The Markovian metamorphosis of a simple turbulent cascade model

Markovian properties of a discrete random multiplicative cascade model of log-normal type are discussed. After taking small-scale resummation and breaking of the ultrametric hierarchy into account, qualitative agreement with Kramers-Moyal coefficients, recently deduced from a fully developed turbulent flow, is achieved.Comment: 6 pages, 2 figure

A late-time transition in the equation of state versus Lambda-CDM

We study a model of the dark energy which exhibits a rapid change in its equation of state w(z), such as occurs in vacuum metamorphosis. We compare the model predictions with CMB, large scale structure and supernova data and show that a late-time transition is marginally preferred over standard Lambda-CDM.Comment: 4 pages, 1 figure, to appear in the proceedings of XXXVIIth Rencontres de Moriond, "The Cosmological Model", March 200

Timing of Metamorphosis in a Freshwater Crustacean: Comparison with Anuran Models

Many crustaceans have complex life cycles characterized by a metamorphosis, yet variation in metamorphic traits, and the causes and consequences of this variation, have rarely been examined. Food concentrations were changed during specific larval stages of the freshwater copepod Mesocyclops edax Forbes (Copepoda: Cyclopoida) to examine whether age and size at metamorphosis remain flexible or become fixed during the larval period. Results were compared to predictions of both flexible (the Wilbur—Collins model) and fixed (Leips—Travis model) rate models for the timing of amphibian metamorphosis. Age and size at metamorphosis were variable in all treatments, and age was always more variable than size. Changes in food concentration early in larval development resulted in significant differences in age at metamorphosis among treatments, but changes initiated when 60% of the larval period had passed had no effect on age at metamorphosis. Development appeared to become fixed later in the larval period, before the ultimate larval stage was reached. These results support predictions of the Leips—Travis model. Early changes in food concentrations had significant effects on size at metamorphosis, but changes initiated during the penultimate larval stage (50—60% of larval development) had no effect on metamorph size. Size at metamorphosis in M. edax also appeared to be fixed before the ultimate larval stage was reached. Fixation of size at metamorphosis during development is not predicted by either model and may be unique to organisms with rigid exoskeletons that constrain growth within any stage. Patterns of covariation between age and size at metamorphosis suggest that food conditions early in larval development exert a large effect on metamorphic traits, in contrast to patterns observed in several amphibian species. The Wilbur—Collins model places a fitness premium on delaying metamorphosis to achieve a maximum size, when growth conditions are favorable; it thus may not apply to crustaceans. Selection pressures on the timing of metamorphosis in crustaceans may differ substantially from those identified for amphibians and other organisms. Because of these differences, incorporating crustaceans into studies of metamorphosis will help to clarify the factors affecting this life cycle transition

TRANSCRIPTIONAL AND MORPHOLOGICAL CHANGES DURING THYROXINE-INDUCED METAMORPHOSIS OF THE MEXICAN AXOLOTL AND AXOLOTL-TIGER SALAMANDER HYBRIDS

For nearly a century, amphibian metamorphosis has served as an important model of how thyroid hormones regulate vertebrate development. Consequently metamorphosis has been studied in a number of ways including: morphologically, developmentally, ecologically, and from an endocrine perspective. Over the last two decades, much has been learned about the molecular basis of anuran (frog) metamorphosis. However, very little is known about the molecular underpinnings of urodele (salamander) metamorphosis. Using the axolotl and axolotl hybrids as models, I present some of the first studies on the gene expression changes that occur during urodele metamorphosis. In Chapter 1, the motivation for the research described in the subsequent chapters is presented and the literature is briefly reviewed. In Chapter 2, the first microarray analysis of urodele metamorphosis is presented. This analysis shows that hundreds of genes are differentially expressed during thyroid hormone-induced metamorphic skin remodeling. Chapter 3 extends the analysis presented in Chapter 2 by showing that the transcriptional patterns associated with metamorphic skin remodeling are robust even when the concentration of thyroid hormone used to induce metamorphosis is varied by an order of magnitude. Chapter 4 makes use of the differentially expressed genes identified in Chapters 2 and 3 to articulate the first model of urodele metamorphosis to integrate changes in morphology, gene expression, and histology. In addition, Chapter 4 outlines a novel application for piecewise linear regression. In turn, Chapter 5 makes use of the model presented in Chapter 4 to demonstrate that full siblings segregating profound variation in metamorphic timing begin to diverge in phenotype early during larval development. In Chapter 6 the conclusions drawn from the research are summarized and future directions are suggested

Habitat deterioration promotes the evolution of direct development in metamorphosing species

Although metamorphosis is widespread in the animal kingdom, several species have evolved life-cycle modifications to avoid complete metamorphosis. Some species, for example, many salamanders and newts, have deleted the adult stage via a process called paedomorphosis. Others, for example, some frog species and marine invertebrates, no longer have a distinct larval stage and reach maturation via direct development. Here we study which ecological conditions can lead to the loss of metamorphosis via the evolution of direct development. To do so, we use size-structured consumer-resource models in conjunction with the adaptive-dynamics approach. In case the larval habitat deteriorates, individuals will produce larger offspring and in concert accelerate metamorphosis. Although this leads to the evolutionary transition from metamorphosis to direct development when the adult habitat is highly favorable, the population will go extinct in case the adult habitat does not provide sufficient food to escape metamorphosis. With a phylogenetic approach we furthermore show that among amphibians the transition of metamorphosis to direct development is indeed, in line with model predictions, conditional on and preceded by the evolution of larger egg sizes

Running gravitational couplings, decoupling, and curved spacetime renormalization

We propose to slightly generalize the DeWitt-Schwinger adiabatic renormalization subtractions in curved space to include an arbitrary renormalization mass scale $\mu$. The new predicted running for the gravitational couplings are fully consistent with decoupling of heavy massive fields. This is a somewhat improvement with respect to the more standard treatment of minimal (DeWitt-Schwinger) subtractions via dimensional regularization. We also show how the vacuum metamorphosis model emerges from the running couplings.Comment: Some points clarified, misprints corrected; to appear in Phys. Rev.

Lagrange-Poincare field equations

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem. The Kelvin-Noether theorem is formulated in this context. Applications to the isoperimetric problem, the Skyrme model for meson interaction, metamorphosis image dynamics, and molecular strands illustrate various aspects of the theory.Comment: Submitted to Journal of Geometry and Physics, 45 pages, 1 figur

Condensate cosmology -- dark energy from dark matter

Imagine a scenario in which the dark energy forms via the condensation of dark matter at some low redshift. The Compton wavelength therefore changes from small to very large at the transition, unlike quintessence or metamorphosis. We study CMB, large scale structure, supernova and radio galaxy constraints on condensation by performing a 4 parameter likelihood analysis over the Hubble constant and the three parameters associated with Q, the condensate field: Omega_Q, w_f and z_t (energy density and equation of state today, and redshift of transition). Condensation roughly interpolates between Lambda CDM (for large z_t) and sCDM (low z_t) and provides a slightly better fit to the data than Lambda CDM. We confirm that there is no degeneracy in the CMB between H and z_t and discuss the implications of late-time transitions for the Lyman-alpha forest. Finally we discuss the nonlinear phase of both condensation and metamorphosis, which is much more interesting than in standard quintessence models.Comment: 13 pages, 13 colour figures. Final version with discussion of TE cross-correlation spectra for condensation and metamorphosis in light of the WMAP result