Cross-scale spatial variability and associations of carbon pools provide insight into regulating carbon sequestration in tropical montane rainforests.

The spatial distribution of plant, soil, and microbial carbon pools, along with their intricate interactions, presents a great challenge for the current carbon cycle research. However, it is not clear what are the characteristics of the spatial variability of these carbon pools, particularly their cross-scale relationships. We investigated the cross-scale spatial variability of microbial necromass carbon (MNC), soil organic carbon (SOC) and plant biomass (PB), as well as their correlation in a tropical montane rainforest using multifractal analysis. The results showed multifractal spatial variations of MNC, SOC, and PB, demonstrating their adherence to power-law scaling. MNC, especially low MNC, exhibited stronger spatial heterogeneity and weaker evenness compared with SOC and PB. The cross-scale correlation between MNC and SOC was stronger than their correlations at the measurement scale. Furthermore, the cross-scale spatial variability of MNC and SOC exhibited stronger and more stable correlations than those with PB. Additionally, this research suggests that when SOC and PB are both low, it is advisable for reforestations to potentiate MNC formation, whereas when both SOC and PB are high some thinning can be advisable to favour MNC formation. Thus, these results support the utilization of management measures such as reforestation or thinning as nature-based solutions to regulate carbon sequestration capacity of tropical forests by affecting the correlations among various carbon pools.

An energy-efficient solution to sludge drying and combustion process through Camellia oleifera shells amended foaming.

Foaming pretreatment has been proven effective in promoting sludge drying, however, the variation in sludge properties significantly influences the foaming efficiency. Inspired by foam stabilizer of solid particles, Camellia oleifera shells (COS) was screened out from various biomasses as an additive incorporated with the CaO for promoting the sludge foaming. For the introduction of COS, this study analyzed the drying behaviors of foamed sludge, quantified the surface cracks information, characterized the combustion performance, and evaluated the energy consumption. The results indicated that 46.72-50.10% of time could be saved in foaming the sludge to 0.70 g/mL by addition of 3.0 wt% COS. Compared with the original sludge (OS), the 0.70 g/mL foamed sludge saved 47.43% of time for sludge drying at 80 °C, and this value further increased to 53.14% with 3.0 wt% COS addition. Combining the multifractal spectra and drying kinetics analysis, the foaming promoted the formation of complex surface cracks in the warm-up period, while COS further improved the complexity of cracks in the constant rate period, and the shrinkage of isolated sludge blocks in the falling rate period, thus enhanced the moisture diffusion and heat transfer. Furthermore, the appropriate porous structure and additional volatile matters promoted the combustion performance. The 0.90 g/mL foamed sludge with COS presented the lowest activation energy of 180.362 kJ/mol in combustion. Overall, compared with OS, the 0.70 g/mL foamed sludge with COS saved 40.65% energy consumption during the foaming, drying and combustion processes, providing an energy-efficient solution for the sludge treatment and disposal.

The environmental capacity of rare heavy metal calculation in the Qinghai‒Tibet Plateau region via multifractal analysis.

Accurate assessments of the soil environmental capacity are important for evaluating heavy metal pollution levels, facilitating effective prevention and control measures against such pollution. However, due to the lack of risk screening values for certain key elements, such as Rb, Sn, and Th, the assessment of the soil environmental capacity is not comprehensive. Therefore, in this study, the Menyuan-Huangzhong area of Qinghai Province was selected as the research area, and local background and risk values were established via multifractal analysis, thereby systematically examining the environmental capacity. The findings indicated that within the study area, the static environmental capacity values of 15 elements could be ranked as follows: Ba, Cu, Zn, Cr, Rb, Ni, La, Pb, Th, As, U, Sn, Tl, Cd, and Hg. In general, the residual capacity distribution of the various elements varied across the study area, with lower values primarily found in the northern and central regions and higher values obtained in the northwestern and southwestern regions. Between 2018 and 2068, there was a notable and rapid decline in the dynamic environmental capacity of Hg, Cu, and Cd in the study area. In the Menyuan-Huangzhong area of Qinghai, the average comprehensive soil environmental capacity index reached 0.91, indicating a moderate environmental capacity and slight associated health risks. The findings of this study could serve as a valuable reference for soil heavy metal pollution assessment, early warning, and management in this area; enhance the study of soil environmental capacity methods; and provide a theoretical foundation for subsequent research.

Fault Diagnosing of Cycloidal Gear Reducer Using Statistical Features of Vibration Signal and Multifractal Spectra.

The article presents a method for diagnosing cycloidal gear damage on a laboratory stand. The damage was simulated by removing the sliding sleeves from two adjacent external pins of the cycloidal gearbox. Damage to the sliding sleeves may occur under operating conditions and can lead to the destruction of the gear unit. Hence, early detection is essential. Signals from torque sensors, rotational speed sensors and vibration acceleration sensors of input and output shafts for various rotational speeds and transmission loads were recorded. The frequency analysis of these signals was carried out. Due to the fluctuation of the rotational speed, the frequency spectrum gives an approximate picture and is not useful in detecting this type of damage. The statistical characteristics of the signal were determined. However, only statistical moments of higher orders, such as kurtosis, are sensitive to the tested damage. Therefore, the use of multifractal analysis of the vibration signal using the wavelet leader method (WLMF) was considered. Then log-cumulants of the multifractal spectrum were selected as the new signal features.

Expecting the Unexpected: Entropy and Multifractal Systems in Finance.

Entropy serves as a measure of chaos in systems by representing the average rate of information loss about a phase point's position on the attractor. When dealing with a multifractal system, a single exponent cannot fully describe its dynamics, necessitating a continuous spectrum of exponents, known as the singularity spectrum. From an investor's point of view, a rise in entropy is a signal of abnormal and possibly negative returns. This means he has to expect the unexpected and prepare for it. To explore this, we analyse the New York Stock Exchange (NYSE) U.S. Index as well as its constituents. Through this examination, we assess their multifractal characteristics and identify market conditions (bearish/bullish markets) using entropy, an effective method for recognizing fluctuating fractal markets. Our findings challenge conventional beliefs by demonstrating that price declines lead to increased entropy, contrary to some studies in the literature that suggest that reduced entropy in market crises implies more determinism. Instead, we propose that bear markets are likely to exhibit higher entropy, indicating a greater chance of unexpected extreme events. Moreover, our study reveals a power-law behaviour and indicates the absence of variance.

Investigating Dynamical Complexity and Fractal Characteristics of Bitcoin/US Dollar and Euro/US Dollar Exchange Rates around the COVID-19 Outbreak.

This article investigates the dynamical complexity and fractal characteristics changes of the Bitcoin/US dollar (BTC/USD) and Euro/US dollar (EUR/USD) returns in the period before and after the outbreak of the COVID-19 pandemic. More specifically, we applied the asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) method to investigate the temporal evolution of the asymmetric multifractal spectrum parameters. In addition, we examined the temporal evolution of Fuzzy entropy, non-extensive Tsallis entropy, Shannon entropy, and Fisher information. Our research was motivated to contribute to the comprehension of the pandemic's impact and the possible changes it caused in two currencies that play a key role in the modern financial system. Our results revealed that for the overall trend both before and after the outbreak of the pandemic, the BTC/USD returns exhibited persistent behavior while the EUR/USD returns exhibited anti-persistent behavior. Additionally, after the outbreak of COVID-19, there was an increase in the degree of multifractality, a dominance of large fluctuations, as well as a sharp decrease of the complexity (i.e., increase of the order and information content and decrease of randomness) of both BTC/USD and EUR/USD returns. The World Health Organization (WHO) announcement, in which COVID-19 was declared a global pandemic, appears to have had a significant impact on the sudden change in complexity. Our findings can help both investors and risk managers, as well as policymakers, to formulate a comprehensive response to the occurrence of such external events.

The Impact of COVID-19 on Weak-Form Efficiency in Cryptocurrency and Forex Markets.

The COVID-19 pandemic has had an unprecedented impact on the global economy and financial markets. In this article, we explore the impact of the pandemic on the weak-form efficiency of the cryptocurrency and forex markets by conducting a comprehensive comparative analysis of the two markets. To estimate the weak-form of market efficiency, we utilize the asymmetric market deficiency measure (MDM) derived using the asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) approach, along with fuzzy entropy, Tsallis entropy, and Fisher information. Initially, we analyze the temporal evolution of these four measures using overlapping sliding windows. Subsequently, we assess both the mean value and variance of the distribution for each measure and currency in two distinct time periods: before and during the pandemic. Our findings reveal distinct shifts in efficiency before and during the COVID-19 pandemic. Specifically, there was a clear increase in the weak-form inefficiency of traditional currencies during the pandemic. Among cryptocurrencies, BTC stands out for its behavior, which resembles that of traditional currencies. Moreover, our results underscore the significant impact of COVID-19 on weak-form market efficiency during both upward and downward market movements. These findings could be useful for investors, portfolio managers, and policy makers.

Broadband Dynamics Rather than Frequency-Specific Rhythms Underlie Prediction Error in the Primate Auditory Cortex.

Detection of statistical irregularities, measured as a prediction error response, is fundamental to the perceptual monitoring of the environment. We studied whether prediction error response is associated with neural oscillations or asynchronous broadband activity. Electrocorticography was conducted in three male monkeys, who passively listened to the auditory roving oddball stimuli. Local field potentials (LFPs) recorded over the auditory cortex underwent spectral principal component analysis, which decoupled broadband and rhythmic components of the LFP signal. We found that the broadband component captured the prediction error response, whereas none of the rhythmic components were associated with statistical irregularities of sounds. The broadband component displayed more stochastic, asymmetrical multifractal properties than the rhythmic components, which revealed more self-similar dynamics. We thus conclude that the prediction error response is captured by neuronal populations generating asynchronous broadband activity, defined by irregular dynamic states, which, unlike oscillatory rhythms, appear to enable the neural representation of auditory prediction error response.SIGNIFICANCE STATEMENT This study aimed to examine the contribution of oscillatory and asynchronous components of auditory local field potentials in the generation of prediction error responses to sensory irregularities, as this has not been directly addressed in the previous studies. Here, we show that mismatch negativity-an auditory prediction error response-is driven by the asynchronous broadband component of potentials recorded in the auditory cortex. This finding highlights the importance of nonoscillatory neural processes in the predictive monitoring of the environment. At a more general level, the study demonstrates that stochastic neural processes, which are often disregarded as neural noise, do have a functional role in the processing of sensory information.

Multifractal analysis of chest CT images of patients with the 2019 novel coronavirus disease (COVID-19).

The present study was done to evaluate chest computed tomography (CT) images of patients with 2019 novel coronavirus disease (COVID-19) by multifractal technique as a new method to find a way for comparing lung infection quantitatively and identifying progression pattern of the disease. The multifractal spectra extracted from analysis of CT images showed that these spectra were correlated with lung infection amount and disease progression so that, multifractal parameters (αmin, αmax, ∆α, f(αmin), f(αmax), ∆f(α), α(q = 0), and f(α) max) were strongly dependent on amount of lung infection. The results demonstrated that multifractality of chest CT images was increased with the increase in lung infection in patients. The interesting and promising result was that capacity dimension (D0) as a new diagnostic parameter varied linearly with progression and reduction of lung infection. A critical value was found for D0, according to which patients with D0 lower than 1.4 can be healed by treatment. Therefore, herein, a way was found for quantitative assessment of lung infection of patients with COVID-19 by analyzing chest CT images using the multifractal method. This method can be very effective for physicians in diagnosis and treatment of pneumonia caused by COVID-19 and timely identification of therapeutic effects.

Population density impact on COVID-19 mortality rate: A multifractal analysis using French data.

The current COVID-19 pandemic caught everyone off guard and is an excellent case study to investigate the real impact of population density on emerging highly contagious infectious diseases. The relationship between the threat of COVID-19 and population density has been widely debated not only in scientific articles, but also in magazines and reports around the world. It appeared both in the columns of experts and in the speeches of politicians, yet without reaching any consensus. In this study, using COVID-19 data from France, we try to shed light on this debate. An alternative density measure, weighted by population, is used. This novel density measure clearly outperforms the commonly used density in terms of relationship with COVID-19 deaths and proved to be competitive with some of the best known predictors, including population. A multifractal analysis, characterizing different space distributions of population in France, is used to further understand the relation between density and COVID-19 mortality rate.

Multifractal dimensions of soil particle size distribution reveal the erodibility and fertility of alpine grassland soils in the Northern Tibet Plateau.

Climate change and human activities have seriously degraded alpine grassland, potentially affecting soil particle size distribution (PSD) and further influencing the nutrient levels and erodibility of soil. Predicting the fertility and erodibility of alpine soil using multifractal dimensions of soil PSD could be used to enhance the management and restoration of degraded alpine grasslands. In the present study, we evaluated three types of alpine grasslands: alpine meadow (AM), alpine steppe (AS), and alpine desert steppe (ADS). Fencing and grazing management measures were conducted at sites containing each grassland type. Then, we analyzed the PSDs, erodibility, and other properties of soil in the 0-20 cm soil layer. Multifractal characterization of soil PSD was calculated using the fractal scale theory. The findings showed that grassland type significantly impacted soil nutrients and the multifractal dimensions of soil PSDs, whereas management measures affected soil erodibility significantly. The proportion of finer particles decreased as follows: AM > AS > ADS. Compared to grazing, fencing enhanced clay content and reduced the proportion of coarser particles under all three grassland types. AM had higher organic carbon and nitrogen levels than AS and ADS. Multifractal dimensions were highest for AM, with ADS having higher erodibility than AM and AS. Multifractal dimensions (except for correlation dimension) also had significantly positive relationships with soil organic carbon and available nutrient content and soil erodibility, but had significantly negative correlations with soil pH, bulk density, and electrical conductivity. Thus, the multifractal dimensions of soil PSDs could be used to characterize the erodibility and fertility characteristics of soil in alpine regions, providing a reference for assessing vegetation restoration measures in the Northern Tibet Plateau.

Head-to-Tail and Head-to-Head Molecular Chains of Poly(p-Anisidine): Combined Experimental and Theoretical Evaluation.

Poly(p-anisidine) (PPA) is a polyaniline derivative presenting a methoxy (-OCH3) group at the para position of the phenyl ring. Considering the important role of conjugated polymers in novel technological applications, a systematic, combined experimental and theoretical investigation was performed to obtain more insight into the crystallization process of PPA. Conventional oxidative polymerization of p-anisidine monomer was based on a central composite rotational design (CCRD). The effects of the concentration of the monomer, ammonium persulfate (APS), and HCl on the percentage of crystallinity were considered. Several experimental techniques such as X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM), multifractal analysis, Nuclear Magnetic Resonance (13C NMR), Fourier-transform Infrared spectroscopy (FTIR), and complex impedance spectroscopy analysis, in addition to Density Functional Theory (DFT), were employed to perform a systematic investigation of PPA. The experimental treatments resulted in different crystal structures with a percentage of crystallinity ranging from (29.2 ± 0.6)% (PPA1HT) to (55.1 ± 0.2)% (PPA16HT-HH). A broad halo in the PPA16HT-HH pattern from 2θ = 10.0-30.0° suggested a reduced crystallinity. Needle and globular-particle morphologies were observed in both samples; the needle morphology might have been related to the crystalline contribution. A multifractal analysis showed that the PPA surface became more complex when the crystallinity was reduced. The proposed molecular structures of PPA were supported by the high-resolution 13C NMR results, allowing us to access the percentage of head-to-tail (HT) and head-to-head (HH) molecular structures. When comparing the calculated and experimental FTIR spectra, the most pronounced changes were observed in ν(C-H), ν(N-H), ν(C-O), and ν(C-N-C) due to the influence of counterions on the polymer backbone as well as the different mechanisms of polymerization. Finally, a significant difference in the electrical conductivity was observed in the range of 1.00 × 10-9 S.cm-1 and 3.90 × 10-14 S.cm-1, respectively, for PPA1HT and PPA16HT-HH.

Multifractal Company Market: An Application to the Stock Market Indices.

Using the multiscale normalized partition function, we exploit the multifractal analysis based on directly measurable shares of companies in the market. We present evidence that markets of competing firms are multifractal/multiscale. We verified this by (i) using our model that described the critical properties of the company market and (ii) analyzing a real company market defined by the S&P500 index. As the valuable reference case, we considered a four-group market model that skillfully reconstructs this index's empirical data. We point out that a four-group company market organization is universal because it can perfectly describe the essential features of the spectrum of dimensions, regardless of the analyzed series of shares. The apparent differences from the empirical data appear only at the level of subtle effects.

Coupled multifractal methods to reveal changes in nitrogen dioxide and tropospheric ozone concentrations during the COVID-19 lockdown.

Due to COVID-19 pandemic, the lockdown effects on air pollution level are undeniable. Several studies around the world have detected an uneven behaviour in tropospheric ozone (O 3) concentrations. In this work, Seville (Spain) is used as example of faced to traffic place in which the nitrogen dioxide (NO 2) is drastically reduced (41%) while O 3 has no significant changes. In order to evaluate the existence of differences in O 3 behaviour that is not detected by statistical procedures, a multifractal approach was used to assess the coupled scale relationship between NO 2 and O 3 during the 2020 lockdown against a period reference (2017-2019). For this purpose, the two main coupled multifractal method were employed: multifractal detrended cross-correlation and joint multifractal analysis. While cross-correlation analysis did not detect differences between the cross-correlated fluctuations of NO 2 and O 3 in the periods analysed, the joint multifractal analysis, based on the partition function and the method of moments, found a loss of variability in O 3 during the lockdown. This leads to a loss of multifractal characteristic of O 3 time series. The drastically reduction of primary pollutants during the lockdown might be the responsible of the tendency to monofractality in O 3 time series. These differences were found for a wide temporal extent ranging from 80 min to ~28 days.

On the multifractal analysis of air quality index time series before and during COVID-19 partial lockdown: A case study of Shanghai, China.

Due to the COVID-19 pandemic, human activities are largely restricted in Shanghai, China and it is a valuable experiment to testify the correlation of air quality and human activities. In consideration of the complexity of air pollution, this study aims to compare the multifractal characteristics of air quality index (AQI) time series before and during COVID-19 partial lockdown, and analyze the correlations between multifractal parameters of AQI time series and human activities in Shanghai, China. The hourly AQI series in Shanghai from November 27, 2019 to March 23, 2020 is used for this study. Firstly, using the MF-DFA method, the multifractal characteristics of the AQI series are explored. Secondly, the causes of the multifractality of the AQI series are determined. Finally, the correlations between multifractal parameters of AQI time series and human activities are investigated. The multifractal analysis results reveal that the AQI series during COVID-19 partial lockdown also has multifractal characteristics, and the slightly weaker multifractal characteristics and marginally smaller multifractal degree are obtained in comparison with the pre-lockdown phase. However, the contribution of the effective or intrinsic multifractality before and during COVID-19 partial lockdown are very close. The results via the sliding window procedure indicate that the multifractal parameters ( Δ H , Δ α , Δ f ) show the similar fluctuations along with the fluctuations of passenger volume in Shanghai Metro. Furthermore, it is found that Δ H , Δ α and Δ f and adjusted passenger volume in Shanghai Metro are positively correlated. The possible trend is that the higher adjusted passenger volume is, the larger the value of Δ H , Δ α , Δ f becomes, which means the stronger multifractal characteristics and larger multifractal degree of air quality system.

Permutation Entropy of Weakly Noise-Affected Signals.

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos.

We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

Complexity in Economic and Social Systems: Cryptocurrency Market at around COVID-19.

Social systems are characterized by an enormous network of connections and factors that can influence the structure and dynamics of these systems. Among them the whole economical sphere of human activity seems to be the most interrelated and complex. All financial markets, including the youngest one, the cryptocurrency market, belong to this sphere. The complexity of the cryptocurrency market can be studied from different perspectives. First, the dynamics of the cryptocurrency exchange rates to other cryptocurrencies and fiat currencies can be studied and quantified by means of multifractal formalism. Second, coupling and decoupling of the cryptocurrencies and the conventional assets can be investigated with the advanced cross-correlation analyses based on fractal analysis. Third, an internal structure of the cryptocurrency market can also be a subject of analysis that exploits, for example, a network representation of the market. In this work, we approach the subject from all three perspectives based on data from a recent time interval between January 2019 and June 2020. This period includes the peculiar time of the Covid-19 pandemic; therefore, we pay particular attention to this event and investigate how strong its impact on the structure and dynamics of the market was. Besides, the studied data covers a few other significant events like double bull and bear phases in 2019. We show that, throughout the considered interval, the exchange rate returns were multifractal with intermittent signatures of bifractality that can be associated with the most volatile periods of the market dynamics like a bull market onset in April 2019 and the Covid-19 outburst in March 2020. The topology of a minimal spanning tree representation of the market also used to alter during these events from a distributed type without any dominant node to a highly centralized type with a dominating hub of USDT. However, the MST topology during the pandemic differs in some details from other volatile periods.

Multifractal Characterization of Butterfly Wings Scales.

A lot of insect families have physical structures created by evolution for coloration. These structures are a source of ideas for new bio-inspired materials. The aim of this study was to quantitatively characterize the micromorphology of butterfly wings scales using atomic force microscopy and multifractal analysis. Two types of butterflies, Euploea mulciber ("striped blue crow") and Morpho didius ("giant blue morpho"), were studied. The three-dimensional (3D) surface texture of the butterfly wings scales was investigated focusing on two areas: where the perceived colors strongly depend on and where they do not depend on the viewing angle. The results highlight a correlation between the surface coloration and 3D surface microtexture of butterfly wings scales.

Wavelet leader multifractal analysis of heart rate variability in atrial fibrillation.

BACKGROUND: Accurate and timely detection of atrial fibrillation (AF) episodes is important in primarily and secondary prevention of ischemic stroke and heart-related problems. In this work, heart rate regularity of ECG inter-beat intervals was investigated in episodes of AF and other rhythms using a wavelet leader based multifractal analysis. Our aim was to improve the detectability of AF episodes. METHODS: Inter-beat intervals from 25 ECG recordings available in the MIT-BIH atrial fibrillation database were analysed. Four types of annotated rhythms (atrial fibrillation, atrial flutter, AV junctional rhythm, and other rhythms) were available. A wavelet leader based multifractal analysis was applied to 5 min non-overlapping windows of each recording to estimate the multifractal spectrum in each window. The width of the multifractal spectrum was analysed for its discrimination power between rhythm episodes. RESULTS: In 10 of 25 recordings, the width of multifractal spectrum was significantly lower in episodes of AF than in other rhythms indicating increased regularity during AF. High classification accuracy (95%) of AF episodes was achieved using a combination of features derived from the multifractal analysis and statistical central moment features. CONCLUSIONS: An increase in the regularity of inter-beat intervals was observed during AF episodes by means of multifractal analysis. Multifractal features may be used to improve AF detection accuracy.