Order Central Moments Research Articles

Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators

In this article, we propose a new kind of q-Stancu-Durrmeyer operators (or shortly q-SD operators). We calculate first and second order moments, for and we give an estimation for the second order central moment, . Furthermore, through the use of the second modulus of continuity, we invent approximation properties of the q-SD operators in the local sense and by using order Lipschitz kind maximal function, we give a direct estimation for the q-SD operators again in the local sense.

Sparsity-Constrained Kernel Generalized Maximum Versoria Criterion With Variable Center

Sparsity-aware kernel adaptive filtering algorithms using maximum correntropy criterion (MCC) and maximum Versoria criterion (MVC) have emerged as a promising candidate for nonlinear sparse parameter estimation under non-Gaussian distortions. However, the existing zero-attracting (ZA) kernel-MCC (ZA-KMCC) and ZA-kernel-MVC (ZA-KMVC) algorithms deliver suboptimal performance for non-zero-mean noise distributions due to the fixed center located at origin. In this brief, first we propose a novel generalized MVC with variable center (GMVC-VC) based learning paradigm by introducing a center at any location, which consists of higher order central moments of error. Next, we propose a novel generalized Versoria zero-attracting kernel GMVC-VC (GVZA-KGMVC-VC) algorithm, which is robust for nonlinear sparse systems under non-Gaussian noise having non-zero-mean. Furthermore, the detailed convergence analysis in both mean and mean-square sense is performed for the proposed algorithm. Simulations demonstrate that the proposed GVZA-KGMVC-VC approach delivers lower mean square deviation over the existing state-of-art benchmarks.

Genuine q-Stancu-Bernstein–Durrmeyer Operators

In the present paper, we introduce the genuine q-Stancu-Bernstein–Durrmeyer operators Znq,α(f;x). We calculate the moments of these operators, Znq,α(tj;x) for j=0,1,2, which follows a symmetric pattern. We also calculate the second order central moment Znq,α((t−x)2;x). We give a Korovkin-type theorem; we estimate the rate of convergence for continuous functions. Furthermore, we prove a local approximation theorem in terms of second modulus of continuity; we obtain a local direct estimate for the genuine q-Stancu-Bernstein–Durrmeyer operators in terms of Lipschitz-type maximal function of order β and we prove a direct global approximation theorem by using the Ditzian-Totik modulus of second order.

Intervened Exponential Distribution: Properties and Applications

This manuscript aims to study the intervention-based probability model. Statistical and reliability properties such as the expressions for, cumulative density function (CDF), mean deviations about mean and median, rth order central and non-central moments, ”generation functions” for moments have been derived. Moreover, the expression for reliability function, hazard rate, reverse hazard rate, aging intensity, mean residual life function, stress-strength reliability, and entropy metrics due to R´enyi and Shannon are also derived. Monte Carlo simulation study performance of maximum likelihood estimates (MLEs) has been carried out, followed by calculations of Average Bias (ABias), and Mean Square Error (MSE). The applicability of the model in real-life situations has been discussed by analyzing the two real-life data sets.

Определение вклада массивной компоненты из анализа искажений формы линии дифракционных спектров для нанокомпозитных материалов

Using the analysis of the elastic lines distortions of the diffraction spectra with the involvement of the high order central moments of the distribution, the sensitivity of the developed technique to the presence of an admixture of a bulk component in nanocomposite materials was estimated. Cases for the main types of instrumental resolution functions of diffractometers and functions describing the response from materials embedded in the pore space of nanomatrices such as SBA-15, MCM-41, MCM-48, etc. are considered.

Determination of the Massive Component Contribution from the Analysis of Line Shape Distortions in Diffraction Spectra for Nanocomposite Materials

Using the analysis of the elastic lines distortions of the diffraction spectra with the involvement of the high order central moments of the distribution, the sensitivity of the developed technique to the presence of an admixture of a bulk component in nanocomposite materials was estimated. Cases for the main types of instrumental resolution functions of diffractometers and functions describing the response from materials embedded in the pore space of nanomatrices such as SBA-15, MCM-41, MCM-48, etc. are considered. Keywords: porous matrices, diffraction, resolution function, nanocomposite materials, elastic peak line shape, higher central moments of distribution.

Some approximation properties of new ( p,q ) -analogue of Bal\xe1zs\u2013Szabados operators

In this paper, a new ( p,q ) -analogue of the Balázs–Szabados operators is defined. Moments up to the fourth order are calculated, and second order and fourth order central moments are estimated. Local approximation properties of the operators are examined and a Voronovskaja type theorem is given.

Approximation Properties of New Modified Gamma Operators

This paper is aimed at constructing new modified Gamma operators using the second central moment of the classic Gamma operators. And we will compute the first, second, fourth, and sixth order central moments by the moment computation formulas, and their quantitative properties are researched. Then, the global results are established in certain weighted spaces and the direct results including the Voronovskaya-type asymptotic formula, and point-wise estimates are investigated. Also, weighted approximation of these operators is discussed. Finally, the quantitative Voronovskaya-type asymptotic formula and Grüss Voronovskaya-type approximation are presented.

Muscle fatigue analysis in isometric contractions using geometric features of surface electromyography signals

In this study, an attempt has been made to differentiate the muscle nonfatigue and fatigue conditions using geometric features of surface Electromyography (sEMG) signals. For this purpose, a new framework is proposed that consists of Fourier descriptor based shape representation and geometric feature extraction. The sEMG signals are acquired from biceps brachii muscle of 25 healthy adult volunteers in isometric contractions. The signals associated with nonfatigue and fatigue conditions are preprocessed and subjected to discrete Fourier transform. The Fourier coefficients are scattered in the complex plane and the envelope is computed using α-shape method. The boundary of the resultant shape represents the Fourier descriptors. The geometric features namely centroid, moments, perimeter, area, circularity, convexity, average bending energy, major axis length, eccentricity and ellipse variance are extracted from the shape. The results show that seven out of twelve features have statistically significant (p < 0.001) difference between the two conditions. The five features namely major axis length, area, perimeter, second order moment and central moment are considered for muscle fatigue classification using k-nearest neighbor, naïve Bayes, decision tree and multilayer perceptron (MLP). Among these classifiers, maximum accuracy of 86 % is achieved with MLP based detection model. Therefore, it appears that the geometric features of sEMG signals could be useful in the detection of muscle fatigue condition in clinical diagnosis, workplace and rehabilitation.

On Higher Order Structures in Thermodynamics.

We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing the average of measurable quantities and extremal measures. Secondly, the variance of random vectors induces the Riemannian structures on the corresponding manifolds. Computing higher order central moments, one drives to the corresponding higher order structures, namely the cubic and the fourth order forms. The cubic form is responsible for the skewness of the extremal distribution. The condition for it to be zero gives us so-called symmetric processes. The positivity of the fourth order structure gives us an additional requirement to thermodynamic state.

Higher order moments of the estimated tangency portfolio weights

In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order non-central and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and t-distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments.

Approximation properties of modified (&lt;i&gt;p, q&lt;/i&gt;)-Sz&amp;#225;sz-Mirakyan-Kantorovich operators

In this paper, we introduce a new kind of modified (p, q)-Szasz-Mirakyan-Kantorovich operators based on (p, q)-calculus. Next, the moments computation formulas, the second and fourth order central moments computation formulas and other quantitative properties are investigated. Then, the approximation properties including local approximation, weighted approximation, rate of convergence and Voronovskaja type theorem are obtained. Finally, we generalize the operators by adding a parameter λ.

An Initial Value Estimation Method for the Kalman and Extended Kalman Filters in Underground Metal Detection

As an underground metal detection technology, the electromagnetic induction (EMI) method is widely used in many cases. Therefore, the EMI detection algorithms with excellent performance are worth studying. One of the EMI detection methods in the underground metal detection is the filter method, which first obtains the secondary magnetic field data and then uses the Kalman filter (KF) and the extended Kalman filter (EKF) to estimate the parameters of metal targets. However, the traditional KF methods used in the underground metal detection have an unsatisfactory performance of the convergence as the algorithms are given a random or a fixed initial value. Here, an initial state estimation algorithm for the underground metal detection is proposed. The initial state of the target’s horizontal position is estimated by the first order central moments of the secondary field strength map. In addition, the initial state of the target’s depth is estimated by the full width at half maximum (FWHM) method. In addition, the initial state of the magnetic polarizability tensor is estimated by the least squares method. Then, these initial states are used as the initial values for KF and EKF. Finally, the position, posture and polarizability of the target are recursively calculated. A simulation platform for the underground metal detection is built in this paper. The simulation results show that the initial value estimation method proposed for the filtering algorithm has an excellent performance in the underground metal detection.

Robust unsupervised domain adaptation for neural networks via moment alignment

A novel approach for unsupervised domain adaptation for neural networks is proposed. It relies on metric-based regularization of the learning process. The metric-based regularization aims at domain-invariant latent feature representations by means of maximizing the similarity between domain-specific activation distributions. The proposed metric results from modifying an integral probability metric such that it becomes less translation-sensitive on a polynomial function space. The metric has an intuitive interpretation in the dual space as the sum of differences of higher order central moments of the corresponding activation distributions. Under appropriate assumptions on the input distributions, error minimization is proven for the continuous case. As demonstrated by an analysis of standard benchmark experiments for sentiment analysis, object recognition and digit recognition, the outlined approach is robust regarding parameter changes and achieves higher classification accuracies than comparable approaches.

Learning using privileged information for HRRP‐based radar target recognition

A novel machine learning method named extended support vector data description with negative examples (ESVDD-neg) is developed to classify the fast Fourier transform-magnitude feature of complex high-resolution range profile (HRRP), motivated by the problem of radar automatic target recognition. The proposed method not only inherits the close non-linear boundary advantage of support vector data description with negative examples model but also incorporates a new learning paradigm named learning using privileged information into the model. It leads to the appealing application with no assumptions regarding the distribution of data and needs less training samples and prior information. Besides, the second order central moment is selected as privileged information for better recognition performance, weakening the effect of translation sensitivity, and the normalisation contributes to eliminating the amplitude sensitivity. Hence, there will be a remarkable improvement of recognition accuracy not only with small training dataset but also under the condition of low signal-to-noise ratio. Numerical experiments based on two publicly UCI datasets and HRRPs of four aircrafts demonstrate the feasibility and superiority of the proposed method. The noise robust ESVDD-neg is ideal for HRRP-based radar target recognition.

Quantitative-Voronovskaya and Gr\xfcss-Voronovskaya type theorems for Sz\xe1sz-Durrmeyer type operators blended with multiple Appell polynomials

In this paper, we establish a link between the Szász-Durrmeyer type operators and multiple Appell polynomials. We study a quantitative-Voronovskaya type theorem in terms of weighted modulus of smoothness using sixth order central moment and Grüss-Voronovskaya type theorem. We also establish a local approximation theorem by means of the Steklov means in terms of the first and the second order modulus of continuity and Voronovskaya type asymtotic theorem. Further, we discuss the degree of approximation by means of the weighted spaces. Lastly, we find the rate of approximation of functions having a derivative of bounded variation.

ECG derived respiration: comparison of time-domain approaches and application to altered breathing patterns of patients with schizophrenia

In life-threatening diseases and in several clinical interventions, monitoring of vital parameters is essential to guarantee the safety of patients. Besides monitoring the electrocardiogram (ECG), it is helpful to assess respiratory activity. If the respiration signal itself is not recorded, it can be extracted from the ECG (i.e. ECG derived respiration, EDR).In the present paper, we compared six EDR approaches, namely RS-decline quantified by central moments, respiratory sinus arrhythmia (RSA), R-wave amplitude, QRS area, RS-distance and maximum RS-slope. In order to evaluate the performance of each approach, we applied each method to a database of ECGs and reference respiration signals of 41 healthy subjects. All considered methods revealed relatively small absolute mean errors of the breathing rate (BR) at rest (0.75–1.3 Bpm). The method based on higher order central moments revealed a minimum mean absolute error of 0.75 Bpm (4.40%) and a maximum correlation and concordance with the reference BR (rp = 0.97, rc = 0.97). Using this technique, we analyzed changes of respiration in patients suffering from acute schizophrenia. An increased respiration rate of about 4 Bpm was found. Additionally, alteration of respiratory ratio and reduced respiratory sinus arrhythmia was demonstrated. We conclude that a precise dynamic monitoring of breathing and the investigation of changes in breathing patterns is possible without recording respiration per se.

A new kind of Bernstein-Schurer-Stancu-Kantorovich-type operators based on q-integers

Agrawal et al. (Boll. Unione Mat. Ital. 8:169-180, 2015) introduced a Stancu-type Kantorovich modification of the operators proposed by Ren and Zeng (Bull. Korean Math. Soc. 50(4):1145-1156, 2013) and studied a basic convergence theorem by using the Bohman-Korovokin criterion, the rate of convergence involving the modulus of continuity, and the Lipschitz function. The concern of this paper is to obtain Voronoskaja-type asymptotic result by calculating an estimate of fourth order central moment for these operators and discuss the rate of convergence for the bivariate case by using the complete and partial moduli of continuity and the degree of approximation by means of a Lipschitz-type function and the Peetre K-functional. Also, we consider the associated GBS (generalized Boolean sum) operators and estimate the rate of convergence for these operators with the help of a mixed modulus of smoothness. Furthermore, we show the rate of convergence of these operators (univariate case) to certain functions with the help of the illustrations using Maple algorithms and in the bivariate case, the rate of convergence of these operators is compared with the associated GBS operators by illustrative graphics.

Rough Set-Based Approach for Automatic Emotion Classification of Music

Music emotion is an important component in the field of music information retrieval and computational musicology. This paper proposes an approach for automatic emotion classification, based on rough set (RS) theory. In the proposed approach, four different sets of music features are extracted, representing dynamics, rhythm, spectral, and harmony. From the features, five different statistical parameters are considered as attributes, including up to the 4th order central moments of each feature, and covariance components of mutual ones. The large number of attributes is controlled by RS-based approach, in which superfluous features are removed, to obtain indispensable ones. In addition, RS-based approach makes it possible to visualize which attributes play a significant role in the generated rules, and also determine the strength of each rule for classification. The experiments have been performed to find out which audio features and which of the different statistical parameters derived from them are important for emotion classification. Also, the resulting indispensable attributes and the usefulness of covariance components have been discussed. The overall classification accuracy with all statistical parameters has recorded comparatively better than currently existing methods on a pair of datasets.

Deriving respiration from high resolution 12-channel-ECG during cycling exercise

Abstract Monitoring of cardiac and respiratory activity, is essential in several clinical interventions like bicycle ergometries. The respiration signal can be derived from the ECG if it is not recorded itself (ECG derived respiration, EDR). In this study, we tried to reconstruct breathing rates (BR) from stress test high resolution 12-channel-ECGs in nine healthy subjects using higher order central moments. A mean absolute error per subjects of 2.9/min and relatively high correlation (r p = 0.85) and concordance coefficient (rc = 0.79) indicated a quite accurate reproduction of respiratory activity. The analysis of the different test stages revealed an increase of BR errors while subjects were effortful cycling compared to rest. During incremental cycling exercise test the mean absolute error per subjects was 3.4/min. Compared to the results reported in other studies at rest in supine position, this seems adequately accurate. In conclusion, our results indicate that EDR using higher order central moments is suited for monitoring BR during physical activity.