5,504 research outputs found
Permutation test for periodicity in short time series data
Abstract Background Periodic processes, such as the circadian rhythm, are important factors modulating and coordinating transcription of genes governing key metabolic pathways. Theoretically, even small fluctuations in the orchestration of circadian gene expression patterns among different tissues may result in functional asynchrony at the organism level and may contribute to a wide range of pathologic disorders. Identification of circadian expression pattern in time series data is important, but equally challenging. Microarray technology allows estimation of relative expression of thousands of genes at each time point. However, this estimation often lacks precision and microarray experiments are prohibitively expensive, limiting the number of data points in a time series expression profile. The data produced in these experiments carries a high degree of stochastic variation, obscuring the periodic pattern and a limited number of replicates, typically covering not more than two complete periods of oscillation. Results To address this issue, we have developed a simple, but effective, computational technique for the identification of a periodic pattern in relatively short time series, typical for microarray studies of circadian expression. This test is based on a random permutation of time points in order to estimate non-randomness of a periodogram. The Permutated time, or Pt-test, is able to detect oscillations within a given period in expression profiles dominated by a high degree of stochastic fluctuations or oscillations of different irrelevant frequencies. We have conducted a comprehensive study of circadian expression on a large data set produced at PBRC, representing three different peripheral murine tissues. We have also re-analyzed a number of similar time series data sets produced and published independently by other research groups over the past few years. Conclusion The Permutated time test (Pt-test) is demonstrated to be effective for detection of periodicity in short time series typical for high-density microarray experiments. The software is a set of C++ programs available from the authors on the open source basis.</p
Delay Parameter Selection in Permutation Entropy Using Topological Data Analysis
Permutation Entropy (PE) is a powerful tool for quantifying the
predictability of a sequence which includes measuring the regularity of a time
series. Despite its successful application in a variety of scientific domains,
PE requires a judicious choice of the delay parameter . While another
parameter of interest in PE is the motif dimension , Typically is
selected between and with or giving optimal results for the
majority of systems. Therefore, in this work we focus solely on choosing the
delay parameter. Selecting is often accomplished using trial and error
guided by the expertise of domain scientists. However, in this paper, we show
that persistent homology, the flag ship tool from Topological Data Analysis
(TDA) toolset, provides an approach for the automatic selection of . We
evaluate the successful identification of a suitable from our TDA-based
approach by comparing our results to a variety of examples in published
literature
Surrogate time series
Before we apply nonlinear techniques, for example those inspired by chaos
theory, to dynamical phenomena occurring in nature, it is necessary to first
ask if the use of such advanced techniques is justified "by the data". While
many processes in nature seem very unlikely a priori to be linear, the possible
nonlinear nature might not be evident in specific aspects of their dynamics.
The method of surrogate data has become a very popular tool to address such a
question. However, while it was meant to provide a statistically rigorous,
foolproof framework, some limitations and caveats have shown up in its
practical use. In this paper, recent efforts to understand the caveats, avoid
the pitfalls, and to overcome some of the limitations, are reviewed and
augmented by new material. In particular, we will discuss specific as well as
more general approaches to constrained randomisation, providing a full range of
examples. New algorithms will be introduced for unevenly sampled and
multivariate data and for surrogate spike trains. The main limitation, which
lies in the interpretability of the test results, will be illustrated through
instructive case studies. We will also discuss some implementational aspects of
the realisation of these methods in the TISEAN
(http://www.mpipks-dresden.mpg.de/~tisean) software package.Comment: 28 pages, 23 figures, software at
http://www.mpipks-dresden.mpg.de/~tisea
A simple method for detecting chaos in nature
Chaos, or exponential sensitivity to small perturbations, appears everywhere
in nature. Moreover, chaos is predicted to play diverse functional roles in
living systems. A method for detecting chaos from empirical measurements should
therefore be a key component of the biologist's toolkit. But, classic
chaos-detection tools are highly sensitive to measurement noise and break down
for common edge cases, making it difficult to detect chaos in domains, like
biology, where measurements are noisy. However, newer tools promise to overcome
these limitations. Here, we combine several such tools into an automated
processing pipeline, and show that our pipeline can detect the presence (or
absence) of chaos in noisy recordings, even for difficult edge cases. As a
first-pass application of our pipeline, we show that heart rate variability is
not chaotic as some have proposed, and instead reflects a stochastic process in
both health and disease. Our tool is easy-to-use and freely available
Inferring long memory processes in the climate network via ordinal pattern analysis
We use ordinal patterns and symbolic analysis to construct global climate
networks and uncover long and short term memory processes. The data analyzed is
the monthly averaged surface air temperature (SAT field) and the results
suggest that the time variability of the SAT field is determined by patterns of
oscillatory behavior that repeat from time to time, with a periodicity related
to intraseasonal oscillations and to El Ni\~{n}o on seasonal-to-interannual
time scales.Comment: 10 pages, 13 figures Enlarged version, new sections and figures.
Accepted in Chao
Periodic behaviour of coronal mass ejections, eruptive events, and solar activity proxies during solar cycles 23 and 24
We report on the parallel analysis of the periodic behaviour of coronal mass
ejections (CMEs) based on 21 years [1996 -- 2016] of observations with the
SOHO/LASCO--C2 coronagraph, solar flares, prominences, and several proxies of
solar activity. We consider values of the rates globally and whenever possible,
distinguish solar hemispheres and solar cycles 23 and 24. Periodicities are
investigated using both frequency (periodogram) and time-frequency (wavelet)
analysis. We find that these different processes, in addition to following the
11-year Solar Cycle, exhibit diverse statistically significant
oscillations with properties common to all solar, coronal, and heliospheric
processes: variable periodicity, intermittence, asymmetric development in the
northern and southern solar hemispheres, and largest amplitudes during the
maximum phase of solar cycles, being more pronounced during solar cycle 23 than
the weaker cycle 24. However, our analysis reveals an extremely complex and
diverse situation. For instance, there exists very limited commonality for
periods of less than one year. The few exceptions are the periods of 3.1--3.2
months found in the global occurrence rates of CMEs and in the sunspot area
(SSA) and those of 5.9--6.1 months found in the northern hemisphere. Mid-range
periods of 1 and 2 years are more wide spread among the
studied processes, but exhibit a very distinct behaviour with the first one
being present only in the northern hemisphere and the second one only in the
southern hemisphere. These periodic behaviours likely results from the
complexity of the underlying physical processes, prominently the emergence of
magnetic flux.Comment: 33 pages, 15 figures, 2 table
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