Multifractal and joint multifractal analysis of soil invertebrate fauna, altitude, and organic carbon

ABSTRACT The objectives of this study were to evaluate the degree of multifractality of the spatial distribution of altitude, organic carbon concentration, and invertebrate fauna diversity, and to characterize the degree of joint multifractal association among these variables. Soil sampling was performed every 20 m across a 2,540 m transect, with a total of 128 sampling points in a sugarcane area in Goiana municipality, Pernambuco State. For each sampling point, the altitude, organic carbon concentration, and macrofauna diversity (diversity indices and functional groups) were evaluated. Spatial distributions of altitude, organic carbon concentration, and macrofauna diversity were characterized by the generalized dimension spectrum (Dq) and singularity spectrums [f(α) versus α], which presented multifractal behavior with different degrees of heterogeneity in scales. Joint multifractal analysis was useful for revealing the relationships at multiple scales between the studied variables, as demonstrated by the non-detected associations using traditional statistical methods. To quantify the spatial variability of edaphic fauna based on the multiple scales and association sets in the joint dimension, the impact of agricultural production systems on biological diversity can be described. All of the studied variables displayed a multifractal behavior with greater or lower heterogeneity degree depending on the variable, with altitude and organic carbon being the most homogeneous attributes.

Investigating efficiency of frontier stock markets using multifractal detrended fluctuation analysis

PurposeThe investigation of the fractal nature of financial data has been growing in the literature. The purpose is to investigate the multifractal behavior of frontier markets using multifractal detrended fluctuation analysis (MFDFA).Design/methodology/approachThis study used daily closing prices of nine frontier stock markets up to 31-Aug-2020. A preliminary analysis reveals that these markets exhibit fat tails and clustering patterns. For a more robust analysis, a combination of Seasonal and Trend Decomposition using Loess (STL) and MFDFA has been employed. The former method is used to decompose daily stock returns, where later detected the long rang dependence in the series.FindingsThe results confirm varying degree of multifractality in frontier stock markets, implying that they exhibit long-range dependence. Based on these multifractality levels, Serbian and Romanian stock markets are the ones exhibiting least long-range dependence, while Slovenian and Mauritius stock markets indicating highest dependence in their series. Furthermore, the markets of Kenya, Morocco, Romania and Serbia exhibit mean reversion (anti-persistent) behavior while the remaining frontier markets show persistent behaviors.Practical implicationsThe information given by the detection of the fractal measure of data can support for investment and policymaking decisions.Originality/valueFrontier markets are of great potential from the perspective of international diversification. However, most of the research focused on other emerging and developed markets, especially in the context of multifractal analysis. This study combines the STL method and a physics-based robust technique, MFDFA to detect the multifractal behavior of frontier stock markets.

Entropy and Multifractal-Multiscale Indices of Heart Rate Time Series to Evaluate Intricate Cognitive-Autonomic Interactions

Recent research has clarified the existence of a networked system involving a cortical and subcortical circuitry regulating both cognition and cardiac autonomic control, which is dynamically organized as a function of cognitive demand. The main interactions span multiple temporal and spatial scales and are extensively governed by nonlinear processes. Hence, entropy and (multi)fractality in heart period time series are suitable to capture emergent behavior of the cognitive-autonomic network coordination. This study investigated how entropy and multifractal-multiscale analyses could depict specific cognitive-autonomic architectures reflected in the heart rate dynamics when students performed selective inhibition tasks. The participants () completed cognitive interference (Stroop color and word task), action cancellation (stop-signal) and action restraint (go/no-go) tasks, compared to watching a neutral movie as baseline. Entropy and fractal markers (respectively, the refined composite multiscale entropy and multifractal-multiscale detrended fluctuation analysis) outperformed other time-domain and frequency-domain markers of the heart rate variability in distinguishing cognitive tasks. Crucially, the entropy increased selectively during cognitive interference and the multifractality increased during action cancellation. An interpretative hypothesis is that cognitive interference elicited a greater richness in interactive processes that form the central autonomic network while action cancellation, which is achieved via biasing a sensorimotor network, could lead to a scale-specific heightening of multifractal behavior.

Random Number Generator with Long-Range Dependence and Multifractal Behavior Based on Memristor

Random number generators are used in areas such as encryption and system modeling, where some of these exhibit fractal behaviors. For this reason, it is interesting to make use of the memristor characteristics for the random number generation. Accordingly, the objective of this article is to evaluate the performance of a chaotic memristive system as a random number generator with fractal behavior and long-range dependence. To achieve the above, modeling memristor and its corresponding chaotic systems is performed, from which a random number generator is constructed. Subsequently, the Hurst parameter for the detection of long-range dependence is estimated and a fractal analysis of the synthesized data is performed. Finally, a comparison between the model proposed in the research and the β-MWM algorithm is made. The results obtained show that the data synthesized from the proposed generator have a variable Hurst parameter and both monofractal and multifractal behavior. The main contribution of this research is the proposal of a new model for the synthesis of traces with long-range dependence and fractal behavior based on the non-linearity of the memristor.

Multifractal behavior of SARS-CoV-2 COVID-19 pandemic spread, case of: Algeria, Russia, USA and Italy.

Here, the multifractal behavior of the SARS-CoV-2 COVID-19 pandemic daily and death cases is investigated through the so-called Wavelet Transform Modulus Maxima lines (WTMM) method, data available via the World Health Organization (WHO) dashboard of Algeria, Russia, USA and Italy are analyzed. The obtained results show the multifractal behavior of the COVID-19 pandemic data with different spectra of singularities. Keywords: Multifractal behavior, daily and death cases, WTMM, COVID-19 pandemic data