E.G. Pavlos’s research while affiliated with University of Crete and other places

We perform non-linear analysis on stock market indices using time-dependent extended Tsallis statistics. Specifically, we evaluate the q-triplet for particular time periods with the purpose of demonstrating the temporal dependence of the extended characteristics of the underlying market dynamics. We apply the analysis on daily close price timeseries of four major global markets (S&P 500, Tokyo-NIKKEI, Frankfurt-DAX, London-LSE). For comparison, we also compute time-dependent Generalized Hurst Exponents (GHE) Hq using the GHE method, thus estimating the temporal evolution of the multiscaling characteristics of the index dynamics. We focus on periods before and after critical market events such as stock market bubbles (2000 dot.com bubble, Japanese 1990 bubble, 2008 US real estate crisis) and find that the temporal trends of q-triplet values significantly differ among these periods indicating that in the rising period before a bubble break, the underlying extended statistics of the market dynamics strongly deviates from purely stochastic behavior, whereas, after the breakdown, it gradually converges to the Gaussian-like behavior which is a characteristic of an efficient market. We also conclude that relative temporal variation patterns of the Tsallis q-triplet can be connected to different aspects of market dynamics and reveals useful information about market conditions especially those underlying the development of a stock market bubble. We found specific temporal patterns and trends in the relative variation of the indices in the q-triplet that distinguish periods just before and just after a stock-market bubble break. Differences between endogenous and exogenous stock market crises are also captured by the temporal changes in the Tsallis q-triplet. Finally, we introduce two new time-dependent empirical metrics (Q-metrics) that are functions of the Tsallis q-triplet.

We perform non-linear analysis on stock market indices using time-dependent extended Tsallis statistics. Specifically, we evaluate the q-triplet for particular time periods with the purpose of demonstrating the temporal dependence of the extended characteristics of the underlying market dynamics. We apply the analysis on daily close price timeseries of four major global markets (S&P 500, Tokyo-NIKKEI, Frankfurt-DAX, London-LSE). For comparison, we also compute time-dependentGeneralized Hurst Exponents (GHE) Hq using the GHE method, thus estimating the temporal evolution of the multiscaling characteristics of the index dynamics. We focus on periods before and after critical market events such as stock market bubbles (2000 dot.com bubble, Japanese 1990 bubble, 2008 US real estate crisis) and find that the temporal trends of q-triplet values significantly differ among these periods indicating that in the rising period before a bubble break, the underlying extended statistics of the market dynamics strongly deviates from purely stochastic behavior, whereas, after the breakdown, it gradually converges to the Gaussian-like behavior which is a characteristic of an efficient market. We also conclude that relative temporal variation patterns of the Tsallis q-triplet can be connected to different aspects of market dynamics and reveals useful information about market conditions especially those underlying the development of a stock market bubble. We found specific temporal patterns and trends in the relative variation of the indices in the q-triplet that distinguish periods just before and just after a stock-market bubble break. Differences between endogenous and exogenous stock market crises are also captured by the temporal changes in the Tsallis q-triplet. Finally, we introduce two new time-dependent empirical metrics (Q-metrics) that are functions of the Tsallis q-triplet. We apply them to the above stock market index price timeseries and discuss the significance of their temporal dependence on market dynamics and the possibility of using them, together with the relative temporal changes of the q-triplet, as signaling tools for future market events such as the development of a market bubble.

Complexity metrics and machine learning (ML) models have been utilized to analyze the lengths of segmental genomic entities of DNA sequences (exonic, intronic, intergenic, repeat, unique) with the purpose to ask questions regarding the segmental organization of the human genome within the size distribution of these sequences. For this we developed an integrated methodology that is based upon the reconstructed phase space theorem, the non-extensive statistical theory of Tsallis, ML techniques and a technical index, integrating the generated information, which we introduce and named it Complexity Factor (COFA). Our analysis revealed that the size distribution of the genomic regions within chromosomes are not random but follow patterns with characteristic features that have been seen through its complexity character and it is part of the dynamics of the whole genome. Finally, this picture of dynamics in DNA is recognized using ML tools for clustering, classification and prediction with high accuracy.

Complexity metrics and machine learning (ML) models have been utilized to analyze the lengths of segmental genomic entities like: exons, introns, intergenic and repeat/unique DNA sequences, in each of the 22 human chromosomes. The purpose of the study was to assess information and order that may be concealed within the size distribution of these sequences. For this purpose, we developed an innovative integrated methodology. Our analysis is based upon the reconstructed phase space theorem, the non-extensive statistical theory of Tsallis, ML techniques and a new technical index, integrating the generated information, which we introduce and named it Complexity Factor (COFA). The low-dimensional deterministic nonlinear chaotic and non-extensive statistical character of the DNA sequences was verified with strong multifractal characteristics and long-range correlations with significant variations per genomic entity and per chromosome. The results of the analysis reveal changes in complexity behavior per genomic entity and chromosome regarding the size distribution of individual genomic segment. The lengths of intron regions show greater complexity behavior in all metrics than the exonic ones, with longer range correlations, and stronger memory effects, for all chromosomes. We conclude from our analysis, that the size distribution of the genomic regions within chromosomes, are not random, but follow a specific pattern with characteristic features, that have been seen here through its complexity character, and it is part of the dynamics of the whole genome according to complexity theory. This picture of dynamics of the redundancy of information in DNA recognized from ML tools for clustering, classification and prediction.

Complexity metrics and machine learning (ML) models have been utilized to analyze the lengths of segmental genomic entities of DNA sequences (exonic, intronic, intergenic, repeat, unique) with the purpose to ask questions regarding the segmental organization of the human genome within the size distribution of these sequences. For this we developed an integrated methodology that is based upon the reconstructed phase space theorem, the non-extensive statistical theory of Tsallis, ML techniques, and a technical index, integrating the generated information, which we introduce and named complexity factor (COFA). Our analysis revealed that the size distribution of the genomic regions within chromosomes are not random but follow patterns with characteristic features that have been seen through its complexity character, and it is part of the dynamics of the whole genome. Finally, this picture of dynamics in DNA is recognized using ML tools for clustering, classification, and prediction with high accuracy.

In this study Tsallis non-extensive statistics and multifractal analysis for the physical description and understanding of the Random Telegraph Noise (RTN), observed in UTBB FD-SOI MOSFET current timeseries is presented. Specifically, we estimate the Tsallis q-triplet and q-entropy production, the Hurst exponent, the multifractal singular spectrum and other topological and dynamical characteristics of this MOSFET-current dynamics as a function of the drain voltage. The analysis shows the existence of microscopic intermittent turbulence and anomalous diffusion processes, underlying the noisy timeseries. The relevant results indicate the existence of a self-organized critical behavior manifested by a percolation mechanism and a fractional transport process. The multifractal character of the dynamics was demonstrated and explained by the maximization of the Tsallis q-entropy function. Final, our analysis revealed the existence of a non-equilibrium topological transition process, taking place when the drain voltage increases and satisfies the basic principles of Tsallis non- extensive statistical theory.

This study combines two independent domains of science, the high throughput DNA sequencing capabilities of Genomics and complexity theory from Physics, to assess the information encoded by the different genomic segments of exonic, intronic and intergenic regions of the Major Histocompatibility Complex (MHC) and identify possible interactive relationships. The dynamic and non-extensive statistical characteristics of two well characterized MHC sequences from the homozygous cell lines, PGF and COX, in addition to two other genomic regions of comparable size, used as controls, have been studied using the reconstructed phase space theorem and the non-extensive statistical theory of Tsallis. The results reveal similar non-linear dynamical behavior as far as complexity and self-organization features. In particular, the low-dimensional deterministic nonlinear chaotic and non-extensive statistical character of the DNA sequences was verified with strong multifractal characteristics and long-range correlations. The nonlinear indices repeatedly verified that MHC sequences, whether exonic, intronic or intergenic include varying levels of information and reveal an interaction of the genes with intergenic regions, whereby the lower the number of genes in a region, the less the complexity and information content of the intergenic region. Finally we showed the significance of the intergenic region in the production of the DNA dynamics. The findings reveal interesting content information in all three genomic elements and interactive relationships of the genes with the intergenic regions. The results most likely are relevant to the whole genome and not only to the MHC. These findings are consistent with the ENCODE project, which has now established that the non-coding regions of the genome remain to be of relevance, as they are functionally important and play a significant role in the regulation of expression of genes and coordination of the many biological processes of the cell.

In this small review, the theoretical framework of non-extensive statistical theory, introduced by Constantino Tsallis in 1988, is presented in relation with the q-triplet estimation concerning experimental time series from climate, seismogenesis, and space plasmas systems. These physical systems reveal common dynamical, geometrical, or statistical characteristics. Such characteristics are low dimensionality, typical intermittent turbulence multifractality, temporal or spatial multiscale correlations, power law scale invariance, non-Gaussian statistics, and others. The aforementioned phenomenology has been attributed in the past to chaotic or self-organized critical (SOC) universal dynamics. However, after two or three decades of theoretical development of the complexity theory, a more compact theoretical description can be given for the underlying universal physical processes which produce the experimental time series complexity. In this picture, the old reductionist view of universality of particles and forces is extended to the modern universality of multiscale complex processes from the microscopic to the macroscopic level of different physical systems. In addition, it can be stated that a basic and universal organizing principle exists creating complex spatio-temporal and multiscale different physical structures or different dynamical scenarios at every physical scale level. The best physical representation of the underline universal organizing principle is the well-known entropy principle. Tsallis introduced a q-entropy (Sq) as a non-extensive (q-extension) of the Boltzmann–Gibbs (BG) entropy (for q = 1, the BG entropy is restored) and statistics in order to describe efficiently the rich phenomenology that complex systems exhibit. Tsallis q-entropy could be a strong candidate for entropy principle according to which nature creates complex structures everywhere, from the microscopic to the macroscopic level, trying to succeed the extremization of the Tsallis entropy. In addition, this Sq entropy principle is harmonized with the q extension of the classic and Gaussian central limit theorem (q-CLT). The q-extension of CLT corresponds to the Levy a-stable extension of the Gaussian attractor of the classic statistical theory. The q-CLT is related to the Tsallis q-triplet theory of random time series with non-Gaussian statistical profile. Moreover Tsallis q-extended entropy principle can be used as the theoretical framework for the unification of some new dynamical characteristics of complex systems such as the spatio-temporal fractional dynamics, the anomalous diffusion processes and the strange dynamics of Hamiltonian and dissipative dynamical systems, the intermittent turbulence theory, the fractional topological and percolation phase transition processes according to Zelenyi and Milovanov non-equilibrium and non-stationary states (NESS) theory, as well as the non-equilibrium renormalization group theory(RNGT) of distributed dynamics and the reduction of dynamical degrees of freedom.

In this paper, we perform statistical analysis of time series deriving from Earth's climate. The time series are concerned with Geopotential Height (GH) and correspond to temporal and spatial components of the global distribution of month average values, during the period (1948-2012). The analysis is based on Tsallis non-extensive statistical mechanics and in particular on the estimation of Tsallis' q-triplet, namely (. qstat, qsens, qrel), the reconstructed phase space and the estimation of correlation dimension and the Hurst exponent of rescaled range analysis (R/S). The deviation of Tsallis q-triplet from unity indicates non-Gaussian (Tsallis q-Gaussian) non-extensive character with heavy tails probability density functions (PDFs), multifractal behavior and long range dependences for all timeseries considered. Also noticeable differences of the q-triplet estimation found in the timeseries at distinct local or temporal regions. Moreover, in the reconstructive phase space revealed a lower-dimensional fractal set in the GH dynamical phase space (strong self-organization) and the estimation of Hurst exponent indicated multifractality, non-Gaussianity and persistence. The analysis is giving significant information identifying and characterizing the dynamical characteristics of the earth's climate.

In this study we present some new and significant results concerning the dynamics of interplanetary coronal mass ejections (ICMEs) observed in the near Earth at L1 solar wind environment, as well as its effect in Earth’s magnetosphere. The results are referred to Tsallis non-extensive statistics and in particular to the estimation of Tsallis -triplet, of magnetic field time series of the ICME observed at the Earth resulting from the solar eruptive activity on March 7, 2012 at the Sun. For this, we used a multi-spacecraft approach based on data experiments from ACE, CLUSTER 4, THEMIS-E and THEMIS-C spacecraft. For the data analysis different time periods were considered, sorted as “quiet”, “shock” and “aftershock”, while different space domains such as the Interplanetary space (near Earth at L1 and upstream of the Earth’s bowshock), the Earth’s magnetosheath and magnetotail, were also taken into account. Our results reveal significant differences in statistical and dynamical features, indicating important variations of the magnetic field dynamics both in time and space domains during the shock event, in terms of rate of entropy production, relaxation dynamics and non-equilibrium meta-stable stationary states.