TY - JOUR
AB - The growth function of populations is central in biomathematics. The main dogma is the existence of density-dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the Population. One important class of regulatory functions is the theta-logistic, which generalizes the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter rho and a competition coefficient theta. Distinct sign combinations of these parameters reproduce not only the family of theta-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population. (c) 2005 Elsevier Ltd. All rights reserved.
AU - de Vladar, Harold
ID - 4237
IS - 2
JF - Journal of Theoretical Biology
TI - Density-dependence as a size-independent regulatory mechanism
VL - 238
ER -
TY - JOUR
AB - We study the extent to which the Hausdorff dimension of a compact subset of an infinite-dimensional Banach space is affected by a typical mapping into a finite-dimensional space. It is possible that the dimension drops under all such mappings, but the amount by which it typically drops is controlled by the ‘thickness exponent’ of the set, which was defined by Hunt and Kaloshin (Nonlinearity12 (1999), 1263–1275). More precisely, let $X$ be a compact subset of a Banach space $B$ with thickness exponent $\tau$ and Hausdorff dimension $d$. Let $M$ be any subspace of the (locally) Lipschitz functions from $B$ to $\mathbb{R}^{m}$ that contains the space of bounded linear functions. We prove that for almost every (in the sense of prevalence) function $f \in M$, the Hausdorff dimension of $f(X)$ is at least $\min\{ m, d / (1 + \tau) \}$. We also prove an analogous result for a certain part of the dimension spectra of Borel probability measures supported on $X$. The factor $1 / (1 + \tau)$ can be improved to $1 / (1 + \tau / 2)$ if $B$ is a Hilbert space. Since dimension cannot increase under a (locally) Lipschitz function, these theorems become dimension preservation results when $\tau = 0$. We conjecture that many of the attractors associated with the evolution equations of mathematical physics have thickness exponent zero. We also discuss the sharpness of our results in the case $\tau > 0$.
AU - OTT, WILLIAM
AU - HUNT, BRIAN
AU - Kaloshin, Vadim
ID - 8514
IS - 3
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
TI - The effect of projections on fractal sets and measures in Banach spaces
VL - 26
ER -
TY - CONF
AB - We consider the evolution of a set carried by a space periodic incompressible stochastic flow in a Euclidean space. We
report on three main results obtained in [8, 9, 10] concerning long time behaviour for a typical realization of the stochastic flow. First, at time t most of the particles are at a distance of order √t away from the origin. Moreover, we prove a Central Limit Theorem for the evolution of a measure carried by the flow, which holds for almost every realization of the flow. Second, we show the existence of a zero measure full Hausdorff dimension set of points, which
escape to infinity at a linear rate. Third, in the 2-dimensional case, we study the set of points visited by the original set by time t. Such a set, when scaled down by the factor of t, has a limiting non random shape.
AU - Kaloshin, Vadim
AU - DOLGOPYAT, D.
AU - KORALOV, L.
ID - 8515
SN - 9789812562012
T2 - XIVth International Congress on Mathematical Physics
TI - Long time behaviour of periodic stochastic flows
ER -
TY - JOUR
AU - Kaloshin, Vadim
AU - Saprykina, Maria
ID - 8513
IS - 2
JF - Discrete & Continuous Dynamical Systems - A
SN - 1553-5231
TI - Generic 3-dimensional volume-preserving diffeomorphisms with superexponential growth of number of periodic orbits
VL - 15
ER -
TY - JOUR
AB - We demonstrate the feasibility of recording 1H–15N correlation spectra of proteins in only one second of acquisition time. The experiment combines recently proposed SOFAST-HMQC with Hadamard-type 15N frequency encoding. This allows site-resolved real-time NMR studies of kinetic processes in proteins with an increased time resolution. The sensitivity of the experiment is sufficient to be applicable to a wide range of molecular systems available at millimolar concentration on a high magnetic field spectrometer.
AU - Schanda, Paul
AU - Brutscher, Bernhard
ID - 8490
IS - 2
JF - Journal of Magnetic Resonance
KW - Nuclear and High Energy Physics
KW - Biophysics
KW - Biochemistry
KW - Condensed Matter Physics
SN - 1090-7807
TI - Hadamard frequency-encoded SOFAST-HMQC for ultrafast two-dimensional protein NMR
VL - 178
ER -