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One-third Hybrid Algorithm for Numerical solution of First-order Models Problems with Initial Condition

One-third Hybrid Algorithm for Numerical solution of First-o...

2024 International Conference on Science, engineering and Business for Driving Sustainable Development Goals, SEB4SDG 2024

作者： Omole, Ezekiel Olaoluwa Kehinde Uwaifor, John Oboni, Atabo Victor Obarhua, Friday O. Ajewole, Kehinde Peter Onu, Peter Folaranmi, Rotimi Oluwafemi Oluwayemi, Mathew O. Amoyedo, Femi Emmanuel Idowu Olaleru, Grace Landmark University Mathematics Programme Department of Physical Sciences Omu-Aran Nigeria University of Abuja Department of Mathematics Abuja Nigeria Confluence University of Science and Technology Department of Mathematics and Statistic Kogi State Osara Nigeria Federal University of Technology Department of Mathematical Sciences Akure Nigeria Landmark University Mathematics Programme Department of Physical Sciences Kwara State Omu-Aran Nigeria Omu-Aran Nigeria ThomasAdewumi University Department of Mathematical and Computing Scineces Kwara State Oko Nigeria Margaret Lawrence University Department of Mathematics and Statistics Galilee Delta State Nigeria Landmark University Department of Electrical and Information Engineering Kwara State Omuaran Nigeria

ISBN: (纸本)9798350358155

The collocation and interpolation technique on the power series approximate solution was used to develop a new continuous implicit hybrid one-third step method capable of solving first-order stiff initial value problems. This method has the advantage of allowing for easy step length changes and function evaluation at off-step points. The block method used to implement the main method ensures that each discrete method resulting from the block's simultaneous solution has the same order of accuracy as the main method. The method provides large intervals of absolute stability;it is consistent, zero stable, and thus converges. Sample examples of linear and nonlinear stiff problems were used to evaluate the method's performance. When compared to other existing methods, our developed method has been shown to be more accurate. © 2024 IEEE.

关键词： Consensus algorithm

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New Trends in the Modeling of Diseases Through Computational Techniques

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Computer Systems Science & engineering 2023年第6期45卷 2935-2951页

作者： Nesreen Althobaiti Ali Raza Arooj Nasir Jan Awrejcewicz Muhammad Rafiq Nauman Ahmed Witold Pawłowski Muhammad Jawaz Emad E.Mahmoud Department of Mathematics and Statistics College of ScienceTaif UniversityP.O.Box 11099Taif21944Saudi Arabia Department of Mathematics Govt.Maulana Zafar Ali Khan Graduate College WazirabadPunjab Higher Education Department(PHED)Lahore54000Pakistan Baqai Medical University Karachi75340Pakistan Shalamar Medical and Dental College Lahore54000Pakistan Department of Automation Biomechanics and MechatronicsLodz University of Technology1/15 Stefanowskiego St.90-924LodzPoland Department of Mathematics Faculty of Sciences and TechnologyUniversity of Central PunjabLahore54000Pakistan Department of Mathematics and Statistics University of LahoreLahore54590Pakistan Institute of Machine Tools and Production Engineering Lodz University of Technology1/15 Stefanowskiego St.90-537LodzPoland

The computational techniques are a set of novel problem-solving methodologies that have attracted wider attention for their excellent *** handling strategies of real-world problems are artificial neural networks(ANN),evolutionary computing(EC),and many *** estimated fifty thousand to ninety thousand new leishmaniasis cases occur annually,with only 25%to 45%reported to the World Health Organization(WHO).It remains one of the top parasitic diseases with outbreak and mortality *** 2020,more than ninety percent of new cases reported to World Health Organization(WHO)occurred in ten countries:Brazil,China,Ethiopia,Eritrea,India,Kenya,Somalia,South Sudan,Sudan,and *** transmission of visceral leishmaniasis is studied dynamically and *** study included positivity,boundedness,equilibria,reproduction number,and local stability of the model in the dynamical *** detailed methods like Runge Kutta and Euler depend on time steps and violate the physical relevance of the *** produce negative and unbounded results,so in disease dynamics,such developments have no biological significance;in other words,these results are *** the implicit nonstandard finite difference method does not depend on time step,positive,bounded,dynamic and *** the computational techniques and their results were compared using computer simulations.

关键词： Real-world problem differential equations computational techniques analysis

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Bioconvection Cross nanofluid flow with Cattaneo-Christov heat and mass fluxes past plate, wedge and cone

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Multiscale and Multidisciplinary Modeling, Experiments and Design 2025年第6期8卷 1-20页

作者： Shah, Muhammad Zameer Khan, Noor Saeed Khan, Waris Boukhris, Imed Kouki, Marouan Agha, Afnan Al Garalleh, Hakim Al Al-Buriahi, M.S. Division of Science and Technology Department of Mathematics University of Education Lahore54000 Pakistan Department of Mathematics and Statistics Hazara University Mansehra Pakistan Central Labs King Khalid University Abha AlQura’aP.O. Box 960 Saudi Arabia Department of Information System Faculty of Computing and Information Technology Northern Border University Rafha Saudi Arabia Department of Mathematical Science College of Engineering University of Business and Technology Jeddah21361 Saudi Arabia Department of Physics Sakarya University Sakarya Turkey

This study examines the bioconvection flow of a Cross nanofluid containing gyrotactic microorganisms over three geometrical configurations: a flat plate, a wedge, and a cone. The significance of this research lies in its incorporation of the Cattaneo-Christov heat and mass flux theory, which accounts for thermal relaxation effects-critical in optimizing heat and mass transfer processes in bioengineering and industrial applications. The study aims to analyze the combined effects of radiative heat transfer, thermophoresis, heat generation/absorption, magnetic field strength and other embedded parameters on fluid behavior. The research employs the Homotopy Analysis Method (HAM) to obtain analytical solution for velocity, temperature, nanoparticle concentration, and gyrotactic microorganism density distribution. The key findings indicate that heat transfer is most efficient over the cone, whereas the wedge exhibits the highest mass transfer rate and microbial concentration. The study further highlights the influence of governing parameters such as buoyancy ratio, relaxation time, and external forces on fluid behavior. These results contribute to a deeper understanding of nanofluid dynamics in biomedical and industrial applications, including microbial-enhanced oil recovery and nanofluid-based drug delivery systems. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

关键词： SARS

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Lignin-based polyurethane composites enhanced with hydroxyapatite for controlled drug delivery and potential cellular scaffold applications

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Polymer Composites 2024年第16期45卷 15159-15172页

作者： Nugroho, Roshid Adi Saputra, Ozi Adi Pradita, Agung Lucky Fajar, Al Bukhori Nur Wibowo, Fajar Rakhman Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Sebelas Maret Central Java Surakarta Indonesia Sustainable Chemical Science and Technology Taiwan International Graduate Program Academia Sinica Taipei Taiwan Institute of Chemistry Academia Sinica Taipei Taiwan Department of Chemical Engineering Collage of Engineering National Taiwan University Taipei Taiwan

Polymer technology has rapidly advanced across diverse domains, particularly in biomedical applications. Among various polymers, polyurethane (PU) hold great potential in developing biomaterials such as biomedical scaffold and drug delivery. In this study, we have innovatively engineered eco-friendly polyurethane using lignin, a sustainable bio-polyol derived from oil palm empty fruit bunches. To enhance the physicochemical properties of the PU, we have incorporated hydroxyapatite (HA) into the composites. The inclusion of HA has led to notable improvements in crucial properties such as density, porosity, and water absorption, making these composites ideal candidates for tissue regeneration scaffolds. Furthermore, to assess their biomedical applicability in drug delivery and cell scaffolding, we have employed the quercetin drug model. The results revealed a sustained kinetic release behavior within the polyurethane/hydroxyapatite (PU/HA) composites, showcasing their potential for controlled drug delivery applications. Moreover, cytotoxicity assays conducted using neuro-2a cell models demonstrated the non-cytotoxic nature of both PU and PU/HA composites. This finding holds significant implications for biomedical applications, indicating that these composites offer biocompatible platforms for tissue engineering and regenerative medicine endeavors. The ability of these composites to support cell viability underscores their potential for a wide range of biomedical applications, including neural tissue engineering and drug delivery systems targeting brain diseases. These findings pave the way for the development of innovative and sustainable biomaterials with diverse biomedical applications. Highlights: An eco-friendly polyurethane has been engineered by harnessing liginin-derived oil palm empty fruit bunches. Incorporation of hydroxyapaptite enhance the physical properties of polyurethane. Controlled kinetic drug release is one of polyurethane/hydroxyapatite (PU/HA) com

关键词： Fruits

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On efficient and scalable computation of the nonparametric maximum likelihood estimator in mixture models

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2024年第1期25卷 439-484页

作者： Yangjing Zhang Ying Cui Bodhisattva Sen Kim-Chuan Toh Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Department of Industrial Engineering and Operations Research University of California Berkeley Department of Statistics Columbia University Department of Mathematics Institute of Operations Research and Analytics National University of Singapore

In this paper, we focus on the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our approach discretizes this infinite dimensional convex optimization problem by setting fixed support points for the NPMLE and optimizing over the mixing proportions. We propose an efficient and scalable semismooth Newton based augmented Lagrangian method (ALM). Our algorithm outperforms the state-of-the-art methods (Kim et al., 2020; Koenker and Gu, 2017), capable of handling n≈106 data points with m ≈ 104 support points. A key advantage of our approach is its strategic utilization of the solution's sparsity, leading to structured sparsity in Hessian computations. As a result, our algorithm demonstrates better scaling in terms of m when compared to the mixsqp method (Kim et al., 2020). The computed NPMLE can be directly applied to denoising the observations in the framework of empirical Bayes. We propose new denoising estimands in this context along with their consistent estimates. Extensive numerical experiments are conducted to illustrate the efficiency of our ALM. In particular, we employ our method to analyze two astronomy data sets: (i) Gaia-TGAS Catalog (Anderson et al., 2018) containing approximately 1.4 × 106 data points in two dimensions, and (ii) a data set from the APOGEE survey (Majewski et al., 2017) with approximately 2.7 × 104 data points.

关键词： augmented Lagrangian method denoising empirical Bayes Gaussian location mixture model heteroscedastic errors semismooth Newton method sparse secondorder information

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Machine Learning and Time Series Approaches for Stock Price Prediction: A Case Study of Indian Banks

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Procedia Computer Science 2025年 260卷 626-634页

作者： Tiya Chaudhary Minirani S Nilkamal School of Mathematics Applied Statistics and Analytics (NSOMASA) NMIMS University Mumbai – 400056 Department of Mathematics Mukesh Patel School Of Technology Management and Engineering NMIMS University Mumbai-400056

The Finance sector plays an important role in the economy of any country. With increased recognition of the stock market and its importance in the economy, correct investments and portfolio management has been the top priority in this sector. With the introduction of machine learning and time series models this has been easier. This research paper focuses on the comparative analysis of three most used machine learning and time series models namely Autoregressive Integrated Moving Average (ARIMA), Seasonal Autoregressive Integrated Moving Average (SARIMA) and Long Term Short Term Memory (LSTM) in predicting the stock prices of the Indian Banks namely ICICI Bank, IndusInd Bank, State Bank Of India, Kotak Mahindra Bank, HDFC Bank and Axis Bank using efficient and time saving means. Each models’ accuracy is evaluated using error metrics like Root Mean Square Error, Mean Squared Error and Mean Absolute Error. The findings aim to provide an insight about the most preferred model in this field and also help financial analysts and investors to make the correct decisions while investing into the market.

关键词： ARIMA SARIMA LSTM Root Mean Square Error Mean Absolute Error Stock price prediction

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Reliability modeling and analysis of mixture of exponential distributions using artificial neural network

Reliability modeling and analysis of mixture of exponential ...

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作者： Shafiq, Anum Çolak, Andaç Batur Lone, Showkat Ahmad Sindhu, Tabassum Naz Muhammad, Taseer School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing China Mechanical Engineering Department Niğde Ömer Halisdemir University Niğde Turkey Department of Basic Sciences College of Science and Theoretical Studies Saudi Electronic University Riyadh Saudi Arabia Department of Statistics Quaid-i-Azam University 45320 Islamabad Pakistan Department of Mathematics College of Sciences King Khalid University Abha Saudi Arabia

In recent years, statisticians have become more and more interested in the study of mixture models, especially in the last decade, without adequately considering the difficulty of modeling the reliability measures of mixture models using artificial neural networks. In this study, in which artificial neural networks and mixed model reliability criteria are analyzed, various reliability parameters are calculated considering different scenarios. In order to estimate the obtained numerical reliability parameters, a multilayer artificial neural network model has been developed. Seven different reliability parameter values have been obtained from the artificial neural network model designed with four input parameters. The prediction values obtained from the artificial neural network model developed with five neurons in the hidden layer have been compared with numerical data, and the performance of the model has been analyzed comprehensively. The mean squared error (MSE) value for the network model has been calculated as 1.98E-08 and the R value as 0.99991. The results clearly revealed that the artificial neural network model developed using data from the appropriate statistical model is an excellent tool that can be used to estimate reliability measures. © 2022 John Wiley & Sons, Ltd.

关键词： Mixtures

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Optimal aggregation of prediction intervals under unsupervised domain shift 24

Optimal aggregation of prediction intervals under unsupervis...

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Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Jiawei Ge Debarghya Mukherjee Jianqing Fan Operations Research & Financial Engineering Princeton University Department of Mathematics and Statistics Boston University

ISBN: (纸本)9798331314385

As machine learning models are increasingly deployed in dynamic environments, it becomes paramount to assess and quantify uncertainties associated with distribution shifts. A distribution shift occurs when the underlying data-generating process changes, leading to a deviation in the model's performance. The prediction interval, which captures the range of likely outcomes for a given prediction, serves as a crucial tool for characterizing uncertainties induced by their underlying distribution. In this paper, we propose methodologies for aggregating prediction intervals to obtain one with minimal width and adequate coverage on the target domain under unsupervised domain shift, under which we have labeled samples from a related source domain and unlabeled covariates from the target domain. Our analysis encompasses scenarios where the source and the target domain are related via i) a bounded density ratio, and ii) a measure-preserving transformation. Our proposed methodologies are computationally efficient and easy to implement. Beyond illustrating the performance of our method through real-world datasets, we also delve into the theoretical details. This includes establishing rigorous theoretical guarantees, coupled with finite sample bounds, regarding the coverage and width of our prediction intervals. Our approach excels in practical applications and is underpinned by a solid theoretical framework, ensuring its reliability and effectiveness across diverse contexts.

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A Non-Singleton Type-3 Fuzzy Modeling: Optimized by Square-Root Cubature Kalman Filter

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Intelligent Automation & Soft Computing 2023年第7期37卷 17-32页

作者： Aoqi Xu Khalid A.Alattas Nasreen Kausar Ardashir Mohammadzadeh Ebru Ozbilge Tonguc Cagin School of Economics Fujian Normal UniversityFuzhou350007China Department of Computer Science and Artificial Intelligence College of Computer Science and EngineeringUniversity of JeddahJeddah23890Saudi Arabia Department of Mathematics Faculty of Arts and ScienceYildiz Technical UniversityEsenler34220IstanbulTurkey Multidisciplinary Center for Infrastructure Engineering Shenyang University of TechnologyShenyang110870China American University of the Middle East Department of Mathematics&Statistics54200EgailaKuwait

In many problems,to analyze the process/metabolism behavior,a mod-el of the system is identiﬁ*** main gap is the weakness of current methods *** *** primary objective of this study is to present a more robust method against *** paper proposes a new deep learning scheme for modeling and identiﬁcation *** suggested approach is based on non-singleton type-3 fuzzy logic systems(NT3-FLSs)that can support measurement errors and high-level *** the rule optimization,the antecedent parameters and the level of secondary memberships are also adjusted by the suggested square root cubature Kalmanﬁlter(SCKF).In the learn-ing algorithm,the presented NT3-FLSs are deeply learned,and their nonlinear structure is *** designed scheme is applied for modeling carbon cap-ture and sequestration problem using real-world data *** various ana-lyses and comparisons,the better efﬁciency of the proposed fuzzy modeling scheme is veriﬁ*** main advantages of the suggested approach include better resistance against uncertainties,deep learning,and good convergence.

关键词： Modeling computational intelligence fuzzy logic systems modeling identiﬁcation deep learning type-3 fuzzy systems optimization

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Kansa–RBF algorithms for elliptic BVPs in annular domains with mixed boundary conditions

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mathematics and Computers in Simulation 2023年 206卷 77-104页

作者： Jankowska, Malgorzata A. Karageorghis, Andreas Chen, C.S. Institute of Applied Mechanics Poznan University of Technology Poznan60–965 Poland Department of Mathematics and Statistics University of Cyprus P.O. Box 20537 Nicosia1678 Cyprus School of Mathematics and Natural Sciences University of Southern Mississippi HattiesburgMS39406 United States Department of Civil Engineering National Taiwan University Taipei Taiwan

We employ a Kansa–radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains with mixed Dirichlet/Neumann boundary conditions. By exploiting the circular boundaries and the properties of circulant matrices we employ, in an efficient way, the pre-conditioned Krylov subspace iterative solvers GMRES and BiCGSTAB for the solution of the resulting linear systems. In particular, we employ block circulant pre-conditioners which allow for the efficient solution of the relevant systems in the iterative solution. Moreover, by exploiting the properties of circulant matrices we perform the matrix–vector multiplications involved in the iterative solvers efficiently. The feasibility of the proposed techniques is illustrated by several numerical examples. © 2022 International Association for mathematics and Computers in Simulation (IMACS)

关键词： Iterative methods

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