992 research outputs found
Modelling Food Webs
We review theoretical approaches to the understanding of food webs. After an
overview of the available food web data, we discuss three different classes of
models. The first class comprise static models, which assign links between
species according to some simple rule. The second class are dynamical models,
which include the population dynamics of several interacting species. We focus
on the question of the stability of such webs. The third class are species
assembly models and evolutionary models, which build webs starting from a few
species by adding new species through a process of "invasion" (assembly models)
or "speciation" (evolutionary models). Evolutionary models are found to be
capable of building large stable webs.Comment: 34 pages, 2 figures. To be published in "Handbook of graphs and
networks" S. Bornholdt and H. G. Schuster (eds) (Wiley-VCH, Berlin
Reconciling cooperation, biodiversity and stability in complex ecological communities
Empirical observations show that ecological communities can have a huge
number of coexisting species, also with few or limited number of resources.
These ecosystems are characterized by multiple type of interactions, in
particular displaying cooperative behaviors. However, standard modeling of
population dynamics based on Lotka-Volterra type of equations predicts that
ecosystem stability should decrease as the number of species in the community
increases and that cooperative systems are less stable than communities with
only competitive and/or exploitative interactions. Here we propose a stochastic
model of population dynamics, which includes exploitative interactions as well
as cooperative interactions induced by cross-feeding. The model is exactly
solved and we obtain results for relevant macro-ecological patterns, such as
species abundance distributions and correlation functions. In the large system
size limit, any number of species can coexist for a very general class of
interaction networks and stability increases as the number of species grows.
For pure mutualistic/commensalistic interactions we determine the topological
properties of the network that guarantee species coexistence. We also show that
the stationary state is globally stable and that inferring species interactions
through species abundance correlation analysis may be misleading. Our
theoretical approach thus show that appropriate models of cooperation naturally
leads to a solution of the long-standing question about complexity-stability
paradox and on how highly biodiverse communities can coexist.Comment: 25 pages, 10 figure
A look at the relationship between industrial dynamics and aggregate fluctuations
The firmly established evidence of right-skewness of the firms’ size distribution is generally modelled recurring to some variant of the Gibrat’s Law of Proportional Effects. In spite of its empirical success, this approach has been harshly criticized on a theoretical ground due to its lack of economic contents and its unpleasant long-run implications. In this chapter we show that a right-skewed firms’ size distribution, with its upper tail scaling down as a power law, arises naturally from a simple choice-theoretic model based on financial market imperfections and a wage setting relationship. Our results rest on a multi-agent generalization of the prey-predator model, firstly introduced into economics by Richard Goodwin forty years ago.Firm size; Prey-predator model; Business Fluctuations
The role of data in model building and prediction: a survey through examples
The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of quantitative sciences, mean abstract mathematical or algorithmical representations. This short review discusses a few key examples from Physics, taken from dynamical systems theory, biophysics, and statistical mechanics, representing three paradigmatic procedures to build models and predictions from available data. In the case of dynamical systems we show how predictions can be obtained in a virtually model-free framework using the methods of analogues, and we briefly discuss other approaches based on machine learning methods. In cases where the complexity of systems is challenging, like in biophysics, we stress the necessity to include part of the empirical knowledge in the models to gain the minimal amount of realism. Finally, we consider many body systems where many (temporal or spatial) scales are at play-and show how to derive from data a dimensional reduction in terms of a Langevin dynamics for their slow components
The Gompertz-Pareto Income Distribution
This work analyzes the Gompertz-Pareto distribution (GPD) of personal income,
formed by the combination of the Gompertz curve, representing the overwhelming
majority of the economically less favorable part of the population of a
country, and the Pareto power law, which describes its tiny richest part.
Equations for the Lorenz curve, Gini coefficient and the percentage share of
the Gompertzian part relative to the total income are all written in this
distribution. We show that only three parameters, determined by linear data
fitting, are required for its complete characterization. Consistency checks are
carried out using income data of Brazil from 1981 to 2007 and they lead to the
conclusion that the GPD is consistent and provides a coherent and simple
analytical tool to describe personal income distribution data.Comment: 13 pages, 5 figures, LaTeX. Accepted for publication in "Physica A
Order out of Randomness : Self-Organization Processes in Astrophysics
Self-organization is a property of dissipative nonlinear processes that are
governed by an internal driver and a positive feedback mechanism, which creates
regular geometric and/or temporal patterns and decreases the entropy, in
contrast to random processes. Here we investigate for the first time a
comprehensive number of 16 self-organization processes that operate in
planetary physics, solar physics, stellar physics, galactic physics, and
cosmology. Self-organizing systems create spontaneous {\sl order out of chaos},
during the evolution from an initially disordered system to an ordered
stationary system, via quasi-periodic limit-cycle dynamics, harmonic mechanical
resonances, or gyromagnetic resonances. The internal driver can be gravity,
rotation, thermal pressure, or acceleration of nonthermal particles, while the
positive feedback mechanism is often an instability, such as the
magneto-rotational instability, the Rayleigh-B\'enard convection instability,
turbulence, vortex attraction, magnetic reconnection, plasma condensation, or
loss-cone instability. Physical models of astrophysical self-organization
processes involve hydrodynamic, MHD, and N-body formulations of Lotka-Volterra
equation systems.Comment: 61 pages, 38 Figure
Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error bounds and Algorithms
Biochemical reactions can happen on different time scales and also the
abundance of species in these reactions can be very different from each other.
Classical approaches, such as deterministic or stochastic approach, fail to
account for or to exploit this multi-scale nature, respectively. In this paper,
we propose a jump-diffusion approximation for multi-scale Markov jump processes
that couples the two modeling approaches. An error bound of the proposed
approximation is derived and used to partition the reactions into fast and slow
sets, where the fast set is simulated by a stochastic differential equation and
the slow set is modeled by a discrete chain. The error bound leads to a very
efficient dynamic partitioning algorithm which has been implemented for several
multi-scale reaction systems. The gain in computational efficiency is
illustrated by a realistically sized model of a signal transduction cascade
coupled to a gene expression dynamics.Comment: 32 pages, 7 figure
Empirical Examination of Lotka’s Law for Information Science and Library Science
The paper presents a bibliometric study on the fit of Lotka’s law on Information Science & Library Science journals indexed in Social Science Citation Index of Journal Citation Report from the period 1956 to 2014. The parameters of the Lotka's law model, C and α, were found using the linear least squares method and the Kolmogorov-Smirnov test was applied to estimate the kindness of adjustment of the results to the Lotka’s distribution. It was found that the pattern of publication of the LIS category articles fits to Lotka’s law
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