Interspecific allometry of bone dimensions: A review of the theoretical models

A fascinating problem in biological scaling is the variation of long-bone length (or diameter) Y with body mass M in mammals, birds, and other vertebrates. It turns out that Y and M are related by a power law, namely Y=Y₀M^b, where Y₀ is a constant and b is the so-called allometric exponent. The origin of these power laws is still unclear because, in general, biological laws do not follow from physical ones in a simple manner.Here we make a historical review of this subject, summarizing the main experimental papers as well as discussing the main theoretical proposals. Long-bone allometry seems to be determined by the need to resist the particular loads applied to each bone in each taxon. Experimental measurements of in vivo stresses have found that mammalian long bones are subjected mainly to compression and bending, while avian wing-bones and reptilian limb-bones suffer a high degree of torsion. A recent model, based on the hypothesis that mammalian long-bone allometry is determined by compressive and bending loads, was able elucidate several aspects of mammalian limb-bone scaling. However, an explanation for avian and reptilian long-bone allometry is still missing.     

A mixed phase transition for a hierarchical spin glass

A proof of the existence of a mixed ferromagnetic (or antiferromagnetic)-spin-glass fixed point for an Ising spin-glass model on the diamond hierarchical lattice is given.     

Allometric scaling laws of metabolism

One of the most pervasive laws in biology is the allometric scaling, whereby a biological variable Y is related to the mass M of the organism by a power law, Y=Y₀M^b, where b is the so-called allometric exponent. The origin of these power laws is still a matter of dispute mainly because biological laws, in general, do not follow from physical ones in a simple manner. In this work, we review the interspecific allometry of metabolic rates, where recent progress in the understanding of the interplay between geometrical, physical and biological constraints has been achieved.

For many years, it was a universal belief that the basal metabolic rate (BMR) of all organisms is described by Kleiber's law (allometric exponent b=3/4). A few years ago, a theoretical basis for this law was proposed, based on a resource distribution network common to all organisms. Nevertheless, the 3/4-law has been questioned recently. First, there is an ongoing debate as to whether the empirical value of b is 3/4 or 2/3, or even nonuniversal. Second, some mathematical and conceptual errors were found these network models, weakening the proposed theoretical arguments. Another pertinent observation is that the maximal aerobically sustained metabolic rate of endotherms scales with an exponent larger than that of BMR. Here we present a critical discussion of the theoretical models proposed to explain the scaling of metabolic rates, and compare the predicted exponents with a review of the experimental literature. Our main conclusion is that although there is not a universal exponent, it should be possible to develop a unified theory for the common origin of the allometric scaling laws of metabolism.     

Static and time-dependent perturbations of the classical elliptical billiard

The elliptical billiard problem defines a two-dimensional integrable discrete dynamical system. Integrability not being a robust property, we study some static and time-dependent perturbations of this problem. For the static case, we observe the transition from integrability to chaos, on some perturbations of the ellipse. Then we study time-dependent perturbations, supposing that the boundary deforms periodically with the time, remaining always an ellipse. We investigate numerically the now four-dimensional phase space, looking mainly at the question of whether or not the velocity of a given trajectory may increase indefinitely.     

LOCAL NEUROTOXICITY OF HEMATOPORPHYRIN DERIVATIVE FOLLOWING INTRACEREBRAL INJECTION

The present study reports on toxicity of hematoporphyrin derivative (HpD) for normal brain tissue in vivo without the addition of light. Hematoporphyrin derivative was injected by slow infusion in rat brains. Histological examination was carried out for intervals after HpD administration, ranging from 0 h to 15 days. Ultrastructural changes were examinated with transmission electron microscopy. The extent of the necrosis was determined for different HpD concentrations and compared with control animals infused with 0.9% saline. Leukocytic infiltration was observed at day 5. Transmission electron microscopy showed that nuclei of neurons were completely disintegrated 4 h after HpD administration. Furthermore disruption of myelin sheaths was observed. The extent of the necrosis decreased with lower HpD doses. Injection of 2 μg HpD in a volume of 4 μL (0.5 mg/mL) resulted in a virtually equal extension of the tissue damage, as compared to the mechanical damage in the control animals caused by the infusion procedure.     

Scaling of dynamical properties of the Fermi-Ulam accelerator

We investigate numerically the chaotic sea of the complete Fermi-Ulam model (FUM) and of its simplified version (SFUM). We perform a scaling analysis near the integrable to non-integrable transition to describe the average energy as function of time t and as function of iteration (or collision) number n. When t is employed as independent variable, the exponents of FUM and SFUM are different. However, when n is used, the exponents are the same for both FUM and SFUM. In the collision number analysis, we present analytical arguments supporting the values of the exponents related to the control paramenter and to the initial velocity. We describe also how the scaling exponents obtained by using t as independent variable are related to the ones obtained with n. In contrast to SFUM, the average energy in FUM saturates for long times. We discuss the origin of the observed differences and similarities between FUM and its simplified version.     

Uniform asymptotics for compound Poisson processes with regularly varying jumps and vanishing drift

This paper addresses heavy-tailed large-deviation estimates for the distribution tail of functionals of a class of spectrally one-sided Lévy processes. Our contribution is to show that these estimates remain valid in a near-critical regime. This complements recent similar results that have been obtained for the all-time supremum of such processes. Specifically, we consider local asymptotics of the all-time supremum, the supremum of the process until exiting $[0,\infty )$, the maximum jump until that time, and the time it takes until exiting $[0,\infty )$. The proofs rely, among other things, on properties of scale functions.     

Fluorogenic Bifunctional trans-Cyclooctenes as Efficient Tools for Investigating Click-to-Release Kinetics

The inverse electron demand Diels–Alder pyridazine elimination reaction between tetrazines and allylic substituted trans-cyclooctenes (TCOs) is a key player in bioorthogonal bond cleavage reactions. Determining the rate of elimination of alkylamine substrates has so far proven difficult. Here, we report a fluorogenic tool consisting of a TCO-linked EDANS fluorophore and a DABCYL quencher for accurate determination of both the click and release rate constants for any tetrazine at physiologically relevant concentrations.     

Chaotic properties of the elliptical stadium

The elliptical stadium is a curve constructed by joining two half-ellipses, with half axesa>1 andb=1, by two straight segments of equal length 2h.Donnay [6] has shown that if 1 <a < and ifh is big enough, then the corresponding billiard map has a positive Lyapunov exponent almost everywhere; moreover,h asa In this work we prove that if , then assures the positiveness of a Lyapunov exponent. And we conclude that, for these values ofa andh, the elliptical stadium billiard mapping is ergodic and has theK-property.During this work, partially supported by Fac. de Ciencias, UruguayPartially supported by CNPq, Brasil