Publications (8)27.07 Total impact
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ABSTRACT: 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=Y0Mb, where b is the socalled 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 3/4law 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.  [Show abstract] [Hide abstract]
ABSTRACT: A fascinating problem in biological scaling is the variation of longbone 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=Y0Mb, where Y0 is a constant and b is the socalled 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. Longbone 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 wingbones and reptilian limbbones suffer a high degree of torsion. A recent model, based on the hypothesis that mammalian longbone allometry is determined by compressive and bending loads, was able elucidate several aspects of mammalian limbbone scaling. However, an explanation for avian and reptilian longbone allometry is still missing.  [Show abstract] [Hide abstract]
ABSTRACT: Extremal dynamics represents a path to selforganized criticality in which the order parameter is tuned to a value of zero. The order parameter is associated with a phase transition to an absorbing state. Given a process that exhibits a phase transition to an absorbing state, we define an "extremal absorbing" process, providing the link to the associated extremal (nonabsorbing) process. Stationary properties of the latter correspond to those at the absorbingstate phase transition in the former. Studying the absorbing version of an extremal dynamics model allows to determine certain critical exponents that are not otherwise accessible. In the case of the BakSneppen (BS) model, the absorbing version is closely related to the "f avalanche" introduced by Paczuski, Maslov, and Bak [Phys. Rev. E 53, 414 (1996)], or, in spreading simulations to the "BS branching process" also studied by these authors. The corresponding nonextremal process belongs to the directed percolation universality class. We revisit the absorbing BS model, obtaining refined estimates for the threshold and critical exponents in one dimension. We also study an extremal version of the usual contact process, using meanfield theory and simulation. The extremal condition slows the spread of activity and modifies the critical behavior radically, defining an "extremal directed percolation" universality class of absorbingstate phase transitions. Asymmetric updating is a relevant perturbation for this class, even though it is irrelevant for the corresponding nonextremal class.  [Show abstract] [Hide abstract]
ABSTRACT: Allometric scaling is one of the most pervasive laws in biology. Its origin, however, is still a matter of dispute. Recent studies have established that maximum metabolic rate scales with an exponent larger than that found for basal metabolism. This unpredicted result sets a challenge that can decide which of the concurrent hypotheses is the correct theory. Here we show that both scaling laws can be deduced from a single network model. Besides the 3/4law for basal metabolism, the model predicts that maximum metabolic rate scales as $M^{6/7}$, maximum heart rate as $M^{1/7}$, and muscular capillary density as $M^{1/7}$, in agreement with data. 
Article: On the thresholds, probability densities, and critical exponents of Bak–Sneppenlike models
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ABSTRACT: We report a simple method to accurately determine the threshold and the exponent ν of the Bak–Sneppen (BS) model and also investigate the BS universality class. For the randomneighbor version of the BS model, we find the threshold x∗=0.33332(3), in agreement with the exact result given by meanfield theory. For the onedimensional original model, we find x∗=0.6672(2) in good agreement with the results reported in the literature; for the anisotropic BS model we obtain x∗=0.7240(1). We study the finite size effect x∗(L)−x∗(L→∞)∝L−ν, observed in a system with L sites, and find ν=1.00(1) for the randomneighbor version, ν=1.40(1) for the original model, and ν=1.58(1) for the anisotropic case. Finally, we discuss the effect of defining the extremal site as the one which minimizes a general function f(x), instead of simply f(x)=x as in the original updating rule. We emphasize that models with extremal dynamics have singular stationary probability distributions p(x). Our simulations indicate the existence of two symmetrybased universality classes.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate, using meanfield theory and simulation, the effect of asymmetry on the critical behavior and probability density of Bak–Sneppen models. Two kinds of anisotropy are investigated: (i) different numbers of sites to the left and right of the central (minimum) site are updated and (ii) sites to the left and right of the central site are renewed in different ways. Of particular interest is the crossover from symmetric to asymmetric scaling for weakly asymmetric dynamics, and the collapse of data with different numbers of updated sites but the same degree of asymmetry. All nonsymmetric rules studied fall, independent of the degree of asymmetry, in the same universality class. Conversely, symmetric variants reproduce the exponents of the original model. Our results confirm the existence of two symmetrybased universality classes for extremal dynamics.  [Show abstract] [Hide abstract]
ABSTRACT: Although there is much data available on mammalian longbone allometry, a theory explaining these data is still lacking. We show that bending and axial compression are the relevant loading modes and elucidate why the elastic similarity model failed to explain the experimental data. Our analysis provides scaling relations connecting bone diameter and length to the axial and transverse components of the force, in good agreement with experimental data. The model also accounts for other important features of longbone allometry.  [Show abstract] [Hide abstract]
ABSTRACT: Extremal dynamics is the mechanism that drives the BakSneppen model into a (selforganized) critical state, marked by a singular stationary probability density p(x). With the aim of understanding this phenomenon, we study the BS model and several variants via meanfield theory and simulation. In all cases, we find that p(x) is singular at one or more points, as a consequence of extremal dynamics. Furthermore we show that the extremal barrier xi always belongs to the ‘prohibited’ interval, in which p(x)=0. Our simulations indicate that the BakSneppen universality class is robust with regard to changes in the updating rule: we find the same value for the exponent π for all variants. Meanfield theory, which furnishes an exact description for the model on a complete graph, reproduces the character of the probability distribution found in simulations. For the modified processes meanfield theory takes the form of a functional equation for p(x).
Publication Stats
108  Citations  
27.07  Total Impact Points  
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Institutions

20032005

Federal University of Minas Gerais
 Departamento de Física
Belo Horizonte, Estado de Minas Gerais, Brazil
