stochastic Resonance in distributed systems due to a selective coupling

Recent massive numerical simulations have shown that the response of a "stochastic resonator" is enhanced as a consequence of spatial coupling. Similar results have been analytically obtained in a reaction-diffusion model, using "nonequilibrium potential" techniques. We now consider a field-dependent diffusivity and show that the "selectivity" of the coupling is more efficient for achieving stochastic-resonance enhancement than its overall value in the constant-diffusivity case.Comment: 10 pgs (RevTex), 4 figures, submitted to Phys.Rev.Let

Exact expression for the diffusion propagator in a family of time-dependent anharmonic potentials

We have obtained the exact expression of the diffusion propagator in the time-dependent anharmonic potential $V(x,t)={1/2}a(t)x^2+b\ln x$. The underlying Euclidean metric of the problem allows us to obtain analytical solutions for a whole family of the elastic parameter a(t), exploiting the relation between the path integral representation of the short time propagator and the modified Bessel functions. We have also analyzed the conditions for the appearance of a non-zero flow of particles through the infinite barrier located at the origin (b<0).Comment: RevTex, 19 pgs. Accepted in Physical Review

Stochastic resonance between dissipative structures in a bistable noise-sustained dynamics

We study an extended system that without noise shows a monostable dynamics, but when submitted to an adequate multiplicative noise, an effective bistable dynamics arise. The stochastic resonance between the attractors of the \textit{noise-sustained dynamics} is investigated theoretically in terms of a two-state approximation. The knowledge of the exact nonequilibrium potential allows us to obtain the output signal-to-noise ratio. Its maximum is predicted in the symmetric case for which both attractors have the same nonequilibrium potential value.Comment: RevTex, 13 pages, 6 figures, accepted in Physical Review

Rates of agonism among female primates: a cross-taxon perspective

Agonism is common in group-living animals, shaping dominance relationships and ultimately impacting individual tness. Rates of agonism vary considerably among taxa, however, and explaining this variation has been central in ecological models of female social relationships in primates. Early iterations of these models posited a link to diet, with more frequent agonism predicted in frugivorous species due to the presumed greater contestability of fruits relative to other food types. Although some more recent studies have suggested that dietary categories may be poor predictors of contest competition among primates, to date there have been no broad, cross-taxa comparisons of rates of female–female agonism in relation to diet. This study tests whether dietary variables do indeed pre- dict rates of female agonism and further investigates the role of group size (i.e., number of competitors) and substrate use (i.e., degree of arboreality) on the frequency of agonism. Data from 44 wild, unprovisioned groups, including 3 strepsirhine species, 3 platyrrhines, 5 colobines, 10 cercopithecines, and 2 hominoids were analyzed using phylogenetically controlled and uncontrolled methods. Results indicate that diet does not predict agonistic rates, with trends actually being in the opposite direction than predicted for all taxa except cercopithecines. In contrast, agonistic rates are positively associated with group size and possibly degree of terrestriality. Competitor density and perhaps the risk of ghting, thus, appear more important than general diet in predicting agonism among female primates. We discuss the implications of these results for socio-ecological hypotheses

Effects of local habitat variation on the behavioral ecology of two sympatric groups of brown howler monkey (alouatta clamitans)

Although the brown howler monkey (Alouatta clamitans) is a relatively well-studied Neotropical primate, its behavioral and dietary flexibility at the intra-population level remains poorly documented. This study presents data collected on the behavior and ecology of two closely located groups of brown howlers during the same period at the RPPN Feliciano Miguel Abdala in southeastern Brazil. One group occupied a primary valley habitat, henceforth the Valley Group (VG), and the other group occupied a regenerating hillside habitat, the Hill Group (HG). We hypothesized differences in the behavior and ecological parameters between these sympatric groups due to the predicted harsher conditions on the hillside, compared to the valley. We measured several habitat parameters within the home range of both groups and collected data on the activity budget, diet and day range lengths, from August to November 2005, between dawn and dusk. In total, behavioral data were collected for 26 (318 h) and 28 (308 h) sampling days for VG and HG, respectively. As we predicted, HG spent significantly more time feeding and consumed less fruit and more leaves than VG, consistent with our finding that the hillside habitat was of lower quality. However, HG also spent less time resting and more time travelling than VG, suggesting that the monkeys had to expend more time and energy to obtain high-energy foods, such as fruits and flowers that were more widely spaced in their hill habitat. Our results revealed that different locations in this forest vary in quality and raise the question of how different groups secure their home ranges. Fine-grained comparisons such as this are important to prioritize conservation and management areas within a reserve

Genetic Diversity and Population History of a Critically Endangered Primate, the Northern Muriqui (Brachyteles hypoxanthus)

Social, ecological, and historical processes affect the genetic structure of primate populations, and therefore have key implications for the conservation of endangered species. The northern muriqui (Brachyteles hypoxanthus) is a critically endangered New World monkey and a flagship species for the conservation of the Atlantic Forest hotspot. Yet, like other neotropical primates, little is known about its population history and the genetic structure of remnant populations. We analyzed the mitochondrial DNA control region of 152 northern muriquis, or 17.6% of the 864 northern muriquis from 8 of the 12 known extant populations and found no evidence of phylogeographic partitions or past population shrinkage/expansion. Bayesian and classic analyses show that this finding may be attributed to the joint contribution of female-biased dispersal, demographic stability, and a relatively large historic population size. Past population stability is consistent with a central Atlantic Forest Pleistocene refuge. In addition, the best scenario supported by an Approximate Bayesian Computation analysis, significant fixation indices (ΦST = 0.49, ΦCT = 0.24), and population-specific haplotypes, coupled with the extirpation of intermediate populations, are indicative of a recent geographic structuring of genetic diversity during the Holocene. Genetic diversity is higher in populations living in larger areas (>2,000 hectares), but it is remarkably low in the species overall (θ = 0.018). Three populations occurring in protected reserves and one fragmented population inhabiting private lands harbor 22 out of 23 haplotypes, most of which are population-exclusive, and therefore represent patchy repositories of the species' genetic diversity. We suggest that these populations be treated as discrete units for conservation management purposes

The long lives of primates and the ‘invariant rate of ageing’ hypothesis

Is it possible to slow the rate of ageing, or do biological constraints limit its plasticity? We test the ‘invariant rate of ageing’ hypothesis, which posits that the rate of ageing is relatively fixed within species, with a collection of 39 human and nonhuman primate datasets across seven genera. We first recapitulate, in nonhuman primates, the highly regular relationship between life expectancy and lifespan equality seen in humans. We next demonstrate that variation in the rate of ageing within genera is orders of magnitude smaller than variation in pre-adult and age-independent mortality. Finally, we demonstrate that changes in the rate of ageing, but not other mortality parameters, produce striking, species-atypical changes in mortality patterns. Our results support the invariant rate of ageing hypothesis, implying biological constraints on how much the human rate of ageing can be slowed

A Feedback Quenched Oscillator Produces Turing Patterning with One Diffuser

Efforts to engineer synthetic gene networks that spontaneously produce patterning in multicellular ensembles have focused on Turing's original model and the “activator-inhibitor” models of Meinhardt and Gierer. Systems based on this model are notoriously difficult to engineer. We present the first demonstration that Turing pattern formation can arise in a new family of oscillator-driven gene network topologies, specifically when a second feedback loop is introduced which quenches oscillations and incorporates a diffusible molecule. We provide an analysis of the system that predicts the range of kinetic parameters over which patterning should emerge and demonstrate the system's viability using stochastic simulations of a field of cells using realistic parameters. The primary goal of this paper is to provide a circuit architecture which can be implemented with relative ease by practitioners and which could serve as a model system for pattern generation in synthetic multicellular systems. Given the wide range of oscillatory circuits in natural systems, our system supports the tantalizing possibility that Turing pattern formation in natural multicellular systems can arise from oscillator-driven mechanisms