Narrow Results

This work explores the use of the Higuchi fractal dimension (HFD) to characterize the complexity of the Standard and Poor’s (S&P) Index for the period from 1928 to 2023. It is found that the fractal dimension is not constant but exhibits large time fluctuations. In line with adaptive market hypothesis notions, such a feature can be seen as the response of the stock market to a complex and changing environment formed by a diversity of participants and exogenous shocks. The concept of fractal dimension was extended to consider scale dependence and multifractality. It is shown that the fractality dimension approaches an integer value when the time scale increases, which reflects smoother price fluctuation profiles. It was also shown that the multifractal HFD exhibits large fluctuations for scales of weeks, months, and quarters, which can be linked to the seasonal periods of the operation of the stock market. The impact of salient events was also assessed. It was found that the 1987 and 2008 market crashes had the highest effect on the multifractal HFD, suggesting that these events involved multiple factors. Overall, the results in the present work showed that the fractal dimension tools and notions provide a useful and complementary framework for characterizing the behavior of financial indices.

Protein sequence similarity analysis (PSSA) is a significant task in bioinformatics, which can obtain information about unknown sequences such as protein structures and homology relationships. Protein sequence refers to the series of amino acids with rich physical and chemical properties, namely the basic structure of proteins. However, sequence similarity analysis and phylogenetic analysis between different species which have complex amino acid sequences is a challenging problem. In this paper, nine properties of amino acids were considered and the sequence was converted into numerical values by principal component analysis (PCA); with Haar Wavelet Transform, and Higuchi fractal dimension (HFD), a new feature vector is constructed to represent the sequence; Spearman distance was selected to calculate the distance matrix and the phylogenetic tree was constructed. In this paper, two representative protein sequences (9 ND5 (NADH dehydrogenase 5) and 8 ND6 (NADH dehydrogenase 6)) were selected for similarity analysis and phylogenetic analysis, and compared with MEGA software and other existing methods. The extensive results show that our method is outperforming and results consistent with the known facts.

In this paper, a new irregularity criterion based on fractal dimensions is introduced. In fact, this criterion (which is called ONH criterion) is the state space version of Higuchi fractal dimension, which can discriminate stochastic and deterministic time series from each other. To compute this criterion, we have exploited "the amount of state vectors fluctuations" in embedding space. By varying the reconstruction delay in embedding space, one can obtain a logarithmic diagram of overall changes corresponding to reconstructed state space versus delays. The slope of the linear region of this diagram could be considered as a new irregularity criterion. To discriminate random and deterministic time series, this criterion is adopted as a new statistic for hypothesis testing. Probability density function of this statistic under H₀ hypothesis is constructed and regarding to a certain confidence level, one can determine whether randomness is accepted or rejected.

The complexity, entropy and other non-linear measures of the electroencephalogram (EEG), such as Higuchi fractal dimension (FD), have been recently proposed as the measures of anesthesia depth and sedation. We hypothesized that during unconciousness in rats induced by the general anesthetics with opposite mechanism of action, behaviorally and poligraphically controlled as appropriately achieved stable anesthesia, we can detect distinct inter-structure brain dynamic using mean FDs. We used the surrogate data test for nonlinearity in order to establish the existence of nonlinear dynamics, and to justify the use of FD as a nonlinear measure in the time series analysis. The surrogate data of predefined probability distribution and autocorrelation properties have been generated using the algorithm of statically transformed autoregressive process (STAP). FD then is applied to quantify EEG signal complexity at the cortical, hippocampal and pontine level during stable general anesthesia (ketamine/xylazine or nembutal anesthesia).

Our study showed for the first time that global neuronal inhibition caused by different mechanisms of anesthetic action induced distinct brain inter-structure complexity gradient in Sprague Dawley rats. EEG signal complexities were higher at cortical and hippocampal level in ketamine/xylazine vs. nembutal anesthesia, with the dominance of hippocampal complexity. In nembutal anesthesia the complexity dominance moved to pontine level, and ponto-hippocampo-cortical decreasing complexity gradient was established. This study has proved the Higuchi fractal dimension as a valuable tool for measuring the anesthesia induced inter-structure EEG complexity.