54 research outputs found
Particle algorithms for population dynamics in flows
We present and discuss particle based algorithms to numerically study the dynamics of population subjected to an advecting flow condition. We discuss few possible variants of the algorithms and compare them in a model compressible flow. A comparison against appropriate versions of the continuum stochastic Fisher equation (sFKPP) is also presented and discussed. The algorithms can be used to study populations genetics in fluid environments.Postprint (published version
Macroscopic equations for the adiabatic piston
A simplified version of a classical problem in thermodynamics -- the
adiabatic piston -- is discussed in the framework of kinetic theory. We
consider the limit of gases whose relaxation time is extremely fast so that the
gases contained on the left and right chambers of the piston are always in
equilibrium (that is the molecules are uniformly distributed and their
velocities obey the Maxwell-Boltzmann distribution) after any collision with
the piston. Then by using kinetic theory we derive the collision statistics
from which we obtain a set of ordinary differential equations for the evolution
of the macroscopic observables (namely the piston average velocity and
position, the velocity variance and the temperatures of the two compartments).
The dynamics of these equations is compared with simulations of an ideal gas
and a microscopic model of gas settled to verify the assumptions used in the
derivation. We show that the equations predict an evolution for the macroscopic
variables which catches the basic features of the problem. The results here
presented recover those derived, using a different approach, by Gruber, Pache
and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).Comment: 13 pages, 7 figures (revTeX4) The paper has been completely rewritten
with new derivation and results, supplementary information can be found at
http://denali.phys.uniroma1.it/~cencini/Papers/cppv07_supplements.pd
Growth, competition and cooperation in spatial population genetics
We study an individual based model describing competition in space between
two different alleles. Although the model is similar in spirit to classic
models of spatial population genetics such as the stepping stone model, here
however space is continuous and the total density of competing individuals
fluctuates due to demographic stochasticity. By means of analytics and
numerical simulations, we study the behavior of fixation probabilities,
fixation times, and heterozygosity, in a neutral setting and in cases where the
two species can compete or cooperate. By concluding with examples in which
individuals are transported by fluid flows, we argue that this model is a
natural choice to describe competition in marine environments.Comment: 29 pages, 14 figures; revised version including a section with
results in the presence of fluid flow
How Gaussian competition leads to lumpy or uniform species distributions
A central model in theoretical ecology considers the competition of a range
of species for a broad spectrum of resources. Recent studies have shown that
essentially two different outcomes are possible. Either the species surviving
competition are more or less uniformly distributed over the resource spectrum,
or their distribution is 'lumped' (or 'clumped'), consisting of clusters of
species with similar resource use that are separated by gaps in resource space.
Which of these outcomes will occur crucially depends on the competition kernel,
which reflects the shape of the resource utilization pattern of the competing
species. Most models considered in the literature assume a Gaussian competition
kernel. This is unfortunate, since predictions based on such a Gaussian
assumption are not robust. In fact, Gaussian kernels are a border case
scenario, and slight deviations from this function can lead to either uniform
or lumped species distributions. Here we illustrate the non-robustness of the
Gaussian assumption by simulating different implementations of the standard
competition model with constant carrying capacity. In this scenario, lumped
species distributions can come about by secondary ecological or evolutionary
mechanisms or by details of the numerical implementation of the model. We
analyze the origin of this sensitivity and discuss it in the context of recent
applications of the model.Comment: 11 pages, 3 figures, revised versio
A Universal Lifetime Distribution for Multi-Species Systems
Lifetime distributions of social entities, such as enterprises, products, and
media contents, are one of the fundamental statistics characterizing the social
dynamics. To investigate the lifetime distribution of mutually interacting
systems, simple models having a rule for additions and deletions of entities
are investigated. We found a quite universal lifetime distribution for various
kinds of inter-entity interactions, and it is well fitted by a
stretched-exponential function with an exponent close to 1/2. We propose a
"modified Red-Queen" hypothesis to explain this distribution. We also review
empirical studies on the lifetime distribution of social entities, and
discussed the applicability of the model.Comment: 10 pages, 6 figures, Proceedings of Social Modeling and Simulations +
Econophysics Colloquium 201
Phase Synchronization in Railway Timetables
Timetable construction belongs to the most important optimization problems in
public transport. Finding optimal or near-optimal timetables under the
subsidiary conditions of minimizing travel times and other criteria is a
targeted contribution to the functioning of public transport. In addition to
efficiency (given, e.g., by minimal average travel times), a significant
feature of a timetable is its robustness against delay propagation. Here we
study the balance of efficiency and robustness in long-distance railway
timetables (in particular the current long-distance railway timetable in
Germany) from the perspective of synchronization, exploiting the fact that a
major part of the trains run nearly periodically. We find that synchronization
is highest at intermediate-sized stations. We argue that this synchronization
perspective opens a new avenue towards an understanding of railway timetables
by representing them as spatio-temporal phase patterns. Robustness and
efficiency can then be viewed as properties of this phase pattern
Population dynamics in compressible flows
Organisms often grow, migrate and compete in liquid environments, as well as
on solid surfaces. However, relatively little is known about what happens when
competing species are mixed and compressed by fluid turbulence. In these
lectures we review our recent work on population dynamics and population
genetics in compressible velocity fields of one and two dimensions. We discuss
why compressible turbulence is relevant for population dynamics in the ocean
and we consider cases both where the velocity field is turbulent and when it is
static. Furthermore, we investigate populations in terms of a continuos density
field and when the populations are treated via discrete particles. In the last
case we focus on the competition and fixation of one species compared to
anotherComment: 16 pages, talk delivered at the Geilo Winter School 201
Scaling Laws in Human Language
Zipf's law on word frequency is observed in English, French, Spanish,
Italian, and so on, yet it does not hold for Chinese, Japanese or Korean
characters. A model for writing process is proposed to explain the above
difference, which takes into account the effects of finite vocabulary size.
Experiments, simulations and analytical solution agree well with each other.
The results show that the frequency distribution follows a power law with
exponent being equal to 1, at which the corresponding Zipf's exponent diverges.
Actually, the distribution obeys exponential form in the Zipf's plot. Deviating
from the Heaps' law, the number of distinct words grows with the text length in
three stages: It grows linearly in the beginning, then turns to a logarithmical
form, and eventually saturates. This work refines previous understanding about
Zipf's law and Heaps' law in language systems.Comment: 6 pages, 4 figure
Artificial Sequences and Complexity Measures
In this paper we exploit concepts of information theory to address the
fundamental problem of identifying and defining the most suitable tools to
extract, in a automatic and agnostic way, information from a generic string of
characters. We introduce in particular a class of methods which use in a
crucial way data compression techniques in order to define a measure of
remoteness and distance between pairs of sequences of characters (e.g. texts)
based on their relative information content. We also discuss in detail how
specific features of data compression techniques could be used to introduce the
notion of dictionary of a given sequence and of Artificial Text and we show how
these new tools can be used for information extraction purposes. We point out
the versatility and generality of our method that applies to any kind of
corpora of character strings independently of the type of coding behind them.
We consider as a case study linguistic motivated problems and we present
results for automatic language recognition, authorship attribution and self
consistent-classification.Comment: Revised version, with major changes, of previous "Data Compression
approach to Information Extraction and Classification" by A. Baronchelli and
V. Loreto. 15 pages; 5 figure
Patchiness and Demographic Noise in Three Ecological Examples
Understanding the causes and effects of spatial aggregation is one of the
most fundamental problems in ecology. Aggregation is an emergent phenomenon
arising from the interactions between the individuals of the population, able
to sense only -at most- local densities of their cohorts. Thus, taking into
account the individual-level interactions and fluctuations is essential to
reach a correct description of the population. Classic deterministic equations
are suitable to describe some aspects of the population, but leave out features
related to the stochasticity inherent to the discreteness of the individuals.
Stochastic equations for the population do account for these
fluctuation-generated effects by means of demographic noise terms but, owing to
their complexity, they can be difficult (or, at times, impossible) to deal
with. Even when they can be written in a simple form, they are still difficult
to numerically integrate due to the presence of the "square-root" intrinsic
noise. In this paper, we discuss a simple way to add the effect of demographic
stochasticity to three classic, deterministic ecological examples where
aggregation plays an important role. We study the resulting equations using a
recently-introduced integration scheme especially devised to integrate
numerically stochastic equations with demographic noise. Aimed at scrutinizing
the ability of these stochastic examples to show aggregation, we find that the
three systems not only show patchy configurations, but also undergo a phase
transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy
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