{"title":"Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems","authors":"Baiying Dong, Zhilin Li, Juan Ruiz-Álvarez","doi":"10.37256/rrcs.2120232118","DOIUrl":"https://doi.org/10.37256/rrcs.2120232118","url":null,"abstract":"In this paper, third-order compact and fourth-order finite element methods (FEMs) based on simple modifications of traditional FEMs are proposed for solving one-dimensional Sturm-Liouville boundary value problems (BVPs). The key idea is based on interpolation error estimates. A simple posterior error analysis of the original piecewise linear finite element space leads to a third-order accurate solution in the L2 norm, second-order in the H1, and the energy norm. The novel idea is also applied to obtain a fourth-order FEM based on the quadratic finite element space. The basis functions in the new fourth-order FEM are more compact compared with that of the classic cubic basis functions. Numerical examples presented in this paper have confirmed the convergence order and analysis. A generalization to a class of nonlinear two-point BVPs is also discussed and tested.","PeriodicalId":377142,"journal":{"name":"Research Reports on Computer Science","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116870467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Z. Dou, Ke Peng, Yajing Wang, Zhenmei Li, Qinqin Wei
{"title":"Design and Application of Virtual Flexible Simulation Experiment Teaching Platform for Relay Protection","authors":"Z. Dou, Ke Peng, Yajing Wang, Zhenmei Li, Qinqin Wei","doi":"10.37256/rrcs.2120232119","DOIUrl":"https://doi.org/10.37256/rrcs.2120232119","url":null,"abstract":"Abstract: Power system relay protection (PSRP) is a comprehensive course in electrical engineering undergraduate stage, which has a very strong engineering application. However, due to the influence of many factors, such as the power system security, high experimental cost, limited course hours, insufficient open conditions, and so on, traditional experimental teaching combined with hardware is difficult to meet the needs of students in various scenarios anytime and anywhere. Therefore, a low-cost virtual flexible simulation experiment teaching platform (VFSETP) is developed. The platform uses Simulink to build the simulation model of power system primary system and uses graphical user interface (GUI) to design the human-computer interaction interface. Through the communication between GUI and Simulink model, the protection experiments in various scenarios are successfully simulated. The VFSETP has many advantages such as simple interface, good visualization effect, and simple operation. The teachers can easily use it for classroom demonstration, and the students can use it for verification, analysis, expansion, and exploration of experiments in a variety of application scenarios without relying on the laboratory environment. This experimental mode is very conducive to the understanding of knowledge and the cultivation of practical innovation ability. The results of the student survey show that the design method and application mode of the platform can provide a reference for similar courses.","PeriodicalId":377142,"journal":{"name":"Research Reports on Computer Science","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129253507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Note on Reinforcement Learning","authors":"Ying Tan","doi":"10.37256/rrcs.1220222153","DOIUrl":"https://doi.org/10.37256/rrcs.1220222153","url":null,"abstract":"In the past decade, deep reinforcement learning (DRL) has drawn much attention in theoretical research, meanwhile, it has seen huge success across multiple application areas, such as combinatorial optimization, recommender systems, autonomous driving, intelligent healthcare system and robotics. As one of three basic machine learning paradigms, reinforcement learning concerns with how intelligent agents learn in an interactive environment through trial and error to maximize the total cumulative reward of the agents. Even though many progresses of reinforcement learning have been presented, there are still many challenging research topics due to the complexity of the problems.","PeriodicalId":377142,"journal":{"name":"Research Reports on Computer Science","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126625684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme","authors":"Navnit Jha, P. Lin","doi":"10.37256/rrcs.1120211466","DOIUrl":"https://doi.org/10.37256/rrcs.1120211466","url":null,"abstract":"A two-level implicit compact formulation with quasi-variable meshes is reported for solving three-dimensions second-order nonlinear parabolic partial differential equations. The new nineteen-point compact scheme exhibit fourth and second-order accuracy in space and time on a variable mesh steps and uniformly spaced mesh points. We have also developed an operator-splitting technique to implement the alternating direction implicit (ADI) scheme for computing the 3D advection-diffusion equation. Thomas algorithm computes each tri-diagonal matrix that arises from ADI steps in minimal computing time. The operator-splitting form is unconditionally stable. The improved accuracy is achieved at a lower cost of computation and storage because the spatial mesh parameters tune the mesh location according to solution values' behavior. The new method is successfully applied to the Navier-Stokes equation, advection-diffusion equation, and Burger's equation for the computational illustrations that corroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The main highlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, and its superiority over the comparable uniform meshes high-order compact scheme.","PeriodicalId":377142,"journal":{"name":"Research Reports on Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130554199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Learning Pinball TWSVM efficiently using Privileged Information and their applications","authors":"R. Rastogi, Aman Pal, Suresh Chandra","doi":"10.37256/rrcs.1120211325","DOIUrl":"https://doi.org/10.37256/rrcs.1120211325","url":null,"abstract":"In any learning framework, an expert knowledge always plays a crucial role. But, in the field of machine learning, the knowledge offered by an expert is rarely used. Moreover, machine learning algorithms (SVM based) generally use hinge loss function which is sensitive towards the noise. Thus, in order to get the advantage from an expert knowledge and to reduce the sensitivity towards the noise, in this paper, we propose a fast and novel Twin Support Vector Machine classifier based on privileged information with pinball loss function which has been termed as Pin-TWSVMPI where expert's knowledge is in the form of privileged information. The proposed Pin-TWSVMPI incorporates privileged information by using correcting function so as to obtain two nonparallel decision hyperplanes. Further, in order to make computations more efficient and fast, we use Sequential Minimal Optimization (SMO) technique for obtaining the classifier and have also shown its application for Pedestrian detection and Handwritten digit recognition. Further, for UCI datasets, we first implement a procedure which extracts privileged information from the features of the dataset which are then further utilized by Pin-TWSVMPI to which lead to enhancement in classification accuracy with comparatively lesser computational time.","PeriodicalId":377142,"journal":{"name":"Research Reports on Computer Science","volume":"373 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131894531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multi-label Minimax Probability Machine with Multi-manifold Regularisation","authors":"Sambhav Jain, R. Rastogi","doi":"10.37256/rrcs.1120211193","DOIUrl":"https://doi.org/10.37256/rrcs.1120211193","url":null,"abstract":"Semi-supervised learning i.e., learning from a large number of unlabelled data and exploiting a small percentage of labelled data has attracted centralised attention in recent years. Semi-supervised problem is handled mainly using graph based Laplacian and Hessian regularisation methods. However, neither the Laplacian method which leads to poor generalisation nor the Hessian energy can properly forecast the data points beyond the range of the domain. Thus, in this paper, the Laplacian-Hessian semi-supervised method is proposed, which can both predict the data points and enhance the stability of Hessian regulariser. In this paper, we propose a Laplacian-Hessian Multi-label Minimax Probability Machine, which is Multi-manifold regularisation framework. The proposed classifier requires mean and covariance information; therefore, assumptions related to the class conditional distributions are not required; rather, a upper bound on the misclassification probability of future data is obtained explicitly. Furthermore, the proposed model can effectively utilise the geometric information via a combination of Hessian-Laplacian manifold regularisation. We also show that the proposed method can be kernelised on the basis of a theorem similar to the representer theorem for handling non-linear cases. Extensive experimental comparisons of our proposed method with related multi-label algorithms on well known multi-label datasets demonstrate the validity and comparable performance of our proposed approach.","PeriodicalId":377142,"journal":{"name":"Research Reports on Computer Science","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132068182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linked List Elimination from Hashing Methods","authors":"Mahmoud Naghibzadeh, B. Naghibzadeh","doi":"10.37256/rrcs.1120211145","DOIUrl":"https://doi.org/10.37256/rrcs.1120211145","url":null,"abstract":"Hashing has been used for decades in many fields such as encryption, password verification, and pattern search. Hash systems consist mainly of three components: the hash function, the hash table, and the linked lists that are attached to the hash table. One of the major benefits of using a hash function is reduction in the runtime of the hash-based software systems. However, their linked lists are a major source of time consumption. In this paper, an innovative method is proposed to remove all the linked lists attached to the hash table and collect the necessary information in a one-dimensional array. The method can be used to create an index for the human genome. The human genome is the size of a million-page book with no index, and it is difficult to find the needed information. The proposed method transforms list search operations with linear time complexity into array searches with logarithmic time complexity. In a sample problem, finding inversions in genomic sequences, the proposed indexing system is compared with traditional hashing systems with linked lists. It is demonstrated that, in addition to time complexity reduction, the proposed method reduces the space required for the hash system to one half of what is used by linked list based methods.","PeriodicalId":377142,"journal":{"name":"Research Reports on Computer Science","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133157913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francis J. Vasko, Anthony Dellinger, Yun Lu, Bryan McNally, Myung Soon Song
{"title":"A Simple and Efficient Technique to Generate Bounded Solutions for the Generalized Assignment Problem: A Guide for OR Practitioners","authors":"Francis J. Vasko, Anthony Dellinger, Yun Lu, Bryan McNally, Myung Soon Song","doi":"10.37256/rrcs.1120211039","DOIUrl":"https://doi.org/10.37256/rrcs.1120211039","url":null,"abstract":"The generalized assignment problem (GAP) is a NP-hard problem that has a large and varied number of important applications in business and industry. Approximate solution approaches for the GAP do not require excessive computation time, but typically there are no guarantees on solution quality. In this article, a methodology called the simple sequential increasing tolerance (SSIT) matheuristic that iteratively uses any general-purpose integer programming software is discussed. This methodology uses a sequence of increasing tolerances in conjunction with optimization software to generate a solution that is guaranteed to be within a specified percentage of the optimum in a short time. SSIT requires no problem-specific coding and can be used with any commercial optimization software to generate bounded solutions in a timely manner. Empirically, SSIT is tested on 51 GAP instances (24 medium and 27 large) in the literature. The performance of CPLEX versus Gurobi on these 51 GAP test instances is also statistically analyzed.","PeriodicalId":377142,"journal":{"name":"Research Reports on Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130334077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hybridization of Convolutional Neural Networks with Wavelet Architecture for COVID-19 Detection","authors":"R. Manavalan, S. Priya","doi":"10.37256/rrcs.1120211112","DOIUrl":"https://doi.org/10.37256/rrcs.1120211112","url":null,"abstract":"Coronavirus disease is an infectious disease caused by perilous viruses. According to the World Health Organization (WHO) updated reports, the number of people infected with Coronavirus-2019 (COVID-19) and death rate rises rapidly every day. The limited number of COVID-19 test kits available in hospitals could not meet with the demand of daily growing cases. The ability to diagnose COVID-19 suspected cases accurately and quickly is essential for prompt quarantine and medical treatment. The goal of this research is to implement a novel system called Convolution Neural Network with Wavelet Transformation (CNN-WT) to assist radiologists for the automatic COVID-19 detection through chest X-ray images to counter the outbreak of SARS-CoV-2. The proposed CNN-WT method employing X-ray imaging has the potential to be very beneficial for the medical sector in dealing with mass testing circumstances in pandemics like COVID-19. The dataset used for experimentation consists of 219 chest X-Ray images with confirmed COVID-19 cases and 219 images of healthy people. The suggested model's efficacy is evaluated using 5-fold cross-validation. The CNN-WT model yielded an average accuracy of 98.63%, which is 1.36% higher than the general CNN architecture.","PeriodicalId":377142,"journal":{"name":"Research Reports on Computer Science","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123166451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}