2,685 research outputs found
Adaptation dynamics of the quasispecies model
We study the adaptation dynamics of an initially maladapted population
evolving via the elementary processes of mutation and selection. The evolution
occurs on rugged fitness landscapes which are defined on the multi-dimensional
genotypic space and have many local peaks separated by low fitness valleys. We
mainly focus on the Eigen's model that describes the deterministic dynamics of
an infinite number of self-replicating molecules. In the stationary state, for
small mutation rates such a population forms a {\it quasispecies} which
consists of the fittest genotype and its closely related mutants. The
quasispecies dynamics on rugged fitness landscape follow a punctuated (or
step-like) pattern in which a population jumps from a low fitness peak to a
higher one, stays there for a considerable time before shifting the peak again
and eventually reaches the global maximum of the fitness landscape. We
calculate exactly several properties of this dynamical process within a
simplified version of the quasispecies model.Comment: Proceedings of Statphys conference at IIT Guwahati, to be published
in Praman
Sample-Dependent Phase Transitions in Disordered Exclusion Models
We give numerical evidence that the location of the first order phase
transition between the low and the high density phases of the one dimensional
asymmetric simple exclusion process with open boundaries becomes sample
dependent when quenched disorder is introduced for the hopping rates.Comment: accepted in Europhysics Letter
Records and sequences of records from random variables with a linear trend
We consider records and sequences of records drawn from discrete time series
of the form , where the are independent and identically
distributed random variables and is a constant drift. For very small and
very large drift velocities, we investigate the asymptotic behavior of the
probability of a record occurring in the th step and the
probability that all entries are records, i.e. that . Our work is motivated by the analysis of temperature time series in
climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure
Geofysisch onderzoek binnen het \u27Nieuwerck\u27 van de kathedraal van Antwerpen (Antwerpen, provincie Antwerpen)
Van 11 tot en met 15 februari 2013 werd door ADEDE bvba in de tuin van het Nieuwerck te Antwerpen een non-destructieve geofysische prospectie uitgevoerd. Deze tuin bevindt zich ten oosten van de Onze-Lieve-Vrouwekathedraal, tussen de Groenplaats, de Melkmarkt en de Lijnwaadmarkt. De totale toegankelijke oppervlakte van het onderzoeksterrein (i. e. vrij van vegetatie) bedroeg 415m². Ondanks een verstoorde (puin)bodem en het versnipperde onderzoeksgebied (bomen, struiken en een vijver) was de inzet van geofysische detectiemethoden zinvol. De grondradar met 200MHz antenne leverde daarbij wel betere resultaten op dan de conductiviteits- en de magnetische susceptibiliteitmetingen met behulp van de EM31-MK2. Binnen het dossier van het Nieuwerck hebben de gekozen geofysische methodes aangetoond dat er een groot aantal structuren in de bodem kunnen geregistreerd worden, ook al is er een hoge graad van verstoring (door heterogene grond met puin). Na uitvoering van de detectie en terugkoppeling met bestaande boorgegevens konden met zekerheid drie en waarschijnlijk twaalf structuren herkend worden, alsook werd er een beeld gevormd van hoe de opbouw van de opvulling van het Nieuwerck in elkaar zit. Door de dikte van de opvulling konden dieperliggende structuren niet vastgesteld worden
Records in a changing world
In the context of this paper, a record is an entry in a sequence of random
variables (RV's) that is larger or smaller than all previous entries. After a
brief review of the classic theory of records, which is largely restricted to
sequences of independent and identically distributed (i.i.d.) RV's, new results
for sequences of independent RV's with distributions that broaden or sharpen
with time are presented. In particular, we show that when the width of the
distribution grows as a power law in time , the mean number of records is
asymptotically of order for distributions with a power law tail (the
\textit{Fr\'echet class} of extremal value statistics), of order
for distributions of exponential type (\textit{Gumbel class}), and of order
for distributions of bounded support (\textit{Weibull class}),
where the exponent describes the behaviour of the distribution at the
upper (or lower) boundary. Simulations are presented which indicate that, in
contrast to the i.i.d. case, the sequence of record breaking events is
correlated in such a way that the variance of the number of records is
asymptotically smaller than the mean.Comment: 12 pages, 2 figure
Evolutionary trajectories in rugged fitness landscapes
We consider the evolutionary trajectories traced out by an infinite
population undergoing mutation-selection dynamics in static, uncorrelated
random fitness landscapes. Starting from the population that consists of a
single genotype, the most populated genotype \textit{jumps} from a local
fitness maximum to another and eventually reaches the global maximum. We use a
strong selection limit, which reduces the dynamics beyond the first time step
to the competition between independent mutant subpopulations, to study the
dynamics of this model and of a simpler one-dimensional model which ignores the
geometry of the sequence space. We find that the fit genotypes that appear
along a trajectory are a subset of suitably defined fitness \textit{records},
and exploit several results from the record theory for non-identically
distributed random variables. The genotypes that contribute to the trajectory
are those records that are not \textit{bypassed} by superior records arising
further away from the initial population. Several conjectures concerning the
statistics of bypassing are extracted from numerical simulations. In
particular, for the one-dimensional model, we propose a simple relation between
the bypassing probability and the dynamic exponent which describes the scaling
of the typical evolution time with genome size. The latter can be determined
exactly in terms of the extremal properties of the fitness distribution.Comment: Figures in color; minor revisions in tex
Spontaneous Jamming in One-Dimensional Systems
We study the phenomenon of jamming in driven diffusive systems. We introduce
a simple microscopic model in which jamming of a conserved driven species is
mediated by the presence of a non-conserved quantity, causing an effective long
range interaction of the driven species. We study the model analytically and
numerically, providing strong evidence that jamming occurs; however, this
proceeds via a strict phase transition (with spontaneous symmetry breaking)
only in a prescribed limit. Outside this limit, the nearby transition
(characterised by an essential singularity) induces sharp crossovers and
transient coarsening phenomena. We discuss the relevance of the model to two
physical situations: the clustering of buses, and the clogging of a suspension
forced along a pipe.Comment: 8 pages, 4 figures, uses epsfig. Submitted to Europhysics Letter
Kinetic roughening of surfaces: Derivation, solution and application of linear growth equations
We present a comprehensive analysis of a linear growth model, which combines
the characteristic features of the Edwards--Wilkinson and noisy Mullins
equations. This model can be derived from microscopics and it describes the
relaxation and growth of surfaces under conditions where the nonlinearities can
be neglected. We calculate in detail the surface width and various correlation
functions characterizing the model. In particular, we study the crossover
scaling of these functions between the two limits described by the combined
equation. Also, we study the effect of colored and conserved noise on the
growth exponents, and the effect of different initial conditions. The
contribution of a rough substrate to the surface width is shown to decay
universally as , where is
the time--dependent correlation length associated with the growth process,
is the initial roughness and the correlation length of the
substrate roughness, and is the surface dimensionality. As a second
application, we compute the large distance asymptotics of the height
correlation function and show that it differs qualitatively from the functional
forms commonly used in the intepretation of scattering experiments.Comment: 28 pages with 4 PostScript figures, uses titlepage.sty; to appear in
Phys. Rev.
Non-neutral theory of biodiversity
We present a non-neutral stochastic model for the dynamics taking place in a
meta-community ecosystems in presence of migration. The model provides a
framework for describing the emergence of multiple ecological scenarios and
behaves in two extreme limits either as the unified neutral theory of
biodiversity or as the Bak-Sneppen model. Interestingly, the model shows a
condensation phase transition where one species becomes the dominant one, the
diversity in the ecosystems is strongly reduced and the ecosystem is
non-stationary. This phase transition extend the principle of competitive
exclusion to open ecosystems and might be relevant for the study of the impact
of invasive species in native ecologies.Comment: 4 pages, 3 figur
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