SCALING IN COGNITION

Fractals ◽  
2001 ◽  
Vol 09 (04) ◽  
pp. 379-391 ◽  
Author(s):  
VASILE V. MORARIU ◽  
AUREL COZA ◽  
MINERVA ALOUETTE CHIS ◽  
ADRIANA ISVORAN ◽  
LAURA-CORNELIA MORARIU
Keyword(s):  
Human Subjects ◽  
Approximate Entropy ◽  
Characteristic Number ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Random Series ◽  
Dimension Analysis ◽  
Range Correlation ◽  
Short Memory ◽  
Detrended Fluctuation

Conscious activity is generally consistent with a deterministic mode of action, however some activities demand randomness. The goal of this study was to find whether mind can produce randomness. We asked various human subjects, aged between 21 and 57, to produce sequences of random integers. The non-repetition of the terms in the series was the "algorithm" generally used by all the subjects. The series were analyzed by using spectral analysis (SA), detrended fluctuation analysis (DFA), information (I2) and approximate entropy (AE) and correlation dimension analysis (CDA). SA of the series revealed 1/fβ(-0.4<β<1) types of spectra. The α scaling exponent resulting from DFA ranged between 0.2 and 1.1. The maximum of the distribution of α was centered at about 0.62. This is equivalent to a quarter power law in spectral terms. A significant percentage of subjects were able to produce random series. I2 of mental series revealed short-range correlation for pairs of successive numbers in the series. The correlation decreased gradually and it disappeared at a delay step of about 7 which is the characteristic number of short memory. AE had a minimum value at α=1 and a maximum value at α=0.5 for mental and random series, respectively. CDA showed no presence of attractors in the series, therefore none of the randomness produced by the subjects was of deterministic origin. A comparison of the scaling exponents revealed that the mental series have a certain long-range characteristic which is common to the human language as evident in the literature writings.

QUARTER POWER SCALING IN DYNAMICS: EXPERIMENTAL EVIDENCE FROM CELL BIOLOGY AND COGNITIVE PSYCHOLOGY

2001 ◽  
Vol 01 (03) ◽  
pp. L111-L116 ◽  
Author(s):  
VASILE V. MORARIU ◽  
AUREL COZA
Keyword(s):  
Cell Biology ◽  
Detrended Fluctuation Analysis ◽  
Human Subjects ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Random Generation ◽  
Present Evidence ◽  
Biological Variables ◽  
Different Types ◽  
Detrended Fluctuation

1/4 scaling of various biological variables in relation to body mass is universal in biology. Recent models provided evidence that such a scaling is a result of optimization of the processes in the system. We present evidence for 1/4 scaling in dynamical processes from two different types of experiments: fluctuation of the erythrocyte diameter and a task of random generation of series of numbers by human subjects. The time series obtained for different cells and human subjects respectively were analyzed by detrended fluctuation analysis. The exponents from different individuals presented a gaussian distribution centered at a scaling exponent equivalent to 1/4 for both types of experiments. While this proves the existence of 1/4 scaling in dynamics, it also shows that processes do not proceed equally efficient in various individuals. Consequently the deviation from the 1/4 scaling individuals can be used as a universal tool of investigation for the efficiency, or the optimization of various biological, psychological or other types of variables.

SCALING ANALYSIS OF THE A-PHASE DYNAMICS DURING SLEEP

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050050
Author(s):  
V. E. ARCE-GUEVARA ◽  
M. O. MENDEZ ◽  
J. S. MURGUÍA ◽  
A. ALBA ◽  
H. GONZÁLEZ-AGUILAR ◽  
...  
Keyword(s):  
Binary Sequence ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Scaling Exponent ◽  
Sleep State ◽  
Phase Dynamics ◽  
A Value ◽  
Sleep Condition ◽  
Detrended Fluctuation

In this work, the scaling behavior of the sleep process is evaluated by using detrended fluctuation analysis based on wavelets. The analysis is carried out from arrivals of short and recurrent cortical events called A-phases, which in turn build up the Cyclic Alternating Pattern phenomenon, and are classified in three types: A1, A2 and A3. In this study, 61 sleep recordings corresponding to healthy, nocturnal frontal lobe epilepsy patients and sleep-state misperception subjects, were analyzed. From the A-phase annotations, the onsets were extracted and a binary sequence with one second resolution was generated. An item in the sequence has a value of one if an A-phase onset occurs in the corresponding window, and a value of zero otherwise. In addition, we consider other different temporal resolutions from 2[Formula: see text]s to 256[Formula: see text]s. Furthermore, the same analysis was carried out for sequences obtained from the different types of A-phases and their combinations. The results of the numerical analysis showed a relationship between the time resolutions and the scaling exponents; specifically, for higher time resolutions a white noise behavior is observed, whereas for lower time resolutions a behavior towards to [Formula: see text]-noise is exhibited. Statistical differences among groups were observed by applying various wavelet functions from the Daubechies family and choosing the appropriate sequence of A-phase onsets. This scaling analysis allows the characterization of the free-scale dynamic of the sleep process that is specific for each sleep condition. The scaling exponent could be useful as a diagnosis parameter in clinics when sleep macrostructure does not offer enough information.

scholarly journals Fatigue reduces the complexity of knee extensor torque during fatiguing sustained isometric contractions

2018 ◽  
Author(s):  
Jamie Pethick ◽  
Mark Burnley ◽  
Samantha Lee Winter
Keyword(s):  
Temporal Structure ◽  
Femoral Nerve ◽  
Knee Extensor ◽  
Approximate Entropy ◽  
Task Demands ◽  
Peripheral Fatigue ◽  
Knee Extensors ◽  
Fluctuation Analysis ◽  
Isometric Contractions ◽  
Scaling Exponent

The temporal structure, or complexity, of muscle torque output reflects the adaptability of motor control to changes in task demands. This complexity is reduced by neuromuscular fatigue during intermittent isometric contractions. We tested the hypothesis that sustained fatiguing isometric contractions would result in a similar loss of complexity. To that end, nine healthy participants performed, on separate days, sustained isometric contractions of the knee extensors at 20% MVC to task failure and at 100% MVC for 60 seconds. Torque and surface EMG signals were sampled continuously. Complexity and fractal scaling were quantified by calculating approximate entropy (ApEn) and the detrended fluctuation analysis (DFA) α scaling exponent. Global, central and peripheral fatigue were quantified using maximal voluntary contractions (MVCs) with femoral nerve stimulation. Fatigue reduced the complexity of both submaximal (ApEn from 1.02 ± 0.06 to 0.41 ± 0.04, P &lt; 0.05) and maximal contractions (ApEn from 0.34 ± 0.05 to 0.26 ± 0.04, P &lt; 0.05; DFA α from 1.41 ± 0.04 to 1.52 ± 0.03, P &lt; 0.05). The losses of complexity were accompanied by significant global, central and peripheral fatigue (all P &lt; 0.05). These results demonstrate that a fatigue-induced loss of torque complexity is evident not only during fatiguing intermittent isometric contractions, but also during sustained fatiguing contractions.

scholarly journals Early Warning Signals for Bearing Failure Using Detrended Fluctuation Analysis

2020 ◽  
Vol 10 (23) ◽  
pp. 8489
Author(s):  
Laith Shalalfeh ◽  
Ashraf AlShalalfeh
Keyword(s):  
Long Range ◽  
Early Warning ◽  
Detrended Fluctuation Analysis ◽  
Short Range ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Bearing Failure ◽  
Kendall’S Tau ◽  
Vibration Data ◽  
Detrended Fluctuation

Prognostic techniques play a critical role in predicting upcoming faults and failures in machinery or a system by monitoring any deviation in the operation. This paper presents a novel method to analyze multidimensional sensory data and use its characteristics in bearing health prognostics. Firstly, detrended fluctuation analysis (DFA) is exploited to evaluate the long-range correlations in ball bearing vibration data. The results reveal the existence of the crossover phenomenon in vibration data with two scaling exponents at the short-range and long-range scales. Among several data sets, applying the DFA method to vibration signals shows a consistent increase in the short-range scaling exponent toward bearing failure. Finally, Kendall’s tau is used as a ranking coefficient to quantify the trend in the scaling exponent. It was found that the Kendall’s tau coefficient of the vibration scaling exponent could provide an early warning signal (EWS) for bearing failure.

scholarly journals Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Gopa Bhoumik ◽  
Argha Deb ◽  
Swarnapratim Bhattacharyya ◽  
Dipak Ghosh
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Heavy Ion ◽  
Projectile Energy ◽  
Fluctuation Analysis ◽  
Data Set ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Range Correlation ◽  
Multifractal Property ◽  
Detrended Fluctuation

We have studied the multifractality of pion emission process in16O-AgBr interactions at 2.1 AGeV  and  60 AGeV,12C-AgBr  and  24Mg-AgBr interactions at 4.5 AGeV, and32S-AgBr interactions at 200 AGeV using Multifractal Detrended Fluctuation Analysis (MFDFA) method which is capable of extracting the actual multifractal property filtering out the average trend of fluctuation. The analysis reveals that the pseudorapidity distribution of the shower particles is multifractal in nature for all the interactions; that is, pion production mechanism has inbuilt multiscale self-similarity property. We have employed MFDFA method for randomly generated events for32S-AgBr interactions at 200 AGeV. Comparison of expt. results with those obtained from randomly generated data set reveals that the source of multifractality in our data is the presence of long range correlation. Comparing the results obtained from different interactions, it may be concluded that strength of multifractality decreases with projectile mass for the same projectile energy and for a particular projectile it increases with energy. The values of ordinary Hurst exponent suggest that there is long range correlation present in our data for all the interactions.

DETRENDED FLUCTUATION ANALYSIS OF CHROMATIN TEXTURE FOR DIAGNOSIS IN BREAST CYTOLOGY

Fractals ◽  
2002 ◽  
Vol 10 (01) ◽  
pp. 19-25 ◽  
Author(s):  
ANDREW J. EINSTEIN ◽  
HAI-SHAN WU ◽  
JUAN GIL
Keyword(s):  
Logistic Regression ◽  
Epithelial Cell ◽  
Epithelial Cells ◽  
Detrended Fluctuation Analysis ◽  
Breast Epithelial Cell ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Breast Epithelial Cells ◽  
Breast Epithelial ◽  
Detrended Fluctuation

Chromatin appearance in breast epithelial cells has been shown to have fractal properties, and detrended fluctuation analysis (DFA) is an effective method for characterizing the scaling in non-stationary fractal signals in terms of a scaling exponent. This study examines the use of DFA for the characterization of chromatin appearance in breast epithelial cells. Images of nuclei representative of fine-needle aspiration biopsies of the breast are characterized in terms of the scaling exponent for 19 patients with benign lesions and 22 patients with invasive ductal carcinoma. Characterizing patients by the standard deviations of the values of the scaling exponent for their representative nuclei, a statistically significant difference is noted between benign and malignant cases. This reflects that malignancies exhibit less variability in chromatin roughness than do benign cases. Previous logistic regression models for the diagnosis of breast epithelial cell lesions are improved upon by incorporating the standard deviation of the scaling exponent. Using leave-one-out cross-validation, the best logistic regression classifiers demonstrate a sensitivity of 95% and a specificity of 100%. A combination of DFA and lacunarity analysis is seen to provide the best approach to characterizing chromatin in breast epithelial cell nuclei.

The Application of Detrended Fluctuation Analysis in Rice Blast in the Early Warning

2014 ◽  
Vol 644-650 ◽  
pp. 6011-6014
Author(s):  
Xin Zhao ◽  
Yan Hong Huang Fu ◽  
Qian Sun ◽  
Lian Jun Yu
Keyword(s):  
Relative Humidity ◽  
Rice Blast ◽  
Detrended Fluctuation Analysis ◽  
Statistical Significance ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Temperature And Humidity ◽  
Detrended Fluctuation ◽  
Uniform Scaling ◽  
Scaling Index

In this paper, the 5-9 months of 2000-2011 temperature and humidity data, used the detrended fluctuation analysis, obtained how the two data series’ non-uniform scaling index changes with time. In order to comprehensive influence of temperature and relative humidity of the two meteorological factors, the temperature and humidity coefficient is introduced. We also proposed a new non-uniform scaling index taking into account the information of temperature and relative humidity, and discusses the possible correlation between temperature and humidity and rice blast. The preliminary results show, A long-range power-law correlation can be found in the time series of temperature and humidity. About 5-15 days before the occurrence of rice blast will appear anomalies of non-uniform scaling index. It reflects the rice blast made a difference of statistical significance to the characteristic of nonlinear system internal of temperature and humidity coefficient. It can predict the occurrence and prevalence of rice blast according to the abnormal changes of temperature and humidity coefficient scaling exponent.

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