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.

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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In this paper, the multifractal properties of the ion current time series in the fast-activating vacuolar (FV) channels of Beta vulgaris L. taproot cells were investigated. These channels are permeable for only monovalent cations and mediate K+ at very low concentrations of cytosolic Ca2+ and large voltages of either polarity. Using the patch clamp technique, the currents of the FV channels in red beet taproot vacuoles were recorded and analysed by using the multifractal detrended fluctuation analysis (MFDFA) method. The activity of the FV channels depended on the external potential and was sensitive to the auxin. It was also shown that the singularity spectrum of the ion current in the FV channels is non-singular, and the multifractal parameters, i.e., the generalised Hurst exponent and the singularity spectrum, were modified in the presence of IAA. Taking into account the obtained results, it can be suggested that the multifractal properties of fast-activating vacuolar (FV) K+ channels, indicating the existence of long-term memory, should be taken into account in the molecular mechanism of the auxin-induced growth of plant cells.

In the last 40 years, Chinese cities have seen extensive development across a wide array of spheres. In this study, we applied a power-law and multifractal analysis to characterise 22 indices for 288 prefecture-level cities in mainland China. The data used to characterise the indices is representative of the year 2012. The results show that the Gross domestic product (GDP) is regular and exhibits multifractal spatial characteristics. Specifically, most developmental fields exhibit coupling in conjunction with being chaotic. Furthermore, eight indices with multifractal characteristics clearly reflect the spatial complexity of the corresponding fields and the volatility between prefecture-level cities. Overall, the tertiary industry has undergone nongeneralised development. On the other hand, the construction industry resembles a bubble economy, and the spatial layout of traditional industries has a homogenising effect in Middle and East China. This study examines China\'s overall spatial characteristics and states based on the above-mentioned analyses; additionally, the study focuses on the early 2010s. The contribution of this study provides a quantitative analysis paradigm based on a multifractal approach.

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.