Using space-filling curves and fractals to reveal spatial and temporal patterns in neuroimaging data.

Objective Magnetic resonance imaging (MRI), functional MRI (fMRI) and other neuroimaging techniques are routinely used in medical diagnosis, cognitive neuroscience or recently in brain decoding. They produce three- or four-dimensional scans reflecting the geometry of brain tissue or activity, which is highly correlated temporally and spatially. While there exist numerous theoretically guided methods for analyzing correlations in one-dimensional data, they often cannot be readily generalized to the multidimensional geometrically embedded setting.

Classification of ROI-based fMRI data in short-term memory tasks using discriminant analysis and neural networks.

Understanding brain function relies on identifying spatiotemporal patterns in brain activity. In recent years, machine learning methods have been widely used to detect connections between regions of interest (ROIs) involved in cognitive functions, as measured by the fMRI technique. However, it's essential to match the type of learning method to the problem type, and extracting the information about the most important ROI connections might be challenging.

Quantifying multifractal anisotropy in two dimensional objects.

An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis into 2D. It is tested on synthetic structures to ensure its effectiveness, with results indicating consistency.

Investigating structural and functional aspects of the brain's criticality in stroke.

This paper addresses the question of the brain's critical dynamics after an injury such as a stroke. It is hypothesized that the healthy brain operates near a phase transition (critical point), which provides optimal conditions for information transmission and responses to inputs. If structural damage could cause the critical point to disappear and thus make self-organized criticality unachievable, it would offer the theoretical explanation for the post-stroke impairment of brain function.

Genuine multifractality in time series is due to temporal correlations.

Based on the mathematical arguments formulated within the multifractal detrended fluctuation analysis (MFDFA) approach it is shown that, in the uncorrelated time series from the Gaussian basin of attraction, the effects resembling multifractality asymptotically disappear for positive moments when the length of time series increases. A hint is given that this applies to the negative moments as well and extends to the Lévy stable regime of fluctuations. The related effects are also illustrated and confirmed by numerical simulations.

Analysis of fMRI Signals from Working Memory Tasks and Resting-State of Brain: Neutrosophic-Entropy-Based Clustering Algorithm.

This study applies a neutrosophic-entropy-based clustering algorithm (NEBCA) to analyze the fMRI signals. We consider the data obtained from four different working memory tasks and the brain's resting state for the experimental purpose. Three non-overlapping clusters of data related to temporal brain activity are determined and statistically analyzed.

Complexity in Economic and Social Systems.

During recent years we have witnessed a systematic progress in the understanding of complex systems, both in the case of particular systems that are classified into this group and, in general, as regards the phenomenon of complexity [...

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.

Competition of noise and collectivity in global cryptocurrency trading: Route to a self-contained market.

Cross correlations in fluctuations of the daily exchange rates within the basket of the 100 highest-capitalization cryptocurrencies over the period October 1, 2015-March 31, 2019 are studied. The corresponding dynamics predominantly involve one leading eigenvalue of the correlation matrix, while the others largely coincide with those of Wishart random matrices. However, the magnitude of the principal eigenvalue, and thus the degree of collectivity, strongly depends on which cryptocurrency is used as a base.

High-dimensional dynamics in a single-transistor oscillator containing Feynman-Sierpiński resonators: Effect of fractal depth and irregularity.

Fractal structures pervade nature and are receiving increasing engineering attention towards the realization of broadband resonators and antennas. We show that fractal resonators can support the emergence of high-dimensional chaotic dynamics even in the context of an elementary, single-transistor oscillator circuit. Sierpiński gaskets of variable depth are constructed using discrete capacitors and inductors, whose values are scaled according to a simple sequence.

Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects.

Based on 1-min price changes recorded since year 2012, the fluctuation properties of the rapidly emerging Bitcoin market are assessed over chosen sub-periods, in terms of return distributions, volatility autocorrelation, Hurst exponents, and multiscaling effects. The findings are compared to the stylized facts of mature world markets. While early trading was affected by system-specific irregularities, it is found that over the months preceding April 2018 all these statistical indicators approach the features hallmarking maturity.

Apparent remote synchronization of amplitudes: A demodulation and interference effect.

A form of "remote synchronization" was recently described, wherein amplitude fluctuations across a ring of non-identical, non-linear electronic oscillators become entrained into spatially-structured patterns. According to linear models and mutual information, synchronization and causality dip at a certain distance, then recover before eventually fading. Here, the underlying mechanism is finally elucidated through novel experiments and simulations.

Atypical transistor-based chaotic oscillators: Design, realization, and diversity.

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date.

Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations.

Based on a recently proposed q-dependent detrended cross-correlation coefficient, ρ_{q} [J. Kwapień, P. Oświęcimka, and S.

Self-similarity and quasi-idempotence in neural networks and related dynamical systems.

Self-similarity across length scales is pervasively observed in natural systems. Here, we investigate topological self-similarity in complex networks representing diverse forms of connectivity in the brain and some related dynamical systems, by considering the correlation between edges directly connecting any two nodes in a network and indirect connection between the same via all triangles spanning the rest of the network. We note that this aspect of self-similarity, which is distinct from hierarchically nested connectivity (coarse-grain similarity), is closely related to idempotence of the matrix representing the graph.

Multifractal cross-correlation effects in two-variable time series of complex network vertex observables.

We investigate the scaling of the cross-correlations calculated for two-variable time series containing vertex properties in the context of complex networks. Time series of such observables are obtained by means of stationary, unbiased random walks. We consider three vertex properties that provide, respectively, short-, medium-, and long-range information regarding the topological role of vertices in a given network.

Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations.

The detrended cross-correlation coefficient ρ(DCCA) has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, nonstationary time series. It is based on the detrended cross-correlation and detrended fluctuation analyses (DCCA and DFA, respectively) and can be viewed as an analog of the Pearson coefficient in the case of the fluctuation analysis. The coefficient ρ(DCCA) works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross-correlated, without the possibility to obtain information on the amplitude of fluctuations that are responsible for those cross-correlations.

Modeling the average shortest-path length in growth of word-adjacency networks.

We investigate properties of evolving linguistic networks defined by the word-adjacency relation. Such networks belong to the category of networks with accelerated growth but their shortest-path length appears to reveal the network size dependence of different functional form than the ones known so far. We thus compare the networks created from literary texts with their artificial substitutes based on different variants of the Dorogovtsev-Mendes model and observe that none of them is able to properly simulate the novel asymptotics of the shortest-path length.

Detecting and interpreting distortions in hierarchical organization of complex time series.

Hierarchical organization is a cornerstone of complexity and multifractality constitutes its central quantifying concept. For model uniform cascades the corresponding singularity spectra are symmetric while those extracted from empirical data are often asymmetric. Using selected time series representing such diverse phenomena as price changes and intertransaction times in financial markets, sentence length variability in narrative texts, Missouri River discharge, and sunspot number variability as examples, we show that the resulting singularity spectra appear strongly asymmetric, more often left sided but in some cases also right sided.

Detrended cross-correlation analysis consistently extended to multifractality.

We propose an algorithm, multifractal cross-correlation analysis (MFCCA), which constitutes a consistent extension of the detrended cross-correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods, like multifractal extension, have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross-correlations when there are none. The principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments.

Wavelet versus detrended fluctuation analysis of multifractal structures.

We perform a comparative study of applicability of the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus maxima (WTMM) method in proper detecting of monofractal and multifractal character of data. We quantify the performance of both methods by using different sorts of artificial signals generated according to a few well-known exactly soluble mathematical models: monofractal fractional Brownian motion, bifractal Lévy flights, and different sorts of multifractal binomial cascades. Our results show that in the majority of situations in which one does not know a priori the fractal properties of a process, choosing MFDFA should be recommended.