Multifractality and Network Analysis of Phase Transition

Multifractal fluctuations in zebrafish (Danio rerio) polarization time series

In this work, we study the polarization time series obtained from experimental observation of a group of zebrafish (Danio rerio) confined in a circular tank. The complex dynamics of the individual trajectory evolution lead to the appearance of multiple characteristic scales. Employing the Multifractal Detrended Fluctuation Analysis (MF-DFA), we found distinct behaviors according to the parameters used. The polarization time series are multifractal at low fish densities and their average scales with ρ - 1 / 4 . On the other hand, they tend to be monofractal, and their average scales with ρ - 1 / 2 for high fish densities. These two regimes overlap at critical density ρ c , suggesting the existence of a phase transition separating them. We also observed that for low densities, the polarization velocity shows a non-Gaussian behavior with heavy tails associated with long-range correlation and becomes Gaussian for high densities, presenting an uncorrelated regime.

Evidence of Critical Dynamics in Movements of Bees inside a Hive

Social insects such as honey bees exhibit complex behavioral patterns, and their distributed behavioral coordination enables decision-making at the colony level. It has, therefore, been proposed that a high-level description of their collective behavior might share commonalities with the dynamics of neural processes in brains. Here, we investigated this proposal by focusing on the possibility that brains are poised at the edge of a critical phase transition and that such a state is enabling increased computational power and adaptability. We applied mathematical tools developed in computational neuroscience to a dataset of bee movement trajectories that were recorded within the hive during the course of many days. We found that certain characteristics of the activity of the bee hive system are consistent with the Ising model when it operates at a critical temperature, and that the system's behavioral dynamics share features with the human brain in the resting state.

Spatial patterns of urbanising landscapes in the North Indian Punjab show features predicted by fractal theory

Understanding and governing human settlement patterns is a major challenge of the urban age. While rural settlements emerge as parts of agricultural landscapes, cities typically evolve in economically strategic locations, and over time form hierarchical systems of cities. Purposeful planning and the collective, self-organized behavior of the inhabitants interact in the development of regional settlement patterns. Since self-organizing systems often produce fractal patterns in nature, this study combines approaches of land use science, city ranking, and urban planning under a fractal theory framework, to analyze the settlement system of the Indian Punjab. Scaling levels were defined by discontinuities in the size distribution of built-up areas (Global Urban Footprint), which correlated to population-based classifications (r = 0.9591). Self-similarity across scales was supported by geo-statistical similarity (p < 0.05) of distances and angles between settlements of successive classes, and the overall fractal dimension of D_B = 1.95. When compared to a modeled Sierpinski Carpet, more than 50% of the settlements met the fractal geometry rules at larger scales. The spatial distribution of small villages, however, deviated, indicating a scale-related shift in organizing principles. Explicitly acknowledging cross-scale relations and self-organisation in regional planning policies may lead to more sustainable settlement structures that are in harmony with natural system properties.

Analysis of Korean Peninsula Earthquake Network Based on Event Shuffling and Network Shuffling

In this work, a Korean peninsula earthquake network, constructed via event-sequential linking known as the Abe–Suzuki method, was investigated in terms of network properties. A significance test for these network properties was performed via comparisons with those of two random networks, constructed from two approaches, that is, EVENT (SEQUENCE) SHUFFLING and NETWORK (MATRIX) SHUFFLING. The Abe–Suzuki earthquake network has a clear difference from the two random networks. However, the two shuffled networks exhibited completely different functions, and even some network properties for one shuffled datum are significantly high and those of the other shuffled data are low compared to actual data. For most cases, the event-shuffled network showed a functional similarity to the real network, but with different exponents/parameters. This result strongly claims that the Korean peninsula earthquake network has a spatiotemporal causal relation. Additionally, the Korean peninsula network properties are mostly similar to those found in previous studies on the US and Japan. Further, the Korean earthquake network showed strong linearity in a specific range of spatial resolution, that is, 0.20°~0.80°, implying that macroscopic properties of the Korean earthquake network are highly regular in this range of resolution.

Research on risk early warning algorithm for asymmetric samples in multifractal financial market

This paper takes 11-year 5-minute high-frequency trading data of the Shanghai and Shenzhen 300 Index (CSI300) as a research sample. First, it proposes a method to define the normal state and the state of attention of the financial market based on multi-fractal characteristics, and randomly owes it Sampling (RU), synthetic minority oversampling (SMOTE) and traditional support vector machine (SVM) are combined to propose an improved SVM model—RU-SMOTE-SVM model to predict extreme risks in China’s financial market, and compare Traditional SVM, SMOTE-SVM, RU-SMOTE-NN and RU-SMOTE-DT are compared. The empirical results show that the price fluctuations of China’s emerging financial markets have significant multi-fractal characteristics; the normal and concerned states defined based on the multi-fractal feature parameters are not only accurate, but also have obvious statistical test significance and clear practical significance; and traditional SVM and Compared with BP neural network (NN), RU-SMOTE-SVM is not only significantly higher in prediction accuracy, but also in terms of prediction stability. That is, RU-SMOTE-SVM can effectively solve the problems of other early warning models to solve the symmetrical sample problem.

Temporal Signatures of Criticality in Human Cortical Excitability as Probed by Early Somatosensory Responses

Brain responses vary considerably from moment to moment, even to identical sensory stimuli. This has been attributed to changes in instantaneous neuronal states determining the system's excitability. Yet the spatiotemporal organization of these dynamics remains poorly understood. Here we test whether variability in stimulus-evoked activity can be interpreted within the framework of criticality, which postulates dynamics of neural systems to be tuned toward the phase transition between stability and instability as is reflected in scale-free fluctuations in spontaneous neural activity. Using a novel noninvasive approach in 33 male human participants, we tracked instantaneous cortical excitability by inferring the magnitude of excitatory postsynaptic currents from the N20 component of the somatosensory evoked potential. Fluctuations of cortical excitability demonstrated long-range temporal dependencies decaying according to a power law across trials, a hallmark of systems at critical states. As these dynamics covaried with changes in prestimulus oscillatory activity in the alpha band (8-13 Hz), we establish a mechanistic link between ongoing and evoked activity through cortical excitability and argue that the co-emergence of common temporal power laws may indeed originate from neural networks poised close to a critical state. In contrast, no signatures of criticality were found in subcortical or peripheral nerve activity. Thus, criticality may represent a parsimonious organizing principle of variability in stimulus-related brain processes on a cortical level, possibly reflecting a delicate equilibrium between robustness and flexibility of neural responses to external stimuli.SIGNIFICANCE STATEMENT Variability of neural responses in primary sensory areas is puzzling, as it is detrimental to the exact mapping between stimulus features and neural activity. However, such variability can be beneficial for information processing in neural networks if it is of a specific nature, namely, if dynamics are poised at a so-called critical state characterized by a scale-free spatiotemporal structure. Here, we demonstrate the existence of a link between signatures of criticality in ongoing and evoked activity through cortical excitability, which fills the long-standing gap between two major directions of research on neural variability: the impact of instantaneous brain states on stimulus processing on the one hand and the scale-free organization of spatiotemporal network dynamics of spontaneous activity on the other.

Analysis of properties of Ising and Kuramoto models that are preserved in networks constructed by visualization algorithms

Recently it has been shown that building networks from time series allows to study complex systems to characterize them when they go through a phase transition. This give us the opportunity to study this systems from a entire new point of view. In the present work we have used the natural and horizontal visualization algorithms to built networks of two popular models, which present phase transitions: the Ising model and the Kuramoto model. By measuring some topological quantities as the average degree, or the clustering coefficient, it was found that the networks retain the capability of detecting the phase transition of the system. From our results it is possible to establish that both visibility algorithms are capable of detecting the critical control parameter, as in every quantity analyzed (the average degree, the average path and the clustering coefficient) there is a minimum or a maximum value. In the case of the natural visualization algorithm, the average path results are much more noisy than in the other quantities in the study. Specially for the Kuramoto Model, which in this case does not allow a detection of the critical point at plain sight as for the other quantities. The horizontal visualization algorithm has proven to be more explicit in every quantity, as every one of them show a clear change of behavior before and after the critical point of the transition.