Constantinos Papadimitriou

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.

THE MAJOR GEOEFFECTIVE SOLAR ERUPTIONS OF 2012 MARCH 7: COMPREHENSIVE SUN-TO-EARTH ANALYSIS

During the interval 2012 March 7–11 the geospace experienced a barrage of intense space weather phenomena including the second largest geomagnetic storm of solar cycle 24 so far. Significant ultra-low-frequency wave enhancements and relativistic-electron dropouts in the radiation belts, as well as strong energetic-electron injection events in the magnetosphere were observed. These phenomena were ultimately associated with two ultra-fast (>2000 km s) coronal mass ejections (CMEs), linked to two X-class flares launched on early 2012 March 7. Given that both powerful events originated from solar active region NOAA 11429 and their onsets were separated by less than an hour, the analysis of the two events and the determination of solar causes and geospace effects are rather challenging. Using satellite data from a flotilla of solar, heliospheric and magnetospheric missions a synergistic Sun-to-Earth study of diverse observational solar, interplanetary and magnetospheric data sets was performed. It was found that only the second CME was Earth-directed. Using a novel method, we estimated its near-Sun magnetic field at 13 Re to be in the range [0.01, 0.16] G. Steep radial fall-offs of the near-Sun CME magnetic field are required to match the magnetic fields of the corresponding interplanetary CME (ICME) at 1 AU. Perturbed upstream solar-wind conditions, as resulting from the shock associated with the Earth-directed CME, offer a decent description of its kinematics. The magnetospheric compression caused by the arrival at 1 AU of the shock associated with the ICME was a key factor for radiation-belt dynamics.

Magnetospheric ULF wave studies in the frame of Swarm mission: a time-frequency analysis tool for automated detection of pulsations in magnetic and electric field observations

We combine the advantages of multi-spacecraft and ground-based monitoring of the geospace environment in order to analyze and study magnetospheric ultra low frequency (ULF) waves. In line with this aim, we also develop and deliver relevant analysis tools based on wavelet transforms and tailored to the Swarm mission. In the preparation phase as well as the lifetime of the Swarm mission, the analysis of isolated ULF wave events— especially those detected in the Pc3 frequency range (20–100 mHz) that a topside ionosphere mission efficiently resolves—can help to elucidate the processes that play a crucial role in the generation of waves and their most defining propagation characteristics. Additionally, we offer a useful platform to monitor the wave evolution from the outer boundaries of Earth’s magnetosphere through the topside ionosphere down to the surface. Data from a single Low Earth Orbit (LEO) satellite (CHAMP), a multi-satellite LEO mission (ST5) and the ongoing multi-satellite magnetospheric mission (Cluster) along with a ground-based magnetic network (CARISMA) are used to demonstrate the potential of our analysis technique in studying wave evolution in detail. A better understanding of the generation and propagation of waves will also allow to geophysically validate some of Swarm’s data products, especially those related to the magnetic and electric fields in geospace. With a carefully selected case study focusing on the recovery phase of a moderate magnetic storm (9 April 2006 with a minimum Dst value of −82 nT) as a starting point, we clearly demonstrate the capabilities offered by our wavelet analysis tools and highlight the options opened to treat various categories of multipoint multi-instrument measurements (both spaceborne and ground-based) for signatures of ULF wave signals as well as the effects of various other sources.

Emerin expression in tubular aggregates.

Emerin is an inner nuclear membrane protein that is mutated or not expressed in patients with X-linked Emery-Dreifuss muscular dystrophy (X-EDMD/EMD). Cytoplasmic localization of emerin in cultured cells or tissues has been reported, although this remains a controversial issue. Tubular aggregates (TAs) are pathological structures seen in the sarcoplasm of human skeletal muscle fibers in various disorders. The TAs derive from the sarcoplasmic reticulum (SR) and represent, probably, an adaptive response of the SR to various insults to the muscle fibers. In the present study, we present immunohistochemical evidence of emerin expression in TAs. Muscle biopsies with tubular aggregates from four male, unrelated patients were studied. The percentage of muscle fibers containing TAs varied between 5 and 20%. Routine histochemistry revealed intense reaction of TAs with NADH-TR, AMPDA, and NSE, but not with COX, SDH, myosin ATPase (pH 9.4, 4.3, 4.6), PAS, and Oil red O staining. Immunohistochemical study revealed strong immunostaining of TAs with antibodies against emerin and7 SERCA2-ATPase. Immunostaining of TAs was also seen with antibodies against heat shock protein and dysferlin, but not with antibodies to lamin A, dystrophin, adhalin, β, γ, δ sarcoglycans, and merosin. These results suggest that emerin, an inner nuclear membrane protein, is present at the TAs. The interpretation and significance of this finding is discussed in relation to experimental data suggesting that normal emerin localization at the inner nuclear membrane depends on lamin A and mutations in the N-terminal domain of emerin cause mislocalization of the protein to the sarcoplasmic membranes.

Quantifying Dynamical Complexity of Magnetic Storms and Solar Flares via Nonextensive Tsallis Entropy

Over the last couple of decades nonextensive Tsallis entropy has shown remarkable applicability to describe nonequilibrium physical systems with large variability and multifractal structure. Herein, we review recent results from the application of Tsallis statistical mechanics to the detection of dynamical changes related with the occurrence of magnetic storms. We extend our review to describe attempts to approach the dynamics of magnetic storms and solar flares by means of universality through Tsallis statistics. We also include a discussion of possible implications on space weather forecasting efforts arising from the verification of Tsallis entropy in the complex system of the magnetosphere.

Word-length Entropies and Correlations of Natural Language Written Texts

Abstract We study the frequency distributions and correlations of the word lengths of 10 European languages. Our findings indicate that (a) the word-length distribution of short words quantified by the mean value and the entropy distinguishes the Uralic (Finnish) corpus from the others, (b) the tails at long words, manifested in the high-order moments of the distributions, differentiate the Germanic languages (except for English) from the Romanic languages and Greek and (c) the correlations between nearby word lengths measured by the comparison of the real entropies with those of the shuffled texts are found to be smaller in the case of Germanic and Finnish languages.

ENTROPY ANALYSIS OF WORD-LENGTH SERIES OF NATURAL LANGUAGE TEXTS: EFFECTS OF TEXT LANGUAGE AND GENRE

We estimate the n-gram entropies of natural language texts in word-length representation and find that these are sensitive to text language and genre. We attribute this sensitivity to changes in the probability distribution of the lengths of single words and emphasize the crucial role of the uniformity of probabilities of having words with length between five and ten. Furthermore, comparison with the entropies of shuffled data reveals the impact of word length correlations on the estimated n-gram entropies.

Nonstorm loss of relativistic electrons in the outer radiation belt

We report observations of electron Phase Space Density (PSD) dropout and evidence that supports the loss mechanism of magnetopause shadowing and outward radial diffusion during a nonstorm period characterized by persistently positive values of the SYM-H index. On 14 April 2013 an electron PSD dropout of 2 orders of magnitude was observed at the nightside magnetosphere by the Van Allen Probes. The magnetopause shadowing was associated with a strong pulse attributed to the arrival of an interplanetary coronal mass ejection. It is shown, for the first time in detail, that significant losses to the magnetosheath may occur even in the absence of significant reconnection and magnetic storm activity. Signatures of substorm injections that penetrate the outer belt and enhance the low-energy electrons were also observed right after the interplanetary pressure pulse. Moreover, particle measurements from THEMIS constellation also show a PSD depletion in the dayside magnetosphere.

Extreme relativistic electron fluxes in the Earth's outer radiation belt: Analysis of INTEGRAL IREM data

Relativistic electrons (E > 500 keV) cause internal charging and are an important space weather hazard. To assess the vulnerability of the satellite fleet to these so-called “killer” electrons, it is essential to estimate reasonable worst cases, and, in particular, to estimate the flux levels that may be reached once in 10 and once in 100 years. In this study we perform an extreme value analysis of the relativistic electron fluxes in the Earths outer radiation belt as a function of energy and L∗. We use data from the Radiation Environment Monitor (IREM) on board the International Gamma Ray Astrophysical Laboratory (INTEGRAL) spacecraft from 17 October 2002 to 31 December 2016. The 1 in 10 year flux at L∗=4.5, representative of equatorial medium Earth orbit, decreases with increasing energy ranging from 1.36 × 107 cm−2 s−1 sr−1 MeV−1 at E = 0.69 MeV to 5.34 × 105 cm−2 s−1 sr−1 MeV−1 at E = 2.05 MeV. The 1 in 100 year flux at L∗=4.5 is generally a factor of 1.1 to 1.2 larger than the corresponding 1 in 10 year flux. The 1 in 10 year flux at L∗=6.0, representative of geosynchronous orbit, decreases with increasing energy ranging from 4.35 × 106 cm−2 s−1 sr−1 MeV−1 at E = 0.69 MeV to 1.16 × 105 cm−2 s−1 sr−1 MeV−1 at E = 2.05 MeV. The 1 in 100 year flux at L∗=6.0 is generally a factor of 1.1 to 1.4 larger than the corresponding 1 in 10 year flux. The ratio of the 1 in 10 year flux at L∗=4.5 to that at L∗=6.0 increases with increasing energy ranging from 3.1 at E = 0.69 MeV to 4.6 at E = 2.05 MeV.

Long-range correlations and burstiness in written texts: Universal and language-specific aspects

Recently, methods from the statistical physics of complex systems have been applied successfully to identify universal features in the long-range correlations (LRCs) of written texts. However, in real texts, these universal features are being intermingled with language-specific influences. This paper aims at the characterization and further understanding of the interplay between universal and language-specific effects on the LRCs in texts. To this end, we apply the language-sensitive mapping of written texts to word-length series (wls) and analyse large parallel (of same content) corpora from 10 languages classified to four families (Romanic, Germanic, Greek and Uralic). The autocorrelation functions of the wls reveal tiny but persistent LRCs decaying at large scales following a power-law with a language-independent exponent ∼0.60–0.65. The impact of language is displayed in the amplitude of correlations where a relative standard deviation >40% among the analyzed languages is observed. The classification to language families seems to play a significant role since, the Finnish and Germanic languages exhibit more correlations than the Greek and Roman families. To reveal the origins of the LRCs, we focus on the long words and perform burst and correlation analysis in their positions along the corpora. We find that the universal features are linked more to the correlations of the inter-long word distances while the language-specific aspects are related more to their distributions.