Presence Of Long-range Correlations Research Articles

Effects of electron-to-ion mass ratio in driving magnetic oscillations of magnetohydrodynamic plasmas and self-organized criticality

Evolutions of nonlinear magnetic fields have been shown to be governed by a set of coupled nonlinear equations of second order in magnetohydrodynamic (MHD) plasmas by Lee and Parks [Geophys. Res. Lett. 19, 637–640 (1992)]. We have considered the same set of coupled nonlinear equations for further analysis in this work by neglecting the presence of external forcing term in it. Different modes of oscillations of magnetic field have been found to exist in special limiting cases of this set of undriven second order coupled nonlinear equations having frequencies that are multiples of lower hybrid frequency. Numerical solutions of these coupled equations have been analysed revealing a quasi-periodic route to chaotic oscillations of the nonlinear magnetic fields as electron-to-ion mass ratio signifying presence of linear coupling effects is increased. Some signatures of the phenomenon of self-organized criticality (SOC) in typical quasi-periodic oscillations of magnetic field have also been noticed using Fourier analysis. The presence of long range correlations has been witnessed in quasi-periodic oscillations whereas both long range correlations and anticorrelations are found in chaotic oscillations using rescaled range analysis. Concluding remarks are provided in addition to various results and discussions.

Extensive entropy: the case of zero entropy defect

This paper shows that the Rényi and Boltzmann-Gibbs (BG) extensive entropies share the same functional relationship with the nonextensive entropy associated with kappa distributions, which coincides with the well-known Havrda/Charvát/Daróczy/Tsallis (HCDT) entropy. We find that while the relationship between kappa/HCDT and Rényi entropies is merely a mathematical identity between their entropic statistical definitions, the relationship between kappa/HCDT and BG entropies is based on their thermodynamic connection. The latter connects the entropy between a system characterized by correlations among their all constituents (kappa/HCDT entropy) and the entropy of the same system but with no correlations among their constituents (BG entropy). The origin of this relationship, and its connection with thermodynamics, is examined using the concept of entropy defect, that is, the decrease in a system’s entropy caused by the presence of long-range correlations among its constituents; in the limiting case of zero correlations, the entropy defect vanishes and the entropy becomes extensive and expressed by the BG formulation.

Random Matrix Analysis of Protein Families

Proteins are vital for almost all biochemical and cellular processes. Although there is an enormous growth in the protein sequence data, the statistical characterization, structure, and function of many of these sequences are still unknown. The statistical and spectral analysis of the Pearson correlation matrices between positions based on physiochemical properties of amino acids of seven protein families is performed and compared with the random Wishart matrix model results. A detailed analysis shows that the protein families significantly diverge from the Marcenko-Pastur distribution with many eigenvalues (outliers) outside the Wishart lower and upper bound. It is shown that level spacing distribution of protein families is similar to the Gaussian orthogonal ensemble. Further, the number variance varies as log of the system size indicating the presence of long range correlations within the protein families.

Data-driven fractional subgrid-scale modeling for scalar turbulence: A nonlocal LES approach

Filtering the passive scalar transport equation in the large-eddy simulation (LES) of turbulent transport gives rise to the closure term corresponding to the unresolved scalar flux. Understanding and respecting the statistical features of subgrid-scale (SGS) flux is a crucial point in robustness and predictability of the LES. In this work, we investigate the intrinsic nonlocal behavior of the SGS passive scalar flux through studying its two-point statistics obtained from the filtered direct numerical simulation (DNS) data for passive scalar transport in homogeneous isotropic turbulence (HIT). Presence of long-range correlations in true SGS scalar flux urges to go beyond the conventional local closure modeling approaches that fail to predict the non-Gaussian statistical features of turbulent transport in passive scalars. Here, we propose an appropriate statistical model for microscopic SGS motions by taking into account the filtered Boltzmann transport equation (FBTE) for passive scalar. In FBTE, we approximate the filtered equilibrium distribution with an α-stable Lévy distribution that essentially incorporates a power-law behavior to resemble the observed nonlocal statistics of SGS scalar flux. Generic ensemble-averaging of such FBTE lets us formulate a continuum level closure model for the SGS scalar flux appearing in terms of fractional-order Laplacian that is inherently nonlocal. Through a data-driven approach, we infer the optimal version of our SGS model using the high-fidelity data for the two-point correlation function between the SGS scalar flux and filtered scalar gradient, and sparse linear regression. In an a priori test, the optimal fractional-order model yields a promising performance in reproducing the probability distribution function (PDF) of the SGS dissipation of the filtered scalar variance compared to its true PDF obtained from the filtered DNS data.

Scaling Properties and Persistence of Long-Term Solar Activity

The long-range correlations associated with the presence of persistence are investigated by applying the detrended fluctuation analysis (DFA) on three different proxies of long-term solar activity. The considered datasets are a sunspot number reconstruction (SNR04) obtained from the atmospheric activity of the cosmogenic isotope 14C derived from tree rings, a total solar irradiance reconstruction (TSIR12) obtained from several 10Be ice core records from Greenland and Antarctica in combination with the global record of 14C in tree rings and a new multi-proxy sunspot number reconstruction (SNR18), also derived from 10Be datasets and the global 14C production series. The DFA scaling exponents found for the three time series are similar (lying in the range between 0.70 and 0.77) and the scaling ranges are comparable. These results indicate the presence of long-range correlations with persistence, in substantial agreement with the findings of previous studies carried out on other solar activity indices and proxies.

Experimental study of shear deformation of the medium formed by the massif of ribbed grains

The approach to the study of the seismically active zone as an open system that is in a state of self-organized criticality is becoming increasingly used in modern research. The models used in this approach should reflect the most characteristic features of such media: discreteness, nonequilibrium, nonlinear and nonlocal nature of interactions. In this paper, the medium is modeled by a granular massif with ribbed grains. Three different massifs are used in the research. Within one massif, all grains are identical, while grains from different massifs differ in shape (cubic or irregular ribbed) and characteristic size.
 A number of experiments of shear deformation of such granular massifs were carried out in order to study the influence of the shape and size of grains on the statistical charac-teristics of the process. The influence of the stress state on the deformation properties of these media was also studied. The experiments proved the qualitative similarity of the behavior of different granular media. Obtained experimentally force jumps, represen-ting the reaction of the granular medium to shear deformation, obey the distributions in the form of power dependencies. However, the magnitudes of the forces arising in the massifs depend on the grain shape and size as well as the stress state in the massifs. The experiments with shear deformation of the granular media under the external action of small impulse stresses have shown that such action causes a smoother, devoid of sharp jumps, deformation. External perturbations shift the distribution of the force jumps towards smaller values, leaving their exponents unchanged.
 The analysis of experimental results using nonadditive statistical mechanics confirmed the presence of long-range correlations in the massif of ribbed granules during its shear deformation.

Long-range temporal correlations in the broadband resting state activity of the human brain revealed by neuronal avalanches

Resting-state brain activity is characterized by the presence of neuronal avalanches showing absence of characteristic size. Such evidence has been interpreted in the context of criticality and associated with the normal functioning of the brain. A distinctive attribute of systems at criticality is the presence of long-range correlations. Thus, to verify the hypothesis that the brain operates close to a critical point and consequently assess deviations from criticality for diagnostic purposes, it is of primary importance to robustly and reliably characterize correlations in resting-state brain activity. Recent works focused on the analysis of narrow-band electroencephalography (EEG) and magnetoencephalography (MEG) signal amplitude envelope, showing evidence of long-range temporal correlations (LRTC) in neural oscillations. However, brain activity is a broadband phenomenon, and a significant piece of information useful to precisely discriminate between normal (critical) and pathological behavior (non-critical), may be encoded in the broadband spatio-temporal cortical dynamics. Here we propose to characterize the temporal correlations in the broadband brain activity through the lens of neuronal avalanches. To this end, we consider resting-state EEG and long-term MEG recordings, extract the corresponding neuronal avalanche sequences, and study their temporal correlations. We demonstrate that the broadband resting-state brain activity consistently exhibits long-range power-law correlations in both EEG and MEG recordings, with similar values of the scaling exponents. Importantly, although we observe that the avalanche size distribution depends on scale parameters, scaling exponents characterizing long-range correlations are quite robust. In particular, they are independent of the temporal binning (scale of analysis), indicating that our analysis captures intrinsic characteristics of the underlying dynamics. Because neuronal avalanches constitute a fundamental feature of neural systems with universal characteristics, the proposed approach may serve as a general, systems- and experiment-independent procedure to infer the existence of underlying long-range correlations in extended neural systems, and identify pathological behaviors in the complex spatio-temporal interplay of cortical rhythms.

Characterization of an operational quantum resource in a critical many-body system

Quantum many-body systems have been extensively studied from the perspective of quantum technology, and conversely, critical phenomena in such systems have been characterized by operationally relevant resources like entanglement. In this paper, we investigate robustness of magic (RoM), the resource in magic state injection based quantum computation schemes, in the context of the transverse field anisotropic XY model. We show that the the factorizable ground state in the symmetry broken configuration is composed of an enormous number of highly magical H states. We find the existence of a point very near the quantum critical point where magic contained explicitly in the correlation between two distant qubits attains a sharp maxima. Unlike bipartite entanglement, this persists over very long distances, capturing the presence of long range correlation near the phase transition. We derive scaling laws and extract corresponding exponents around criticality. Finally, we study the effect of temperature on two-qubit RoM and show that it reveals a crossover between dominance of quantum and thermal fluctuations.

Multifractal behavior in return and volatility series of Bitcoin and gold in comparison

Abstract In this study, we investigate multifractal nature of return and volatility (proxied by absolute and squared returns) series of Bitcoin and gold throughout full sample periods and sub-sample periods which are decided accordingly the results of the structural breaks in the full sample periods. Applying the Multifractal Detrended Fluctuation Analysis (MFDFA), it is found that Bitcoin return series have distinctly different multifractal properties than of gold. Our evidence shows that all return and volatility series of Bitcoin have a persistent behavior, and have higher degree of multifractality than of gold. Using rolling windows approach, we confirm the persistence and the higher degree of multifractality of Bitcoin time series. Return series of gold have uncorrelated behavior while volatility series of gold have persistent behavior. Moreover, applying structural break test for the series of complexity parameters retrieved from the multifractal analysis of the return and volatility series of gold and Bitcoin, our results indicate that time series of gold have different regimes with different characteristics of multifractality. Furthermore, impact of temporal correlations and fat-tails is also examined and both are found to be the source of multifractality in the return series of Bitcoin and gold. In volatility series of Bitcoin, multifractality arises mostly due to long-range correlations and fat-tails. However, presence of long-range correlations and fat-tails in the original volatility series of gold mostly yields to less degree of multifractality.

Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: effect of disorder correlations

We study numerically the effects of short- and long-range correlations on the localization properties of the eigenstates in a one-dimensional disordered lattice characterized by a random non-Hermitian Hamiltonian, where the imaginary part of the on-site potential is random. We calculate the participation number versus strengths of disorder and correlation. In the short-ranged case and when the correlation length is sufficiently small, we find that there exists a critical value of the disorder strength, below which enhancement and above which suppression of localization occurs as the correlation length increases. In the region where the correlation length is larger, localization is suppressed in all cases. Similar behavior is obtained for long-range correlations as the disorder strength and the correlation exponent are varied. Unlike in the case of a long-range correlated real random potential, no signature of the localization transition is found in a long-range correlated imaginary random potential. In the region where localization is enhanced in the presence of long-range correlations, we find that the enhancement occurs in the whole energy band, but is strongest near the band center. In addition, we find that the anomalous localization enhancement effect occurs near the band center in the long-range correlated case.

Tsallis conditional mutual information in investigating long range correlation in symbol sequences

The presence of long range correlation (LRC) as opposed to Markov chain of a finite order is of primary interest in the study of symbol sequences, such as DNA. Among others, methods using information theory have been developed for Markov chain order estimation. In this work, we consider the Tsallis entropy and define the Tsallis conditional mutual information (TCMI) for Markov chain order estimation, which is more suitable to identify large orders suggesting effectively LRC. The TCMI of order m for a Tsallis parameter q is computed for increasing m and a significance test is performed for each m until TCMI is found non-significant. Randomization and parametric significance tests for TCMI are developed. For the latter, the null distribution of TCMI is approximated with a gamma distribution deriving analytic expressions for its parameters. We assess the accuracy of order estimation with the two tests for TCMI and compare them to the respective tests using the Shannon entropy. Extended simulations on Markov chains of different orders and structures of the transition probability matrix show that Shannon and Tsallis tests with parameter q=2 have similar performance for small orders. When the problem becomes more demanding for higher Markov chain orders and LRCs, Tsallis tests for q=2 have better approximation to the correct order with the sequence length N. Finally, the Tsallis tests are favorably compared to Shannon tests to real DNA sequences.

Non-Gaussian behavior of reflected fractional Brownian motion

A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary increments, is a prototypical model for this situation. Here, we extend the previous results found for unbiased reflected fractional Brownian motion (Wada et al 2018 Phys. Rev. E 97 020102) to the biased case by means of Monte Carlo simulations and scaling arguments. We demonstrate that the interplay between the reflecting wall and the correlations leads to highly non-Gaussian probability densities of the particle position x close to the reflecting wall. Specifically, the probability density develops a power-law singularity with if the correlations are positive (persistent) and if the correlations are negative (antipersistent). We also analyze the behavior of the large-x tail of the stationary probability density reached for bias towards the wall, the average displacements of the walker, and the first-passage time, i.e. the time it takes for the walker reach position x for the first time.

Non-extensive statistics in free-electron metals and thermal effective mass

We have applied the non-extensive statistical mechanics to free electrons in several metals to calculate the electronic specific heat at low temperature. In this case, the Fermi–Dirac (FD) function is modified from its Boltzmann–Gibbs (BG) form, with the exponential part going to a q-exponential, in its non-extensive form. In most cases, the non-extensive parameter, q, is found to be greater than unity to produce the correct thermal effective mass, m∗, of electrons. The ratio m∗∕m is found to show a nice systematic dependence on q. Results indicate, electrons in metals, in the presence of long range correlations are reasonably well described by Tsallis statistics.

Long-range temporal correlation in Auditory Brainstem Responses to Spoken Syllable/da/

The speech auditory brainstem response (sABR) is an objective clinical tool to diagnose particular impairments along the auditory brainstem pathways. We explore the scaling behavior of the brainstem in response to synthetic /da/ stimuli using a proposed pipeline including Multifractal Detrended Moving Average Analysis (MFDMA) modified by Singular Value Decomposition. The scaling exponent confirms that all normal sABR are classified into the non-stationary process. The average Hurst exponent is H = 0:77 ± 0:12 at 68% confidence interval indicating long-range correlation which shows the first universality behavior of sABR. Our findings exhibit that fluctuations in the sABR series are dictated by a mechanism associated with long-term memory of the dynamic of the auditory system in the brainstem level. The q-dependency of h(q) demonstrates that underlying data sets have multifractal nature revealing the second universality behavior of the normal sABR samples. Comparing Hurst exponent of original sABR with the results of the corresponding shuffled and surrogate series, we conclude that its multifractality is almost due to the long-range temporal correlations which are devoted to the third universality. Finally, the presence of long-range correlation which is related to the slow timescales in the subcortical level and integration of information in the brainstem network is confirmed.

Tunneling probe of fluctuating superconductivity in disordered thin films

Disordered thin films close to the superconducting-insulating phase transition (SIT) hold the key to understanding quantum phase transition in strongly correlated materials. The SIT is governed by superconducting quantum fluctuations, which can be revealed for example by tunneling measurements. These experiments detect a spectral gap, accompanied by suppressed coherence peaks that do not fit the BCS prediction. To explain these observations, we consider the effect of finite-range superconducting fluctuations on the density of states, focusing on the insulating side of the SIT. We perform a controlled diagrammatic resummation and derive analytic expressions for the tunneling differential conductance. We find that short-range superconducting fluctuations suppress the coherence peaks, even in the presence of long-range correlations. Our approach offers a quantitative description of existing measurements on disordered thin films and accounts for tunneling spectra with suppressed coherence peaks observed, for example, in the pseudo gap regime of high-temperature superconductors.

A long memory property of economic and financial news flows

One of the tools for examining the processes and time series with self-similarity is the long-range correlation exponent (the Hurst exponent). Many methods have been developed for estimating the long-range correlation exponent using experimental time series over the last years. In this paper we estimate the Hurst exponent parameter obtained by different methods using news analytics time series. We exploit the most commonly used methods for estimating the Hurst exponents: fluctuation analysis, the detrended fluctuation analysis and the detrending moving average analysis. Following some previous studies, empirical results show the presence of long-range correlations for the time series of news intensity data. In particular, the paper shows that the behaviour of long range dependence for time series of news intensity in the recent period from 1 January 2015 to 22 September 2015 did not change in comparison to the period from 1 September 2010 to 29 October 2010. Moreover, the change of the news analytics provider and the consideration of more recent data did not significantly affect estimates of the Hurst exponent. The results show that the self-similarity property is a stable characteristic of the news flow of information which serves the financial industry and stock markets.

An investigation of Renyi entropy in high-energy nucleus–nucleus collisions

A study of Renyi entropy of shower particles has been carried out using 16O, 28Si, and 32S projectiles in interaction with AgBr and CNO target present in nuclear emulsion at an incident momentum of 4.5 AGeV/c. The analysis reveals interesting experimental observations for both groups of targets. A comparison of the experimental results with the results obtained from analyzing the event sample generated by the UrQMD code is also presented. Renyi entropy values increase with the increase of projectile mass. This increase is weaker in case of CNO target. The calculated values of second-order Renyi entropy H2 are shown to vary linearly with the logarithm of average particle multiplicity ln⟨n⟩ for both targets. The dependence of Renyi entropy on the logarithm of average particle multiplicity ln⟨n⟩ indicates the presence of long-range correlation in high-energy nucleus–nucleus interactions. The variation is found to be stronger in the case of experimental events in comparison to the UrQMD simulated events indicating stronger long-range correlation for the experimental data.

Event-by-Event pseudorapidity fluctuation analysis: An outlook to multiplicity and phase space dependence

A detailed study of Event-by-Event pseudorapidity fluctuation of the pions produced in 16O -AgBr interactions at 60A GeV and 32S -AgBr interactions at 200A GeV has been carried out in terms of \( \phi\) , a variable defined as a measure of fluctuation. Non-zero \( \phi\) values indicate the presence of strong correlation among the pions for both interactions. Multiplicity and rapidity dependence of the Event-by-Event pseudorapidity fluctuation has been investigated. A decrease of \( \phi\) with average multiplicity and increase of the same variable with pseudorapidity width are observed. Decrease of \( \phi\) with average multiplicity is concluded as the particle emission by several independent sources occurs for higher-multiplicity events. The increase in \( \phi\) values with pseudorapidity width, taken around central rapidity, might hint towards the presence of long-range correlation and its dominance over short range one. We have compared our experimental results with Monte Carlo simulation generated assuming independent particle emission. Comparison shows that the source of correlation and fluctuation is the dynamics of the pion production process. We have also compared our results with events generated by FRITIOF code. Such events also show the presence of fluctuation and correlation; however they fail to replicate the experimental findings.

Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

We have studied the multifractality of pion emission process in16O-AgBr interactions at 2.1 AGeV and 60 AGeV,12C-AgBr and 24Mg-AgBr interactions at 4.5 AGeV, and32S-AgBr interactions at 200 AGeV using Multifractal Detrended Fluctuation Analysis (MFDFA) method which is capable of extracting the actual multifractal property filtering out the average trend of fluctuation. The analysis reveals that the pseudorapidity distribution of the shower particles is multifractal in nature for all the interactions; that is, pion production mechanism has inbuilt multiscale self-similarity property. We have employed MFDFA method for randomly generated events for32S-AgBr interactions at 200 AGeV. Comparison of expt. results with those obtained from randomly generated data set reveals that the source of multifractality in our data is the presence of long range correlation. Comparing the results obtained from different interactions, it may be concluded that strength of multifractality decreases with projectile mass for the same projectile energy and for a particular projectile it increases with energy. The values of ordinary Hurst exponent suggest that there is long range correlation present in our data for all the interactions.

The effect of footwear and footfall pattern on running stride interval long-range correlations and distributional variability

The presence of long-range correlations (self-similarity) in the stride-to-stride fluctuations in running stride interval has been used as an indicator of a healthy adaptable system. Changes to footfall patterns when running with minimalist shoes could cause a less adaptable running gait. The purpose of this study was to investigate stride interval variability and the degree of self-similarity of stride interval in runners wearing minimalist and conventional footwear. Twenty-six trained habitual rearfoot footfall runners, unaccustomed to running in minimalist footwear, performed 6-min sub-maximal treadmill running bouts at 11, 13 and 15 km·h−1 in minimalist and conventional shoes. Force sensitive resistors were placed in the shoes to quantify stride interval (time between successive foot contacts). Footfall position, stride interval mean and coefficient of variation (CV), were used to assess performance as a function of shoe type. Long-range correlations of stride interval were assessed using detrended fluctuation analysis (α). Mean stride interval was 1-1.3% shorter (P=0.02) and 27% of runners adopted a midfoot footfall (MFF) in the minimalist shoe. There was a significant shoe effect on α and shoe*speed*footfall interaction effect on CV (P<0.05). Runners that adopted a MFF in minimalist shoes, displayed reduced long-range correlations (P<0.05) and CV (P<0.06) in their running stride interval at the 15 km·h−1 speed. The reduced variability and self-similarity observed for runners that changed to a MFF in the minimalist shoe may be suggestive of a system that is less flexible and more prone to injury.