Publication Date: 2007
Applied Mathematics and Computation (963003)189(1)pp. 341-345
In this paper, an application of homotopy perturbation method is applied to solve the nonlinear two-dimensional wave equation. The analytic solution of the nonlinear wave equation is calculated in the form of a series with easily computable components. The non-homogenous equation is effectively solved by employing the phenomena of the self-canceling "noise" terms, where sum of components vanishes in the limit. Comparing the methodology with some known techniques shows that the present approach is powerful and reliable. Its remarkable accuracy properties are finally demonstrated by an example. © 2006 Elsevier Inc. All rights reserved.
Publication Date: 2007
International Journal of Computer Mathematics (10290265)84(1)pp. 75-79
In this paper we propose new ideas for the implementation of the Adomian decomposition method to solve nonlinear Volterra integral equations. Numerical examples are presented to illustrate the method for nonlinear Volterra integral equations of the second kind.
Publication Date: 2024
Journal of Information Security and Applications (22142134)83
Today, due to the unparalleled growth of multimedia data sharing, especially digital images, between users over insecure channels in real-time applications, cryptography algorithms have gained increasing attention for the secure and efficient transmission. In classical chaos-based image cryptosystems, the confusion and diffusion operations are often applied as two separate and independent phases, which threatens the cryptosystem security. To address these problems, in this paper, a fast image cryptosystem based on parallel simultaneous diffusion–confusion strategy has been proposed using Latin squares, called PSDCLS. It consists of three main steps. First, the initial parameters of the Hénon-Sine chaotic map are produced from SHA256 of both the plain image content and the user's secret key. Second, a chaos-based random Latin square is constructed by employing the chaotic sequence produced through the Hénon-Sine chaotic map. Third, a parallel simultaneous diffusion–confusion scheme is proposed by using Latin square and vectorization technique to overcome the problems of computational complexity and high risk of separable and iterative confusion–diffusion operations in the classical chaos-based image cryptosystems. To analyze and evaluate the security and performance of PSDCLS cryptosystem, we conducted extensive simulations and experiments on various benchmark images. Experimental results and analyses show that PSDCLS achieves excellent scores for information entropy (>7.99), correlation coefficients close to 0, key space (2512), NPCR (>99.60%), UACI (>33.46%). The encryption time for test images of size 512 × 512 and 512×512×3 was around 0.026 and 0.081 s, respectively. Therefore, PSDCLS is highly robust against common cryptographic attacks and serves as a swift cryptosystem for real-time encryption applications. The source code of PSDCLS is accessible at: https://github.com/EbrahimZarei64/PSDCLS. © 2024 Elsevier Ltd
Publication Date: 2019
Journal of Parallel and Distributed Computing (07437315)129pp. 14-35
Nested loops are main source of the parallelism in many scientific applications. Partitioning the iteration space of nested loops with data dependencies into tiles and assigning them to processing nodes for parallel execution is essential for achieving high performance. Although most of the previous work focused on tiling on fully connected homogeneous distributed systems, some studies have been devoted to tiling on partially connected distributed systems. In this paper, we address the parallelization of perfectly nested loops with dependencies on partially connected heterogeneous distributed systems and present a topology and computational-power aware tile mapping. This work aims to take into account not only the node's computational power when tiling iteration space of nested loops but also the exploitation of the network topology when mapping tiles to processing nodes. This approach allows minimizing the parallel execution time by improving the load balancing and minimizing the communication costs. We demonstrate the performance of proposed method by comparing it with the computational-power aware tile mapping and the topology aware tile mapping. The experimental results show that the proposed method improves the parallel execution time by up to 62% and 28% compared with the computational-power aware tile mapping and the topology aware tile mapping, respectively. © 2019 Elsevier Inc.
Publication Date: 2017
Concurrency and Computation: Practice and Experience (15320626)29(5)
Nested loops are the largest source of parallelism in many data-parallel scientific applications. Heterogeneous distributed systems are popular computing platforms for data-parallel applications. Data partitioning is critical in exploiting the computational power of such systems, and existing data partitioning algorithms try to maximize performance of data-parallel applications by finding a data distribution that balances the workload between the processing nodes while minimizing communication costs. This paper addresses the problem of 3-dimensional data partitioning for 3-level perfectly nested loops on heterogeneous distributed systems. The primary aim is to minimize the execution time by improving the load balancing and minimizing the internode communications. We propose a new data partitioning algorithm using dynamic programming, build a theoretical model to estimate the execution time of each partition, and select a partition with minimum execution time as a near-optimal solution. We demonstrate the effectiveness of the new algorithm for 2 data-parallel scientific applications on heterogeneous distributed systems. The new algorithm reduces the execution time by between 7% and 17%, on average, compared with leading data partitioning methods on 3 heterogeneous distributed systems. Copyright © 2016 John Wiley & Sons, Ltd.
Publication Date: 2016
Scalable Computing (18951767)17(4)pp. 331-349
Nested loops are one of the most time-consuming parts and the largest sources of parallelism in many scientific applications. In this paper, we address the problem of 3-dimensional tiling and scheduling of three-level perfectly nested loops with dependencies on heterogeneous systems. To exploit the parallelism, we tile and schedule nested loops with dependencies by awareness of computational power of the processing nodes and execute them in pipeline mode. The tile size plays an important role to improve the parallel execution time of nested loops. We develop and evaluate a theoretical model to estimate the parallel execution time of tilled nested loops. Also, we propose a tiling genetic algorithm that used the proposed model to find the near-optimal tile size, minimizing the parallel execution time of dependence nested loops. We demonstrate the accuracy of theoretical model and effectiveness of the proposed tiling genetic algorithm by several experiments on heterogeneous systems. The 3D tiling reduces the parallel execution time by a factor of 1.2× to 2× over the 2D tiling, while parallelizing 3D heat equation as a benchmark. © 2016 SCPE.
Publication Date: 2015
Malaysian Journal Of Computer Science (01279084)28(1)pp. 46-58
Image reconstruction is an important part of computed tomography imaging systems, which converts the measured data into images. Because of high computational cost and slow convergence of iterative reconstruction algorithms, these methods are not widely used in practice. In this paper, we propose a hybrid iterative algorithm by combining multigrid method,Tikhonov regularization and Simultaneous Iterative Reconstruction Technique (SIRT) for reconstruction of the computed tomography image that reduces this drawback. To do so, we reduce the time and the volume of computations considerably by finding astable and appropriate starting point. The experimental results indicate that the proposed iterative algorithm has more rapid convergence and reconstructs high quality images in short computational time than the classical ones.
This paper presents a novel image security system based on the replacement of the pixel values using recursive Cellular automata (CA) substitution. The advantages of our proposed method are that it is computationally efficient and it is reasonably passing sensibility analysis tests. The proposed method is carried out by using one half of image data to encrypt the other half of the image mutually. Our algorithm can encrypt image in parallel and be also applied to color image encryption. In this proposed method, size of key is dynamic and by changing a bit of security key the image cannot retrieve because our method is key sensitive. Simulation results obtained using color; white-black and gray-level images demonstrate the good performance of the proposed image security system. © 2011 IEEE.
Alamatsaz, N.,
Tabatabaei, L.,
Yazdchi, M.,
Payan, H.,
Alamatsaz, N.,
Nasimi, F. Publication Date: 2024
Biomedical Signal Processing and Control (17468108)90
Objective: Electrocardiogram (ECG) is the most frequent and routine diagnostic tool used for monitoring heart electrical signals and evaluating its functionality. The human heart can suffer from a variety of diseases, including cardiac arrhythmias. Arrhythmia is an irregular heart rhythm that in severe cases can lead to stroke and can be diagnosed via ECG recordings. Since early detection of cardiac arrhythmias is of great importance, computerized and automated classification and identification of these abnormal heart signals have received much attention for the past decades. Methods: This paper introduces a light Deep Learning (DL) approach for high accuracy detection of 8 different cardiac arrhythmias and normal rhythms. To employ DL techniques, the ECG signals were preprocessed using resampling and baseline wander removal techniques. The classification was performed using an 11-layer network employing a combination of Convolutional Neural Network (CNN) and Long Short Term Memory (LSTM). Results: In order to evaluate the proposed technique, ECG signals are chosen from the two physionet databases, the MIT-BIH arrhythmia database and the long-term AF database. The proposed DL framework based on the combination of CNN and LSTM showed promising results than most of the state-of-the-art methods. The proposed method reaches the mean diagnostic accuracy of 98.24%. Conclusion: A trained model for arrhythmia classification using diverse ECG signals were successfully developed and tested. Significance: This study presents a lightweight classification technique with high diagnostic accuracy compared to other notable methods, making it a potential candidate for implementation in Holter monitor devices for arrhythmia detection. Finally, we used SHapley Additive exPlanations (SHAP), the most popular Explainable Artificial Intelligence (XAI) method to understand how our model make predictions. The results indicate that those features (ECG samples) that have contributed the most to a prediction are consonant with clinicians’ decisions. Therefore, the use of interpretable models increases the trust of clinicians in AI and thus leads to decreasing the number of misdiagnoses of cardiovascular diseases. © 2023 Elsevier Ltd
Publication Date: 2022
PLoS ONE (19326203)17(2 February)
Differentiating between shockable and non-shockable Electrocardiogram (ECG) signals would increase the success of resuscitation by the Automated External Defibrillators (AED). In this study, a Deep Neural Network (DNN) algorithm is used to distinguish 1.4-second segment shockable signals from non-shockable signals promptly. The proposed technique is frequency-independent and is trained with signals from diverse patients extracted from MIT-BIH, MIT-BIH Malignant Ventricular Ectopy Database (VFDB), and a database for ventricular tachyarrhythmia signals from Creighton University (CUDB) resulting, in an accuracy of 99.1%. Finally, the raspberry pi minicomputer is used to load the optimized version of the model on it. Testing the implemented model on the processor by unseen ECG signals resulted in an average latency of 0.845 seconds meeting the IEC 60601-2-4 requirements. According to the evaluated results, the proposed technique could be used by AED’s. Copyright: © 2022 Nasimi, Yazdchi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Publication Date: 2024
Journal Of The Iranian Statistical Society (17264057)23(1)pp. 99-115
This paper examines a novel extension of the geometric distribution characterized by two parameters, that is not created based on discretizing existing continuous models. This model, due to its analytical form of the cumulative distribution function and simple structure, can be of interest from mathematical perspectives, particularly in cases where the analysis of stochastic orders is desired. In addition, it is a suitable candidate for analyzing monotone hazard rate discrete data, in view of the fact that its hazard rate function exhibits monotonicity in both increasing and decreasing directions. Additionally, the behavior of the survival function of residual lifetime is briefly addressed. The parameters of the distribution are estimated using the maximum likelihood method, and a real-world data set is scrutinized to assess the distribution's adequacy in providing satisfactory fits. © (2024), (Iranian Statistical Society). All rights reserved.
Publication Date: 2019
Communications in Statistics - Theory and Methods (1532415X)48(14)pp. 3464-3481
Recently, Lee and Cha proposed two general classes of discrete bivariate distributions. They have discussed some general properties and some specific cases of their proposed distributions. In this paper we have considered one model, namely bivariate discrete Weibull distribution, which has not been considered in the literature yet. The proposed bivariate discrete Weibull distribution is a discrete analogue of the Marshall–Olkin bivariate Weibull distribution. We study various properties of the proposed distribution and discuss its interesting physical interpretations. The proposed model has four parameters, and because of that it is a very flexible distribution. The maximum likelihood estimators of the parameters cannot be obtained in closed forms, and we have proposed a very efficient nested EM algorithm which works quite well for discrete data. We have also proposed augmented Gibbs sampling procedure to compute Bayes estimates of the unknown parameters based on a very flexible set of priors. Two data sets have been analyzed to show how the proposed model and the method work in practice. We will see that the performances are quite satisfactory. Finally, we conclude the paper. © 2018, © 2018 Taylor & Francis Group, LLC.
Publication Date: 2019
Sequential Analysis (07474946)38(3)pp. 279-300
In this article, using purely and two-stage sequential procedures, the problem of minimum risk point estimation of the reliability parameter (R) under the stress–strength model, in case the loss function is squared error plus sampling cost, is considered when the random stress (X) and the random strength (Y) are independent and both have exponential distributions with different scale parameters. The exact distribution of the total sample size and explicit formulas for the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Using the law of large numbers and Monte Carlo integration, the exact distribution of the stopping rule under the purely sequential procedure is approximated. Moreover, it is shown that both proposed sequential procedures are finite and for special cases the exact distribution of stopping times has a degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally, using a real data set, the procedures are clearly illustrated. © 2019, © 2019 Taylor & Francis Group, LLC.
Publication Date: 2018
Journal of Statistical Theory and Practice (15598616)12(3)pp. 595-614
In 1997, Marshall and Olkin introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions that brings more flexibility to the model. They demonstrated their method for the exponential and Weibull classes. In the same paper they briefly indicated its bivariate extension. The main aim of this article is to introduce the same method, for the first time, to the class of discrete generalized exponential distributions both for the univariate and bivariate cases. We investigate several properties of the proposed univariate and bivariate classes. The univariate class has three parameters, whereas the bivariate class has five parameters. It is observed that depending on the parameter values, the univariate class can be zero inflated as well as heavy tailed. We propose to use an expectation–maximization (EM) algorithm to estimate the unknown parameters. Small simulation experiments have been performed to see the effectiveness of the proposed EM algorithm, and a bivariate data set has been analyzed; it is observed that the proposed models and the EM algorithm work quite well in practice. © 2018, © 2018 Grace Scientific Publishing, LLC.
Publication Date: 2017
Statistics (02331888)51(5)pp. 1143-1158
In this paper, we develop a bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distribution as proposed by Nekoukhou, Alamatsaz and Bidram [Discrete generalized exponential distribution of a second type. Statistics. 2013;47:876–887]. It is observed that the proposed bivariate distribution is a very flexible distribution and the bivariate geometric distribution can be obtained as a special case of this distribution. The proposed distribution can be seen as a natural discrete analogue of the bivariate generalized exponential distribution proposed by Kundu and Gupta [Bivariate generalized exponential distribution. J Multivariate Anal. 2009;100:581–593]. We study different properties of this distribution and explore its dependence structures. We propose a new EM algorithm to compute the maximum-likelihood estimators of the unknown parameters which can be implemented very efficiently, and discuss some inferential issues also. The analysis of one data set has been performed to show the effectiveness of the proposed model. Finally, we propose some open problems and conclude the paper. © 2017 Informa UK Limited, trading as Taylor & Francis Group.
Publication Date: 2013
Communications in Statistics - Theory and Methods (1532415X)42(13)pp. 2324-2334
Skew-symmetric distributions of various types have been the center of attraction by many researchers in the literature. In this article, we will introduce a uni/bimodal generalization of the Azzalini's skew-normal distribution which is indeed an extension of the skew-generalized normal distribution obtained by Arellano-Valle et al. (2004). Our new distribution contains more parameters and thus it is more flexible in data modeling. Indeed, certain univariate case of the so called flexible skew-symmetric distribution of Ma and Genton (2004) is also a particular case of our proposed model. We will first study some basic distributional properties of the new extension, such as its distribution function, limiting behavior and moments. Then, we will investigate some useful results regarding its relation with other known distributions, such as student's t and skew-Cauchy distributions. In addition, we will present certain methods to generate the new distribution and, finally, we shall apply the model to a real data set to illustrate its behavior comparing to some rival models. © Taylor and Francis Group, LLC.
Publication Date: 2012
Statistical Papers (09325026)53(3)pp. 685-696
Skew-symmetric distributions of various types have been the center of attraction by many researchers in the literature. In this article, we shall introduce another more general class of skew distributions, specially related to the Laplace distribution. This new class contains some previously known skew distributions. We shall investigate different characteristics of members of this class such as its moments, thus generalizing a result of Umbach (Stat Probab Lett 76:507-512, 2006), limiting behavior, moment generating function, unimodality and reveal its natural occurrence as the distribution of some order statistics. In addition, we will generalize a result of Aryal and Rao (Nonlinear Anal 63:639-646, 2005) in connection with truncated skew-Laplace distribution and study its certain stochastic orderings. Some illustrative examples are also provided. © 2011 Springer-Verlag.
Publication Date: 2023
Kyoto Journal of Mathematics (21543321)63(4)pp. 829-849
Let C be a locally bounded k-category, where k is a field.We prove that C is pure-semisimple, that is, every object of Mod-C is pure-projective if and only if every family of morphisms between indecomposable finitely generated C-modules is Noetherian. Our formalism establishes the pure-semisimplicity of Galois coverings, that is, if C is a G-category with a free G-action on ind-C, then C is pure-semisimple if and only if C/G is so. © 2023 by Kyoto University.
Publication Date: 2016
Forum Mathematicum (09337741)28(2)pp. 377-389
We describe explicitly the Auslander-Reiten translation in the category of bounded complexes of finitely generated maximal Cohen-Macaulay modules, Cb(CM R), over a commutative local Cohen-Macaulay ring R with a canonical module ω. Then the Auslander-Reiten formula is generalized for complexes in Cb(CM R) and we prove the existence theorem of Auslander-Reiten sequences. As an application of our results, we investigate the existence of Auslander-Reiten triangles in the category of perfect complexes as a full triangulated subcategory of Db(mod R). © 2016 by De Gruyter 2016.
Publication Date: 2015
Journal of Algebra and its Applications (17936829)14(3)
Let λ be an artin algebra. By letting the Nakayama functor act degree-wise, we define a translation ? in the category of complexes of finitely generated λ-modules, C(mod λ). Then we investigate the existence of almost split sequences in the category C(mod λ). As an application of our results, we see that the full subcategory of D(mod λ) consisting of complexes isomorphic to perfect complexes admits almost split sequences. © World Scientific Publishing Company.
Publication Date: 2024
Journal Of Mathematics And Modeling In Finance (27830578)4(1)pp. 19-35
This article proposes a new numerical technique for pricing asset-or-nothing options using the Black-Scholes partial differential equation (PDE). We first use the θ−weighted method to discretize the time domain, and then use Haar wavelets to approximate the functions and derivatives with respect to the asset price variable. By using some vector and matrix calculations, we reduce the PDE to a system of linear equations that can be solved at each time step for different asset prices. We perform an error analysis to show the convergence of our technique. We also provide some numerical examples to compare our technique with some existing methods and to demonstrate its efficiency and accuracy. © 2024, Allameh Tabataba'i University. All rights reserved.
Publication Date: 2023
Computational Methods For Differential Equations (23453982)11(2)pp. 281-290
A numerical method based on the Haar wavelet is introduced in this study for solving the partial differential equation which arises in the pricing of European options. In the first place, and due to the change of variables, the related partial differential equation (PDE) converts into a forward time problem with a spatial domain ranging from 0 to 1. In the following, the Haar wavelet basis is used to approximate the highest derivative order in the equation concerning the spatial variable. Then the lower derivative orders are approximated using the Haar wavelet basis. Finally, by substituting the obtained approximations in the main PDE and doing some computations using the finite differences approach, the problem reduces to a system of linear equations that can be solved to get an approximate solution. The provided examples demonstrate the effectiveness and precision of the method. © 2023 University of Tabriz. All rights reserved.
Publication Date: 2018
Journal of Computational and Applied Mathematics (03770427)328pp. 252-266
One of the most important subject in financial mathematics is the option pricing. The most famous result in this area is Black–Scholes formula for pricing European options. This paper is concerned with a method for solving a generalized Black–Scholes equation in a reproducing kernel Hilbert space. Subsequently, the convergence of the proposed method is studied under some hypotheses which provide the theoretical basis of the proposed method. Furthermore, the error estimates for obtained approximation in reproducing kernel Hilbert space are presented. Finally, a numerical example is considered to illustrate the computation efficiency and accuracy of the proposed method. © 2017 Elsevier B.V.
Publication Date: 2015
CMES - Computer Modeling in Engineering and Sciences (15261492)109(3)pp. 247-262
In this paper we present a meshless collocation method based on the moving least squares (MLS) approximation for numerical solution of the multiasset (d-dimensional) American option in financial mathematics. This problem is modeled by the Black-Scholes equation with moving boundary conditions. A penalty approach is applied to convert the original problem to one in a fixed domain. In finite parts, boundary conditions satisfy in associated (d-1)-dimensional Black-Scholes equations while in infinity they approach to zero. All equations are treated by the proposed meshless approximation method where the method of lines is employed for handling the time variable. Numerical examples for single- and two-asset options are illustrated. Copyright © 2015 Tech Science Press.
Publication Date: 2014
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics (12237027)76(1)pp. 51-58
In this paper, we consider an integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. We use the continuous linear Legendre multi-wavelets on the interval [0, 1) to solve this equation. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Tavassoli kajani m., ,
Vahdati, S.,
Abbas, Z.,
Maleki, M. Publication Date: 2012
Journal Of Applied Mathematics (16870042)2012
Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞). This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. Test examples are considered to show the high accuracy, simplicity, and efficiency of this method. © 2012 M. Tavassoli Kajani et al.
