The Application of Tsallis Entropy Based Self-Adaptive Algorithm for Multi-Threshold Image Segmentation.

Tsallis entropy has been widely used in image thresholding because of its non-extensive properties. The non-extensive parameter q contained in this entropy plays an important role in various adaptive algorithms and has been successfully applied in bi-level image thresholding. In this paper, the relationships between parameter q and pixels' long-range correlations have been further studied within multi-threshold image segmentation. It is found that the pixels' correlations are remarkable and stable for images generated by a known physical principle, such as infrared images, medical CT images, and color satellite remote sensing images. The corresponding non-extensive parameter q can be evaluated by using the self-adaptive Tsallis entropy algorithm. The results of this algorithm are compared with those of the Shannon entropy algorithm and the original Tsallis entropy algorithm in terms of quantitative image quality evaluation metrics PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity). Furthermore, we observed that for image series with the same background, the q values determined by the adaptive algorithm are consistently kept in a narrow range. Therefore, similar or identical scenes during imaging would produce similar strength of long-range correlations, which provides potential applications for unsupervised image processing.

Age-Related Distinctions in EEG Signals during Execution of Motor Tasks Characterized in Terms of Long-Range Correlations.

The problem of revealing age-related distinctions in multichannel electroencephalograms (EEGs) during the execution of motor tasks in young and elderly adults is addressed herein. Based on the detrended fluctuation analysis (DFA), differences in long-range correlations are considered, emphasizing changes in the scaling exponent α. Stronger responses in elderly subjects are confirmed, including the range and rate of increase in α. Unlike elderly subjects, young adults demonstrated about 2.5 times more pronounced differences between motor task responses with the dominant and non-dominant hand. Knowledge of age-related changes in brain electrical activity is important for understanding consequences of healthy aging and distinguishing them from pathological changes associated with brain diseases. Besides diagnosing age-related effects, the potential of DFA can also be used in the field of brain-computer interfaces.

ALUminating the Path of Atherosclerosis Progression: Chaos Theory Suggests a Role for Alu Repeats in the Development of Atherosclerotic Vascular Disease.

Atherosclerosis (ATH) and coronary artery disease (CAD) are chronic inflammatory diseases with an important genetic background; they derive from the cumulative effect of multiple common risk alleles, most of which are located in genomic noncoding regions. These complex diseases behave as nonlinear dynamical systems that show a high dependence on their initial conditions; thus, long-term predictions of disease progression are unreliable. One likely possibility is that the nonlinear nature of ATH could be dependent on nonlinear correlations in the structure of the human genome. In this review, we show how chaos theory analysis has highlighted genomic regions that have shared specific structural constraints, which could have a role in ATH progression. These regions were shown to be enriched with repetitive sequences of the Alu family, genomic parasites that have colonized the human genome, which show a particular secondary structure and are involved in the regulation of gene expression. Here, we show the impact of Alu elements on the mechanisms that regulate gene expression, especially highlighting the molecular mechanisms via which the Alu elements alter the inflammatory response. We devote special attention to their relationship with the long noncoding RNA (lncRNA); antisense noncoding RNA in the INK4 locus (ANRIL), a risk factor for ATH; their role as microRNA (miRNA) sponges; and their ability to interfere with the regulatory circuitry of the (nuclear factor kappa B) NF-κB response. We aim to characterize ATH as a nonlinear dynamic system, in which small initial alterations in the expression of a number of repetitive elements are somehow amplified to reach phenotypic significance.

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

We analyze temporal autocorrelations and the scaling behaviour of EEG microstate sequences during wakeful rest. We use the recently introduced random walk approach and compute its fluctuation function analytically under the null hypothesis of a short-range correlated, first-order Markov process. The empirical fluctuation function and the Hurst parameter H as a surrogate parameter of long-range correlations are computed from 32 resting state EEG recordings and for a set of first-order Markov surrogate data sets with equilibrium distribution and transition matrices identical to the empirical data. In order to distinguish short-range correlations (H ≈ 0.5) from previously reported long-range correlations (H > 0.5) statistically, confidence intervals for H and the fluctuation functions are constructed under the null hypothesis. Comparing three different estimation methods for H, we find that only one data set consistently shows H > 0.5, compatible with long-range correlations, whereas the majority of experimental data sets cannot be consistently distinguished from Markovian scaling behaviour. Our analysis suggests that the scaling behaviour of resting state EEG microstate sequences, though markedly different from uncorrelated, zero-order Markov processes, can often not be distinguished from a short-range correlated, first-order Markov process. Our results do not prove the microstate process to be Markovian, but challenge the approach to parametrize resting state EEG by single parameter models.

Breakdown of long-range temporal dependence in default mode and attention networks during deep sleep.

The integration of segregated brain functional modules is a prerequisite for conscious awareness during wakeful rest. Here, we test the hypothesis that temporal integration, measured as long-term memory in the history of neural activity, is another important quality underlying conscious awareness. For this aim, we study the temporal memory of blood oxygen level-dependent signals across the human nonrapid eye movement sleep cycle. Results reveal that this property gradually decreases from wakefulness to deep nonrapid eye movement sleep and that such decreases affect areas identified with default mode and attention networks. Although blood oxygen level-dependent spontaneous fluctuations exhibit nontrivial spatial organization, even during deep sleep, they also display a decreased temporal complexity in specific brain regions. Conversely, this result suggests that long-range temporal dependence might be an attribute of the spontaneous conscious mentation performed during wakeful rest.

Indication of long-range correlations governing city size.

City systems are characterized by the functional organization of cities on a regional or country scale. While there is a relatively good empirical and theoretical understanding of city size distributions, insights about their spatial organization remain on a conceptual level. Here, we analyze empirically the correlations between the sizes of cities (in terms of area) across long distances. Therefore, we (i) define city clusters, (ii) obtain the neighborhood network from Voronoi cells, and (iii) apply a fluctuation analysis along all shortest paths. We find that most European countries exhibit long-range correlations but in several cases these are anti-correlations. In an analogous way, we study a model inspired by Central Places Theory and find that it leads to positive long-range correlations, unless there is strong additional spatial disorder-contrary to intuition. We conclude that the interactions between cities extend over large distances reaching the country scale. Our findings have policy relevance as urban development or decline can affect cities at a considerable distance.

Nonlinear analysis of neuronal firing modulated by sinusoidal stimulation at axons in rat hippocampus.

Introduction: Electrical stimulation of the brain has shown promising prospects in treating various brain diseases. Although biphasic pulse stimulation remains the predominant clinical approach, there has been increasing interest in exploring alternative stimulation waveforms, such as sinusoidal stimulation, to improve the effectiveness of brain stimulation and to expand its application to a wider range of brain disorders. Despite this growing attention, the effects of sinusoidal stimulation on neurons, especially on their nonlinear firing characteristics, remains unclear. Methods: To address the question, 50 Hz sinusoidal stimulation was applied on Schaffer collaterals of the rat hippocampal CA1 region in vivo. Single unit activity of both pyramidal cells and interneurons in the downstream CA1 region was recorded and analyzed. Two fractal indexes, namely the Fano factor and Hurst exponent, were used to evaluate changes in the long-range correlations, a manifestation of nonlinear dynamics, in spike sequences of neuronal firing. Results: The results demonstrate that sinusoidal electrical stimulation increased the firing rates of both pyramidal cells and interneurons, as well as altered their firing to stimulation-related patterns. Importantly, the sinusoidal stimulation increased, rather than decreased the scaling exponents of both Fano factor and Hurst exponent, indicating an increase in the long-range correlations of both pyramidal cells and interneurons. Discussion: The results firstly reported that periodic sinusoidal stimulation without long-range correlations can increase the long-range correlations of neurons in the downstream post-synaptic area. These results provide new nonlinear mechanisms of brain sinusoidal stimulation and facilitate the development of new stimulation modes.

Computational insight into the effect of alkyl chain length in tetraalkylammonium-based deep eutectic solvents.

The effect of the increase in the alkyl chain length of cation on the properties of deep eutectic solvents based on ethylene glycol has been investigated employing classical molecular dynamics simulations. The change in the structural and dynamic properties in both the bulk and liquid-vapor interface is explored through various analyses. The interaction between the anion and the ethylene glycol increases with an increase in the alkyl chain length of the cation, as observed in the increase of the lifetime of the hydrogen bond formed between the two. The terminal carbon atoms are found to be closer to each other when the cation changes from tetraethylammonium to tetrabutylammonium. The cations are located closer to the interface, and the association of the alkyl chains becomes more significant with increased alkyl chain length, decreasing the surface tension values.

Application of vibration to the soles increases long-range correlations in the stride parameters during walking.

Temporal fluctuations in the stride parameters during human walking exhibit long-range correlations, but these long-range correlations in the stride parameters decrease due to aging or neuromuscular diseases. These observations suggest that any quantified index of the long-range correlation can be regarded as an indicator of gait functionality. Considering the effect of task-relevant sensory feedback on augmenting human motor performance, we devised shoes with active insoles that could deliver noisy vibration to the soles of feet and assessed their efficacy in enhancing the long-range correlations in the stride parameters for healthy young adults. The vibration could be wirelessly controlled using a smartphone. The actuators, control unit, and battery in the devised shoes were light and embedded in the shoes. By virtue of this compactness, the shoes could be easily used for daily walking outside a laboratory. We performed walking experiments with 20 healthy adults and evaluated the effects of sub- and supra-threshold vibration on long-range correlations in stride interval and length. We performed detrended fluctuation analysis to quantify the long-range correlation of temporal changes in stride interval and length. We found that supra-threshold vibration, applied to the soles with the amplitude of 130 % of the sensory threshold, significantly increased the long-range correlations in stride interval and length by 10.3 % (p = 0.009) and 10.1 % (p = 0.021), respectively. On the other hand, sub-threshold vibration with the amplitude of 90 % of the sensory threshold had no significant effect. These results demonstrate that additional somatosensory feedback through barely detectable vibrations, which are supplied by compact shoes with active insoles, can enhance the indices of "healthy" complexity of locomotor function.

Characterization of Anesthesia in Rats from EEG in Terms of Long-Range Correlations.

Long-range correlations are often used as diagnostic markers in physiological research. Due to the limitations of conventional techniques, their characterizations are typically carried out with alternative approaches, such as the detrended fluctuation analysis (DFA). In our previous works, we found EEG-related markers of the blood-brain barrier (BBB), which limits the penetration of major drugs into the brain. However, anesthetics can penetrate the BBB, affecting its function in a dose-related manner. Here, we study two types of anesthesia widely used in experiments on animals, including zoletil/xylazine and isoflurane in optimal doses not associated with changes in the BBB. Based on DFA, we reveal informative characteristics of the electrical activity of the brain during such doses that are important for controlling the depth of anesthesia in long-term experiments using magnetic resonance imaging, multiphoton microscopy, etc., which are crucial for the interpretation of experimental results. These findings provide an important informative platform for the enhancement and refinement of surgery, since the EEG-based DFA analysis of BBB can easily be used during surgery as a tool for characterizing normal BBB functions under anesthesia.

Multifractal detrended fluctuation analysis of insole pressure sensor data to diagnose vestibular system disorders.

The vestibular system (VS) is a sensory system that has a vital function in human life by serving to maintain balance. In this study, multifractal detrended fluctuation analysis (MFDFA) is applied to insole pressure sensor data collected from subjects in order to extract features to identify diseases related to VS dysfunction. We use the multifractal spectrum width as the feature to distinguish between healthy and diseased people. It is observed that multifractal behavior is more dominant and thus the spectrum is wider for healthy subjects, where we explain the reason as the long-range correlations of the small and large fluctuations of the time series for this group. We directly process the instantaneous pressure values to extract features in contrast to studies in the literature where gait analysis is based on investigation of gait dynamics (stride time, stance time, etc.) requiring long walking time. Thus, as the main innovation of this work, we detrend the data to give meaningful information even for a relatively short walk. Extracted feature set was input to fundamental classification algorithms where the Support-Vector-Machine (SVM) performed best with an average accuracy of 98.2% for the binary classification as healthy or suffering. This study is a substantial part of a big project where we finally aim to identify the specific VS disease that causes balance disorder and also determine the stage of the disease, if any. Within this scope, the achieved performance gives high motivation to work more deeply on the issue.

Stride-to-stride variability and fluctuations at intensities around lactate threshold in distance runners.

Stride-to-stride variability and fluctuations in running have been widely investigated in relation to fatigue, injury, and other factors. However, no studies have examined the relationship of stride-to-stride variability and fluctuations with lactate threshold (LT), a well-known performance indicator for distance runners that represents the threshold at which fast-twitch muscle fibers are activated and the glycolytic system is hyperactivated. In this study, we examined a relationship between LT and stride-to-stride variability and fluctuations in trained middle- and long-distance runners (n = 33). All runners were asked to perform multistage graded exercise tests while wearing accelerometers on the upper surface of their shoes. The LT was determined by measuring blood lactate concentrations after each stage. Three gait parameters for each step were calculated based on the acceleration data: stride time (ST), ground contact time (CT), and peak acceleration (PA). The coefficient of variation (CV) and the long-range correlations (α) for each parameter were also calculated. The effects of the runner's group and the relative intensity for CV and α on gait parameters were evaluated using a two-way repeated measures analysis of variance. Although no significant effect was observed in the CV and α of ST, significant intensity main effects were observed for the CV and α of CT and PA. The lack of significant changes in ST might be the result of runners' adequate control of ST to minimize energy cost. All the parameters showing significant changes with increasing intensity decreased dramatically when they were close to LT. This might have been caused by an increase in physiological load near LT and be interpreted as a variation in motor control because of alternations in the mobilized muscle fibers and physiological changes around the LT. The α should be useful for non-invasive LT detection.

Running gait produces long range correlations: A systematic review.

BACKGROUND: Walking and running are common forms of locomotion, both of which exhibit variability over many gait cycles. Many studies have investigated the patterns generated from that ebb and flow, and a large proportion suggests human gait exhibits Long Range Correlations (LRCs). LRCs refer to the observation that healthy gait characteristic, like stride times, are positively correlated to themselves over time. Literature on LRCs in walking gait is well known but less attention has been given to LRCs in running gait. RESEARCH QUESTION: What is the state of the art concerning LRCs in running gait? METHODS: We conducted a systematic review to identify the typical LRC patterns present in human running gait, in addition to disease, injury, and running surface effects on LRCs. Inclusion criteria were human subjects, running related experiments, computed LRCs, and experimental design. Exclusion criteria were studies on animals, non-humans, walking only, non-running, non-LRC analysis, and non-experiments. RESULTS: The initial search returned 536 articles. After review and deliberation, our review included 26 articles. Almost every article produced strong evidence for LRCs apparent in running gait and in all running surfaces. Additionally, LRCs tended to decrease due to fatigue, past injury, increased load carriage and seem to be lowest at preferred running speed on a treadmill. No studies investigated disease effects on LRCs in running gait. SIGNIFICANCE: LRCs seem to increase with deviations away from preferred running speed. Previously injured runners produced decreased LRCs compared to non-injured runners. LRCs also tended to decrease due to an increase in fatigue rate, which has been associated with increased injury rate. Lastly, there is a need for research on the typical LRCs in an overground environment, for which the typical LRCs found in a treadmill environment may or may not transfer.

A fractal scaling analysis of the SARS-CoV-2 genome sequence.

An approach based on fractal scaling analysis to characterize the organization of the SARS-CoV-2 genome sequence was used. The method is based on the detrended fluctuation analysis (DFA) implemented on a sliding window scheme to detect variations of long-range correlations over the genome sequence regions. The nucleotides sequence is mapped in a numerical sequence by using four different assignation rules: amino-keto, purine-pyrimidine, hydrogen-bond and hydrophobicity patterns. The originally reported sequence from Wuhan isolates (Wuhan Hu-1) was considered as a reference to contrast the structure of the 2002-2004 SARS-CoV-1 strain. Long-range correlations, quantified in terms of a scaling exponent, depended on both the mapping rule and the sequence region. Deviations from randomness were attributed to serial correlations or anti-correlations, which can be ascribed to ordered regions of the genome sequence. It was found that the Wuhan Hu-1 sequence was more random than the SARS-CoV-1 sequence, which suggests that the SARS-CoV-2 possesses a more efficient genomic structure for replication and infection. In general, the virus isolated in the early 2020 months showed slight correlation differences with the Wuhan Hu-1 sequence. However, early isolates from India and Italy presented visible differences that led to a more ordered sequence organization. It is apparent that the increased sequence order, particularly in the spike region, endowed some early variants with a more efficient mechanism to spreading, replicating and infecting. Overall, the results showed that the DFA provides a suitable framework to assess long-term correlations hidden in the internal organization of the SARS-CoV-2 genome sequence.

Assessing the Temporal Organization of Walking Variability: A Systematic Review and Consensus Guidelines on Detrended Fluctuation Analysis.

Human physiological signals are inherently rhythmic and have a hallmark feature in that even distant intrasignal measurements are related to each other. This relationship is termed long-range correlation and has been recognized as an indicator of the optimal state of the observed physiological systems, among which the locomotor system. Loss of long-range correlations has been found as a result of aging as well as disease, which can be evaluated with detrended fluctuation analysis (DFA). Recently, DFA and the scaling exponent α have been employed for understanding the degeneration of temporal regulation of human walking biorhythms in, for example, Parkinson disease (PD). However, heterogeneous evidence on scaling exponent α values reported in the literature across different population groups has put into question what constitutes a healthy physiological pattern. Therefore, the purpose of this systematic review was to investigate the functional thresholds of scaling exponent α in young vs. older adults, as well as between patients with PD and age-matched asymptomatic controls. Aging and PD exhibited a negative effect size (i.e., led to decreased long-range correlations) of -0.20 and -0.53, respectively. Our meta-analysis based on 14 studies provides evidence that a mean scaling exponent α threshold of 0.86 [2 standard error (0.76, 0.96)] is able to optimally discriminate temporal organization of stride interval between young and old, whereas 0.82 (0.72, 0.92) differentiates patients with PD and age-matched asymptomatic controls. The optimal thresholds presented in this review together with the consensus guidelines for using DFA might allow a more sensitive and reliable application of this metric for understanding human walking physiology than has been achieved to date.

Detrended fluctuation analysis detects altered coordination of running gait in athletes following a heavy period of training.

OBJECTIVES: To investigate whether functional overreaching affects locomotor system behaviour when running at fixed relative intensities and if any effects were associated with changes in running performance. DESIGN: Prospective intervention study. METHODS: Ten trained male runners completed three training blocks in a fixed order. Training consisted of one week of light training (baseline), two weeks of heavy training designed to induce functional overreaching, and ten days of light taper training designed to allow athletes to recover from, and adapt to, the heavy training. Locomotor behaviour, 5-km time trial performance, and subjective reports of training status (Daily Analysis of Life Demands for Athletes (DALDA) questionnaire) were assessed at the completion of each training block. Locomotor behaviour was assessed using detrended fluctuation analysis of stride intervals during running at speeds corresponding to 65% and 85% of maximum heart rate (HRmax) at baseline. RESULTS: Time trial performance (effect size ±95% confidence interval (ES): 0.16±0.06; p<0.001), locomotor behaviour at 65% HRmax (ES: -1.12±0.95; p=0.026), and DALDA (ES: 2.55±0.80; p<0.001) were all detrimentally affected by the heavy training. Time trial performance improved relative to baseline after the taper (ES: -0.16±0.10; p=0.003) but locomotor behaviour at 65% HRmax (ES: -1.18±1.17; p=0.048) and DALDA (ES: 0.92±0.90; p=0.045) remained impaired. CONCLUSIONS: Locomotor behaviour during running at 65% HRmax was impaired by functional overreaching and remained impaired after a 10-day taper, despite improved running performance. Locomotor changes may increase injury risk and should be considered within athlete monitoring programs independently of performance changes.

Temporal Structure in Haptic Signaling Under a Cooperative Task.

Haptic communication between humans plays an important role in society. Although this form of communication is ubiquitous at all levels of society and of human development, little is known about how synchronized coordination of motion between two persons leads to higher-order cognitive functions used in communication. In this study, we developed a novel experimental paradigm of a coin-collecting task in which participants used their hands to control a rod to jointly collect the coins on the screen. We characterized the haptic interactions between paired participants while they were taking part in a cooperative task. The individual participants first completed this task on their own and then with a randomly assigned partner for the cooperative task. Single participant experiments were used as a baseline to compare results of the paired participants. Forces applied to the rod were translated to four possible haptic states which encode the combination of the haptic interactions. As a next step, pairs of consecutive haptic states were then combined into 16 possible haptic signals which were classified in terms of their temporal patterns using a Tsallis q-exponential function. For paired participants, 80% of the haptic signals could be fit by the Tsallis q-exponential. On the other hand, only 30% of the signals found in the single-participant trials could be fit by the Tsallis q-exponential. This shows a clear difference in the temporal structures of haptic signals when participants are interacting with each other and when they are not. We also found a large difference in the number of haptic signals used by paired participants and singles. Single participants only used 1/4 of the possible haptic signals. Paired participants, on the other hand, used more than half of the possible signals. These results suggest that temporal structures present in haptic communication could be linked to the emergence of language at an evolutionary level.

Factorization of Force and Timing in Sensorimotor Performance: Long-Range Correlation Properties of Two Different Task Goals.

Long-range correlations are often manifested in the form of 1/fß noise in a series of repeated measurements of the same neural or behavioral variable. Recent work has demonstrated that the magnitude and nature of these long-range correlations reliably capture individual differences and variation in task performance. In sensorimotor timing experiments, task characteristics such as tapping or circle drawing affect these long-range correlations during the production of isochronous time intervals. Such correlations are highly reproducible across multiple trials for the same task but do not correlate between tasks. In the present experiment, we investigate whether two behavioral variables that are simultaneously controlled by the same participant in a given experimental condition can show such differentially organized fluctuations. In order to answer this question, 13 participants were asked to produce repetitive movements with their right index finger at a specified time interval (500 ms) and a specified force (8N) in the absence of an auditory metronome and visual feedback of force levels following a synchronization-continuation paradigm. Although participants showed high levels of consistency in the long-range correlations for each task component separately over multiple trials/observations, the long-range fluctuations for force and timing were found to show no correlations with each other for each participant. Cross recurrence quantification analyses (CRQA) revealed that there was limited shared structure between the timing and force time series data. Taken together, these results suggest that complex systems can organize multiple processes in a relatively independent manner while maintaining a high degree of reliability within one task parameter.

The visualCMAT: A web-server to select and interpret correlated mutations/co-evolving residues in protein families.

The visualCMAT web-server was designed to assist experimental research in the fields of protein/enzyme biochemistry, protein engineering, and drug discovery by providing an intuitive and easy-to-use interface to the analysis of correlated mutations/co-evolving residues. Sequence and structural information describing homologous proteins are used to predict correlated substitutions by the Mutual information-based CMAT approach, classify them into spatially close co-evolving pairs, which either form a direct physical contact or interact with the same ligand (e.g. a substrate or a crystallographic water molecule), and long-range correlations, annotate and rank binding sites on the protein surface by the presence of statistically significant co-evolving positions. The results of the visualCMAT are organized for a convenient visual analysis and can be downloaded to a local computer as a content-rich all-in-one PyMol session file with multiple layers of annotation corresponding to bioinformatic, statistical and structural analyses of the predicted co-evolution, or further studied online using the built-in interactive analysis tools. The online interactivity is implemented in HTML5 and therefore neither plugins nor Java are required. The visualCMAT web-server is integrated with the Mustguseal web-server capable of constructing large structure-guided sequence alignments of protein families and superfamilies using all available information about their structures and sequences in public databases. The visualCMAT web-server can be used to understand the relationship between structure and function in proteins, implemented at selecting hotspots and compensatory mutations for rational design and directed evolution experiments to produce novel enzymes with improved properties, and employed at studying the mechanism of selective ligand's binding and allosteric communication between topologically independent sites in protein structures. The web-server is freely available at https://biokinet.belozersky.msu.ru/visualcmat and there are no login requirements.

Nonlinear temperature effects on multifractal complexity of metabolic rate of mice.

Complex physiological dynamics have been argued to be a signature of healthy physiological function. Here we test whether the complexity of metabolic rate fluctuations in small endotherms decreases with lower environmental temperatures. To do so, we examine the multifractal temporal scaling properties of the rate of change in oxygen consumption r(VO2), in the laboratory mouse Mus musculus, assessing their long range correlation properties across seven different environmental temperatures, ranging from 0 °C to 30 °C. To do so, we applied multifractal detrended fluctuation analysis (MF-DFA), finding that r(VO2) fluctuations show two scaling regimes. For small time scales below the crossover time (approximately 102 s), either monofractal or weak multifractal dynamics are observed depending on whether Ta < 15 °C or Ta > 15 °C respectively. For larger time scales, r(VO2) fluctuations are characterized by an asymptotic scaling exponent that indicates multifractal anti-persistent or uncorrelated dynamics. For both scaling regimes, a generalization of the multiplicative cascade model provides very good fits for the Renyi exponents τ(q), showing that the infinite number of exponents h(q) can be described by only two independent parameters, a and b. We also show that the long-range correlation structure of r(VO2) time series differs from randomly shuffled series, and may not be explained as an artifact of stochastic sampling of a linear frequency spectrum. These results show that metabolic rate dynamics in a well studied micro-endotherm are consistent with a highly non-linear feedback control system.