A comparative analysis of fracture mechanisms in high- and very high- cycle fatigue (HCF, VHCF) regimes was carried out based on the results of multifractal analysis of the fracture surfaces of additively manufactured 316L stainless steel samples. In terms of scale invariants, the morphology of fracture surfaces in HCF and VHCF regimes inside and outside the fine granular area is shown. The analysis demonstrated that chaotic patterns of relief formation prevail in the crack initiation zone of VHCF samples. However, there is a self-similar relief with a pronounced correlation in the crack propagation area. The relief of the crack growth areas for HCF and VHCF samples are similar to each other.

The aim of this paper is to investigate whether a multifractal analysis can be applied to study choroidal blood vessels and help ophthalmologists in the early diagnosis of retinitis pigmentosa (RP). In a case study, we used spectral domain optical coherence tomography (SDOCT), which is a noninvasive and highly sensitive imaging technique of the retina and choroid. The image of a choroidal branching pattern can be regarded as a multifractal. Therefore, we calculated the generalized Renyi point-centered dimensions, which are considered a measure of the inhomogeneity of data, to prove that it increases in patients with RP as compared to those in the control group.

The characteristics of biomedical signals are not captured by conventional measures like the average amplitude of the signal. The methodologies derived from fractal geometry have been a very useful approach to study the degree of irregularity of a signal. The monofractal analysis of a signal is defined by a single power-law exponent in assuming a scale invariance in time and space. However, temporal and spatial variation in the scale-invariant structure of the biomedical signal often appears. In this case, multifractal analysis is well-suited because it is defined by a multifractal spectrum of power-law exponents. There are several approaches to the implementation of this analysis, and there are numerous ways to present these.In this chapter, we review the use of multifractal analysis for the purpose of characterizing signals in neuroimaging. After describing the tenets of multifractal analysis, we present several approaches to estimating the multifractal spectrum. Finally, we describe the applications of this spectrum on biomedical signals in the characterization of several diseases in neurosciences.

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 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.

Type 2 diabetes mellitus (T2DM) is characterized by several complications, such as retinopathy, renal failure, cardiovascular disease, and diabetic neuropathy. Among these, neuropathy is the most severe complication, due to the challenging nature of its early detection. The linear Hearth Rate Variability (HRV) analysis is the most common diagnosis technique for diabetic neuropathy, and it is characterized by the determination of the sympathetic-parasympathetic balance on the peripheral nerves through a linear analysis of the tachogram obtained using photoplethysmography. We aimed to perform a multifractal analysis to identify autonomic neuropathy, which was not yet manifest and not detectable with the linear HRV analysis. We enrolled 10 healthy controls, 10 T2DM-diagnosed patients with not-full-blown neuropathy, and 10 T2DM diagnosed patients with full-blown neuropathy. The tachograms for the HRV analysis were obtained using finger photoplethysmography and a linear and/or multifractal analysis was performed. Our preliminary results showed that the linear analysis could effectively differentiate between healthy patients and T2DM patients with full-blown neuropathy; nevertheless, no differences were revealed comparing the full-blown to not-full-blown neuropathic diabetic patients. Conversely, the multifractal HRV analysis was effective for discriminating between full-blown and not-full-blown neuropathic T2DM patients. The multifractal analysis can represent a powerful strategy to determine neuropathic onset, even without clinical diagnostic evidence.

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.

The binding of conidia to surfaces is a prerequisite for biofouling by fungal species. In this study, Aspergillus niger subtypes 1957 and 1988 were used which produced differently shaped conidia (round or spikey respectively). Test surfaces were characterised for their surface topography, wettability, and hardness. Conidial assays included perpendicular and lateral force measurements, as well as attachment, adhesion and retention assays. Anionic surfaces were less rough (Ra 2.4 nm), less wettable (54°) and harder (0.72 GPa) than cationic surfaces (Ra 5.4 nm, 36° and 0.5 GPa, respectively). Perpendicular and lateral force assays demonstrated that both types of conidia adhered with more force to the anionic surfaces and were influenced by surface wettability. Following the binding assays, fewer A. niger 1957 and A. niger 1988 conidia bound to the anionic surface. However, surface wettability affected the density and dispersion of the conidia on the coatings, whilst clustering was affected by their spore shapes. This work demonstrated that anionic surfaces were more repulsive to A. niger 1998 spores than cationic surfaces were, but once attached, the conidia bound more firmly to the anionic surfaces. This work informs on the importance of understanding how conidia become tightly bound to surfaces, which can be used to prevent biofouling.

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.

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