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Distinguishing cause from effect is a scientific challenge resisting solutions from mathematics, statistics, information theory and computer science. Compression-Complexity Causality (CCC) is a recently proposed interventional measure of causality, inspired by Wiener-Granger's idea. It estimates causality based on change in dynamical compression-complexity (or compressibility) of the effect variable, given the cause variable. CCC works with minimal assumptions on given data and is robust to irregular-sampling, missing-data and finite-length effects. However, it only works for one-dimensional time series. We propose an ordinal pattern symbolization scheme to encode multidimensional patterns into one-dimensional symbolic sequences, and thus introduce the Permutation CCC (PCCC), which retains all advantages of the original CCC and can be applied to data from multidimensional systems with potentially hidden variables. PCCC is tested on numerical simulations and applied to paleoclimate data characterized by irregular and uncertain sampling and limited numbers of samples., Comment: 14 pages, 3 figures, 1 table

Within the context of social balance theory, much attention has been paid to the attainment and stability of unipolar or bipolar societies. However, multipolar societies are commonplace in the real world, despite the fact that the mechanism of their emergence is much less explored. Here, we investigate the evolution of a society of interacting agents with friendly (positive) and enmity (negative) relations into a final stable multipolar state. Triads are assigned energy according to the degree of tension they impose on the network. Agents update their connections in order to decrease the total energy (tension) of the system, on average. Our approach is to consider a variable energy $\epsilon\in[0,1]$ for triads which are entirely made of negative relations. We show that the final state of the system depends on the initial density of the friendly links $\rho_0$. For initial densities greater than an $\epsilon$ dependent threshold $\rho^c_0(\epsilon)$ unipolar (paradise) state is reached. However, for $\rho_0 \leq \rho^c_0(\epsilon)$ multi-polar and bipolar states can emerge. We observe that the number of stable final poles increases with decreasing $\epsilon$ where the first transition from bipolar to multipolar society occurs at $\epsilon^*\approx 0.67$. We end the paper by providing a mean-field calculation that provides an estimate for the critical ($\epsilon$ dependent) initial positive link density, which is consistent with our simulations.

Recently, we introduced [Physical Review E 100, 022303 (2019)] a stochastic social balance model with Glauber dynamics which takes into account the role of randomness in the individual's behavior. One important finding of our study was a phase transition from a balance state to an imbalance state as the randomness crosses a critical value, which was shown to vanish in the thermodynamic limit. In a recent similar study [K. Malarz and K. Ku\l akowskiy, (2020), arXiv:2009.10136], it was shown that the critical randomness tends to infinity as the system size diverges. This led the authors to question our results. Here, we show that this apparent inconsistency is the results of different definitions of energy in each model. We also demonstrate that synchronous and sequential updating rules can largely affect the results, in contrast with the claims made by the aforementioned authors.

Evolutionary games provide the theoretical backbone for many aspects of our social life: from cooperation to crime, from climate inaction to imperfect vaccination and epidemic spreading, from antibiotics overuse to biodiversity preservation. An important, and so far overlooked, aspect of reality is the diverse strategic identities of individuals. While applying the same strategy to all interaction partners may be an acceptable assumption for simpler forms of life, this fails to account} for the behavior of more complex living beings. For instance, we humans act differently around different people. Here we show that allowing individuals to adopt different strategies with different partners yields a very rich evolutionary dynamics, including time-dependent coexistence of cooperation and defection, system-wide shifts in the dominant strategy, and maturation in individual choices. Our results are robust to variations in network type and size, and strategy updating rules. Accounting for diverse strategic identities thus has far-reaching implications in the mathematical modeling of social games., Comment: 9 pages, 4 figures

Correlations in multifractal series have been investigated, extensively. Almost all approaches try to find scaling features of a given time series. However, the analysis of such scaling properties has some difficulties such as finding a proper scaling region. On the other hand, such correlation detection methods may be affected by the probability distribution function of the series. In this article, we apply the horizontal visibility graph algorithm to map stochastic time series into networks. By investigating the magnitude and sign of a multifractal time series, we show that one can detect linear as well as nonlinear correlations, even for situations that have been considered as uncorrelated noises by typical approaches like MFDFA. In this respect, we introduce a topological parameter that can well measure the strength of nonlinear correlations. This parameter is independent of the probability distribution function and calculated without the need to find any scaling region. Our findings may provide new insights about the multifractal analysis of time series in a variety of complex systems.

We study the evolution of a social network with friendly/enmity connections into a balanced state by introducing a dynamical model with an intrinsic randomness, similar to Glauber dynamics in statistical mechanics. We include the possibility of the tension promotion as well as the tension reduction in our model. Such a more realistic situation enables the system to escape from local minima in its energy landscape and thus to exit out of frozen imbalanced states, which are unwanted outcomes observed in previous models. On the other hand, in finite networks the dynamics takes the system into a balanced phase, if the randomness is lower than a critical value. For large networks, we also find a sharp phase transition at the initial positive link density of $\rho_0^*=1/2$, where the system transitions from a bipolar state into a paradise. This modifies the gradual phase transition at a nontrivial value of $\rho_0^*=0.65$, observed in recent studies.

The records statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a universal behavior for the whole range of Hurst exponents. However, for non-stationary fractional Brownian motions the record dynamics is crucially dependent on the memory, which plays the role of a non-stationarity index, here. Indeed, the deviation from the results of the stationary case increases by increasing the Hurst exponent in fractional Brownian motions. We demonstrate that the memory governs the dynamics of the records as long as it causes non-stationarity in fractal stochastic processes, otherwise, it has no impact on the records statistics., Comment: 7 pages, 7 figures

In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacency matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.

We employ the horizontal visibility algorithm to map the velocity and acceleration time series in turbulent flows with different Reynolds numbers, onto complex networks. The universal nature of velocity fluctuations in high Reynolds turbulent Helium flow is found to be inherited in the corresponding network topology. The degree distributions of the acceleration series are shown to have stretched exponential forms with the Reynolds number dependent fitting parameter. Furthermore, for acceleration time series, we find a transitional behavior in terms of the Reynolds number in all network features which is in agreement with recent empirical studies.

Typically, contagion strength is modeled by a transmission rate $\lambda$, whereby all nodes in a network are treated uniformly in a mean-field approximation. However, local agents react differently to the same contagion based on their local characteristics. Following our recent work [EPL \textbf{99}, 58002 (2012)], we investigate contagion spreading models with local dynamics on complex networks. We therefore quantify contagions by their quality, $0 \leq \alpha \leq 1$, and follow their spreading as their transmission condition (fitness) is evaluated by local agents. We choose various deterministic local rules. Initial spreading with exponential quality-dependent time scales is followed by a stationary state with a prevalence depending on the quality of the contagion. We also observe various interesting phenomena, for example, high prevalence without the participation of the hubs. This is in sharp contrast with the general belief that hubs play a central role in a typical spreading process. We further study the role of network topology in various models and find that as long as small-world effect exists, the underlying topology does not contribute to the final stationary state but only affects the initial spreading velocity., Comment: 18 pages, 6 figures, to appear

Understanding how contagions (information, infections, etc) are spread on complex networks is important both from practical as well as theoretical point of view. Considerable work has been done in this regard in the past decade or so. However, most models are limited in their scope and as a result only capture general features of spreading phenomena. Here, we propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local (probabilistic) dynamics occurring at various nodes. Transmission occurs only after the quality-based fitness of the contagion has been evaluated by the local agent. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. Low prevalence is seen for a wide range of contagion quality for arbitrary large networks. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. Our results are consistent with recent empirical observations., Comment: 7 pages, 8 figures. (Submitted)

We report on a novel stochastic analysis of seismic time series for the Earth's vertical velocity, by using methods originally developed for complex hierarchical systems, and in particular for turbulent flows. Analysis of the fluctuations of the detrended increments of the series reveals a pronounced change of the shapes of the probability density functions (PDF) of the series' increments. Before and close to an earthquake the shape of the PDF and the long-range correlation in the increments both manifest significant changes. For a moderate or large-size earthquake the typical time at which the PDF undergoes the transition from a Gaussian to a non-Gaussian is about 5-10 hours. Thus, the transition represents a new precursor for detecting such earthquakes., Comment: 12 pages, 5 figures