Convergent Chaos

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the 'butterfly effect' needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts

Inhomogeneous magnetization in dipolar ferromagnetic liquids

At high densities fluids of strongly dipolar spherical particles exhibit spontaneous long-ranged orientational order. Typically, due to demagnetization effects induced by the long range of the dipolar interactions, the magnetization structure is spatially inhomogeneous and depends on the shape of the sample. We determine this structure for a cubic sample by the free minimization of an appropriate microscopic density functional using simulated annealing. We find a vortex structure resembling four domains separated by four domain walls whose thickness increases proportional to the system size L. There are indications that for large L the whole configuration scales with the system size. Near the axis of the mainly planar vortex structure the direction of the magnetization escapes into the third dimension or, at higher temperatures, the absolute value of the magnetization is strongly reduced. Thus the orientational order is characterized by two point defects at the top and the bottom of the sample, respectively. The equilibrium structure in an external field and the transition to a homogeneous magnetization for strong fields are analyzed, too.Comment: 17 postscript figures included, submitted to Phys. Rev.

Conditional stability of unstable viscous shock waves in compressible gas dynamics and MHD

Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic--parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small $L^1\cap H^3$ perturbations, converging time-asymptotically to a translate of the unperturbed wave. That is, for a shock with $p$ unstable eigenvalues, we establish conditional stability on a codimension-$p$ manifold of initial data, with sharp rates of decay in all $L^p$. For $p=0$, we recover the result of unconditional stability obtained by Mascia and Zumbrun. The main new difficulty in the hyperbolic--parabolic case is to construct an invariant manifold in the absence of parabolic smoothing.Comment: 32p

Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential

The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schr\"odinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.Comment: 12 pages, 17 figure

Safety of low-carbohydrate diets

Low-carbohydrate diets have re-emerged into the public spotlight and are enjoying a high degree of popularity as people search for a solution to the population\u27s ever-expanding waistline. The current evidence though indicates that low-carbohydrate diets present no significant advantage over more traditional energy-restricted diets on long-term weight loss and maintenance. Furthermore, a higher rate of adverse side-effects can be attributed to low-carbohydrate dieting approaches. Short-term efficacy of low-carbohydrate diets has been demonstrated for some lipid parameters of cardiovascular risk and measures of glucose control and insulin sensitivity, but no studies have ascertained if these effects represent a change in primary outcome measures. Low-carbohydrate diets are likely effective and not harmful in the short term and may have therapeutic benefits for weight-related chronic diseases although weight loss on such a program should be undertaken under medical supervision. While new commercial incarnations of the low-carbohydrate diet are now addressing overall dietary adequacy by encouraging plenty of high-fibre vegetables, fruit, low-glycaemic-index carbohydrates and healthier fat sources, this is not the message that reaches the entire public nor is it the type of diet adopted by many people outside of the world of a well-designed clinical trial. Health effects of long-term ad hoc restriction of inherently beneficial food groups without a concomitant reduction in body weight remains unanswered.<br /

Reappraising Sexual Coevolution and the Sex Roles

Over recent decades, new ideas have radically altered how we see sex and reproduction. The implications of these ideas are still being explored, yielding intriguing discoveries

Evolution of Female Preference for Younger Males

Previous theoretical work has suggested that females should prefer to mate with older males, as older males should have higher fitness than the average fitness of the cohort into which they were born. However, studies in humans and model organisms have shown that as males age, they accumulate deleterious mutations in their germ-line at an ever-increasing rate, thereby reducing the quality of genes passed on to the next generation. Thus, older males may produce relatively poor-quality offspring. To better understand how male age influences female mate preference and offspring quality, we used a genetic algorithm model to study the effect of age-related increases in male genetic load on female mate preference. When we incorporate age-related increases in mutation load in males into our model, we find that females evolve a preference for younger males. Females in this model could determine a male's age, but not his inherited genotype nor his mutation load. Nevertheless, females evolved age-preferences that led them to mate with males that had low mutation loads, but showed no preference for males with respect to their somatic quality. These results suggest that germ-line quality, rather than somatic quality, should be the focus of female preference in good genes models

Localized breathing solutions for Bose-Einstein condensates in periodic traps

We demonstrate the existence of localized oscillatory breathers for quasi-one-dimensional Bose-Einstein condensates confined in periodic potentials. The breathing behavior corresponds to position-oscillations of individual condensates about the minima of the potential lattice. We deduce the structural stability of the localized oscillations from the construction. The stability is confirmed numerically for perturbations to the initial state of the condensate, to the potential trap, as well as for external noise. We also construct periodic and chaotic extended oscillations for the chain of condensates. All our findings are verified by direct numerical integration of the Gross-Pitaevskii equation in one dimension.Comment: LaTeX, 6 pages, 7 postscript figures, extended version of previous uploa

The untapped potential of reptile biodiversity for understanding how and why animals age

1.The field of comparative aging biology has greatly expanded in the past 20 years. Longitudinal studies of populations of reptiles with a range of maximum lifespans have accumulated and been analyzed for evidence of mortality senescence and reproductive decline. While not as well represented in studies of amniote senescence, reptiles have been the subjects of many recent demographic and mechanistic studies of the biology of aging. 2. We review recent literature on reptile demographic senescence, mechanisms of senescence, and identify unanswered questions. Given the ecophysiological and demographic diversity of reptiles, what is the expected range of reptile senescence rates? Are known mechanisms of aging in reptiles consistent with canonical hallmarks of aging in model systems? What are the knowledge gaps in our understanding of reptile aging? 3. We find ample evidence of increasing mortality with advancing age in many reptiles. Testudines stand out as slower aging than other orders, but data on crocodilians and tuatara are sparse. Sex‐specific analyses are generally not available. Studies of female reproduction suggest that reptiles are less likely to have reproductive decline with advancing age than mammals. 4. Reptiles share many physiological and molecular pathways of aging with mammals, birds, and laboratory model organisms. Adaptations related to stress physiology coupled with reptilian ectothermy suggest novel comparisons and contrasts that can be made with canonical aging phenotypes in mammals. These include stem cell and regeneration biology, homeostatic mechanisms, IIS/TOR signaling, and DNA repair. 5. To overcome challenges to the study of reptile aging, we recommend extending and expanding long‐term monitoring of reptile populations, developing reptile cell lines to aid cellular biology, conducting more comparative studies of reptile morphology and physiology sampled along relevant life‐history axes, and sequencing more reptile genomes for comparative genomics. Given the diversity of reptile life histories and adaptations, achieving these directives will likely greatly benefit all aging biology

Direct Selection on Genetic Robustness Revealed in the Yeast Transcriptome

Evolutionary theory predicts that organisms should evolve the ability to produce high fitness phenotypes in the face of environmental disturbances (environmental robustness) or genetic mutations (genetic robustness). While several studies have uncovered mechanisms that lead to both environmental and genetic robustness, we have yet to understand why some components of the genome are more robust than others. According to evolutionary theory, environmental and genetic robustness will have different responses to selective forces. Selection on environmental robustness for a trait is expected to be strong and related to the fitness costs of altering that trait. In contrast to environmental robustness, selection on genetic robustness for a trait is expected to be largely independent of the fitness cost of altering the trait and instead should correlate with the standing genetic variation for the trait that can potentially be buffered. Several mechanisms that provide both environmental and genetic robustness have been described, and this correlation could be explained by direct selection on both forms of robustness (direct selection hypothesis), or through selection on environmental robustness and a correlated response in genetic robustness (congruence hypothesis).Using both published and novel data on gene expression in the yeast Saccharomyces cerevisiae, we find that genetic robustness is correlated with environmental robustness across the yeast genome as predicted by the congruence hypothesis. However, we also show that environmental robustness, but not genetic robustness, is related to per-gene fitness effects. In contrast, genetic robustness is significantly correlated with network position, suggesting that genetic robustness has been under direct selection.We observed a significant correlation between our measures of genetic and environmental robustness, in agreement with the congruence hypothesis. However, this correlation alone cannot explain the co-variance of genetic robustness with position in the protein interaction network. We therefore conclude that direct selection on robustness has played a role in the evolution of genetic robustness in the transcriptome