Statistical Behavior Research Articles

Inhomogeneous turbulence for the Wick Nonlinear Schrödinger equation

AbstractWe introduce a simplified model for wave turbulence theory—the Wick nonlinear Schrödinger equation, of which the main feature is the absence of all self‐interactions in the correlation expansions of its solutions. For this model, we derive several wave kinetic equations that govern the effective statistical behavior of its solutions in various regimes. In the homogeneous setting, where the initial correlation is translation invariant, we obtain a wave kinetic equation similar to the one predicted by the formal theory. In the inhomogeneous setting, we obtain a wave kinetic equation that describes the statistical behavior of the wavepackets of the solutions, accounting for both the transport of wavepackets and collisions among them. Another wave kinetic equation, which seems new in the literature, also appears in a certain scaling regime of this setting and provides a more refined collision picture.

A robust beamforming with antenna selection approach for dense antenna arrays under limited CSI

This paper introduces a novel approach for dense antenna arrays, which integrates beamforming and antenna selection. The proposed method aims to optimize the number of transmit antennas to reduce power consumption and enhance spectral efficiency at the transmitter. By employing optimal beamforming weights, our approach steers signals toward the intended receiver to maximize the transmit power of the desired signal while mitigating side-lobe interference under channel uncertainty. To adapt beamforming parameters dynamically to changing channel conditions, we develop a channel estimation approach that obtains accurate channel state information (CSI). In contrast to prior studies, our channel estimation method utilizes a generalized Gaussian distribution (GGD) model, capable of accommodating both matched and mismatched CSI features by modeling heavy-tailed and light-tailed distributions. This allows our method to capture diverse channel statistical behaviors resulting from phenomena such as fading and interference under various propagation conditions. Furthermore, we introduce an angle entropy metric, which measures angle of departure (AoD) variations, indicating the degree of uncertainty regarding the directionality of transmitted signals. Simulation results validate the accuracy of our analytical findings and demonstrate the superior performance of the proposed approach in terms of robustness and bit-error-rate (BER) performance.

Analysis of short-term polarization stability using Allan variance

The application of Allan variance to characterize the stability of optical signals affected by stochastic polarization fluctuations and the identification of the underlying power law noise processes is explored. Allan variance can ease the comparison regarding polarization stability of optical systems affected by polarization noise and define a near-optimum integration interval to reveal trends. Examples of the application of Allan variance to optical systems with stable polarization conditions show that white noise and random walk terms can be observed. Additionally, experiments show that the three Stokes parameters can exhibit different statistical behaviors in the Brownian-noise regime. Allan analysis can easily be used to define, in real-time systematically, the denoising strategy in polarization-based sensing and for the optimization of polarization-sensitive optical systems instead of the conventional approach relying on heuristics or information criteria.

Developing Non-Stationary Frequency Relationships for Greater Pamba River basin, Kerala India incorporating dominant climatic precursors

Abstract. Global climate changes significantly contribute to increased frequency of hydrologic extremes. This significantly underestimates the hydrologic design parameters, bringing of hydro systems to increased failure risk. In order to address this concern, the current practice of development of hydrologic frequency tools need to be updated accounting for non-stationarity. This study first considered a diverse set of statistical tests to examine the trend, change points, non-stationarity and randomness of streamflow, rainfall and temperature time series of scales ranging from daily to annual. The annual maxima time series indicated non stationarity against the stationary behaviour of daily series of hydro-meteorological datasets of the basin. Subsequently, this study developed the Temperature Duration Frequency (TDF), Rainfall Intensity Duration Frequency (IDF) and Flood Frequency (FF) curves of Greater Pamba river basin in Kerala India, the part of which was most severely affected by the near century return period flood event of 2018. The analysis was performed for a multitude of combinations of variations in distribution parameters with time and climatic drivers as physical covariates in the extreme value formulations. The study proposed a novel wavelet coherence (WC) based driver selection of most dominant combination of climatic precursors in developing FF and IDF relations of three locations of Kalloopara, Malakkara and Thumpamon and TDF curve of Kuttanad region in the basin, considering data of 1985–2015 period. The proposed WC framework considers bi-multi-and partial effects of climatic oscillations (COs) like El Niño Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), Pacific Decadal Oscillation (PDO) and North Atlantic Oscillation (NAO) in identifying potential drivers. The different WC formulations captured in-phase relationships of streamflows and rainfall with COs at intra-annual, annual and inter annual scales up to 4 years. The methods showed that addition of climatic precursors improved the NS estimates of flood and rainfall quantiles by more accurately capturing the magnitudes of extreme streamflows and rainfalls of 2018, 2021 than the time covariate formulations. However, the role of COs on extreme temperature is not found to be influential in developing TDF relationships, which needs further investigation.

Thermodynamic geometry of a system with unified quantum statistics.

We investigate the thermodynamic characteristics of unified quantum statistics, a framework exhibiting a crossover between Bose-Einstein and Fermi-Dirac statistics by varying a generalization parameter δ. An intrinsic statistical interaction becomes attractive for δ≤0.5, maintaining positive thermodynamic curvature across the entire physical range. In the range 0.5<δ<1, the system predominantly displays Fermi-like behavior at high temperatures. Conversely, at low temperatures, the thermodynamic curvature is positive, resembling bosonic behavior. Further temperature reduction induces a transition into the condensate phase. We introduce a critical fugacity (z=Z^{*}) at which the thermodynamic curvature changes sign. Below (z<Z^{*}) and above (z>Z^{*}) this critical point, the statistical behavior mimics fermions and bosons, respectively. We explore the system's statistical behavior for various δ values with respect to temperature, determining the critical fugacity and temperature-dependent condensation. Finally, we analyze specific heat as a function of temperature and condensation phase transition temperature for different δ values in various dimensions.

Forecasting with an N-dimensional Langevin equation and a neural-ordinary differential equation.

Accurate prediction of electricity day-ahead prices is essential in competitive electricity markets. Although stationary electricity-price forecasting techniques have received considerable attention, research on non-stationary methods is comparatively scarce, despite the common prevalence of non-stationary features in electricity markets. Specifically, existing non-stationary techniques will often aim to address individual non-stationary features in isolation, leaving aside the exploration of concurrent multiple non-stationary effects. Our overarching objective here is the formulation of a framework to systematically model and forecast non-stationary electricity-price time series, encompassing the broader scope of non-stationary behavior. For this purpose, we develop a data-driven model that combines an N-dimensional Langevin equation (LE) with a neural-ordinary differential equation (NODE). The LE captures fine-grained details of the electricity-price behavior in stationary regimes but is inadequate for non-stationary conditions. To overcome this inherent limitation, we adopt a NODE approach to learn, and at the same time predict, the difference between the actual electricity-price time series and the simulated price trajectories generated by the LE. By learning this difference, the NODE reconstructs the non-stationary components of the time series that the LE is not able to capture. We exemplify the effectiveness of our framework using the Spanish electricity day-ahead market as a prototypical case study. Our findings reveal that the NODE nicely complements the LE, providing a comprehensive strategy to tackle both stationary and non-stationary electricity-price behavior. The framework's dependability and robustness is demonstrated through different non-stationary scenarios by comparing it against a range of basic naïve methods.

What can we learn from long hydrological time-series? The case of rainfall data at Collegio Romano, Rome, Italy

In this work, we explore the statistical behavior of one of the longest rainfall time-series in Italy and in the world, covering the period 1782–2017. Some standard and innovative statistical tools are applied to test the variability and change of the process across all values (in average, but also in terms of extremes) and scales (from days to years). An oscillation pattern occurs across all the time scales, from years to decades, limited by the sample length. It implies that there are no particular periods of variability, apart from seasonality, and no statistically significant trends, such that the process can be fully characterized in terms of the Hurst coefficient. Despite its exceptional length, the dataset is still insufficient to adequately capture the complex behavior of rainfall over the time scales, especially with regards to extremes, and to separate anthropogenically induced change from natural variability based on the data alone. Our findings suggest that samples of limited length do not allow robust statistical predictions, raising concerns about statistical analyses based on a limited dataset, even a relatively large one.

Charged particle collisionless transport near the X-point of the two-wire model

Collisionless charged particle motion and its transport in the two-wire model (TWM) with no axial magnetic fields is investigated numerically. The TWM configuration contains a magnetic X-point, and single particle motions in such a field have two conserved quantities: the total kinetic energy and the base field line value which is a quantity derived from the axial canonical momentum. As gyrating particles travel along the field lines, they may reach near the X-point region where the magnetic moment, the first adiabatic invariant, can be occasionally shifted due to a large gradient of the field. When the magnetic moment becomes large, resulting in a large Larmor radius, particles probabilistically cross the X-point to migrate to the opposite side of the TWM configuration. These phenomena are investigated with single particle simulations. We find that the statistical behaviour of the seemingly chaotic magnetic moment shifts are completely determined by the two aforementioned conserved quantities, and also that there exists a threshold energy, determined by the base field line value, allowing only particles with a higher energy to cross the separatrix and migrate. It is found that the crossing time is distributed exponentially, and that the migration confinement time, which is the average crossing time, is shorter for particles with a base field line closer to the separatrix and a higher energy. We provide an empirical expression, derived with the simulations, for estimating the collisionless migration confinement time.

Grid‐forming converters in interconnected power systems: Requirements, testing aspects, and system impact

AbstractIn this study, the integration of grid‐forming (GFM) converters in power systems is discussed in terms of both the fundamental aspects of system stability and the technical possibilities of converter‐based resources. The paper provides a survey and comparison of various GFM control concepts with respect to their transient and stationary behavior. A method for black box characterization and conformity testing of GFM converters is presented and relevant results of lab and field tests with GFM converters are discussed. Finally, important system aspects are addressed. This includes an approach to consider the behavior of GFM converters in distribution grid models and investigations on the minimum share of GFM units required to ensure system stability. The findings of this paper provide valuable insights for the design and implementation of GFM converters in modern converter‐based power systems.

Avalanche scaling law for heterogeneous interfacial fracture

A new approach is proposed to study the statistical law of avalanches due to the fracture of a heterogeneous interface. Firstly, a discrete interface is considered as a bundle of fibers clamped with two elastic circular plates, fiber strength being either a random variable or a stochastic field. Based on the theory of solid mechanics, equations governing the dynamic fracture process of fibers under tension are exactly derived and solved. The statistical law of fracture avalanches is accurately obtained. By tuning parameters, the model covers the whole scheme of stress-transfer mechanism due to fiber breaking from local load sharing to equal load sharing. Results show that the distribution of avalanche size of interfacial fracture follows a power-law relation, with the power exponent in the range [1.5,2.5], depending on both disorders of interface and stiffness of plates. Particularly, the exponent monotonically increases with plate stiffness to the value 2.5, a universal constant obtained by Hemmer and Hansen (1992). Then, the fracture of a laminated interface is analyzed. By discretizing the interface to a set of prismatic elements, the problem reduces to that of a discrete interface. Similar statistical behaviors are also observed. Furthermore, the temporal variation of avalanche scaling law is investigated. It is shown that in the vicinity of collapse point, the exponent of each time window is smaller than the exponent evaluated with the whole time series of event, probably a precursor for imminent catastrophic failure of interface.

Modelling of the Flame Surface Density Transport During Flame-Wall Interaction of Premixed Flames within Turbulent Boundary Layers

ABSTRACT A priori Direct Numerical Simulation (DNS) analysis of the modelling of the generalised flame surface density (FSD) transport equation in the framework of Reynolds Averaged Navier-Stokes (RANS) simulations has been conducted with a focus on flame-wall interaction (FWI) within turbulent boundary layers. The analysis was performed using two different scenarios: one involving the unsteady head-on interaction of a statistically planar premixed flame as it propagates through a turbulent boundary layer, and the other addressing statistically stationary oblique-wall interaction of a V-shaped premixed flame within a turbulent channel flow. Flame-wall interaction has been observed to exert a significant influence on the statistical behavior of the terms in the FSD transport equation. Throughout all phases of flame-wall interaction in both configurations, the primary source and sink terms in the FSD transport equation are consistently associated with the tangential strain rate and curvature terms. The relative importance of the contributions of the propagation and turbulent transport terms in the FSD transport equation have been found to be influenced by the flame-wall interaction configuration. Existing models for the tangential strain rate term in the FSD transport equation have been identified as inadequate based on a priori DNS assessment. Hence, adjustments to these models have been proposed to address the impact of flame orientation and near-wall effects specifically in the context of flame-wall interaction within turbulent boundary layers. The alignment between the flame normal vector and the wall normal vector has been identified as a crucial factor in modelling the contributions of unresolved dilatation rate and unresolved normal strain rate to the FSD transport equation. New models for these terms have been demonstrated to exhibit satisfactory agreement with the corresponding terms extracted from DNS data.

Timescales Associated with the Evolution of Reactive Scalar Gradient in Premixed Turbulent Combustion: A Direct Numerical Simulation Analysis

The fractional change in the reaction progress variable gradient depends on the flow normal straining within the flame and also upon the corresponding normal gradients of the reaction rate and its molecular diffusion transport. The statistical behaviours of the normal strain rate and the contributions arising from the normal gradients of the reaction rate and molecular diffusion rate within the flame were analysed by means of a Direct Numerical Simulation (DNS) database of statistically planar turbulent premixed flames ranging from the wrinkled/corrugated flamelets regime to the thin reaction zones regime. The interaction of flame-normal straining with the flame-normal gradient of molecular diffusion rate was found to govern the reactive scalar gradient transport in the preheat zone, where comparable timescales for turbulent straining and molecular diffusion are obtained for small values of Karlovitz numbers. However, the molecular diffusion timescale turns out to be smaller than the turbulent straining timescale for high values of Karlovitz numbers. By contrast, the reaction and hot product zones of the flame remain mostly unaffected by turbulence, and the reactive scalar gradient transport in this zone is determined by the interaction between the flame-normal gradients of molecular diffusion and chemical reaction rates.

What is the nature of responses of energy security to shocks in the E7 countries? Fresh evidence by applying unit root tests

ABSTRACT Energy security, characterized by equitable distribution of sustainable, acceptable and affordable energy sources, carries significant social, economic,\\ and environmental consequences. Achieving energy security is influenced by unanticipated shocks, such as oil price volatility, and policy decisions, including diversifying energy sources and developing green technologies. To gauge the efficiency of shocks and policies in altering energy security dynamics of E7 countries, the present study uses the Energy Security Risk Index (ESRI) as a proxy of energy security and employs panel Lagrange multiplier (LM) with smooth breaks and univariate LM unit root test with sharp breaks. In addition, both tests allow for cross-sectional dependence. Our findings reveal distinct dynamics across countries over the period 1980–2018. Specifically, Brazil, India, Indonesia and Turkey exhibit stationary behaviour in their ESRI, while China shows a unit root process. The stochastic properties of Mexico are inconclusive. Our results have important implications, which are discussed in detail.

Time scales in the dynamics of political opinions and the voter model

Opinions in human societies are measured by political polls on time scales of months to years. Such opinion polls do not resolve the effects of individual interactions but constitute a stochastic process. Voter models with zealots (individuals who do not change their opinions) can describe the mean-field dynamics in systems where no consensus is reached. We show that for large populations, the voter model with zealots is equivalent to the noisy voter model and it has a single characteristic time scale associated with the number of zealots in the population. We discuss which parameters are observable in real data by analysing time series of approval ratings of several political leaders that match the statistical behaviour of the voter model using the technique of the time-averaged mean squared displacement. The characteristic time scale of political opinions in societies is around 12 months, so it cannot be resolved by analysing election data, for which the resolution is several years. The effective population size in all fitted data sets is much smaller than the real population size, which indicates positive correlations of successive voter model steps. We also discuss the heterogeneity of voters as a cause of subdiffusion on long time scales, i.e. slow changes in the society.

Statistical behavior of the European Energy Exchange-Zero Carbon Freight Index (EEX-ZCFI) assessments in the context of Carbon Emissions Fraction Analysis (CEFA)

Greenhouse gas (GHG) emissions through freight transportation have received growing concerns and are one of the critical issues for the United Nation's Sustainability Development Goals (SDGs). The literature survey reveals that freight transportation makes up global GHG emissions and its carbon emissions may double by 2050. In European Union (EU) carbon taxes are a promising way to reduce CO2Carbon di oxide and other GHG emissions. The European Energy Exchange (EEX) recently launched its new Zero Carbon Freight Index (ZCFI). EEX-ZCFI provides the first insight into how much the price of carbon will add to freight costs. This work developed the analysis of a ZCFI using a statistical model (i.e. GARCH and FBM) with the intention of offering a reference for understating the wide-range ramifications of such indices. Preprocessing methods (descriptive statistics, unit root test, and an ARCH effect test) are performed to verify the validity of the GARCH (1,1) model for forecasting volatility. This work employs the EEX-ZCFI time series for January 2020 to August 2022. To further examine the carbon freight indices, a Ljung-Box test method based on the GARCH model was applied. The bootstrapped returns are forming a linear relation with the forecast data; therefore, it concluded that the model designed strongly fits with the time series. With GARCH optimal model parameters we have forecasted the carbon freight index time series data and hypothetically examined the influence on the carbon emission with C5TC time series, which can also be applied in the Asia-pacific region.

Statistical behaviour of laser Doppler vibrometer detector signals and application of statistics for signal diversity

The problem of speckle noise and the so-called signal dropouts is well-known by many LDV sensors. Signal power is reduced when less light power is scattered into the detection aperture due to laser speckle. Signal dropouts occur when the carrier-to-noise ratio (C/N) of the photodetector signal falls below the frequency modulation (FM) threshold. This problem can be resolved with signal diversity. However, the influence of the speckle noise and signal dropouts has not been quantitatively analysed the state of the art. We introduce in this paper a new mathematical model of the statistical behaviour of detector signals of LDV sensors. This allows us to calculate the influence of speckle noise and signal dropouts on the detector signals of LDV sensors. Furthermore, we optimize the signal combination method of signal diversity according to the state of the art. Finally, we present some experimental results to prove our mathematical model and signal diversity for reducing speckle noise and signal dropouts.

Efficient Cumulant-Based Automatic Modulation Classification Using Machine Learning.

This paper introduces a new technique for automatic modulation classification (AMC) in Cognitive Radio (CR) networks. The method employs a straightforward classifier that utilizes high-order cumulant for training. It focuses on the statistical behavior of both analog modulation and digital schemes, which have received limited attention in previous works. The simulation results show that the proposed method performs well with different signal-to-noise ratios (SNRs) and channel conditions. The classifier's performance is superior to that of complex deep learning methods, making it suitable for deployment in CR networks' end units, especially in military and emergency service applications. The proposed method offers a cost-effective and high-quality solution for AMC that meets the strict demands of these critical applications.

Statistical inference for agreement between multiple raters on a binary scale.

Agreement studies often involve more than two raters or repeated measurements. In the presence of two raters, the proportion of agreement and of positive agreement are simple and popular agreement measures for binary scales. These measures were generalized to agreement studies involving more than two raters with statistical inference procedures proposed on an empirical basis. We present two alternatives. The first is a Wald confidence interval using standard errors obtained by the delta method. The second involves Bayesian statistical inference not requiring any specific Bayesian software. These new procedures show better statistical behaviour than the confidence intervals initially proposed. In addition, we provide analytical formulas to determine the minimum number of persons needed for a given number of raters when planning an agreement study. All methods are implemented in the R package simpleagree and the Shiny app simpleagree.

Square Root Statistics of Density Matrices and Their Applications.

To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures-Hall ensemble, extending known results obtained recently over the Hilbert-Schmidt ensemble.

Some Results on Statistically Pre-Cauchy Sequences of Fuzzy Variables Defined by Orlicz Functions in Credibility Space

This study introduces the concept of statistically pre-Cauchy sequences of fuzzy variables in five directions of credibility theory: almost surely, in measure, in mean, in distribution, and uniformly almost surely. However, the main focus is kept on statistically pre-Cauchy sequences in measure, in mean, and in distribution. Furthermore, a correlation between statistically pre-Cauchy sequences and statistically convergent sequences is established using fuzzy variables. Additionally, the exploration of statistically pre-Cauchy sequences of fuzzy variables is initiated through the application of Orlicz functions. The objective is to enhance the understanding of the statistical behavior and convergence properties of fuzzy variables in various credibility scenarios.