6,812 research outputs found
Chaos in computer performance
Modern computer microprocessors are composed of hundreds of millions of
transistors that interact through intricate protocols. Their performance during
program execution may be highly variable and present aperiodic oscillations. In
this paper, we apply current nonlinear time series analysis techniques to the
performances of modern microprocessors during the execution of prototypical
programs. Our results present pieces of evidence strongly supporting that the
high variability of the performance dynamics during the execution of several
programs display low-dimensional deterministic chaos, with sensitivity to
initial conditions comparable to textbook models. Taken together, these results
show that the instantaneous performances of modern microprocessors constitute a
complex (or at least complicated) system and would benefit from analysis with
modern tools of nonlinear and complexity science
Practical implementation of nonlinear time series methods: The TISEAN package
Nonlinear time series analysis is becoming a more and more reliable tool for
the study of complicated dynamics from measurements. The concept of
low-dimensional chaos has proven to be fruitful in the understanding of many
complex phenomena despite the fact that very few natural systems have actually
been found to be low dimensional deterministic in the sense of the theory. In
order to evaluate the long term usefulness of the nonlinear time series
approach as inspired by chaos theory, it will be important that the
corresponding methods become more widely accessible. This paper, while not a
proper review on nonlinear time series analysis, tries to make a contribution
to this process by describing the actual implementation of the algorithms, and
their proper usage. Most of the methods require the choice of certain
parameters for each specific time series application. We will try to give
guidance in this respect. The scope and selection of topics in this article, as
well as the implementational choices that have been made, correspond to the
contents of the software package TISEAN which is publicly available from
http://www.mpipks-dresden.mpg.de/~tisean . In fact, this paper can be seen as
an extended manual for the TISEAN programs. It fills the gap between the
technical documentation and the existing literature, providing the necessary
entry points for a more thorough study of the theoretical background.Comment: 27 pages, 21 figures, downloadable software at
http://www.mpipks-dresden.mpg.de/~tisea
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A chaotic approach to rainfall disaggregation
The importance of high-resolution rainfall data to understanding the intricacies of the dynamics of hydrological processes and describing them in a sophisticated and accurate way has been increasingly realized. The last decade has witnessed a number of studies and numerous approaches to the possibility of transformation of rainfall data from one scale to another, nearly unanimously pointing to such a possibility. However, an important limitation of such approaches is that they treat the rainfall process as a realization of a stochastic process, and therefore there seems to be a lack of connection between the structure of the models and the underlying physics of the rainfall process. The present study introduces a new framework based on the notion of deterministic chaos to investigate the behavior of the dynamics of rainfall transformation between different temporal scales aimed toward establishing this connection. Rainfall data of successively doubled resolutions (i.e., 6, 12, 24, 48, 96, and 192 hours) observed at Leaf River basin, in the state of Mississippi, United States of America, are studied. The correlation dimension method is employed to investigate the presence of chaos in the rainfall transformation. The finite and low correlation dimensions obtained for the distributions of weights between rainfall data of different scales indicate the existence of chaos in the rainfall transformation, suggesting the applicability of a chaotic model. The formulation of a simple chaotic disaggregation model and its application to the Leaf River rainfall data provides encouraging results with practical potential. The disaggregation model results themselves indicate the presence of chaos in the dynamics of rainfall transformation, providing support for the results obtained using the correlation dimension method
The chaotic solar cycle II. Analysis of cosmogenic 10Be data
Context. The variations of solar activity over long time intervals using a
solar activity reconstruction based on the cosmogenic radionuclide 10Be
measured in polar ice cores are studied. Methods. By applying methods of
nonlinear dynamics, the solar activity cycle is studied using solar activity
proxies that have been reaching into the past for over 9300 years. The
complexity of the system is expressed by several parameters of nonlinear
dynamics, such as embedding dimension or false nearest neighbors, and the
method of delay coordinates is applied to the time series. We also fit a damped
random walk model, which accurately describes the variability of quasars, to
the solar 10Be data and investigate the corresponding power spectral
distribution. The periods in the data series were searched by the Fourier and
wavelet analyses. The solar activity on the long-term scale is found to be on
the edge of chaotic behavior. This can explain the observed intermittent period
of longer lasting solar activity minima. Filtering the data by eliminating
variations below a certain period (the periods of 380 yr and 57 yr were used)
yields a far more regular behavior of solar activity. A comparison between the
results for the 10Be data with the 14C data shows many similarities. Both
cosmogenic isotopes are strongly correlated mutually and with solar activity.
Finally, we find that a series of damped random walk models provides a good fit
to the 10Be data with a fixed characteristic time scale of 1000 years, which is
roughly consistent with the quasi-periods found by the Fourier and wavelet
analyses.Comment: 8 pages, 11 figure
A survey of random processes with reinforcement
The models surveyed include generalized P\'{o}lya urns, reinforced random
walks, interacting urn models, and continuous reinforced processes. Emphasis is
on methods and results, with sketches provided of some proofs. Applications are
discussed in statistics, biology, economics and a number of other areas.Comment: Published at http://dx.doi.org/10.1214/07-PS094 in the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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