Search results for: Gaussian approximation

Authors: Kairat T. Mynbaev, Elena N. Lomakina

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We consider a Hardy-type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion, and bounds for its approximation numbers. Previously, bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness earlier have been found using different methods by G. Sinnamon and K. Mynbaev. Our approach is different in that we use domain partitions for all problems under consideration.

Keywords: approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space

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Authors: Chandra Prayaga, Aaron Wade, Lakshmi Prayaga, Gopi Shankar Mallu

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This paper presents the use of machine learning algorithms to predict the success of students in an introductory physics course. Data having 140 rows pertaining to the performance of two batches of students was used. The lack of sufficient data to train robust machine learning models was compensated for by generating synthetic data similar to the real data. CTGAN and CTGAN with Gaussian Copula (Gaussian) were used to generate synthetic data, with the real data as input. To check the similarity between the real data and each synthetic dataset, pair plots were made. The synthetic data was used to train machine learning models using the PyCaret package. For the CTGAN data, the Ada Boost Classifier (ADA) was found to be the ML model with the best fit, whereas the CTGAN with Gaussian Copula yielded Logistic Regression (LR) as the best model. Both models were then tested for accuracy with the real data. ROC-AUC analysis was performed for all the ten classes of the target variable (Grades A, A-, B+, B, B-, C+, C, C-, D, F). The ADA model with CTGAN data showed a mean AUC score of 0.4377, but the LR model with the Gaussian data showed a mean AUC score of 0.6149. ROC-AUC plots were obtained for each Grade value separately. The LR model with Gaussian data showed consistently better AUC scores compared to the ADA model with CTGAN data, except in two cases of the Grade value, C- and A-.

Keywords: machine learning, student success, physics course, grades, synthetic data, CTGAN, gaussian copula CTGAN

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Authors: Septimia Sarbu

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The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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Authors: Kejal Khatri, Vishnu Narayan Mishra

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We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

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Authors: Ahmad Alwosheel, Ahmed Alqaraawi

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This work proposes an unsupervised text-independent probabilistic approach to recognize Quran reciter voice. It is an accurate approach that works on real time applications. This approach does not require a prior information about reciter models. It has two phases, where in the training phase the reciters' acoustical features are modeled using Gaussian Mixture Models, while in the testing phase, unlabeled reciter's acoustical features are examined among GMM models. Using this approach, a high accuracy results are achieved with efficient computation time process.

Keywords: Quran, speaker recognition, reciter recognition, Gaussian Mixture Model

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Authors: Prerana Sharma

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Effect of relativistic nonlinearity on stimulated Raman scattering of the propagating laser beam carrying null intensity in center (hollow Gaussian beam) by excited plasma wave are studied in a collisionless plasma. The construction of the equations is done employing the fluid theory which is developed with partial differential equation and Maxwell’s equations. The analysis is done using eikonal method. The phenonmenon of Stimulated Raman scattering is shown along with the excitation of seed plasma wave. The power of plasma wave and back reflectivity is observed for higher order of hollow Gaussian beam. Back reflectivity is studied numerically for various orders of HGLB with different value of plasma density, laser power and beam radius. Numerical analysis shows that these parameters play vital role on reflectivity characteristics.

Keywords: Hollow Gaussian beam, relativistic nonlinearity, plasma physics, Raman scattering

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Authors: Hacene Benkhoula, Mohamed Badreddine Benabdella, Hamid Bouzeboudja, Abderrahmane Asraoui

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The wind is a random variable difficult to master, for this, we developed a mathematical and statistical methods enable to modeling and forecast wind power. Gaussian Processes (GP) is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space or time and space. GP is an underlying process formed by unrecognized operator’s uses to solve a problem. The purpose of this paper is to present how to forecast wind power by using the GP. The Gaussian process method for forecasting are presented. To validate the presented approach, a simulation under the MATLAB environment has been given.

Keywords: wind power, Gaussien process, modelling, forecasting

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Authors: Wanatchapong Kongkaew

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This paper proposes an application of probabilistic technique, namely Gaussian process regression, for estimating an optimal sequence of the single machine with total weighted tardiness (SMTWT) scheduling problem. In this work, the Gaussian process regression (GPR) model is utilized to predict an optimal sequence of the SMTWT problem, and its solution is improved by using an iterated local search based on simulated annealing scheme, called GPRISA algorithm. The results show that the proposed GPRISA method achieves a very good performance and a reasonable trade-off between solution quality and time consumption. Moreover, in the comparison of deviation from the best-known solution, the proposed mechanism noticeably outperforms the recently existing approaches.

Keywords: Gaussian process regression, iterated local search, simulated annealing, single machine total weighted tardiness

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Authors: Mohammadamin Abbasnejad

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The analysis of expression and facial Action Units (AUs) detection are very important tasks in fields of computer vision and Human Computer Interaction (HCI) due to the wide range of applications in human life. Many works have been done during the past few years which has their own advantages and disadvantages. In this work, we present a new model based on Gaussian Conditional Random Field. We solve our objective problem using ADMM and we show how well the proposed model works. We train and test our work on two facial expression datasets, CK+, and RU-FACS. Experimental evaluation shows that our proposed approach outperform state of the art expression recognition.

Keywords: Gaussian Conditional Random Field, ADMM, convergence, gradient descent

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Authors: Serge B. Provost, Yishan Zhang

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A moment-based adjustment to the saddlepoint approximation is introduced in the context of density estimation. First applied to univariate distributions, this methodology is extended to the bivariate case. It then entails estimating the density function associated with each marginal distribution by means of the saddlepoint approximation and applying a bivariate adjustment to the product of the resulting density estimates. The connection to the distribution of empirical copulas will be pointed out. As well, a novel approach is proposed for estimating the support of distribution. As these results solely rely on sample moments and empirical cumulant-generating functions, they are particularly well suited for modeling massive data sets. Several illustrative applications will be presented.

Keywords: empirical cumulant-generating function, endpoints identification, saddlepoint approximation, sample moments, density estimation

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Authors: Funda Kul, İsmail Gür

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Pension scheme providers have to price mortality risk by accurate mortality forecasting method. There are many mortality-forecasting methods constructed and used in literature. The Lee-Carter model is the first model to consider stochastic improvement trends in life expectancy. It is still precisely used. Mortality forecasting is done by mortality index in the Lee-Carter model. It is assumed that mortality index fits ARIMA time series model. In this paper, we propose and use dynamic normal inverse gaussian distribution to modeling mortality indes in the Lee-Carter model. Using population mortality data for Italy, France, and Turkey, the model is forecasting capability is investigated, and a comparative analysis with other models is ensured by some well-known benchmarking criterions.

Keywords: mortality, forecasting, lee-carter model, normal inverse gaussian distribution

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Authors: Smita Sonker

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Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski.

Keywords: signals, trigonometric fourier approximation, class W(L^r, \xi(t), conjugate fourier series

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Authors: Ying Li, Yan Li

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A new algorithm for single hidden layer feedforward neural networks (SLFN), Orthogonal Basis Extreme Learning (OBEL) algorithm, is proposed and the algorithm derivation is given in the paper. The algorithm can decide both the NNs parameters and the neuron number of hidden layer(s) during training while providing extreme fast learning speed. It will provide a practical way to develop NNs. The simulation results of function approximation showed that the algorithm is effective and feasible with good accuracy and adaptability.

Keywords: neural network, orthogonal basis extreme learning, function approximation

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Authors: Sunghoon Park, Hank Kim, Jinwon An, Sungzoon Cho

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Internet of Things allows one to collect data from facilities which are then used to monitor them and even predict malfunctions in advance. Conventional quality control methods focus on setting a normal range on a sensor value defined between a lower control limit and an upper control limit, and declaring as an anomaly anything falling outside it. However, interactions among sensor values are ignored, thus leading to suboptimal performance. We propose a multivariate approach which takes into account many sensor values at the same time. In particular Gaussian Mixture Model is used which is trained to maximize likelihood value using Expectation-Maximization algorithm. The number of Gaussian component distributions is determined by Bayesian Information Criterion. The negative Log likelihood value is used as an anomaly score. The actual usage scenario goes like a following. For each instance of sensor values from a facility, an anomaly score is computed. If it is larger than a threshold, an alarm will go off and a human expert intervenes and checks the system. A real world data from Building energy system was used to test the model.

Keywords: facility anomaly detection, gaussian mixture model, anomaly score, expectation maximization algorithm

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Authors: B. Bahloul, K. Babesse, A. Dkhira, Y. Bahloul, L. Amirouche

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Structural and electronic properties of the rock-salt BaxSr1−xS are calculated using the first-principles calculations based on the density functional theory (DFT) within the generalized gradient approximation (GGA), the local density approximation (LDA) and the virtual-crystal approximation (VCA). The calculated lattice parameters at equilibrium volume for x=0 and x=1 are in good agreement with the literature data. The BaxSr1−xS alloys are found to be an indirect band gap semiconductor. Moreoever, for the composition (x) ranging between [0-1], we think that our results are well discussed and well predicted.

Keywords: semiconductor, Ab initio calculations, rocksalt, band structure, BaxSr1−xS

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Authors: Suyeb Ahmed Khan, Mahmood Mian

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Simulation plays an important role during all phases of the design and engineering of communications systems, from early stages of conceptual design through the various stages of implementation, testing, and fielding of the system. In the present paper, a simulation model has been constructed for the WCDMA system in order to evaluate the performance. This model describes multiusers effects and calculation of BER (Bit Error Rate) in 3G mobile systems using Simulink MATLAB 7.1. Gaussian Approximation defines the multi-user effect on system performance. BER has been analyzed with comparison between transmitting data and receiving data.

Keywords: WCDMA, simulations, BER, MATLAB

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Authors: Jean-Pierre Lomaliza, Kwang-Seok Moon, Hanhoon Park

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It is well-known that Ramer Douglas Peucker (RDP) algorithm greatly depends on the method of choosing starting points. Therefore, this paper focuses on finding such starting points that will optimize the results of RDP algorithm. Specifically, this paper proposes a curve approximation algorithm that finds flat points, called essential points, of an input curve, divides the curve into corner-like sub-curves using the essential points, and applies the RDP algorithm to the sub-curves. The number of essential points play a role on optimizing the approximation results by balancing the degree of shape information loss and the amount of data reduction. Through experiments with curves of various types and complexities of shape, we compared the performance of the proposed algorithm with three other methods, i.e., the RDP algorithm itself and its variants. As a result, the proposed algorithm outperformed the others in term of maintaining the original shapes of the input curve, which is important in various applications like pattern recognition.

Keywords: curve approximation, essential point, RDP algorithm

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Authors: S. B. Provost, Susan Sheng

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An alternative bivariate density estimation methodology is introduced in this presentation. The proposed approach involves estimating the density function associated with the marginal distribution of each of the two variables by means of the saddlepoint approximation technique and applying a bivariate polynomial adjustment to the product of these density estimates. Since the saddlepoint approximation is utilized in the context of density estimation, such estimates are determined from empirical cumulant-generating functions. In the univariate case, the saddlepoint density estimate is itself adjusted by a polynomial. Given a set of observations, the coefficients of the polynomial adjustments are obtained from the sample moments. Several illustrative applications of the proposed methodology shall be presented. Since this approach relies essentially on a determinate number of sample moments, it is particularly well suited for modeling massive data sets.

Keywords: density estimation, empirical cumulant-generating function, moments, saddlepoint approximation

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Authors: S. Benkraouda, Z. Djelloul-Khedda, B. Yagoubi

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we present a method for early detection of forest fires from a thermal infrared satellite image, using the image matrix of the probability of belonging. The principle of the method is to compare a theoretical mathematical model to an experimental model. We considered that each line of the image matrix, as an embodiment of a non-stationary random process. Since the distribution of pixels in the satellite image is statistically dependent, we divided these lines into small stationary and ergodic intervals to characterize the image by an adequate mathematical model. A standard deviation was chosen to generate random variables, so each interval behaves naturally like white Gaussian noise. The latter has been selected as the mathematical model that represents a set of very majority pixels, which we can be considered as the image background. Before modeling the image, we made a few pretreatments, then the parameters of the theoretical Gaussian model were extracted from the modeled image, these settings will be used to calculate the probability of each interval of the modeled image to belong to the theoretical Gaussian model. The high intensities pixels are regarded as foreign elements to it, so they will have a low probability, and the pixels that belong to the background image will have a high probability. Finally, we did present the reverse of the matrix of probabilities of these intervals for a better fire detection.

Keywords: forest fire, forest fire detection, satellite image, normal distribution, theoretical gaussian model, thermal infrared matrix image

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Authors: Hossein Javidnia, Salehe Taheri

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The Electrocardiogram (ECG) is the recording of the heart’s electrical potential versus time. ECG signals are often contaminated with noise such as baseline wander and muscle noise. As these signals have been widely used in clinical studies to detect heart diseases, it is essential to filter these noises. In this paper we compare performance of Wiener Filtering and Median Filtering methods to filter Additive White Gaussian (AWG) noise with the determined signal to noise ratio (SNR) ranging from 3 to 5 dB applied to long-term ECG recordings samples. Root mean square error (RMSE) and coefficient of determination (R2) between the filtered ECG and original ECG was used as the filter performance indicator. Experimental results show that Wiener filter has better noise filtering performance than Median filter.

Keywords: ECG noise filtering, Wiener filtering, median filtering, Gaussian noise, filtering performance

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

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Performance of different filtering approaches depends on modeling of dynamical system and algorithm structure. For modeling and smoothing the data the evaluation of posterior distribution in different filtering approach should be chosen carefully. In this paper different filtering approaches like filter KALMAN, EKF, UKF, EKS and smoother RTS is simulated in some trajectory tracking of path and accuracy and limitation of these approaches are explained. Then probability of model with different filters is compered and finally the effect of the noise variance to estimation is described with simulations results.

Keywords: Gaussian approximation, Kalman smoother, parameter estimation, noise variance

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Authors: Edlira Donefski, Lorenc Ekonomi, Tina Donefski

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Edgeworth approximation is one of the most important statistical methods that has a considered contribution in the reduction of the sum of standard deviation of the independent variables’ coefficients in a Quantile Regression Model. This model estimates the conditional median or other quantiles. In this paper, we have applied approximating statistical methods in an economical problem. We have created and generated a quantile regression model to see how the profit gained is connected with the realized sales of the cosmetic products in a real data, taken from a local business. The Linear Regression of the generated profit and the realized sales was not free of autocorrelation and heteroscedasticity, so this is the reason that we have used this model instead of Linear Regression. Our aim is to analyze in more details the relation between the variables taken into study: the profit and the finalized sales and how to minimize the standard errors of the independent variable involved in this study, the level of realized sales. The statistical methods that we have applied in our work are Edgeworth Approximation for Independent and Identical distributed (IID) cases, Bootstrap version of the Model and the Edgeworth approximation for Bootstrap Quantile Regression Model. The graphics and the results that we have presented here identify the best approximating model of our study.

Keywords: bootstrap, edgeworth approximation, IID, quantile

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Authors: John Lorenzo Bautista, Yoon-Joong Kim

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This paper presents the development of a Filipino speech recognition tool using the HTK System. The system was trained from a subset of the Filipino Speech Corpus developed by the DSP Laboratory of the University of the Philippines-Diliman. The speech corpus was both used in training and testing the system by estimating the parameters for phonetic HMM-based (Hidden-Markov Model) acoustic models. Experiments on different mixture-weights were incorporated in the study. The phoneme-level word-based recognition of a 5-state HMM resulted in an average accuracy rate of 80.13 for a single-Gaussian mixture model, 81.13 after implementing a phoneme-alignment, and 87.19 for the increased Gaussian-mixture weight model. The highest accuracy rate of 88.70% was obtained from a 5-state model with 6 Gaussian mixtures.

Keywords: Filipino language, Hidden Markov Model, HTK system, speech recognition

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Jian-Heng Wu, Bor-Shen Lin

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The temperature-salinity relationship is one of the most important characteristics used for identifying water masses in marine research. Temperature-salinity characteristics, however, may change dynamically with respect to the geographic location and is quite sensitive to the depth at the same location. When depth is taken into consideration, however, it is not easy to compare the characteristics of different water masses efficiently for a wide range of areas of the ocean. In this paper, the Gaussian mixture model was proposed to analyze the temperature-salinity-depth characteristics of water masses, based on which comparison between water masses may be conducted. Gaussian mixture model could model the distribution of a random vector and is formulated as the weighting sum for a set of multivariate normal distributions. The temperature-salinity-depth data for different locations are first used to train a set of Gaussian mixture models individually. The distance between two Gaussian mixture models can then be defined as the weighting sum of pairwise Bhattacharyya distances among the Gaussian distributions. Consequently, the distance between two water masses may be measured fast, which allows the automatic and efficient comparison of the water masses for a wide range area. The proposed approach not only can approximate the distribution of temperature, salinity, and depth directly without the prior knowledge for assuming the regression family, but may restrict the complexity by controlling the number of mixtures when the amounts of samples are unevenly distributed. In addition, it is critical for knowledge discovery in marine research to represent, manage and share the temperature-salinity-depth characteristics flexibly and responsively. The proposed approach has been applied to a real-time visualization system of ocean data, which may facilitate the comparison of water masses by aggregating the data without degrading the discriminating capabilities. This system provides an interface for querying geographic locations with similar temperature-salinity-depth characteristics interactively and for tracking specific patterns of water masses, such as the Kuroshio near Taiwan or those in the South China Sea.

Keywords: water mass, Gaussian mixture model, data visualization, system framework

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Authors: Balachandra Kumaraswamy, P. G. Poonacha

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Automatic Music Information Retrieval has been one of the challenging topics of research for a few decades now with several interesting approaches reported in the literature. In this paper we have developed a pitch extraction method based on a finite Fourier series approximation to the given window of samples. We then estimate pitch as the fundamental period of the finite Fourier series approximation to the given window of samples. This method uses analysis of the strength of harmonics present in the signal to reduce octave as well as harmonic errors. The performance of our method is compared with three best known methods for pitch extraction, namely, Yin, Windowed Special Normalization of the Auto-Correlation Function and Harmonic Product Spectrum methods of pitch extraction. Our study with artificially created signals as well as music files show that Fourier Approximation method gives much better estimate of pitch with less octave and harmonic errors.

Keywords: pitch, fourier series, yin, normalization of the auto- correlation function, harmonic product, mean square error

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: Valeria Bondarenko

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We proposed algorithms for: estimation of parameters fBm (volatility and Hurst exponent) and for the approximation of random time series by functional of fBm. We proved the consistency of the estimators, which constitute the above algorithms, and proved the optimal forecast of approximated time series. The adequacy of estimation algorithms, approximation, and forecasting is proved by numerical experiment. During the process of creating software, the system has been created, which is displayed by the hierarchical structure. The comparative analysis of proposed algorithms with the other methods gives evidence of the advantage of approximation method. The results can be used to develop methods for the analysis and modeling of time series describing the economic, physical, biological and other processes.

Keywords: mathematical model, random process, Wiener process, fractional Brownian motion

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Authors: Kai Chen, Shuguang Cui, Feng Yin

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Gaussian process (GP) with spectral mixture (SM) kernel demonstrates flexible non-parametric Bayesian learning ability in modeling unknown function. In this work a novel time-varying and non-stationary convolution spectral mixture (TN-CSM) kernel with a significant enhancing of interpretability by using process convolution is introduced. A way decomposing the SM component into an auto-convolution of base SM component and parameterizing it to be input dependent is outlined. Smoothly, performing a convolution between two base SM component yields a novel structure of non-stationary SM component with much better generalized expression and interpretation. The TN-CSM perfectly allows compatibility with the stationary SM kernel in terms of kernel form and spectral base ignored and confused by previous non-stationary kernels. On synthetic and real-world datatsets, experiments show the time-varying characteristics of hyper-parameters in TN-CSM and compare the learning performance of TN-CSM with popular and representative non-stationary GP.

Keywords: Gaussian process, spectral mixture, non-stationary, convolution

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Authors: Preeti Sharma

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This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

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