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Marathons are one of the ultimate challenges of human endeavor. In this paper, we apply recently introduced multifractal techniques which yield a new classification parameter in the processing of physiological data captured on marathon…

Signal Processing · Electrical Eng. & Systems 2025-01-13 Véronique Billat , Wejdene Nasr Ben Hadj Amor , Guillaume Saës , Stéphane Jaffard , Florent Palacin

We review the central results concerning wavelet methods in multifractal analysis, which consists in analysis of the pointwise singularities of a signal, and we describe its recent extension to multivariate multifractal analysis, which…

Signal Processing · Electrical Eng. & Systems 2022-09-30 Stéphane Jaffard , Guillaume Saës , Wejdene Ben Nasr , Florent Palacin , Véronique Billat

An analysis of marathon pacing and elevation change is presented. It is based on an empirical observation of how the pace of elite and non-elite marathon runners change over the course of the marathon and a simple approximation of the…

Popular Physics · Physics 2012-10-03 J. B. Elliott

Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a…

Amateur marathon runners who exercise excessively over time have pathological structural changes in their hearts and aortas. Amateur marathon runners' cardiovascular system adaptations and dangers are discussed in this article. After…

Other Quantitative Biology · Quantitative Biology 2025-07-16 Saeid Aghasoleymani Najafabadi , Hadi Jabbari Saray

We present a multivariate functional mixed effects model for kinematic data from a large number of recreational runners. The runners' sagittal plane hip and knee angles are modelled jointly as a bivariate function with random effects…

The characterization of heart dynamics with a view to distinguish abnormal from normal behavior is an interesting topic in clinical sciences. Here we present an analysis of the Electro-cardiogram (ECG) signals obtained under controlled…

Tissues and Organs · Quantitative Biology 2018-09-05 Snehal M. Shekatkar , Yamini Kotriwar , K. P. Harikrishnan , G. Ambika

We investigate the recovery dynamics of healthy cardiac activity after physical exertion using multimodal biosignals recorded with a polycardiograph. Multifractal features derived from the singularity spectrum capture the scale-invariant…

Pattern Formation and Solitons · Physics 2025-09-30 A. Maluckov , D. Stojanovic , M. Miletic , Lj. Hadzievski , J. Petrovic

We develop the mathematical properties of a multifractal analysis of data based on the weak scaling exponent. The advantage of this analysis is that it does not require any a priori global regularity assumption on the analyzed signal, in…

Signal Processing · Electrical Eng. & Systems 2025-03-24 Patrice Abry , Phipippe Ciuciu , Merlin Dumeur , Stéphane Jaffard , Guillaume Saës

Fluctuations of the human heart beat constitute a complex system that has been studied mostly under resting conditions using conventional time series analysis methods. During physical exercise, the variability of the fluctuations is…

Data Analysis, Statistics and Probability · Physics 2020-08-13 Matti Molkkari , Giorgio Angelotti , Thorsten Emig , Esa Räsänen

Amateur runners are increasingly using wearable devices to track their training, and often do so through simple metrics such as heart rate and pace. However, these metrics are typically analyzed in isolation and lack the explainability…

Human-Computer Interaction · Computer Science 2025-09-16 Evgeny V. Votyakov , Marios Constantinides , Fotis Liarokapis

We present the multiscale entropy analysis of short term physiological time series of simultaneously acquired samples of heart rate, blood pressure and lung volume, from healthy subjects and from subjects with Chronic Heart Failure.…

Medical Physics · Physics 2007-05-23 L. Angelini , R. Maestri , D. Marinazzo , L. Nitti , M. Pellicoro , G. D. Pinna , S. Stramaglia , S. A. Tupputi

Power spectral density is an accepted measure of heart rate variability. Two estimators of multifractal properties: Wavelet Transform Modulus Maxima and Multifractal Detrended Fluctuation Analysis are used to investigate multifractal…

Quantitative Methods · Quantitative Biology 2007-05-23 Danuta Makowiec , Aleksandra Dudkowska , Rafal Galaska , Andrzej Rynkiewicz

Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and…

Classical Analysis and ODEs · Mathematics 2016-08-03 Roberto Leonarduzzi , Herwig Wendt , Patrice Abry , Stéphane Jaffard , Clothilde Melot , Stéphane G. Roux , Maria E. Torres

Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov et al., Nature {\bf 399}, 461 (1999)]. This multifractal character could be…

Chaotic Dynamics · Physics 2009-11-13 Emily S. C. Ching , Yue-Kin Tsang

A multiplicative effects model is introduced for the identification of the factors that are influential to the performance of highly-trained endurance runners. The model extends the established power-law relationship between performance…

Applications · Statistics 2015-07-02 Ioannis Kosmidis , Louis Passfield

Human heart rate fluctuates in a complex and non-stationary manner. Elaborating efficient and adequate tools for the analysis of such signals has been a great challenge for the researchers during last decades. Here, an overview of the main…

Medical Physics · Physics 2007-05-23 J. Kalda , M. Sakki , M. Vainu , M. Laan

Multifractal analysis has become a standard signal processing tool,for which a promising new formulation, the p-leader multifractal formalism, has recently been proposed. It relies on novel multiscale quantities, the p-leaders, defined as…

Numerical Analysis · Mathematics 2017-05-05 Roberto Leonarduzzi , Herwig Wendt , Patrice Abry , Stéphane Jaffard , Clothilde Melot

In order to interpret and explain the physiological signal behaviors, it can be interesting to find some constants among the fluctuations of these data during all the effort or during different stages of the race (which can be detected…

Applications · Statistics 2011-12-06 Imen Kammoun , Véronique Billat , Jean-Marc Bardet

We study the connection between multi-fractality and crucial events. Multi-fractality is frequently used as a measure of physiological variability. Crucial events are known to play a fundamental role in the transport of information between…

Adaptation and Self-Organizing Systems · Physics 2018-01-03 Gyanendra Bohara , David Lambert , Bruce J. West , Paolo Grigolini
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