19 research outputs found
Exact scaling in the expansion-modification system
This work is devoted to the study of the scaling, and the consequent
power-law behavior, of the correlation function in a mutation-replication model
known as the expansion-modification system. The latter is a biology inspired
random substitution model for the genome evolution, which is defined on a
binary alphabet and depends on a parameter interpreted as a \emph{mutation
probability}. We prove that the time-evolution of this system is such that any
initial measure converges towards a unique stationary one exhibiting decay of
correlations not slower than a power-law. We then prove, for a significant
range of mutation probabilities, that the decay of correlations indeed follows
a power-law with scaling exponent smoothly depending on the mutation
probability. Finally we put forward an argument which allows us to give a
closed expression for the corresponding scaling exponent for all the values of
the mutation probability. Such a scaling exponent turns out to be a piecewise
smooth function of the parameter.Comment: 22 pages, 2 figure
Challenges in Complex Systems Science
FuturICT foundations are social science, complex systems science, and ICT.
The main concerns and challenges in the science of complex systems in the
context of FuturICT are laid out in this paper with special emphasis on the
Complex Systems route to Social Sciences. This include complex systems having:
many heterogeneous interacting parts; multiple scales; complicated transition
laws; unexpected or unpredicted emergence; sensitive dependence on initial
conditions; path-dependent dynamics; networked hierarchical connectivities;
interaction of autonomous agents; self-organisation; non-equilibrium dynamics;
combinatorial explosion; adaptivity to changing environments; co-evolving
subsystems; ill-defined boundaries; and multilevel dynamics. In this context,
science is seen as the process of abstracting the dynamics of systems from
data. This presents many challenges including: data gathering by large-scale
experiment, participatory sensing and social computation, managing huge
distributed dynamic and heterogeneous databases; moving from data to dynamical
models, going beyond correlations to cause-effect relationships, understanding
the relationship between simple and comprehensive models with appropriate
choices of variables, ensemble modeling and data assimilation, modeling systems
of systems of systems with many levels between micro and macro; and formulating
new approaches to prediction, forecasting, and risk, especially in systems that
can reflect on and change their behaviour in response to predictions, and
systems whose apparently predictable behaviour is disrupted by apparently
unpredictable rare or extreme events. These challenges are part of the FuturICT
agenda
Scaling concepts and complex fluids : long-range power-law correlations in DNA
We review recent evidencee supporting the discovery of long-range power-law correlations in DNA sequences that contain non-coding regions. The possible interpretation of this finding is also discussed.Nous présentons les récentes évidences supportant la découverte de la corrélation de la loi puissance sur des séquences à longue distance d'ADN qui contiennent des régions non-codantes. L'interprétation de cette découverte est également discutée
Scaling in Nature: from DNA through Heartbeats to Weather
The purpose of this talk is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent ff quantifying the scaling in DNA is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent ff is smaller during sleep periods compared to wake periods. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations. Key words: DNA, heartbeat, weather, time series, scaling, fractals In the last decade it was realized that many systems in nature have no characteristic length or time scale, i.e., they have fractal -- or, more generally, scaling -- properties [1--15]. However, the fractal properties in different..
Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics
We discuss examples of complex systems composed of many interacting subsystems. We focus on those systems displaying nontrivial long-range correlations. These include the one-dimensional sequence of base pairs in DNA, the sequence of flight times of the large seabird Wandering Albatross, and the annual fluctuations in the growth rate of business firms. We review formal analogies in the models that describe the observed long-range correlations, and conclude by discussing the possibility that behavior of large numbers of humans (as measured, e.g., by economic indices) might conform to analogs of the scaling laws that have proved useful in describing systems composed of large numbers of inanimate objects