arXiv subjects

Van M. Savage

Publications and source records attributed to Van M. Savage.

10 recordsLinked to original sources

arXiv2020

Branching principles of animal and plant networks identified by combining extensive data, machine learning, and modeling

Branching in vascular networks and in overall organismic form is one of the most common and ancient features of multicellular plants, fungi, and animals. By combining machine-learning techniques with new theory that relates vascular form to metabolic function, we enable novel classification of diverse branching networks--mouse lung, human head and torso, angiosperm and gymnosperm plants. We find that ratios of limb radii--which dictate essential biologic functions related to resource transport and supply--are best at distinguishing branching networks. We also show how variation in vascular and branching geometry persists despite observing a convergent relationship across organisms for how metabolic rate depends on body mass.

q-bio.QM↗

arXiv2015

Asymmetries arising from the space-filling nature of vascular networks

Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the capillary level. The structural features of the network that accomplish this density and ubiquity of capillaries are often called space-filling. There are multiple strategies to fill a space, but some strategies do not lead to biologically adaptive structures by requiring too much construction material or space, delivering resources too slowly, or using too much power to move blood through the system. We empirically measure the structure of real networks (18 humans and 1 mouse) and compare these observations with predictions of model networks that are space-filling and constrained by a few guiding biological principles. We devise a numerical method that enables the investigation of space-filling strategies and determination of which biological principles influence network structure. Optimization for only a single principle creates unrealistic networks that represent an extreme limit of the possible structures that could be observed in nature. We first study these extreme limits for two competing principles, minimal total material and minimal path lengths. We combine these two principles and enforce various thresholds for balance in the network hierarchy, which provides a novel approach that highlights the trade-offs faced by biological networks and yields predictions that better match our empirical data.

physics.med-ph↗

arXiv2015

Scaling from traits to ecosystems: Developing a general Trait Driver Theory via integrating trait-based and metabolic scaling theories

The rise of trait-based ecology has led to an increased focus on the distribution and dynamics of traits in communities. However, a general theory of trait-based ecology, that can apply across different scales (e.g., species that differ in size) and gradients (e.g., temperature), has yet to be formulated. While research focused on metabolic and allometric scaling theory provides the basis for such a theory it does not explicitly account for differences traits within and across taxa, such as variation in the optimal temperature for growth. Here we synthesize trait-based and metabolic scaling approaches into a framework that we term Trait Drivers Theory or TDT. It shows that the shape and dynamics of trait distributions can be uniquely linked to fundamental drivers of community assembly and how the community will respond to future drivers. To assess predictions and assumptions of TDT, we review several theoretical studies, recent empirical studies spanning local and biogeographic gradients. Further, we analyze how the shift in trait distributions influences ecosystem productivity across an elevational gradient and a 140-year long ecological experiment. We argue that our general TDT provides a baseline for (i) recasting the predictions of ecological theories based on species richness in terms of the shape of trait distributions; and (ii) integrating how specific traits, including body size, and functional diversity scale up to influence the dynamics of species assemblages across climatic gradients and how shifts in functional composition influences ecosystem functioning. Further, it offers a novel framework to integrate trait, metabolic/allometric, and species-richness based approaches in order to build a more predictive functional biogeography to show how assemblages of species have and will respond to climate change.

q-bio.PE↗

arXiv2005

Towards a Quantitative, Metabolic Theory for Mammalian Sleep

Sleep is one of the most noticeable and widespread phenomena occurring in multicellular animals. Nevertheless, no consensus for a theory of its origins has emerged. In particular, no explicit, quantitative theory exists that elucidates or distinguishes between the myriad hypotheses proposed for sleep. Here, we develop a general, quantitative theory for mammalian sleep that relates many of its fundamental parameters to metabolic rate and body size. Most mechanisms suggested for the function of sleep can be placed in this framework, e.g., cellular repair of damage caused by metabolic processes and cortical reorganization to process sensory input. Our theory leads to predictions for sleep time, sleep cycle time, and REM (rapid-eye-movement) time as functions of body and brain mass, and explains, for example, why mice sleep \~14 hours per day relative to the 3.5 hours per day that elephants sleep. Data for 96 species of mammals, spanning six orders of magnitude in body size, are consistent with these predictions and provide strong evidence that time scales for sleep are set by the brain's, not the whole-body, metabolic rate.

q-bio.OT↗

arXiv2002

Red herrings and rotten fish

A longstanding problem in biology has been the origin of pervasive quarter-power allometric scaling laws that relate many characteristics of organisms to body mass (M) across the entire spectrum of life from molecules and microbes to ecosystems and mammals. In particular, whole-organism metabolic rate, B=aM^b, where a is a taxon-dependent normalisation constant and b is approximately equal to 3/4 for both animals and plants. Recently Darveau et al. (hereafter referred to as DSAH) proposed a "multiple-causes model" for B as "the sum of multiple contributors to metabolism", B_i, which were assumed to scale as M^(b_i). They obtained for average values of b: 0.78 for the basal rate and 0.86 for the maximally active rate. In this note we show that DSAH contains serious technical, theoretical and conceptual errors, including misrepresentations of published data and of our previous work. We also show that, within experimental error, there is no empirical evidence for an increase in b during aerobic activity as suggested by DSAH. Moreover, since DSAH consider only metabolic rates of mammals and make no attempt to explain why metabolic rates for other taxa and many other attributes in diverse organisms also scale with quarter-powers (including most of their input data), their formulation is hardly the "unifying principle" they claim. These problems were not addressed in commentaries by Weibel and Burness.

physics.bio-ph↗

arXiv2002

Dynamics of the chiral phase transition in the 2+1 dimensional Gross-Neveu model

The phase diagram of the Gross-Neveu (G-N) model in 2+1 dimensions as a function of chemical potential and temperature has a simple curve separating the broken symmetry and unbroken symmetry phases, with chiral symmetry being restored both at high temperature and high density. We study, in leading order in the 1/N expansion, the dynamics of the chiral phase transition for an expanding plasma of quarks in the Gross-Neveu model in 2+1 dimensions assuming boost invariant kinematics. We compare the time evolution of the order parameter (mass of the fermion) for evolutions starting in the unbroken and broken phases. The proper time evolution of the order parameter resembles previous results in the 1+1 dimensional G-N model in the same approximation. The time needed to traverse the transition is insensitive to mu.

hep-ph↗

arXiv2001

Numerical Simulations of PT-Symmetric Quantum Field Theories

Many non-Hermitian but PT-symmetric theories are known to have a real positive spectrum. Since the action is complex for there theories, Monte Carlo methods do not apply. In this paper the first field-theoretic method for numerical simulations of PT-symmetric Hamiltonians is presented. The method is the complex Langevin equation, which has been used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one-point and two-point Green's functions in zero and one dimension, where comparisons to known results can be made. The method should also be applicable in four-dimensional space-time. Our approach may also give insight into how to formulate a probabilistic interpretation of PT-symmetric theories.

hep-lat↗

arXiv1999

Solution of Schwinger-Dyson Equations for ${\cal PT}$-Symmetric Quantum Field Theory

In recent papers it has been observed that non-Hermitian Hamiltonians, such as those describing $igϕ^3$ and $-gϕ^4$ field theories, still possess real positive spectra so long as the weaker condition of ${\cal PT}$ symmetry holds. This allows for the possibility of new kinds of quantum field theories that have strange and quite unexpected properties. In this paper a technique based on truncating the Schwinger-Dyson equations is presented for renormalizing and solving such field theories. Using this technique it is argued that a $-gϕ^4$ scalar quantum field theory in four-dimensional space-time is renormalizable, is asymptotically free, has a nonzero value of $<0|ϕ|0>$, and has a positive definite spectrum. Such a theory might be useful in describing the Higgs boson.

hep-th↗

arXiv1999

Variational Ansatz for PT-Symmetric Quantum Mechanics

A variational calculation of the energy levels of a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian H= p^2 - (ix)^N with N positive and x complex is presented. Excellent agreement is obtained for the ground state and low lying excited state energy levels and wave functions. We use an energy functional with a three parameter class of PT-symmetric trial wave functions in obtaining our results.

quant-ph↗

arXiv1999

Complex Square Well --- A New Exactly Solvable Quantum Mechanical Model

Recently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian $H=p^2+x^2(ix)^ε$ was studied. It was found that the energy levels for this theory are real for all $ε\geq0$. Here, the limit as $ε\to\infty$ is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, $H=p^2+x^{2M}(ix)^ε$ (M=1,2,3,...) is also studied, and this PT-symmetric Hamiltonian becomes exactly solvable in the large-εlimit as well. In effect, what is obtained in each case is a complex analog of the Hamiltonian for the square well potential. Expansions about the large-εlimit are obtained.

quant-ph↗