Statistical Behavior Research Articles

Investigation of statistical correlation of negative parity energy levels in Tm nucleus with A=170

In this paper, the statistical properties of 1- to 7- negative parity levels in the 170Tm nucleus are considered with emphasis on the nearest neighbor spacing distribution in the framework of random matrix theory. The latest available experimental data for different negative parity energy levels in the E≤ 3000 keV region are used to classifiy in different sequences and are analysed. The Berry – Robnik distribution function and the least square extraction method have been used to determine the parameter of distribution function in considered sequences. The results show the adaptation of the statistical behavior of all considered negative parity levels with the Wigner distribution function and therefore, the statistical correlation of such levels. Also, the strong correlations are yield for the sequences prepared by levels with odd spin values while the 2- levels show a weak correlation and a Poisson-like behavior. The dependence of the statistical behavior of the negative parity levels to the energy was investigated which suggests the maximum correlation in the 1300 <E < 2100 keV energy region.

Exploring the Potential of Neural Networks to Predict Statistics of Solar Wind Turbulence

AbstractTime series data sets often have missing or corrupted entries, which need to be handled in subsequent data analysis. For example, in the context of space physics, calibration issues, satellite telemetry issues, and unexpected events can make parts of a time series unusable. This causes problems for understanding the dynamics of the heliosphere and space weather environment. Various approaches exist to tackle this problem, including mean/median imputation, linear interpolation, and autoregressive modeling. Here, we study the utility of artificial neural networks (ANNs) to predict statistics of sparse time series. Our focus is not on time series prediction but on gleaning the best possible information about the statistical behavior of the system. As an example application, we focus on the structure functions of turbulent time series measured in the solar wind. Using a data set with artificial gaps, a neural network is trained to predict second‐order structure functions and then tested on an unseen data set to quantify its performance. A small feedforward ANN, with only 20 hidden neurons, can predict the large‐scale fluctuation amplitudes better than mean imputation or linear interpolation when the percentage of missing data is high. Although they perform worse than the other methods when it comes to capturing both the shape and fluctuation amplitude together, their performance is better in a statistical sense for large fractions of missing data. Caveats regarding their utility, the optimization procedure, and potential future improvements are discussed.

Hydrodynamic slip significantly alters chaotic advection and scattering of small particles

We present a computational study of the effect of hydrodynamic slip at the surface of a particle on the statistical behavior of an ensemble of spherical particles in a two-dimensional von Karman flow in the wake of a cylinder. We predict that slip can lead to significant differences in escape rates, more initial positions that lead to vortex trapping at long times, and a greater uncertainty in scattering predictions. Thus, our work highlights that hydrodynamic slip significantly affects particle trajectories in unsteady flows.

Bivariate symmetric Heckman models and their characterization

A sample selection bias problem arises when a variable of interest or response is correlated with a latent variable. This problem is presented when the response variable has part of its observations censored. The Heckman sample selection model is based on the bivariate normality assumption and fits both response and latent variables. Recently, this assumption has been relaxed to more flexible models based on the Student-t distribution, which has appealing statistical properties. In this article, we introduce an extention of the Heckman sample selection model to the wide class of symmetric distributions. In the new class of sample selection models, covariates are used to describe its dispersion and correlation parameters explaining heteroscedasticity and sample selection bias, respectively. We derive mathematical and statistical properties of the introduced model, and estimate its parameters with the maximum likelihood method. The case of the bivariate Heckman-Student-t model, as a special member of the family of symmetric Heckman models, is analyzed. Monte Carlo simulations are performed to assess the statistical behavior of the estimation method. Two real data sets are analyzed to illustrate our results.

Fluctuations in pedestrian dynamics routing choices.

Routing choices of walking pedestrians in geometrically complex environments are regulated by the interplay of a multitude of factors such as local crowding, (estimated) time to destination, and (perceived) comfort. As individual choices combine, macroscopic traffic flow patterns emerge. Understanding the physical mechanisms yielding macroscopic traffic distributions in environments with complex geometries is an outstanding scientific challenge, with implications in the design and management of crowded pedestrian facilities. In this work, we analyze, by means of extensive real-life pedestrian tracking data, unidirectional flow dynamics in an asymmetric setting, as a prototype for many common complex geometries. Our environment is composed of a main walkway and a slightly longer detour. Our measurements have been collected during a dedicated high-accuracy pedestrian tracking campaign held in Eindhoven (The Netherlands). We show that the dynamics can be quantitatively modeled by introducing a collective discomfort function, and that fluctuations on the behavior of single individuals are crucial to correctly recover the global statistical behavior. Notably, the observed traffic split substantially departs from an optimal, transport-wise, partition, as the global pedestrian throughput is not maximized.

Furstenberg systems of Hardy field sequences and applications

We study measure preserving systems, called Furstenberg systems, that model the statistical behavior of sequences defined by smooth functions with at most polynomial growth. Typical examples are the sequences (\({n^{{3 \over 2}}}\)), (n log n), and (\([{n^{{3 \over 2}}}]\)), α ∈ ℝ ℚ, where the entries are taken mod 1. We show that their Furstenberg systems arise from unipotent transformations on finite-dimensional tori with some invariant measure that is absolutely continuous with respect to the Haar measure and deduce that they are disjoint from every ergodic system. We also study similar problems for sequences of the form (\(g({S^{[{n^{{3 \over 2}}}]}}y)\)), where S is a measure preserving transformation on the probability space (Y, ν), g ∈ L∞(ν), and y is a typical point in Y. We prove that the corresponding Furstenberg systems are strongly stationary and deduce from this a multiple ergodic theorem and a multiple recurrence result for measure preserving transformations of zero entropy that do not satisfy any commutativity conditions.

Cubic Transmuted Rayleigh Distribution: Theory and Application

In this paper, the Rayleigh distribution is generalized using the cubic transmuted (CT) family studied by Rahman et al. (in EJPAM, 12(3), 1106-1121, 2019) to propose a cubic transmuted Rayleigh distribution. An overall description is presented here for the distributional properties, parameter estimation, inference procedure, reliability behavior, and distribution of different order statistics. A real-life data set is used to demonstrate the applicability of the proposed distribution for modeling data.

Statistical correlation investigation of a single-doweled timber-to-timber joint

Dowel-type joints are widely used in timber structures given their ease of construction, strength, and capacity to deform before failure. The embedment strength of timber and the bending moment capacity of dowels are considered key properties in the design. On the other hand, these properties have an inherent variability that increases the uncertainties related to the connection’s strength and associated failure modes. This study proposes to quantify the uncertainty related to the statistical correlation behavior between the timber embedment strength and dowel bending moment capacity while comparing analytical solutions to the results of double shear single doweled timber joints. Traditional distribution fitting procedures, as well as copula functions, are implemented to capture their marginal and dependence behavior. Since their source of mutual correlation is known, the effectiveness of the different approaches in describing the statistical dependence structure can be assessed. This is done by investigating how equivalent are the descriptions of dependence by copula functions and directly from the correlation origin. Results obtained here indicate that, for single dowel-type connections in double shear, the impact of the copulas on the results is small, which means that improving their joint characterization represents a minor improvement in the reliability results. Besides the minor differences, the results show that copula functions are a viable tool capable of capturing the nuances of the joint behavior between random variables.

Analysis of Flow Behavior as Influenced by Reservoir with Flow Regularization

Understanding the behavior of reservoirs with flow regularization formed by hydroelectric power plants is essential for assessing water availability. The operationalization of reservoirs can be influenced both by climatic characteristics and by the consequences resulting from human actions in the basin. The objective of this study was to evaluate the existing relationships between the inflows and outflows of a reservoir, as well as with the conventional streamflow gauge stations downstream of the dam. Also evaluated were trends in the behavior of minimum, average and maximum flows, in the post-operation period, considering the characteristics of rainfall and irrigation in the region. The results indicated that reservoir operationalization is strongly related to the behavior of inflows. Moreover, a reduction was also verified in all the variables analyzed related to inflows and outflows, as well as in the stations downstream of the dam, except for the maximum flow in the station farthest from the reservoir, which showed a stationary behavior. The reductions in the flows may be related to the almost three-fold increase in the area irrigated by the center pivot in the basin; however, the same cannot be said in relation to the annual rainfall regime of the region, since it showed a stationary behavior for most of the stations evaluated. The work demonstrates the importance of trend analysis of flows over the years in order to identify possible factors responsible for their variability and assist in decision making regarding measures for the recovery and preservation of water resources.

Augmenting covariance estimation for ensemble-based data assimilation in multiple-query scenarios

We present and assess a method to reduce the computational cost of performing ensemble-based data assimilation (DA) for reacting flows in multiple-query scenarios, i.e. scenarios where multiple simulations are performed on systems with similar underlying dynamics. The accuracy of the DA, which depends on the accuracy of the sample covariance, improves with the ensemble size, but results in a commensurate increase to computational cost. To reduce the ensemble size while maintaining accurate covariance, we propose a data-driven approach to augment the covariance based on the statistical behaviour learned from previous model evaluations. We assess our augmentation method using one-dimensional model problems and a two-dimensional synthetic reacting flow problem. We show in all these cases that ensemble size, and thus computational cost, may be reduced by a factor of three to four while maintaining accuracy.

Disordered Complex Networks: Energy Optimal Lattices and Persistent Homology

Disordered complex networks are of fundamental interest in statistical physics, and they have attracted recent interest as stochastic models for information transmission over wireless networks. While mathematically tractable, a network based on the regulation Poisson point process model offers challenges vis-a-vis network efficiency. Strongly correlated alternatives, such as networks based on random matrix spectra (the Ginibre network), on the other hand offer formidable challenges in terms of tractability and robustness issues. In this work, we demonstrate that network models based on random perturbations of Euclidean lattices <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">interpolate</i> between Poisson and rigidly structured networks, and allow us to achieve the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">best of both worlds</i> : significantly improve upon the Poisson model in terms of network efficacy measured by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Signal to Interference plus Noise Ratio</i> (abbrv. SINR) and the related concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coverage probabilities</i> , at the same time retaining a considerable measure of mathematical and computational simplicity and robustness to erasure and noise. We investigate the optimal choice of the base lattice in this model, connecting it to the celebrated problem optimality of Euclidean lattices with respect to the Epstein Zeta function, which is in turn related to notions of lattice energy. This leads us to the choice of the triangular lattice in 2D and face centered cubic lattice in 3D, whose Gaussian perturbations we consider. We provide theoretical analysis and empirical investigations to demonstrate that the coverage probability decreases with increasing strength of perturbation, eventually converging to that of the Poisson network. In the regime of low disorder, our studies suggest an approximate statistical behaviour of the coverage function near a base station as a log-normal distribution with parameters depending on the Epstein Zeta function of the lattice, and related approximate dependencies for a power-law constant that governs the network coverage probability at large thresholds. In 2D, we determine the disorder strength at which the perturbed triangular lattice (abbrv. PTL) and the Ginibre networks are the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closest</i> measured by comparing their network topologies via a comparison of their <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Persistence Diagrams</i> in the total variation as well as the symmetrized nearest neighbour distances. We demonstrate that, at this very same disorder, the PTL and the Ginibre networks exhibit very similar coverage probability distributions, with the PTL performing at least as well as the Ginibre. Thus, the PTL network at this disorder strength can be taken to be an effective substitute for the Ginibre network model, while at the same time offering the advantages of greater tractability both from theoretical and empirical perspectives.

An affine combination of two augmented CLMS adaptive filters for processing noncircular Gaussian signals

This paper investigates the statistical behavior of an affine combination of two augmented complex least mean-square (ACLMS) adaptive filters for processing noncircular Gaussian signals. First, the optimal affine combiner is studied and its steady state mean behavior is explicitly quantified. This makes it possible to reveal the impact of the input second-order noncircularity coefficient on the combiner. Next, the mean square error analysis of the proposed affine-combined ACLMS filters is provided, proving that the combined scheme performs no less than the best of the individual ACLMS subfilters. Besides, to facilitate physically realization of the combination strategy, an error power based algorithm that can iterate the affine combiner to the optimal one is also proposed. Finally, illustrative numerical simulations are provided to support the theoretical results.

Predicting a Person’s Next Activity Region with a Dynamic Region-Relation-Aware Graph Neural Network

The understanding of people’s inter-regional mobility behaviors, such as predicting the next activity region (AR) or uncovering the intentions for regional mobility, is of great value to public administration or business interests. While there are numerous studies on human mobility, these studies are mainly from a statistical view or study movement behaviors within a region. The work on individual-level inter-regional mobility behavior is limited. To this end, in this article, we propose a dynamic region-relation-aware graph neural network (DRRGNN) for exploring individual mobility behaviors over ARs. Specifically, we aim at developing models that can answer three questions: (1) Which regions are the ARs? (2) Which region will be the next AR, and (3) Why do people make this regional mobility? To achieve these tasks, we first propose a method to find out people’s ARs. Then, the designed model integrates a dynamic graph convolution network (DGCN) and a recurrent neural network (RNN) to depict the evolution of relations between ARs and mine the regional mobility patterns. In the learning process, the model further considers peoples’ profiles and visited point-of-interest (POIs). Finally, extensive experiments on two real-world datasets show that the proposed model can significantly improve accuracy for both the next AR prediction and mobility intention prediction.

Overload wave-memory induces amnesia of a self-propelled particle

Information storage is a key element of autonomous, out-of-equilibrium dynamics, especially for biological and synthetic active matter. In synthetic active matter however, the implementation of internal memory in self-propelled systems is often absent, limiting our understanding of memory-driven dynamics. Recently, a system comprised of a droplet generating its guiding wavefield appeared as a prime candidate for such investigations. Indeed, the wavefield, propelling the droplet, encodes information about the droplet trajectory and the amount of information can be controlled by a single scalar experimental parameter. In this work, we show numerically and experimentally that the accumulation of information in the wavefield induces the loss of time correlations, where the dynamics can then be described by a memory-less process. We rationalize the resulting statistical behavior by defining an effective temperature for the particle dynamics where the wavefield acts as a thermostat of large dimensions, and by evidencing a minimization principle of the generated wavefield.

On local weak limit and subgraph counts for sparse random graphs

AbstractWe use an inequality of Sidorenko to show a general relation between local and global subgraph counts and degree moments for locally weakly convergent sequences of sparse random graphs. This yields an optimal criterion to check when the asymptotic behaviour of graph statistics, such as the clustering coefficient and assortativity, is determined by the local weak limit.As an application we obtain new facts for several common models of sparse random intersection graphs where the local weak limit, as we see here, is a simple random clique tree corresponding to a certain two-type Galton–Watson branching process.

Applied Bibliometric in the Advancement of Solar Energy Research

Bibliometrics has proven to be an efficient method for quantitative research on the statistical behavior of academic production, which allows analyzing existing data and documents to resolve trends in specific research fields. Considering the database downloaded from Web of Science, with the help of Hitscite and VOSviewer data analysis tool and Microsoft Excel table, 7,259 publications related to solar energy research from 2010 to 2020 were obtained. The purpose of this research work is to apply bibliometric analysis methods to the development of scientific research on solar energy, as an important part of renewable energies, to evaluate its progress in the last decades and to describe these trends. The results showed that since 2015, research on solar energy has increased, especially in countries such as the United States and China, due to the Paris treaties where the goal is that the average temperature of the earth by the year 2100 does not exceed 1.5 °C. Since greenhouse gases are the cause of the greatest impact of the increase in global temperature, it is expected that researchers will focus on harnessing green energy and take a step further to reduce fossil fuels.

A reduced order model for space–time wave statistics using probabilistic decomposition–synthesis method

We present a reduced order model for predicting space–time extreme wave statistics for directionally spread water waves. This reduced order model relies on the probabilistic decomposition–synthesis framework. In this framework, the probabilistic distribution is decomposed into a ‘background’ region, where there are negligible nonlinear effects and a ‘instability’ region where the nonlinear physics leads to heavy-tailed statistical behaviour. In our reduced order model, we approximate the statistics in the background region with linear simulations to reduce the computational cost. The statistics in the instability region are estimated with nonlinear simulations of focused wave groups with carefully chosen initial conditions to capture the nonlinear effects during the formation of the extreme waves. The probabilistic statistics from these two components are synthesised with analytical expressions to model the overall behaviour of weakly nonlinear waves. This reduced order wave statistical model can provide accurate predictions of nonlinear space–time wave statistics at a fraction of computational cost of direct nonlinear Monte-Carlo simulations.

Modelling Intensity Fluctuations of Rayleigh Backscattered Coherent Light in Single-Mode Fibers

This work reportsa thorough analysis of intensity fluctuations of Rayleigh backscattered coherent light in single mode optical fibers. Based on the intermediate range order of silica glasses and on residual stress of optical fibers, a theoretical model was built to calculate intensity fluctuations of Rayleigh backscattered coherent light in the optical frequency domain. Numerical simulation results were compared to experimental results in time domain, strongly supporting the conclusion that Rayleigh backscattering in single mode fibers is an ergodic process exhibiting ergodicity in the time-frequency sense so that the model can be used to determine the statistical behavior of backscattered intensity fading.

Quantum Statistics of Identical Particles

The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical behaviors are excluded a priori. A more general approach is to ask what other many-particle statistics are consistent with the indistinguishability of identical particles. This strategy offers a way to discuss possible violations of the Pauli Exclusion Principle, and it leads to some interesting issues related to preparation of states and a superselection rule arising from invariance under the permutation group.

Parametric Vine Copula Framework in the Trivariate Probability Analysis of Compound Flooding Events

The interaction between oceanographic, meteorological, and hydrological factors can result in an extreme flooding scenario in the low-lying coastal area, called compound flooding (CF) events. For instance, rainfall and storm surge (or high river discharge) can be driven by the same meteorological forcing mechanisms, tropical or extra-tropical cyclones, resulting in a CF phenomenon. The trivariate distributional framework can significantly explain compound events’ statistical behaviour reducing the associated high-impact flood risk. Resolving heterogenous dependency of the multidimensional CF events by incorporating traditional 3D symmetric or fully nested Archimedean copula is quite complex. The main challenge is to preserve all lower-level dependencies. An approach based on decomposing the full multivariate density into simple local building blocks via conditional independence called vine or pair-copulas is a much more comprehensive way of approximating the trivariate flood dependence structure. In this study, a parametric vine copula of a drawable (D-vine) structure is introduced in the trivariate modelling of flooding events with 46 years of observations of the west coast of Canada. This trivariate framework searches dependency by combining the joint impact of annual maximum 24-h rainfall and the highest storm surge and river discharge observed within the time ±1 day of the highest rainfall event. The D-vine structures are constructed in three alternative ways by permutation of the conditioning variables. The most appropriate D-vine structure is selected using the fitness test statistics and estimating trivariate joint and conditional joint return periods. The investigation confirms that the D-vine copula can effectively define the compound phenomenon’s dependency. The failure probability (FP) method is also adopted in assessing the trivariate hydrologic risk. It is observed that hydrologic events defined in the trivariate case produce higher FP than in the bivariate (or univariate) case. It is also concluded that hydrologic risk increases (i) with an increase in the service design life of the hydraulic facilities and (ii) with a decrease in return periods.