1,373 research outputs found
Fluctuation scaling in complex systems: Taylor's law and beyond
Complex systems consist of many interacting elements which participate in
some dynamical process. The activity of various elements is often different and
the fluctuation in the activity of an element grows monotonically with the
average activity. This relationship is often of the form "", where the exponent is predominantly in
the range . This power law has been observed in a very wide range of
disciplines, ranging from population dynamics through the Internet to the stock
market and it is often treated under the names \emph{Taylor's law} or
\emph{fluctuation scaling}. This review attempts to show how general the above
scaling relationship is by surveying the literature, as well as by reporting
some new empirical data and model calculations. We also show some basic
principles that can underlie the generality of the phenomenon. This is followed
by a mean-field framework based on sums of random variables. In this context
the emergence of fluctuation scaling is equivalent to some corresponding limit
theorems. In certain physical systems fluctuation scaling can be related to
finite size scaling.Comment: 33 pages, 20 figures, 2 tables, submitted to Advances in Physic
Singularity and similarity detection for signals using the wavelet transform
The wavelet transform and related techniques are used to analyze singular and fractal signals. The normalized wavelet scalogram is introduced to detect singularities including jumps, cusps and other sharply changing points. The wavelet auto-covariance is applied to estimate the self-similarity exponent for statistical self-affine signals
Detrended fluctuation analysis of intertrade durations
The intraday pattern, long memory, and multifractal nature of the intertrade
durations, which are defined as the waiting times between two consecutive
transactions, are investigated based upon the limit order book data and order
flows of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in
2003. An inverse -shaped intraday pattern in the intertrade durations with
an abrupt drop in the first minute of the afternoon trading is observed. Based
on the detrended fluctuation analysis, we find a crossover of power-law scaling
behaviors for small box sizes (trade numbers in boxes) and large box sizes and
strong evidence in favor of long memory in both regimes. In addition, the
multifractal nature of intertrade durations in both regimes is confirmed by a
multifractal detrended fluctuation analysis for individual stocks with a few
exceptions in the small-duration regime. The intraday pattern has little
influence on the long memory and multifractaility.Comment: 15 Elsart pages including 4 figures and 1 tabl
Spurious memory in non-equilibrium stochastic models of imitative behavior
The origin of the long-range memory in the non-equilibrium systems is still
an open problem as the phenomenon can be reproduced using models based on
Markov processes. In these cases a notion of spurious memory is introduced. A
good example of Markov processes with spurious memory is stochastic process
driven by a non-linear stochastic differential equation (SDE). This example is
at odds with models built using fractional Brownian motion (fBm). We analyze
differences between these two cases seeking to establish possible empirical
tests of the origin of the observed long-range memory. We investigate
probability density functions (PDFs) of burst and inter-burst duration in
numerically obtained time series and compare with the results of fBm. Our
analysis confirms that the characteristic feature of the processes described by
a one-dimensional SDE is the power-law exponent of the burst or
inter-burst duration PDF. This property of stochastic processes might be used
to detect spurious memory in various non-equilibrium systems, where observed
macroscopic behavior can be derived from the imitative interactions of agents.Comment: 11 pages, 5 figure
Complexity-Entropy Causality Plane as a Complexity Measure for Two-dimensional Patterns
Complexity measures are essential to understand complex systems and there are
numerous definitions to analyze one-dimensional data. However, extensions of
these approaches to two or higher-dimensional data, such as images, are much
less common. Here, we reduce this gap by applying the ideas of the permutation
entropy combined with a relative entropic index. We build up a numerical
procedure that can be easily implemented to evaluate the complexity of two or
higher-dimensional patterns. We work out this method in different scenarios
where numerical experiments and empirical data were taken into account.
Specifically, we have applied the method to i) fractal landscapes generated
numerically where we compare our measures with the Hurst exponent; ii) liquid
crystal textures where nematic-isotropic-nematic phase transitions were
properly identified; iii) 12 characteristic textures of liquid crystals where
the different values show that the method can distinguish different phases; iv)
and Ising surfaces where our method identified the critical temperature and
also proved to be stable.Comment: Accepted for publication in PLoS On
An Updated Algorithm for the Generation of Neutral Landscapes by Spectral Synthesis
Background: Patterns that arise from an ecological process can be driven as much from the landscape over which the process is run as it is by some intrinsic properties of the process itself. The disentanglement of these effects is aided if it possible to run models of the process over artificial landscapes with controllable spatial properties. A number of different methods for the generation of so-called ‘neutral landscapes’ have been developed to provide just such a tool. Of these methods, a particular class that simulate fractional Brownian motion have shown particular promise. The existing methods of simulating fractional Brownian motion suffer from a number of problems however: they are often not easily generalisable to an arbitrary number of dimensions and produce outputs that can exhibit some undesirable artefacts. Methodology: We describe here an updated algorithm for the generation of neutral landscapes by fractional Brownian motion that do not display such undesirable properties. Using Monte Carlo simulation we assess the anisotropic properties of landscapes generated using the new algorithm described in this paper and compare it against a popular benchmark algorithm. Conclusion/Significance: The results show that the existing algorithm creates landscapes with values strongly correlated in the diagonal direction and that the new algorithm presented here corrects this artefact. A number of extensions of the algorithm described here are also highlighted: we describe how the algorithm can be employed to generate landscapes that display different properties in different dimensions and how they can be combined with an environmental gradient to produce landscapes that combine environmental variation at the local and macro scales
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