Analytical and empirical fluctuation functions of the EEG microstate random walk - Short-range vs. long-range correlations

NeuroImage ◽  
2016 ◽  
Vol 141 ◽  
pp. 442-451 ◽  
Author(s):  
F. von Wegner ◽  
E. Tagliazucchi ◽  
V. Brodbeck ◽  
H. Laufs
Keyword(s):  
Random Walk ◽  
Long Range ◽  
Short Range ◽  
Long Range Correlations

scholarly journals DETRENDED FLUCTUATION ANALYSIS OF AUTOREGRESSIVE PROCESSES

2007 ◽  
Vol 07 (03) ◽  
pp. L249-L255 ◽  
Author(s):  
VASILE V. MORARIU ◽  
LUIZA BUIMAGA-IARINCA ◽  
CĂLIN VAMOŞ ◽  
ŞTEFAN M. ŞOLTUZ
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Short Range ◽  
Interaction Constant ◽  
Fluctuation Analysis ◽  
Autoregressive Processes ◽  
Long Range Correlations ◽  
Correlation Exponent ◽  
The Relationship ◽  
Detrended Fluctuation

Autoregressive processes (AR) have typical short-range memory. Detrended Fluctuation Analysis (DFA) was basically designed to reveal long-range correlations in non stationary processes. However DFA can also be regarded as a suitable method to investigate both long-range and short-range correlations in non stationary and stationary systems. Applying DFA to AR processes can help understanding the non-uniform correlation structure of such processes. We systematically investigated a first order autoregressive model AR(1) by DFA and established the relationship between the interaction constant of AR(1) and the DFA correlation exponent. The higher the interaction constant the higher is the short-range correlation exponent. They are exponentially related. The investigation was extended to AR(2) processes. The presence of an interaction between distant terms with characteristic time constant in the series, in addition to a near by interaction will increase the correlation exponent and the range of correlation while the effect of a distant negative interaction will significantly decrease the range of interaction, only. This analysis demonstrate the possibility to identify an AR(1) model in an unknown DFA plot or to distinguish between AR(1) and AR(2) models.

scholarly journals LONG-RANGE FRACTAL CORRELATIONS IN LITERARY CORPORA

Fractals ◽  
2002 ◽  
Vol 10 (04) ◽  
pp. 451-461 ◽  
Author(s):  
MARCELO A. MONTEMURRO ◽  
PEDRO A. PURY
Keyword(s):  
Long Range ◽  
Short Range ◽  
Fractal Structure ◽  
Written Language ◽  
Long Range Correlations ◽  
Large Samples ◽  
Sentence Level ◽  
Set Up ◽  
Short Range Correlations ◽  
Linguistic Basis

In this paper, we analyze the fractal structure of long human language records by mapping large samples of texts onto time series. The particular mapping set up in this work is inspired on linguistic basis in the sense that is retains the word as the fundamental unit of communication. The results confirm that beyond the short-range correlations resulting from syntactic rules acting at sentence level, long-range structures emerge in large written language samples that give rise to long-range correlations in the use of words.

scholarly journals Short-range interactions versus long-range correlations in bird flocks

2015 ◽  
Vol 92 (1) ◽  
Author(s):  
Andrea Cavagna ◽  
Lorenzo Del Castello ◽  
Supravat Dey ◽  
Irene Giardina ◽  
Stefania Melillo ◽  
...  
Keyword(s):  
Long Range ◽  
Short Range ◽  
Long Range Correlations

scholarly journals Basic features of correlated ion stopping in plasmas

1996 ◽  
Vol 14 (4) ◽  
pp. 749-763 ◽  
Author(s):  
Günter Zwicknagel ◽  
Claude Deutsch
Keyword(s):  
Long Range ◽  
Correlation Length ◽  
Short Range ◽  
Single Individual ◽  
Screening Length ◽  
Long Range Correlations ◽  
Ion Clusters ◽  
Large Ratio ◽  
Basic Features ◽  
Short Range Correlations

We reconsider correlated ion stopping in plasmas with the aim to emphasize the basic features and their underlying physics. For a better understanding of the effects connected with correlated ion stopping, it is useful to distinguish two types of correlated ion stopping, characterized by a small or large ratio of the correlation length of the ions to the screening length in the plasma. These two types of correlated ion stopping are of rather different character. We describe and explain these differences and give some generic examples of ion structures and ion clusters to demonstrate the basic features of both types of correlated stopping. This shows that only the short-range correlations always yield an enhanced stopping, whereas the long-range correlations, in general, reduce the stopping compared to single, individual ions. We mainly consider classical plasmas; the basic features, however, remain unchanged for a jellium target as well as for a plasma at any degeneracy.

scholarly journals Nucleotide spacing distribution analysis for human genome

2021 ◽  
Author(s):  
Andrzej Z. Górski ◽  
Monika Piwowar
Keyword(s):  
Human Genome ◽  
Long Range ◽  
Short Range ◽  
Fractal Structure ◽  
Random Sequence ◽  
Distribution Analysis ◽  
Long Range Correlations ◽  
Spacing Distribution ◽  
Self Similar ◽  
Characteristic Features

AbstractThe distribution of nucleotides spacing in human genome was investigated. An analysis of the frequency of occurrence in the human genome of different sequence lengths flanked by one type of nucleotide was carried out showing that the distribution has no self-similar (fractal) structure. The results nevertheless revealed several characteristic features: (i) the distribution for short-range spacing is quite similar to the purely stochastic sequences; (ii) the distribution for long-range spacing essentially deviates from the random sequence distribution, showing strong long-range correlations; (iii) the differences between (A, T) and (C, G) nucleotides are quite significant; (iv) the spacing distribution displays tiny oscillations.

LANGUAGE AND CODIFICATION DEPENDENCE OF LONG-RANGE CORRELATIONS IN TEXTS

Fractals ◽  
1994 ◽  
Vol 02 (01) ◽  
pp. 7-13 ◽  
Author(s):  
M. AMIT ◽  
Y. SHMERLER ◽  
E. EISENBERG ◽  
M. ABRAHAM ◽  
N. SHNERB
Keyword(s):  
Random Walk ◽  
Long Range ◽  
Random Walk Model ◽  
Qualitative Explanation ◽  
Algebraic Decay ◽  
One Dimensional ◽  
Long Range Correlations ◽  
The Bible

We study the long-range correlations in various translations of the Bible by mapping them onto a one dimensional random walk model. We show that the exponent α, which characterizes the algebraic decay law of these correlations depends on both the language and the codification. Some considerations concerning the origin of these correlations are suggested in terms of which a qualitative explanation of this dependence is presented.

Pseudorapidity distribution and cluster formation in 50 and 400 GeV/c hadron–nucleus interactions

1984 ◽  
Vol 62 (3) ◽  
pp. 230-238 ◽  
Author(s):  
M. Irfan ◽  
H. Khushnood ◽  
A. Shakeel ◽  
A. R. Khan ◽  
M. Shafi
Keyword(s):  
Long Range ◽  
Short Range ◽  
Dominant Role ◽  
Cluster Formation ◽  
Pseudorapidity Distribution ◽  
Appreciable Change ◽  
Long Range Correlations ◽  
Rapidity Gap ◽  
Rapidity Distributions ◽  
Short Range Correlations

From the study of the pseudorapidity, η, distributions of charged shower particles produced in 50 GeV/c π− – nucleus and 400 GeV/c proton (p)–nucleus collisions, and their dependence on various parameters, the maxima of η distributions are noticed to shift towards smaller values of η with increasing Ng. Bimodality in the η distributions for all Ng groups has been observed to be completely absent in 50 GeV/c π− – nucleus interactions. Furthermore, the value of [Formula: see text] is found to decrease monotonically with increasing Ng, Ns, and Nh. The dispersions of the rapidity distributions D(η) do not, however, demonstrate any tendency of appreciable change with increasing Ng, except in the region of small Ng values. Finally, study of rapidity-gap length distributions reveals that the two-particle short-range correlations play a dominant role while the contribution of long-range correlations seems to be quite small.

Is walking a random walk? Evidence for long-range correlations in stride interval of human gait

1995 ◽  
Vol 78 (1) ◽  
pp. 349-358 ◽  
Author(s):  
J. M. Hausdorff ◽  
C. K. Peng ◽  
Z. Ladin ◽  
J. Y. Wei ◽  
A. L. Goldberger
Keyword(s):  
Time Series ◽  
Random Walk ◽  
Long Range ◽  
Power Law ◽  
Unknown Origin ◽  
Power Spectral Analysis ◽  
Gait Pattern ◽  
Human Gait ◽  
Long Range Correlations ◽  
Stride Interval

Complex fluctuations of unknown origin appear in the normal gait pattern. These fluctuations might be described as being 1) uncorrelated white noise, 2) short-range correlations, or 3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series, we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that successfully accounts for the experimentally observed long-range correlations.

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