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This paper proposes a set of nonparametric statistical tools for analyzing the system resilience of civil structures and infrastructure and its migration upon changes in critical system parameters. The work is founded on the classic theoretic framework that system resilience is defined in multiple dimensions for a constructed system. Consequentially, system resilience can lose its parametric form as a random variable, falling into the realm of nonparametric statistics. With this nonparametric shift, traditional distribution-based statistics are ineffective in characterizing the migration of system resilience due to the variation of system parameters. Three statistical tools are proposed under the nonparametric statistical resilience analysis (npSRA) framework, including nonparametric copula-based sensitivity analysis, two-sample resilience test analysis, and a novel tool for resilience attenuation analysis. To demonstrate the use of this framework, we focus on electric distribution systems, commonly found in many urban, suburban, and rural areas and vulnerable to tropical storms. A novel procedure for considering resourcefulness parameters in the socioeconomic space is proposed. Numerical results reveal the complex statistical relations between the distributions of system resilience, physical aging, and socioeconomic parameters for the power distribution system. The proposed resilience distance computing and resilience attenuation analysis further suggests two proper nonparametric distance metrics, the Earth Moving Distance (EMD) metric and the Cramévon Mises (CVM) metric, for characterizing the migration of system resilience for electric distribution systems.

AbstractBayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to produce samples from the posterior distribution of the component labels. The data are then clustered by minimizing the expectation of a clustering loss function that favors similarity to the component labels. Unfortunately, although these approaches are routinely implemented, clustering results are highly sensitive to kernel misspecification. For example, if Gaussian kernels are used but the true density of data within a cluster is even slightly non-Gaussian, then clusters will be broken into multiple Gaussian components. To address this problem, we develop Fusing of Localized Densities (FOLD), a novel clustering method that melds components together using the posterior of the kernels. FOLD has a fully Bayesian decision theoretic justification, naturally leads to uncertainty quantification, can be easily implemented as an add-on to MCMC algorithms for mixtures, and favors a small number of distinct clusters. We provide theoretical support for FOLD including clustering optimality under kernel misspecification. In simulated experiments and real data, FOLD outperforms competitors by minimizing the number of clusters while inferring meaningful group structure. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

The Kullback–Leibler (KL) divergence is a widely used measure for comparing probability distributions, but it faces limitations such as its unbounded nature and the lack of comparability between distributions with different quantum values (the discrete unit of probability). This study addresses these challenges by introducing the concept of quantized distributions, which are probability distributions formed by distributing a given discrete quantity or quantum. This study establishes an upper bound for the KL divergence between two quantized distributions, enabling the development of a normalized KL divergence that ranges between 0 and 1. The theoretical findings are supported by empirical evaluations, demonstrating the distinct behavior of the normalized KL divergence compared to other commonly used measures. The results highlight the importance of considering the quantum value when applying the KL divergence, offering insights for future advancements in divergence measures. [ABSTRACT FROM AUTHOR]

We consider the problem of approximating a continuous random variable, characterized by a cumulative distribution function (cdf) F(x), by means of k points, x 1 < x 2 < ⋯ < x k , with probabilities p i , i = 1 , ⋯ , k . For a given k, a criterion for determining the x i and p i of the approximating k-point discrete distribution can be the minimization of some distance to the original distribution. Here we consider the weighted Cramér-von Mises distance between the original cdf F(x) and the step-wise cdf F ^ (x) of the approximating discrete distribution, characterized by a non-negative weighting function w(x). This problem has been already solved analytically when w(x) corresponds to the probability density function of the continuous random variable, w (x) = F ′ (x) , and when w(x) is a piece-wise constant function, through a numerical iterative procedure based on a homotopy continuation approach. In this paper, we propose and implement a solution to the problem for different choices of the weighting function w(x), highlighting how the results are affected by w(x) itself and by the number of approximating points k, in addition to F(x); although an analytic solution is not usually available, yet the problem can be numerically solved through an iterative method, which alternately updates the two sub-sets of k unknowns, the x i 's (or a transformation thereof) and the p i 's, till convergence. The main apparent advantage of these discrete approximations is their universality, since they can be applied to most continuous distributions, whether they possess or not the first moments. In order to shed some light on the proposed approaches, applications to several well-known continuous distributions (among them, the normal and the exponential) and to a practical problem where discretization is a useful tool are also illustrated. [ABSTRACT FROM AUTHOR]

We investigate the usefulness of side entanglement in discriminating between two generic qubit channels, up to unitary pre- and post-processing, and determine exact conditions under which it does enhance (as well as conditions under which it does not) the success probability. This is done in a constructive way by first analysing the problem for channels that are extremal in the set of completely positive and trace-preserving qubit linear maps and then for channels that are inside such a set. [ABSTRACT FROM AUTHOR]

The main objective of this article is to identify the location of damage by a new feature extraction technique and to propose some efficient feature analysis tools as statistical distance measures. The proposed algorithm of feature extraction relies on a combination of the well-known Principal Component Analysis (PCA) and convolution strategy. After extracting the features from raw vibration signals of undamaged and damaged conditions, those are applied to the proposed feature analysis approaches called coefficient of variation, Fisher criterion, Fano factor, and relative reliability index, all of which are formulated by using statistical moments of the features extracted from the PCA-convolution algorithm. To localize damage, the sensor location with the distance value exceeding a certain threshold limit is identified as the damaged area. The main innovations of this research are to present a new hybrid technique of feature extraction suitable for Structural Health Monitoring (SHM) applications and four effective statistical measures for feature analysis and damage identification. The performance and reliability of the proposed methods are verified by a four-story shear-building model and a benchmark concrete beam. Results demonstrate that the approaches presented here can substantially identify the location of damage using the features extracted from the proposed PCA-convolution algorithm. [ABSTRACT FROM AUTHOR]

Thyroid disorder affects the regulation of various metabolic processes throughout the human body. Structural and functional disorders can affect the body and the brain. The computer-aided diagnosis system can identify the kind of thyroid disease. One such machine learning framework is presented in this paper to recognize disease existence and type. This paper presents a fuzzy adaptive feature filtration and expansion-based model to generate the most relevant and contributing features. This two-level filtration model is processed in a controlled fuzzy-based multi-measure evaluation. At the first level, the composite-fuzzy measures are combined with expert's recommendations for identifying the ranked and relevant features. At the second level, the statistical computation-based distance measure is applied for expanding the featureset. The fuzzification is applied to the expanded featureset for transiting the continuous values to fuzzy-values. At this level, the fuzzy-based composite-measure is applied for selecting the most contributing and relevant features over the expanded dataset. This processing featureset is processed by the Extreme Learning Machine (ELM) classifier to predict the disease existence and class. Five experiments are conducted on two datasets for validating the performance and reliability of the proposed framework. The comparative analysis is conducted against the Naive Bayes, Decision Tree, Decision Forest, Random Tree, Multilevel Perceptron, and Radial Basis Function (RBF) Networks. The analysis outcome is taken in terms of accuracy, error, and relevancy-based parameters. The proposed framework claims a significant gain in accuracy, relevancy, and reduction in the error rate. [ABSTRACT FROM AUTHOR]

Aimed at the problem of group data anomaly detection with no data labels, a k-nearest neighbor (kNN) algorithm is proposed to detect group data anomalies in the unsupervised mode. In order to reduce false negatives and false positives caused by the mutual interference between abnormal and normal values, a reverse k-nearest neighbor (RkNN) method is proposed to filter the abnormal group data in reverse. First, the RkNN algorithm uses statistical distance as the similarity measure between different groups of data. Then, the anomaly scores of each group and the initial abnormality are obtained by using the kNN algorithm. Finally, the initial abnormality is filtered by using the RkNN method. The experiment results show that the algorithm proposed can not only effectively reduce the false negatives and false positives, but also has a high anomaly detection rate and good stability.

This study presents a novel statistical trajectory-distance metric specialized for nautical route clustering analysis. Based on the dynamic time warping (DTW) metric, one of the most used metrics for trajectory-distance, the statistical trajectory-distance metric was defined by replacing the distance term in DTW with a linear combination of the Jensen-Shannon divergence and Wasserstein distance. Each waypoint from a nautical route was modelled as a discrete and asymmetric binomial normal distribution defined by the cross-track distance (XTD) of the waypoint. The model was then used to compute the statistical distance between waypoints. Nautical route clustering was performed using density-based spatial clustering of applications with noise and the statistical trajectory-distance metric. The nautical route for the clustering analysis, including the XTD information, was extracted from automatic identification system data from the southern sea of the Korean Peninsula. The clustering results were evaluated by comparing them with the results of other popular trajectory-distance metrics. The proposed method was more effective compared to other trajectory-distance when the trajectories pass on both sides of a small island, which is frequent case in coastal route clustering. [ABSTRACT FROM AUTHOR]

In a recent paper devoted to fault analysis of elliptic curve-based signature schemes, Takahashi et al. (TCHES 2018) described several attacks, one of which assumed an equidistribution property that can be informally stated as follows: given an elliptic curve E over 𝔽q in Weierstrass form and a large subgroup H ⊂ E(𝔽q) generated by G(xG, yG), the points in E(𝔽q) whose x-coordinates are obtained from xG by randomly flipping a fixed, sufficiently long substring of bits (and rejecting cases when the resulting value does not correspond to a point in E(𝔽q)) are close to uniformly distributed among the cosets modulo H. The goal of this note is to formally state, prove and quantify (a variant of) that property, and in particular establish sufficient bounds on the size of the subgroup and on the length of the substring of bits for it to hold. The proof relies on bounds for character sums on elliptic curves established by Kohel and Shparlinski (ANTS–IV).

Ambient vibration is an unknown excitation source that may produce stationary or non-stationary signals. Under such circumstances, traditional feature extraction techniques may not yield relevant features to damage and not provide reliable results of damage identification. The main objective of this article is to propose a data-driven method based on the concept of statistical pattern recognition for locating damage under ambient vibration and unpredictable signal nature in terms of simultaneously stationary and non-stationary behavior. This method is generally comprised of a three-level hybrid algorithm for feature extraction and new statistical distance metrics for feature analysis. The proposed feature extraction method aims at providing new damage-sensitive features in three levels including (1) analyzing the nature of measured vibration signals in terms of stationarity or non-stationarity, and normalizing non-stationary signals by detrending and differencing techniques, (2) modeling each vibration signal by an Autoregressive Moving Average (ARMA) model along with extracting the model residuals, and (3) estimating the power spectral density of residual samples as a new spectral-based feature. To identify the location of damage via spectral-based features, this article proposes two new spectral-based measures called Jeffery's and Smith's distances. The major contributions of this study include proposing a new feature extraction method for dealing with the problem of unpredictable vibration nature and introducing two new distance metrics for damage identification. Experimental vibration measurements of a well-known laboratory structure are utilized to verify the proposed methods. Results demonstrate that these approaches succeed in accurately extracting relevant features and locating damage under ambient vibration and unpredictable signal nature. [ABSTRACT FROM AUTHOR]

Text classification is the process of automatically categorizing text documents into predefined labels, gaining increasing importance with the growing volume of data. In the vector space model, terms within documents must be quantified to be used with classifiers. The abundance of unique terms associated with documents can lead to unwieldy vectors. To address this issue, feature selection, reducing the number of terms by removing irrelevant terms, is a common solution. In this paper, a novel feature selection method called Amount of ReDistribution to Establish Neutrality, ARDEN, is proposed for the task of text classification. ARDEN, is designed with statistical distance perspective by measuring the distance of a term to its neutral counterpart, which represents the least distinguishing term having uniform document frequencies across all classes. ARDEN introduces a method to measure the related distance, providing insights into the degree of deviation of the term from neutrality, thus capturing its distinguishing power. ARDEN is experimentally tested against state-of-the-art feature selection methods. The results suggest that it is a competitive feature selection method, exhibiting superior performance in terms of summary statistics, μ and δ ′. Furthermore, ARDEN is designed for multi-class text classification problems, which does not require a globalization function. Additionally, the proposed method is compared against Wasserstein statistical distance metric, and clearly outperforms it. Finally, we also propose δ ′ evaluation criterion in order to facilitate the interpretation of experimental outcomes across multiple feature sizes. • A novel feature selection, ARDEN, is proposed for text classification. • ARDEN measures the amount of redistribution to establish neutrality for ranking. • ARDEN is designed for multi-class problems and does not need globalization functions. • Experimental results suggest that ARDEN is a competitive feature selection method. • δ ′ is proposed to interpret the results of multiple features. [ABSTRACT FROM AUTHOR]

In a theoretical context of side-channel attacks, optimal bounds between success rate, guessing entropy and statistical distance are derived with a simple majorization (Schur-concavity) argument. They are further theoretically refined for different versions of the classical Hamming weight leakage model, in particular assuming a priori equiprobable secret keys and additive white Gaussian measurement noise. Closed-form expressions and numerical computation are given. A study of the impact of the choice of the substitution box with respect to side-channel resistance reveals that its nonlinearity tends to homogenize the expressivity of success rate, guessing entropy and statistical distance. The intriguing approximate relation between guessing entropy and success rate G E = 1 / S R is observed in the case of 8-bit bytes and low noise. The exact relation between guessing entropy, statistical distance and alphabet size G E = M + 1 2 − M 2 S D for deterministic leakages and equiprobable keys is proved. [ABSTRACT FROM AUTHOR]

Physiological and biochemical networks are highly complex, involving thousands of nodes as well as a hierarchical structure. True network structure is also rarely known. This presents major challenges for applying classical network theory to these networks. However, complex systems generally share the property of having a diffuse or distributed signal. Accordingly, we should predict that system state can be robustly estimated with sparse sampling, and with limited knowledge of true network structure. In this review, we summarize recent findings from several methodologies to estimate system state via a limited sample of biomarkers, notably Mahalanobis distance, principal components analysis, and cluster analysis. While statistically simple, these methods allow novel characterizations of system state when applied judiciously. Broadly, system state can often be estimated even from random samples of biomarkers. Furthermore, appropriate methods can detect emergent underlying physiological structure from this sparse data. We propose that approaches such as these are a powerful tool to understand physiology, and could lead to a new understanding and mapping of the functional implications of biological variation.

BackgroundAging and changing age demographics represent critical problems of our time. Physiological functions decline with age, often ending in a systemic process that contributes to numerous impairments and age-related diseases including heart failure (HF). We aimed to analyze whether differences in composite measures of physiological function [health distance (HD)], specifically physical fitness, between healthy individuals and patients with HF, can be observed.MethodsThe COmPLETE Project is a cross-sectional study of 526 healthy participants aged 20–91 years and 79 patients with stable HF. Fifty-nine biomarkers characterizing fitness (cardiovascular endurance, muscle strength, and neuromuscular coordination) and general health were assessed. We computed HDs as the Mahalanobis distance for vectors of biomarkers (all and domain-specific subsets) that quantified deviations of individuals’ biomarker profiles from “optimums” in the “reference population” (healthy participants aged

Biological aging results in changes in an organism that accumulate over age in a complex fashion across different regulatory systems, and their cumulative effect manifests in increased physiological dysregulation (PD) and declining robustness and resilience that increase risks of health disorders and death. Several composite measures involving multiple biomarkers that capture complex effects of aging have been proposed. We applied one such approach, the Mahalanobis distance (DM), to baseline measurements of various biomarkers (inflammation, hematological, diabetes-associated, lipids, endocrine, renal) in 3,279 participants from the Long Life Family Study (LLFS) with complete biomarker data. We used DM to estimate the level of PD by summarizing information about multiple deviations of biomarkers from specified “norms” in the reference population (here, LLFS participants younger than 60 years at baseline). An increase in DM was associated with significantly higher mortality risk (hazard ratio per standard deviation of DM: 1.42; 95% confidence interval: [1.3, 1.54]), even after adjustment for a composite measure summarizing 85 health-related deficits (disabilities, diseases, less severe symptoms), age, and other covariates. Such composite measures significantly improved mortality predictions especially in the subsample of participants from families enriched for exceptional longevity (the areas under the receiver operating characteristic curves are 0.88 vs. 0.85, in models with and without the composite measures, p = 2.9 × 10−5). Sensitivity analyses confirmed that our conclusions are not sensitive to different aspects of computational procedures. Our findings provide the first evidence of association of PD with mortality and its predictive performance in a unique sample selected for exceptional familial longevity.

Physiological and biochemical networks are highly complex, involving thousands of nodes as well as a hierarchical structure. True network structure is also rarely known. This presents major challenges for applying classical network theory to these networks. However, complex systems generally share the property of having a diffuse or distributed signal. Accordingly, we should predict that system state can be robustly estimated with sparse sampling, and with limited knowledge of true network structure. In this review, we summarize recent findings from several methodologies to estimate system state via a limited sample of biomarkers, notably Mahalanobis distance, principal components analysis, and cluster analysis. While statistically simple, these methods allow novel characterizations of system state when applied judiciously. Broadly, system state can often be estimated even from random samples of biomarkers. Furthermore, appropriate methods can detect emergent underlying physiological structure from this sparse data. We propose that approaches such as these are a powerful tool to understand physiology, and could lead to a new understanding and mapping of the functional implications of biological variation. [ABSTRACT FROM AUTHOR]

Background: Aging and changing age demographics represent critical problems of our time. Physiological functions decline with age, often ending in a systemic process that contributes to numerous impairments and age-related diseases including heart failure (HF). We aimed to analyze whether differences in composite measures of physiological function [health distance (HD)], specifically physical fitness, between healthy individuals and patients with HF, can be observed. Methods: The COmPLETE Project is a cross-sectional study of 526 healthy participants aged 20–91 years and 79 patients with stable HF. Fifty-nine biomarkers characterizing fitness (cardiovascular endurance, muscle strength, and neuromuscular coordination) and general health were assessed. We computed HDs as the Mahalanobis distance for vectors of biomarkers (all and domain-specific subsets) that quantified deviations of individuals' biomarker profiles from "optimums" in the "reference population" (healthy participants aged <40 years). We fitted linear regressions with HD outcomes and disease status (HF/Healthy) and relevant covariates as predictors and logistic regressions for the disease outcome and sex, age, and age2 as covariates in the base model and the same covariates plus combinations of one or two HDs. Results: Nine out of 10 calculated HDs showed evidence for group differences between Healthy and HF (p ≤ 0.002) and most models presented a negative estimate of the interaction term age by group (p < 0.05 for eight HDs). The predictive performance of the base model for HF cases significantly increased by adding HD General health or HD Fitness [areas under the receiver operating characteristic (ROC) curve (AUCs) 0.63, 0.89, and 0.84, respectively]. HD Cardiovascular endurance alone reached an AUC of 0.88. Further, there is evidence that the combination of HDs Cardiovascular endurance and General health shows superior predictive power compared to single HDs. Conclusion: HD composed of physical fitness biomarkers differed between healthy individuals and patients with HF, and differences between groups diminished with increasing age. HDs can successfully predict HF cases, and HD Cardiovascular endurance can significantly increase the predictive power beyond classic clinical biomarkers. Applications of HD could strengthen a comprehensive assessment of physical fitness and may present an optimal target for interventions to slow the decline of physical fitness with aging and, therefore, to increase health span. [ABSTRACT FROM AUTHOR]

The radar data association algorithm in the complex environment is one of the most difficult problems in the field of multi-target tracking. Among them, the nearest neighbor algorithm is an effective data association algorithm with small computation and easy application. However, there is a problem that the data association accuracy is not high, the filtering result is not accurate enough, and the multi-target tracking is easy to cause error correlation. In order to improve the data association effect of the algorithm, a nearest neighbor data association algorithm is proposed. By further deepening the entropy of known measurement information, the entropy weight method is used to analyze and determine the weights of the respective measurement indicators. The weight is optimized for the statistical distance association criterion of the nearest neighbor algorithm, thereby improving the problem of the original algorithm in single target tracking. The simulation results show that the improved algorithm proposed has higher data association accuracy, smaller tracking error and faster convergence than the original algorithm. [ABSTRACT FROM AUTHOR]

Given samples from two distributions over an n-element set, we wish to test whether these distributions are statistically close. We present an algorithm which uses sublinear in n, specifically, O (n 2/3ϵ -8/3 log n), independent samples from each distribution, runs in time linear in the sample size, makes no assumptions about the structure of the distributions, and distinguishes the cases when the distance between the distributions is small (less than {ϵ4/3 n-1/3 /32, ϵn-1/2 /4}) or large (more than ϵ) in ℓ1 distance. This result can be compared to the lower bound of Ω(n2/3 ϵ2/3) for this problem given by Valiant [2008]. Our algorithm has applications to the problem of testing whether a given Markov process is rapidly mixing. We present sublinear algorithms for several variants of this problem as well. [ABSTRACT FROM AUTHOR]

We propose an orientation-averaged intermolecular potential model for the accurate computation of relevant thermodynamic and transport properties of steam at conditions typically encountered in extreme environments such as rocky exoplanetary atmospheres, aircraft and rocket engines, high temperature steam reforming and electrochemical reactors, as well as advanced ultra-supercritical steam power generators. We assess the reliability of the potential model to describe accurately the temperature dependence of relevant thermodynamic properties of rarified steam up to and beyond 3000K. Moreover, we discuss some fundamental issues including (i) the conditions at which an orientation-averaged intermolecular potential for a molecular fluid becomes an accurate representation of the fluid behaviour in extreme environments, (ii) the temperature range of validity of the approximations underlying an orientation averaging approach and, (iii) the methodology of force-field parameterisation to obtain an optimised representation, as well as the concomitant modelling of the thermodynamics and transport properties of rarified fluids. Finally, we illustrate how the simultaneous accurate description of the temperature dependence of the fluid's collision integrals and second virial coefficient is crucial to the successful modelling of rarified steam in extreme environments. [ABSTRACT FROM AUTHOR]

A fundamental challenge of mobile sensor networks is automated active reconfiguration of sensors in response to environmental stimuli in order to maximize their total sensing quality (or minimize their total sensing cost) of events occurring over an environment. In this paper, given an event distribution over a convex environment, we consider mobile isotropic sensors with adjustable sensing range and propose a new family of provably correct reactive coverage control algorithms for both continuous- and discrete-time sensor dynamics. The proposed coverage control algorithms constantly (re)configure sensor positions and sensing ranges in order to minimize a statistical distance, in particular, an $f$ -divergence, between the event distribution over the environment and the overall event detection probability of sensors. We show that the standard Voronoi-based coverage control law of homogeneous mobile sensor networks is a special case of our framework where the event detection probability of each sensor has a Gaussian form, the statistical distance is set to be the Kullback–Leibler (KL) divergence and sensor allocation is performed based on Voronoi diagrams. To increase the practicality of our framework, we also present its integration with a Voronoi-based collision avoidance strategy for disk-shaped sensor bodies and its extension to differential drive sensor dynamics, while retaining the stability properties. [ABSTRACT FROM AUTHOR]

The main approaches currently used to construct identity-based encryption (IBE) schemes are based on bilinear mappings, quadratic residues and lattices. Among them, the most attractive approach is the one based on quadratic residues, due to the fact that the underlying security assumption is a well-understood hard problem. The first such IBE scheme was constructed by Cocks, and some of its deficiencies were addressed in subsequent works. In this paper, we focus on two constructions that address the anonymity problem inherent in Cocks’ scheme, and we tackle some of their incomplete theoretical claims. More precisely, we rigorously study Clear et al.’s and Zhao et al.’s schemes and give accurate probabilities of successful decryption and identity detection in the non-anonymized version of the schemes. Furthermore, in the case of Zhao et al.’s scheme, we give a proper description of the underlying security assumptions.

Multiple attribute decision making (MADM) methods are very useful in choosing the best alternative among the available finite but conflicting alternatives. TOPSIS is one of the MADM methods, which is simple in its methodology and logic. In TOPSIS, Euclidean distances of each alternative from the positive and negative ideal solutions are utilized to find the best alternative. In literature, apart from Euclidean distances, the city block distances have also been tried to find the separations measures. In general, the attribute data are distributed with unequal ranges and also possess moderate to high correlations. Hence, in the present paper, use of statistical distances is proposed in place of Euclidean distances. Procedures to find the best alternatives are developed using statistical and weighted statistical distances respectively. The proposed methods are illustrated with some industrial problems taken from literature. Results show that the proposed methods can be used as new alternatives in MADM for choosing the best solutions.