Long-range Correlations Research Articles

Observation of Enhanced Long-Range Elliptic Anisotropies Inside High-Multiplicity Jets in pp Collisions at sqrt[s]=13 TeV.

A search for collective effects inside jets produced in proton-proton collisions is performed via correlation measurements of charged particles using the CMS detector at the CERN LHC. The analysis uses data collected at a center-of-mass energy of sqrt[s]=13 TeV, corresponding to an integrated luminosity of 138 fb^{-1}. Jets are reconstructed with the anti-k_{T} algorithm with a distance parameter of 0.8 and are required to have transverse momentum greater than 550GeV and pseudorapidity |η^{jet}|<1.6. Two-particle correlations among the charged particles within the jets are studied as functions of the particles' azimuthal angle and pseudorapidity separations (Δϕ^{*} and Δη^{*}) in a jet coordinate basis, where particles' η^{*}, ϕ^{*} are defined relative to the direction of the jet. The correlation functions are studied in classes of in-jet charged-particle multiplicity up to N_{ch}^{j}≈100. Fourier harmonics are extracted from long-range azimuthal correlation functions to characterize azimuthal anisotropy for |Δη^{*}|>2. For low-N_{ch}^{j} jets, the long-range elliptic anisotropic harmonic, v_{2}^{*}, is observed to decrease with N_{ch}^{j}. This trend is well described by MonteCarlo event generators. However, a rising trend for v_{2}^{*} emerges at N_{ch}^{j}≳80, hinting at a possible onset of collective behavior, which is not reproduced by the models tested. This observation yields new insights into the dynamics of jet evolution in the vacuum.

Multifractal Analysis of the Impact of Fuel Cell Introduction in the Korean Electricity Market

This study employs multifractal detrended fluctuation analysis to investigate the impact of fuel cell introduction in the Korean electricity market via the lens of multifractal scaling behavior. Using multifractal analysis, the research delineates discrepancies between peak and off-peak hours, accounting for the daily cyclicity of the electricity market, and proposes a crossover point detection method based on the Chow test. Furthermore, the impacts of fuel cell introduction are evidenced through various methods that encompass multifractal spectra and market efficiency. The findings initially indicate a higher degree of multifractality during off-peak hours relative to peak hours. In particular, the crossover points emerged solely during off-peak hours, unveiling short- and long-term dynamics predicated on a near-annual cycle. Additionally, the average Hurst exponent for the short-term was 0.542, while the average for the long-term was 0.098, representing a notable discrepancy. The introduction of fuel cells attenuated the heterogeneity in the scaling behavior, which is potentially attributable to the decreased volatility in both the supply and demand spectra. Remarkably, after the introduction of fuel cells, there was a discernible decrease in the influence of long-range correlation within multifractality, and the market exhibited an increased propensity toward random-walk behavior. This phenomenon was also detected in the market deficiency measure, from an average of 0.536, prior to the introduction, to an average of 0.267, following the introduction, signifying an improvement in market efficiency. This implies that the introduction of fuel cells into the market engendered increased supply stability and a consistent increase in demand, mitigating volatility on both the supply and demand sides, thus increasing market efficiency.

Environment-mediated long-ranged correlations in many-body system

Quantum states in complex aggregates are unavoidably affected by environmental effects, which typically cannot be accurately modeled by simple Markovian processes. As system sizes scale up, nonperturbative simulation becomes thus unavoidable, but they are extremely challenging due to the intimate interplay of intrinsic many-body interaction and time-retarded feedback from environmental degrees of freedom. In this work, we utilize the recently developed quantum dissipation with minimally extended state space approach to address reservoir induced long-ranged temporal correlations in finite size Ising-type spin chains. For thermal reservoirs with ohmic and subohmic spectral density, we simulate the quantum time evolution from finite to zero temperature. The competition between thermal fluctuations, quantum fluctuations, and anti-/ferromagnetic interactions reveals a rich pattern of dynamical phases, including dissipative induced phase transitions and spatiotemporal correlations.

Multifractal properties of Covid-19 data

Multifractal detrended moving average analysis (MFDFA) has been performed on time series of three different epidemiological indices, namely daily number of new cases per million population, reproduction rate and positive rate, recorded during the Covid-19 pandemic. We consider India, Japan, USA and UK for this study. For all the series the scaling behavior of MFDMA fluctuation functions has been examined, and the multifractal variables like the generalised Hurst exponent spectra and singularity spectra have been calculated. It is found that the time series of the Covid-19 indices are of multifractal nature. The degree of multifractality of the reproduction rate series is significantly weaker than the other two series for all the countries. To find out the source(s) of multifractality, we generate a set of one hundred shuffled series and Amplitude-Adjusted Fourier Transform surrogate series for each of the original series. Comparing the results obtained from the original series with those from the shuffled and surrogate series we understand that the main source of multifractality in Covid-19 data is long-range temporal correlation among the series values.

The Application of Tsallis Entropy Based Self-Adaptive Algorithm for Multi-Threshold Image Segmentation.

Tsallis entropy has been widely used in image thresholding because of its non-extensive properties. The non-extensive parameter q contained in this entropy plays an important role in various adaptive algorithms and has been successfully applied in bi-level image thresholding. In this paper, the relationships between parameter q and pixels' long-range correlations have been further studied within multi-threshold image segmentation. It is found that the pixels' correlations are remarkable and stable for images generated by a known physical principle, such as infrared images, medical CT images, and color satellite remote sensing images. The corresponding non-extensive parameter q can be evaluated by using the self-adaptive Tsallis entropy algorithm. The results of this algorithm are compared with those of the Shannon entropy algorithm and the original Tsallis entropy algorithm in terms of quantitative image quality evaluation metrics PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity). Furthermore, we observed that for image series with the same background, the q values determined by the adaptive algorithm are consistently kept in a narrow range. Therefore, similar or identical scenes during imaging would produce similar strength of long-range correlations, which provides potential applications for unsupervised image processing.

Fast generation of spectrally shaped disorder.

Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by means of the nonuniform fast Fourier transform, thus arriving at an algorithm capable of generating systems with arbitrary spectral properties, with a computational cost that scales O(NlogN) with system size. The method is extended to accommodate arbitrary real-space interactions, such as short-range repulsion, to simultaneously control short- and long-range correlations. We thus generate the largest-ever stealthy hyperuniform configurations in 2d (N=10^{9}) and 3d (N>10^{7}) and demonstrate the flexibility of the approach by generating structures with designed spectral features at scale. By an Ewald sphere construction we link the spectral and optical properties at the single-scattering level and show that stealthy hyperuniform structures generically display transmission gaps, providing a concrete example of fine-tuning of a physical property. We also show that large 3d power-law hyperuniformity in particle packings leads to single-scattering properties nearly identical to those of simple hard spheres. Finally, we demonstrate generalizations of the approach to impose features in either continuous or discrete real space, using constraints in either continuous or discrete reciprocal space. In particular, enforcing large spectral power at peaks with the right symmetry leads to the nondeterministic generation of quasicrystalline structures in 2d and 3d. This technique should become an essential tool to embed, and understand the role of, long-range correlations in disordered metamaterials.

Long-range velocity correlations from active dopants

Active matter systems display collective behaviors that are impossible in thermodynamic equilibrium. One such feature, observed in in dense active matter systems is the appearance of long-range velocity correlations without explicit aligning interaction. However, the conditions for the appearance of these correlations remain largely unexplored. Here we show that such long-range velocity correlations can also be generated in a dense athermal passive system by the inclusion of a very small fraction of active Brownian particles. We develop a continuum theory to explain the emergence of velocity correlations generated via such active dopants. We validate the predictions for the effects of magnitude and persistence time of the active force and the area fractions of active and passive particles using extensive Brownian dynamics simulation of a canonical active-passive mixture. Our work decouples the roles that density and activity play in generating long-range velocity correlations in such exotic non-equilibrium steady states.

Deep video compression based on Long-range Temporal Context Learning

Video compression allows for efficient storage and transmission of data, benefiting imaging and vision applications, e.g. computational imaging, photography, and displays by delivering high-quality videos. To exploit more informative contexts of video, we propose DVCL, a novel Deep Video Compression based on Long-range Temporal Context Learning. Aiming at high coding performance, this new compression paradigm makes full use of long-range temporal correlations derived from multiple reference frames to learn richer contexts. Motion vectors (MVs) are estimated to represent the motion relations of videos. By employing MVs, a long-range temporal context learning (LTCL) module is presented to extract context information from multiple reference frames, such that a more accurate and informative temporal contexts can be learned and constructed. The long-range temporal contexts serve as conditions and generate the predicted frames by contextual encoder and decoder. To address the challenge of imbalanced training, we develop a multi-stage training strategy to ensure the whole DVCL framework is trained progressively and stably. Extensive experiments demonstrate the proposed DVCL achieves the highest objective and subjective quality, while maintaining relatively low complexity. Specifically, 25.30% and 45.75% bitrate savings on average can be obtained than x265 codec at the same PSNR and MS-SSIM, respectively.

General Relations between Stress Fluctuations and Viscoelasticity in Amorphous Polymer and Glass-Forming Systems.

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard-Jones particles.

Hebbian plasticity induced by temporally coincident BCI enhances post-stroke motor recovery

Functional electrical stimulation (FES) can support functional restoration of a paretic limb post-stroke. Hebbian plasticity depends on temporally coinciding pre- and post-synaptic activity. A tight temporal relationship between motor cortical (MC) activity associated with attempted movement and FES-generated visuo-proprioceptive feedback is hypothesized to enhance motor recovery. Using a brain–computer interface (BCI) to classify MC spectral power in electroencephalographic (EEG) signals to trigger FES-delivery with detection of movement attempts improved motor outcomes in chronic stroke patients. We hypothesized that heightened neural plasticity earlier post-stroke would further enhance corticomuscular functional connectivity and motor recovery. We compared subcortical non-dominant hemisphere stroke patients in BCI-FES and Random-FES (FES temporally independent of MC movement attempt detection) groups. The primary outcome measure was the Fugl-Meyer Assessment, Upper Extremity (FMA-UE). We recorded high-density EEG and transcranial magnetic stimulation-induced motor evoked potentials before and after treatment. The BCI group showed greater: FMA-UE improvement; motor evoked potential amplitude; beta oscillatory power and long-range temporal correlation reduction over contralateral MC; and corticomuscular coherence with contralateral MC. These changes are consistent with enhanced post-stroke motor improvement when movement is synchronized with MC activity reflecting attempted movement.

Long-range near-side correlation in e+e− collisions at 183-209 GeV with ALEPH archived data

The first measurement of two-particle angular correlations for charged particles with LEP-II data is presented. The study is performed using archived hadronic e+e− data collected by ALEPH at center-of-mass energies up to 209 GeV, above the W+W− production threshold, which provide access to unprecedented charged-particle multiplicities and more complex color-string configurations if compared to previous measurements at LEP-I energies. An intriguing long-range near-side excess is observed in the correlation function measured with respect to the thrust axis in the highest multiplicity interval (Ntrk≥50). Such a structure is not predicted by the Monte-Carlo simulation. The harmonic anisotropy coefficients vn, which result from the Fourier expansion of the two-particle correlation functions, were also measured for the first time in e+e− data, and compared to pythia 6 predictions and to the results obtained in proton-proton collisions. The results presented in the Letter provide novel experimental constraints on the formation of collective phenomena in point-like e+e− collisions.

Cluster Formation Induced by Local Dielectric Saturation in Restricted Primitive Model Electrolytes.

Experiments using the Surface Force Apparatus (SFA) have found anomalously long-ranged charge-charge underscreening in concentrated salt solutions. Meanwhile, theory and simulations have suggested ion clustering to be a possible origin of this behavior. The popular Restricted Primitive Model of electrolyte solutions, in which the solvent is represented by a uniform relative dielectric constant, εr, is unable to resolve the anomalous underscreening seen in experiments. In this work, we modify the Restricted Primitive Model to account for local dielectric saturation within the ion hydration shell. The dielectric "constant" in our model locally decreases from the bulk value to a lower saturated value at the ionic surface. The parameters for the model are deduced so that typical salt solubilities are obtained. Our simulations for both bulk and slit geometries show that our model displays strong cluster formation and these give rise to long-ranged density correlations between charged surfaces, at distances similar to what has been observed in SFA measurements. An electrolyte model wherein the dielectric constant remains uniform does not display similar clusters, even with εr equal to the low saturated value at ion contact. Hence, the observed behaviors are not simply due to an enhanced Coulomb interaction. In the latter case, cluster growth is counteracted by long-ranged repulsions between like-charged ions within clusters; this is an effect that is considerably reduced when the dielectric response drop is local. Our results imply that long-ranged interactions in these systems are mainly due to cluster-cluster correlations, rather than large electrostatic screening lengths.

Capturing and interpreting wildfire spread dynamics: attention-based spatiotemporal models using ConvLSTM networks

Predicting the trajectory of geographical events, such as wildfire spread, presents a formidable task due to the dynamic associations among influential biophysical factors. Geo-events like wildfires frequently display short and long-range spatial and temporal correlations. Short-range effects are the direct contact and near-contact spread of the fire front. Long-range effects are represented by processes such as spotting, where firebrands carried by the wind ignite fires distant from the flaming front, altering the shape and speed of an advancing fire front. This study addresses these modeling challenges by clearly defining and analyzing the scale-dependent spatiotemporal dynamics that influence wildfire spread, focusing on the interplay between biophysical factors and fire behavior. We propose two unique attention-based spatiotemporal models using Convolutional Long Short-Term Memory (ConvLSTM) networks. These models are designed to learn and capture a range of local to global and short and long-range spatiotemporal correlations. The proposed models were tested on two datasets: a high-resolution wildfire spread dataset produced with a semi-empirical percolation model and a satellite observed wildfire spread data in California 2012–2021. Results indicate that attention-based models accurately predict fire front movements that are consistent with known wildfire spread-biophysical dynamics. Our research suggests there is considerable potential for attention mechanisms to capture the spatiotemporal behavior of wildfire spread, with model transferability, that can guide rapid deployment of wildfire management operations. We also highlight directions for future studies that focus on how the self-attention mechanism could enhance model performance for a range of geospatial applications.

Multifractal analysis of heart rate variability in pregnancy during sleep.

Understanding the complex dynamics of heart rate variability (HRV) during pregnancy is crucial for monitoring both maternal well-being and fetal health. In this study, we use the Multifractal Detrended Fluctuations Analysis approach to investigate HRV patterns in pregnant individuals during sleep based on RR interval maxima (MM fluctuations). In addition, we study the type of multifractality within MM fluctuations, that is, if it arises from a broad probability density function or from varying long-range correlations. Furthermore, to provide a comprehensive view of HRV changes during sleep in pregnancy, classical temporal and spectral HRV indices were calculated at quarterly intervals during sleep. Our study population consists of 21 recordings from nonpregnant women, 18 from the first trimester (early-pregnancy) and 18 from the second trimester (middle-pregnancy) of pregnancy. Results. There are statistically significant differences ( -value < 0.05) in mean heart rate, rms heart rate, mean MM fluctuations, and standard deviation of MM fluctuations, particularly in the third and fourth quarter of sleep between pregnant and non-pregnant states. In addition, the early-pregnancy group shows significant differences ( -value < 0.05) in spectral indices during the first and fourth quarter of sleep compared to the non-pregnancy group. Furthermore, the results of our research show striking similarities in the average multifractal structure of MM fluctuations between pregnant and non-pregnant states during normal sleep. These results highlight the influence of different long-range correlations within the MM fluctuations, which could be primarily associated with the emergence of sleep cycles on multifractality during sleep. Finally, we performed a separability analysis between groups using temporal and spectral HRV indices as features per sleep quarter. Employing only three features after Principal Component Analysis (PCA) to the original feature set, achieving complete separability among all groups appears feasible. Using multifractal analysis, our study provides a comprehensive understanding of the complex HRV patterns during pregnancy, which holds promise for maternal and fetal health monitoring. The separability analysis also provides valuable insights into the potential for group differentiation using simple measures such as mean heart rate, rms heart rate, and mean MM fluctuations or in the transformed feature space based on PCA.

Analyzing Monofractal Short and Very Short Time Series: A Comparison of Detrended Fluctuation Analysis and Convolutional Neural Networks as Classifiers

Time series data are a crucial information source for various natural and societal processes. Short time series can exhibit long-range correlations that reveal significant features not easily discernible in longer ones. Such short time series find utility in AI applications for training models to recognize patterns, make predictions, and perform classification tasks. However, traditional methods like DFA fail as classifiers for monofractal short time series, especially when the series are very short. In this study, we evaluate the performance of the traditional DFA method against the CNN-SVM approach of neural networks as classifiers for different monofractal models. We examine their performance as a function of the decreasing length of synthetic samples. The results demonstrate that CNN-SVM achieves superior classification rates compared to DFA. The overall accuracy rate of CNN-SVM ranges between 64% and 98%, whereas DFA’s accuracy rate ranges between 16% and 64%.

Continuum percolation of two-dimensional adaptive dynamics systems.

The percolation phase transition of a continuum adaptive neuron system with homeostasis is investigated. In order to maintain their average activity at a particular level, each neuron (represented by a disk) varies its connection radius until the sum of overlapping areas with neighboring neurons (representing the overall connection strength in the network) has reached a fixed target area for each neuron. Tuning the two key parameters in the model, i.e., the density defined as the number of neurons (disks) per unit area and the sum of the overlapping area of each disk with its adjacent disks, can drive the system into the critical percolating state. These two parameters are inversely proportional to each other at the critical state, and the critical filling factors are fixed about 0.7157, which is much less than the case of the continuum percolation with uniform disks. It is also confirmed that the critical exponents in this model are the same as the two-dimensional standard lattice percolation. Although the critical state is relatively more sensitive and exhibits long-range spatial correlation, local fluctuations do not propagate in a long-range manner through the system by the adaptive dynamics, which renders the system overall robust against perturbations.

Photon-count fluctuations of spontaneous parametric down conversion exhibit long-range correlations

Photon-count fluctuations of spontaneous parametric down conversion exhibit long-range correlations

Quantum advantage and stability to errors in analogue quantum simulators

Several quantum hardware platforms, while being unable to perform fully fault-tolerant quantum computation, can still be operated as analogue quantum simulators for addressing many-body problems. However, due to the presence of errors, it is not clear to what extent those devices can provide us with an advantage with respect to classical computers. In this work, we make progress on this problem for noisy analogue quantum simulators computing physically relevant properties of many-body systems both in equilibrium and undergoing dynamics. We first formulate a system-size independent notion of stability against extensive errors, which we prove for Gaussian fermion models, as well as for a restricted class of spin systems. Remarkably, for the Gaussian fermion models, our analysis shows the stability of critical models which have long-range correlations. Furthermore, we analyze how this stability may lead to a quantum advantage, for the problem of computing the thermodynamic limit of many-body models, in the presence of a constant error rate and without any explicit error correction.

The Rosenzweig–Porter model revisited for the three Wigner–Dyson symmetry classes

Interest in the Rosenzweig–Porter model, a parameter-dependent random-matrix model which interpolates between Poisson and Wigner–Dyson (WD) statistics describing the fluctuation properties of the eigenstates of typical quantum systems with regular and chaotic classical dynamics, respectively, has come up again in recent years in the field of many-body quantum chaos. The reason is that the model exhibits parameter ranges in which the eigenvectors are Anderson-localized, non-ergodic (fractal) and ergodic extended, respectively. The central question is how these phases and their transitions can be distinguished through properties of the eigenvalues and eigenvectors. We present numerical results for all symmetry classes of Dyson’s threefold way. We analyzed the fluctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results. Based on these results we propose characteristics of the short- and long-range correlations as measures to explore the transition from Poisson to WD statistics. Furthermore, we performed in-depth studies of the properties of the eigenvectors in terms of the fractal dimensions, the Kullback–Leibler (KL) divergences and the fidelity susceptibility. The ergodic and Anderson transitions take place at the same parameter values and a finite size scaling analysis of the KL divergences at the transitions yields the same critical exponents for all three WD classes, thus indicating superuniversality of these transitions.

Nonlinear comparative analysis of Greenland and Antarctica ice cores data.

We analyze the temperature time series of the EPICA Dome C ice cores in Antarctica and of the Greenland project, Summit, with durations of 800 000 and 248 000 years, respectively, with a recent mathematical tool defined through the Fourier phases of the series, known as the J-index. This data driven index can differentiate between purely random dynamics and dynamics with a deterministic component. It is sensitive to nonlinear components and robust to the presence of noise. Our J-index data analysis shows that both Greenland and Antarctica climatic fluctuations possess deterministic traits and suggests the presence of an underlying nonlinear dynamics. Furthermore, in both regions, it reveals the simultaneous occurrence of an important global event known as the "Pelukian transgression." For Antarctica, it also detects the marine isotopic stage 11. Additionally, our calculation of the time series Hurst exponents and our detrended fluctuation analysis show the presence of long-range persistent correlations for Antarctica and anti-persistent correlations for Greenland. For the latter case, our fractal dimension determinations are indicative of a more complex climatic dynamics in Greenland with respect to Antarctica. Our results are encouraging for further development of climate variability deterministic models for these regions.