Multiscale assessment of the degree of multifractality for physiological time series

Recent advancements in detrended fluctuation analysis (DFA) allow evaluating multifractal coefficients scale-by-scale, a promising approach for assessing the complexity of biomedical signals. The multifractality degree is typically quantified by the singularity spectrum width ( W SS ), a method that is critically unstable in multiscale applications. Thus, we aim to propose a robust multiscale index of multifractality, compare it with W SS and illustrate its performance on real biosignals. The proposed index is the cumulative function of squared increments between consecutive DFA coefficients at each scale n : α CF ( n ). We compared it with W SS calculated scale-by-scale considering monofractal/monoscale, monofractal/multiscale, multifractal/monoscale and multifractal/multiscale random processes. The two indices provided qualitatively similar descriptions of multifractality, but α CF ( n ) differentiated better the multifractal components from artefacts due to crossovers or detrending overfitting. Applied on 24 h heart rate recordings of 14 participants, the singularity spectrum failed to always satisfy the concavity requirement for providing meaningful W SS , while α CF ( n ) demonstrated a statistically significant heart rate multifractality at night in the scale ranges 16–100 and 256–680 s. Furthermore, α CF ( n ) did not reject the hypothesis of monofractality at daytime, coherently with previous reports of lower nonlinearity and monoscale multifractality during the day. Thus, α CF ( n ) appears a robust index of multiscale multifractality that is useful for quantifying complexity alterations of physiological series. This article is part of the theme issue ‘Advanced computation in cardiovascular physiology: new challenges and opportunities’.

MULTIFRACTAL ANALYSIS OF SOIL RESISTANCE TO PENETRATION IN DIFFERENT PEDOFORMS

ABSTRACT Soils are highly variable across landscapes, which can be assessed and characterized according to scale, as well as fractal and multifractal concepts of scale. Thus, the objective of this study was to analyze the multifractality of the penetration resistance (PR) of vertical profiles from different slope forms (concave and convex). The experimental plot incorporated 44.75 ha, and the PR was measured at 70 sampling points in the 0-0.6 m layer, distributed in concave (Type A: 38 sampling points) and convex pedoforms (Type B: 32 sampling points). Data analysis was performed using the PR value (every 0.01 m depth) for each of the sampling points (PRmean), and their respective maximum (Prmaximun) and minimum (PRminimum) values. Multifractal analysis was performed to assess the changes in the structure, heterogeneity, and uniformity of the vertical profiles according to the scale, characterizing the partition function, generalized dimension, and singularity spectrum. The multifractal parameters of the generalized dimension and singularity spectrum demonstrated greater homogeneity and uniformity in the vertical PR profiles of pedoform B (convex) compared to those of pedoform A (concave). The minimum PR values in pedoform A (PRminimum) showed the greatest scale heterogeneity, indicating that in terms of soil management, it is more relevant to monitor the minimum values than the maximum values. The fractal analysis allowed us to describe the heterogeneity of the data on scales not evaluated by conventional analysis methods, with high potential for use in precision agriculture and the delimitation of specific management zones.

Wavelet Leader Based Multifractal Analysis of Sleep Electroencephalogram

Background: Conventional manual sleep stage classification is time-consuming and relies on the knowledge and experience of the specialists. The emergence of automatic sleep stage classification greatly improves the classification efficiency. The feature extraction in automatic sleep stage classification is particularly important, which usually uses the linear methods based on techniques in the time domain, frequency domain, or time-frequency domain. Electroencephalograms (EEGs) contain a wealth of physiological information, have been widely used for the classification of sleep stage. Due to the nonlinear, non-stationary, and multifractal characteristics of EEGs, some nonlinear methods have been used to extract features of sleep stages in recent years, such as complexity, multifractal theory, and chaos theory. The Wavelet Leader Multifractal Formalism (WLMF) of the multifractal theory is widely applied to different physiological signals. The current researches focus on discussing the mean H¨older exponent (h0) and the width of the multifractal singularity spectrum (WD(h)) estimated by the WLMF method. However, in the field of sleep staging, a number of researches focused on h0, but few studies on WD(h). Results: This paper aims to assess the multifractal characteristic for sleep EEG time series from the Sleep-EDF Expanded Database by the WLMF method. In the young group, the mean h0 increased from the Wake stage to the S3 stage (p<0.01). So did the elderly group (p<0.001). WD(h) of the Wake stage was less than that of the S3 stage for the young group, and this relationship was reversed for the elderly group(χ2=13.769, df=1, p<0.001). Gender did not affect, with statistical significance, WD(h) of the Wake stage and the S3 stage (χ2=0.085, df=1, p=0.608), nor did the brain region (χ2=3.137, df=1, p=0.078). Conclusions: The result shows that WD(h) was influenced by aging. The gender and location of brain regions did not show significant influence on the multifractal characteristics of wakefulness and sleeping. This finding extends the application of the multifractal singularity spectrum on sleep staging, and raises a fundamental question on what might be the underlying mechanisms of the WD(h) reversion.

Динамика морфологии поверхности вольфрамовой фольги под нагрузкой

Morphology dynamics of recrystallized tungsten foil surface under uniaxial stretching was investigated in situ by LEED, Auger, AFM, SEM an X-Ray fluorescent analysis. It has been found that before the rupture of the sample the transition from multifractality to monofractality occurs in a few stages: narrowing of the width of multifractal singularity spectrum of surface defects, turn of structural blocks of dominating face W (112) and transition of the lattice of dominating face into diffractive disordered state.

Three essays on the behavior of real estate and stock markets

Ο σκοπός αυτής της έρευνας είναι να κατανοήσει τη συμπεριφορά της χρηματιστηριακής αγοράς και της αγοράς ακινήτων του Χονγκ Κονγκ, και να εξετάσει τις πολύπλοκες αλλαγές κατά τη διάρκεια σημαντικών οικονομικών μεταβολών, μέσω τριών διαφορετικών προσεγγίσεων. Παρουσιάζουμε τη πολυμορφοκλασματική φύση των χρηματοοικονομικών αγορών με βάση τα scaling exponents και την ανάλυση του singularity spectrum, και μελετούμε τους χρηματιστηριακούς δείκτες του Χονγκ Κονγκ. Επιπλέον εφαρμόζουμε δύο μεθόδους, την πολυμορφοκλασματική ανάλυση διακυμάνσεων μετά την απομάκρυνση των τάσεων (MFDFA) και την πολυμορφοκλασματική ανάλυση κινητού μέσου όρου μετά την απομάκρυνση των τάσεων (MFDMA) για να αξιολογήσουμε την ύπαρξη πολυμορφοκλασματικότητας στις περιόδους υπό ανάλυση, αλλά και τη σύνδεση των περιόδων πριν και μετά την κρίση. Στην περίπτωση της MFDFA, ο χρηματιστηριακός δείκτης του Χονγκ Κονγκ για το 2007 και το 1994 παρουσιάζει τη μεγαλύτερη πολυμορφοκλασματικότητα, ενώ στην MFDMA τα αποτελέσματα δείχνουν ότι ο χρηματιστηριακός δείκτης του Χονγκ Κονγκ για την κρίση του 1997 και αυτός της ακίνητης περιουσίας για το 2007 παρουσιάζουν τη μεγαλύτερη πολυμορφοκλασματικότητα. Τα αποτελέσματα των δύο μεθόδων παρουσιάζουν κάποιες διαφορές. Επιπλέον μελετάμε την αγορά του Χονγκ Κονγκ και παρουσιάζουμε μετρήσεις στατιστικής εντροπίας και τεστ αποτελεσματικότητας, αναλύοντας την αγορά ακινήτων του Χονγκ Κονγκ με βάση το μέγεθος και την περιοχή στην οποία βρίσκεται το ακίνητο, έτσι ώστε να αντιληφθούμε τις επιπτώσεις από την κρίση στις ΗΠΑ το 2007. Το πιο σημαντικό εύρημα είναι η ιδιαίτερη αντίδραση της περιοχής Kowloon που δείχνει ανεπηρέαστη από την κρίση. Ακόμη, με τη μέθοδο των κυλιόμενων παραθύρων και της εντροπίας κατα Shannon και Tsallis-q καταγράφονται και τα γεγονότα που επηρέασαν τους δείκτες, όπως την επιδημία άτυπης πνευμονίας του 2003, και την επιβολή ειδικού στεγαστικού φόρου το 2012. Στο τελευταίο δοκίμιο της διατριβής θέλουμε να αναλύσουμε τη χρονική εξέλιξη της σχέσης αίτιου-αιτιατού κυρίως κατά τη διάρκεια της κρίσης του 2007. Χρησιμοποιήσαμε ένα τμήμα της μεθόδου που ονομάζεται “βέλτιστη θερμική πορεία”, και τη μέθοδο αιτιότητας κατά Granger. Τα αποτελέσματα συμφωνουν με την προηγούμενη ανάλυση και υποστηρίζουν την ιδιαίτερη αντίδραση της περιοχής Kowloon στην κρίση.

Boltzmann and the Statistical Multifractals

We extend the Boltzmann’s ideas that describe the evolution to the equilibrium of many body systems to the multifractal decomposition of the unitary interval 𝕀, in terms of sets Jα conformed by points with the same pointwise dimension, and obtain the D(α) singularity spectrum.

Chapter 6. Mechanisms of changes in dynamic complexity of involuntary oscillations of the human hand with movement disorders

The sixth chapter examines the mechanisms of changes in the dynamic complexity of hand tremor with an increase in the degree of motor disorders. For this, multifractal and wavelet properties of involuntary oscillations that arise during the performance of certain motor tasks by a healthy person and a person with varying degrees of motor pathology are investigated. It was shown that clinical manifestations of pathological tremor correlate, firstly, with a significant increase in the global energy of the wavelet spectrum and, secondly, with a decrease in the width of the singularity spectrum. At the same time, an improvement in the functional state (a decrease in the amplitude of a pathological tremor) corresponds to a decrease in long-term correlations and an increase in the randomness of up-down patterns, which corresponds to a partial shift of the singularity spectrum into the range of values typical for a tremor of the hand of a healthy person. The mechanism for reducing the dynamic complexity of patterns of involuntary oscillations of the human hand with an increase in the degree of motor disorders is based on a decrease in the contribution of strong fluctuations, accompanied by the appearance of long-term correlations of sequential values of tremor. The considered features in changes in tremor patterns make it possible to quantify the degree of movement disorders and can be used to facilitate the differential diagnosis of the parkinsonian and essential tremor in complex clinical cases.

Влияние механического воздействия на рельеф поверхности металлического стекла Fe-=SUB=-77-=/SUB=-Ni-=SUB=-1-=/SUB=-Si-=SUB=-9-=/SUB=-B-=SUB=-13-=/SUB=-

The micro- and nanoreliefs of the loaded surfaces of a Fe_77Ni_1Si_9B_13 metal glass are probed via scanning tunneling and atomic force microscopies, scanning electron microscopy, and X-ray fluorescence. The fractal characteristics of surfaces are evaluated via the multifractal approach. As found, the variations in a singularity spectrum width, calculated from the tunneling and atomic force microscopies, may be useful for predicting the forthcoming fracture. An increase in the breaking strength of ribbons subjected to hydrostatic compression is due to decreasing microporosity of a near-surface layer, which corresponds to the surface smoothing.

Evaluation of nonlinear dynamics of the cell structure damage as a promising method for personalized cancer diagnostics

Background:Modulation interference microscopy is one of the promising technologies for early personalized cancer diagnostics, while it gives the possibility to obtain real-time images of living functioning cells at a nanometer resolution, as well as to assess spatio-temporal changes of their intracellular structures.Aim:To identify the markers of malignant transformation of cells based on a multiple scale spatio-temporal of the data obtained by lase interferometry duringin situregistration of changes in intracellular structures.Materials and methods:The study was performed with the breast adenocarcinoma MCF-7 cell line and human kidney epithelial cells HEK 293 provided by the N.N. Blokhin National Medical Research Centre of Oncology (Moscow, Russia). Changes in fluctuation of the living cell phase thickness were measured with a laser modulation interference microscope MIM-340 (PA UOMZ, Russia). The multifractal detrended fluctuation analysis (MF-DFA) was used to assess the results obtained.Results:By comparison of the scaling exponential spectra and corresponding spectra of the singular fluctuations in the minimal and maximal diameters of the phase pictures of HEK 293 cells and MCF-7 cells, it was shown that the cancer cell dynamics has definite monofractal properties: a linear dependency of the scaling exponentsτfrom the actualqparameter and “dotted” singularity spectrum (the spectral width does not exceed 0.1). The dynamics of healthy cell demonstrated multifractal properties, such as a non-linear dependencyτ(q)and a bell shaped singularity spectrum (the spectral width over 0.1).Conclusion:We have proposed a new approach to assess the intracellular structural damage during oncogenesis. The signs of monofractality are objective criteria of malignization. The results obtained seems promising as early diagnostic markers of cancer transformation (damage) of cells and determination of tumor cell sensitivity / resistance to anti-tumor agents in an individual patient.