559 research outputs found
Recurrence spectrum in smooth dynamical systems
We prove that for conformal expanding maps the return time does have constant
multifractal spectrum. This is the counterpart of the result by Feng and Wu in
the symbolic setting
Replica Symmetry Breaking in the Random Replicant Model
We study the statistical mechanics of a model describing the coevolution of
species interacting in a random way. We find that at high competition replica
symmetry is broken. We solve the model in the approximation of one step replica
symmetry breaking and we compare our findings with accurate numerical
simulations.Comment: 12 pages, TeX, 5 postscript figures are avalaible upon request,
submitted to Journal of Physics A: Mathematical and Genera
Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)
In the context of smooth interval maps, we study an inducing scheme approach
to prove existence and uniqueness of equilibrium states for potentials
with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used
by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of
Perron-Frobenius operators. We demonstrate that this `bounded range' condition
on the potential is important even if the potential is H\"older continuous. We
also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues
and operator norms. Added extra references and corrected some typo
Not all intravenous immunoglobulin preparations are equally well tolerated
Intravenous immunoglobulin (IVIG) is used for many indications beyond the original substitution in primary antibody deficiency. Whereas many reports mention adverse reactions, no comparative data exist concerning the incidence of side-effects among the different brands of IVIG. We describe here our experience with the use of different IVIG formulations and their tolerability in a select cohort of 40 patients. The IVIG dose ranged from 0.4 to 3 g/kg/day and was given for 1–2742 days. Fourteen patients (35%) experienced mild to severe adverse reactions during or within 48 h of administration of standard IVIG preparation, which did not recur after switching to an alternative preparation. Adverse reactions included headache, fever, chills, nausea, emesis, hypotension and muscle cramps. One patient experienced a severe adverse reaction; he had a 3-day headache following IVIG infusion. Among the 16 patients who received alternative preparation initially, none experienced adverse reactions. In conclusion, this study shows that IVIG preparations are not all equally well tolerated in patients. The data suggest that, perhaps to a comparable extent to the preparation itself, the infusion rate has a major effect. If a reduction in the infusion rate does not minimize side-effects, one should consider switching the IVIG formulation
An integrating factor matrix method to find first integrals
In this paper we developed an integrating factor matrix method to derive
conditions for the existence of first integrals. We use this novel method to
obtain first integrals, along with the conditions for their existence, for two
and three dimensional Lotka-Volterra systems with constant terms. The results
are compared to previous results obtained by other methods
Stochastic stability versus localization in chaotic dynamical systems
We prove stochastic stability of chaotic maps for a general class of Markov
random perturbations (including singular ones) satisfying some kind of mixing
conditions. One of the consequences of this statement is the proof of Ulam's
conjecture about the approximation of the dynamics of a chaotic system by a
finite state Markov chain. Conditions under which the localization phenomenon
(i.e. stabilization of singular invariant measures) takes place are also
considered. Our main tools are the so called bounded variation approach
combined with the ergodic theorem of Ionescu-Tulcea and Marinescu, and a random
walk argument that we apply to prove the absence of ``traps'' under the action
of random perturbations.Comment: 27 pages, LaTe
Oscillatory behaviour in a lattice prey-predator system
Using Monte Carlo simulations we study a lattice model of a prey-predator
system. We show that in the three-dimensional model populations of preys and
predators exhibit coherent periodic oscillations but such a behaviour is absent
in lower-dimensional models. Finite-size analysis indicate that amplitude of
these oscillations is finite even in the thermodynamic limit. In our opinion,
this is the first example of a microscopic model with stochastic dynamics which
exhibits oscillatory behaviour without any external driving force. We suggest
that oscillations in our model are induced by some kind of stochastic
resonance.Comment: 7 pages, 10 figures, Phys.Rev.E (Nov. 1999
Evolutionary games and quasispecies
We discuss a population of sequences subject to mutations and
frequency-dependent selection, where the fitness of a sequence depends on the
composition of the entire population. This type of dynamics is crucial to
understand the evolution of genomic regulation. Mathematically, it takes the
form of a reaction-diffusion problem that is nonlinear in the population state.
In our model system, the fitness is determined by a simple mathematical game,
the hawk-dove game. The stationary population distribution is found to be a
quasispecies with properties different from those which hold in fixed fitness
landscapes.Comment: 7 pages, 2 figures. Typos corrected, references updated. An exact
solution for the hawks-dove game is provide
Coexistence and Survival in Conservative Lotka-Volterra Networks
Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time
On the Lebesgue measure of Li-Yorke pairs for interval maps
We investigate the prevalence of Li-Yorke pairs for and
multimodal maps with non-flat critical points. We show that every
measurable scrambled set has zero Lebesgue measure and that all strongly
wandering sets have zero Lebesgue measure, as does the set of pairs of
asymptotic (but not asymptotically periodic) points.
If is topologically mixing and has no Cantor attractor, then typical
(w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally
admits an absolutely continuous invariant probability measure (acip), then
typical pairs have a dense orbit for . These results make use of
so-called nice neighborhoods of the critical set of general multimodal maps,
and hence uniformly expanding Markov induced maps, the existence of either is
proved in this paper as well.
For the setting where has a Cantor attractor, we present a trichotomy
explaining when the set of Li-Yorke pairs and distal pairs have positive
two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure
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