In this article we proposed three explicit Improved Runge-Kutta (IRK) methods for solving first-order ordinary differential equations. These methods are two-step in nature and require lower number of stages compared to the classical Runge-Kutta method. Therefore the new scheme is computationally more efficient at achieving the same order of local accuracy. The order conditions of the new methods are obtained up to order five using Taylor series expansion and the third and fourth order methods with different stages are derived based on the order conditions. The free parameters are obtained through minimization of the error norm. Convergence of the method is proven and the stability regions are presented. To illustrate the efficiency of the method a number of problems are solved and numerical results showed that the method is more efficient compared with the existing Runge-Kutta method.
This study was concerned with shape preserving interpolation of 2D data. A piecewise C1 univariate rational quadratic trigonometric spline including three positive parameters was devised to produce a shaped interpolant for given shaped data. Positive and monotone curve interpolation schemes were presented to sustain the respective shape features of data. Each scheme was tested for plentiful shaped data sets to substantiate the assertion made in their construction. Moreover, these schemes were compared with conventional shape preserving rational quadratic splines to demonstrate the usefulness of their construction.
Diagnostic radiology is a core and integral part of modern medicine, paving ways for the primary care physicians in the disease diagnoses, treatments and therapy managements. Obviously, all recent standard healthcare procedures have immensely benefitted from the contemporary information technology revolutions, apparently revolutionizing those approaches to acquiring, storing and sharing of diagnostic data for efficient and timely diagnosis of diseases. Connected health network was introduced as an alternative to the ageing traditional concept in healthcare system, improving hospital-physician connectivity and clinical collaborations. Undoubtedly, the modern medicinal approach has drastically improved healthcare but at the expense of high computational cost and possible breach of diagnosis privacy. Consequently, a number of cryptographical techniques are recently being applied to clinical applications, but the challenges of not being able to successfully encrypt both the image and the textual data persist. Furthermore, processing time of encryption-decryption of medical datasets, within a considerable lower computational cost without jeopardizing the required security strength of the encryption algorithm, still remains as an outstanding issue. This study proposes a secured radiology-diagnostic data framework for connected health network using high-performance GPU-accelerated Advanced Encryption Standard. The study was evaluated with radiology image datasets consisting of brain MR and CT datasets obtained from the department of Surgery, University of North Carolina, USA, and the Swedish National Infrastructure for Computing. Sample patients' notes from the University of North Carolina, School of medicine at Chapel Hill were also used to evaluate the framework for its strength in encrypting-decrypting textual data in the form of medical report. Significantly, the framework is not only able to accurately encrypt and decrypt medical image datasets, but it also successfully encrypts and decrypts textual data in Microsoft Word document, Microsoft Excel and Portable Document Formats which are the conventional format of documenting medical records. Interestingly, the entire encryption and decryption procedures were achieved at a lower computational cost using regular hardware and software resources without compromising neither the quality of the decrypted data nor the security level of the algorithms.
The partial integrals of the N-fold Fourier integrals connected with elliptic polynomials (not necessarily
homogeneous; principal part of which has a strictly convex level surface) are considered. It is proved that if a + s > (N – 1)/2 and ap = N then the Riesz means of the nonnegative order s of the N-fold Fourier integrals of continuous finite functions from the Sobolev spaces Wpa (RN) converge uniformly on every compact set, and if a + s > (N – 1)/2 and ap = N, then for any x0 ∈ RN there exists a continuous finite function from the Sobolev space such, that the corresponding Riesz means of the N-fold Fourier integrals diverge to infinity at x0. AMS 2000 Mathematics Subject Classifications: Primary 42B08; Secondary 42C14.
Orthogonal Frequency Division Multiplexing (OFDM) is a successful technique in wireless communication systems. Frequency offset in the OFDM system leads to loss of orthogonality among subcarriers which results in the occurrence of intercarrier interference (ICI). To improve the efficiency of bandwidth performance in the ICI self-cancellation scheme, frequency domain partial response signaling (PRS) was investigated. In this study, the integer polynomial partial response coefficients were exploited to enhance carrier-to-interference power ratio (CIR) in the OFDM system. CIR was enhanced up to 4.1 dB to 5 dB when the lengths of PRS polynomial, K was 2 and 5, respectively.
Open-loop unstable systems with time-delays are often encountered in process industry, which are often more difficult to control than stable processes. In this paper, the stabilization by PID controller of second-order unstable processes, which can be represented as second-order deadtime with an unstable pole (SODUP) and second-order deadtime with two unstable poles (SODTUP), is performed via the necessary and sufficient criteria of Routh-Hurwitz stability analysis. The stability analysis provides improved understanding on the existence of a stabilizing range of each PID parameter. Three simple PID tuning algorithms are proposed to provide desired closed-loop performance-robustness within the stable regions of controller parameters obtained via the stability analysis. The proposed PID controllers show improved performance over those derived via some existing methods.
Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters.
The parallelisation of big data is emerging as an important framework for large-scale parallel data applications such as seismic data processing. The field of seismic data is so large or complex that traditional data processing software is incapable of dealing with it. For example, the implementation of parallel processing in seismic applications to improve the processing speed is complex in nature. To overcome this issue, a simple technique which that helps provide parallel processing for big data applications such as seismic algorithms is needed. In our framework, we used the Apache Hadoop with its MapReduce function. All experiments were conducted on the RedHat CentOS platform. Finally, we studied the bottlenecks and improved the overall performance of the system for seismic algorithms (stochastic inversion).
In this work, a non-abelian metabelian group is represented by G while represents conjugacy class graph. Conjugacy class graph of a group is that graph associated with the conjugacy classes of the group. Its vertices are the non-central conjugacy classes of the group, and two distinct vertices are joined by an edge if their cardinalities are not coprime. A group is referred to as metabelian if there exits an abelian normal subgroup in which the factor group is also abelian. It has been proven earlier that 25 non-abelian metabelian groups which have order less than 24, which are considered in this work, exist. In this article, the conjugacy class graphs of non-abelian metabelian groups of order less than 24 are determined as well as examples of some finite groups associated to other graphs are given.
The aim of the present paper is to investigate coefficient estimates, Fekete-Szegő inequality, and upper bound of third Hankel determinant for some families of starlike and convex functions of reciprocal order.
Security-mediated cryptography was first introduced by Boneh et al. in 2001. The main motivation behind security-mediated cryptography was the capability to allow instant revocation of a user's secret key by necessitating the cooperation of a security mediator in any given transaction. Subsequently in 2003, Boneh et al. showed how to convert a RSA-based security-mediated encryption scheme from a traditional public key setting to an identity-based one, where certificates would no longer be required. Following these two pioneering papers, other cryptographic primitives that utilize a security-mediated approach began to surface. However, the security-mediated identity-based identification scheme (SM-IBI) was not introduced until Chin et al. in 2013 with a scheme built on bilinear pairings. In this paper, we improve on the efficiency results for SM-IBI schemes by proposing two schemes that are pairing-free and are based on well-studied complexity assumptions: the RSA and discrete logarithm assumptions.
Although ray tracing based propagation prediction models are popular for indoor radio wave propagation characterization, most of them do not provide an integrated approach for achieving the goal of optimum coverage, which is a key part in designing wireless network. In this paper, an accelerated technique of three-dimensional ray tracing is presented, where rough surface scattering is included for making a more accurate ray tracing technique. Here, the rough surface scattering is represented by microfacets, for which it becomes possible to compute the scattering field in all possible directions. New optimization techniques, like dual quadrant skipping (DQS) and closest object finder (COF), are implemented for fast characterization of wireless communications and making the ray tracing technique more efficient. In conjunction with the ray tracing technique, probability based coverage optimization algorithm is accumulated with the ray tracing technique to make a compact solution for indoor propagation prediction. The proposed technique decreases the ray tracing time by omitting the unnecessary objects for ray tracing using the DQS technique and by decreasing the ray-object intersection time using the COF technique. On the other hand, the coverage optimization algorithm is based on probability theory, which finds out the minimum number of transmitters and their corresponding positions in order to achieve optimal indoor wireless coverage. Both of the space and time complexities of the proposed algorithm surpass the existing algorithms. For the verification of the proposed ray tracing technique and coverage algorithm, detailed simulation results for different scattering factors, different antenna types, and different operating frequencies are presented. Furthermore, the proposed technique is verified by the experimental results.
We will consider a class of neutral functional differential equations. Some infinite integral conditions for the oscillation of all solutions are derived. Our results extend and improve some of the previous results in the literature.
The vector evaluated particle swarm optimisation (VEPSO) algorithm was previously improved by incorporating nondominated solutions for solving multiobjective optimisation problems. However, the obtained solutions did not converge close to the Pareto front and also did not distribute evenly over the Pareto front. Therefore, in this study, the concept of multiple nondominated leaders is incorporated to further improve the VEPSO algorithm. Hence, multiple nondominated solutions that are best at a respective objective function are used to guide particles in finding optimal solutions. The improved VEPSO is measured by the number of nondominated solutions found, generational distance, spread, and hypervolume. The results from the conducted experiments show that the proposed VEPSO significantly improved the existing VEPSO algorithms.
A new iterative scheme has been constructed for finding minimal solution of a rational matrix equation of the form X + A*X (-1) A = I. The new method is inversion-free per computing step. The convergence of the method has been studied and tested via numerical experiments.
Time series clustering is an important solution to various problems in numerous fields of research, including business, medical science, and finance. However, conventional clustering algorithms are not practical for time series data because they are essentially designed for static data. This impracticality results in poor clustering accuracy in several systems. In this paper, a new hybrid clustering algorithm is proposed based on the similarity in shape of time series data. Time series data are first grouped as subclusters based on similarity in time. The subclusters are then merged using the k-Medoids algorithm based on similarity in shape. This model has two contributions: (1) it is more accurate than other conventional and hybrid approaches and (2) it determines the similarity in shape among time series data with a low complexity. To evaluate the accuracy of the proposed model, the model is tested extensively using syntactic and real-world time series datasets.
Linear constraint minimum variance (LCMV) is one of the adaptive beamforming techniques that is commonly applied to cancel interfering signals and steer or produce a strong beam to the desired signal through its computed weight vectors. However, weights computed by LCMV usually are not able to form the radiation beam towards the target user precisely and not good enough to reduce the interference by placing null at the interference sources. It is difficult to improve and optimize the LCMV beamforming technique through conventional empirical approach. To provide a solution to this problem, artificial intelligence (AI) technique is explored in order to enhance the LCMV beamforming ability. In this paper, particle swarm optimization (PSO), dynamic mutated artificial immune system (DM-AIS), and gravitational search algorithm (GSA) are incorporated into the existing LCMV technique in order to improve the weights of LCMV. The simulation result demonstrates that received signal to interference and noise ratio (SINR) of target user can be significantly improved by the integration of PSO, DM-AIS, and GSA in LCMV through the suppression of interference in undesired direction. Furthermore, the proposed GSA can be applied as a more effective technique in LCMV beamforming optimization as compared to the PSO technique. The algorithms were implemented using Matlab program.
Flyrock is one of the major disturbances induced by blasting which may cause severe damage to nearby structures. This phenomenon has to be precisely predicted and subsequently controlled through the changing in the blast design to minimize potential risk of blasting. The scope of this study is to predict flyrock induced by blasting through a novel approach based on the combination of imperialist competitive algorithm (ICA) and artificial neural network (ANN). For this purpose, the parameters of 113 blasting operations were accurately recorded and flyrock distances were measured for each operation. By applying the sensitivity analysis, maximum charge per delay and powder factor were determined as the most influential parameters on flyrock. In the light of this analysis, two new empirical predictors were developed to predict flyrock distance. For a comparison purpose, a predeveloped backpropagation (BP) ANN was developed and the results were compared with those of the proposed ICA-ANN model and empirical predictors. The results clearly showed the superiority of the proposed ICA-ANN model in comparison with the proposed BP-ANN model and empirical approaches.
Multiobjective (MO) optimization is an emerging field which is increasingly being encountered in many fields globally. Various metaheuristic techniques such as differential evolution (DE), genetic algorithm (GA), gravitational search algorithm (GSA), and particle swarm optimization (PSO) have been used in conjunction with scalarization techniques such as weighted sum approach and the normal-boundary intersection (NBI) method to solve MO problems. Nevertheless, many challenges still arise especially when dealing with problems with multiple objectives (especially in cases more than two). In addition, problems with extensive computational overhead emerge when dealing with hybrid algorithms. This paper discusses these issues by proposing an alternative framework that utilizes algorithmic concepts related to the problem structure for generating efficient and effective algorithms. This paper proposes a framework to generate new high-performance algorithms with minimal computational overhead for MO optimization.
Protein domains contain information about the prediction of protein structure, function, evolution and design since the protein sequence may contain several domains with different or the same copies of the protein domain. In this study, we proposed an algorithm named SplitSSI-SVM that works with the following steps. First, the training and testing datasets are generated to test the SplitSSI-SVM. Second, the protein sequence is split into subsequence based on order and disorder regions. The protein sequence that is more than 600 residues is split into subsequences to investigate the effectiveness of the protein domain prediction based on subsequence. Third, multiple sequence alignment is performed to predict the secondary structure using bidirectional recurrent neural networks (BRNN) where BRNN considers the interaction between amino acids. The information of about protein secondary structure is used to increase the protein domain boundaries signal. Lastly, support vector machines (SVM) are used to classify the protein domain into single-domain, two-domain and multiple-domain. The SplitSSI-SVM is developed to reduce misleading signal, lower protein domain signal caused by primary structure of protein sequence and to provide accurate classification of the protein domain. The performance of SplitSSI-SVM is evaluated using sensitivity and specificity on single-domain, two-domain and multiple-domain. The evaluation shows that the SplitSSI-SVM achieved better results compared with other protein domain predictors such as DOMpro, GlobPlot, Dompred-DPS, Mateo, Biozon, Armadillo, KemaDom, SBASE, HMMPfam and HMMSMART especially in two-domain and multiple-domain.