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A rational optimal block hybrid method for enhanced accuracy in solving Lane–Emden equations

Partial Differential Equations in Applied Mathematics 2024年 12卷

作者： Motsa, Sandile Ahmedai, Salma Nefale, Mpho Otegbeye, Olumuyiwa School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa School of Mathematics Statistics and Computer Science University of KwaZulu-Natal Pietermaritzburg South Africa Faculty of Mathematical Sciences and Statistics Al Neelain University Khartoum Sudan

This paper introduces a block hybrid method designed for the effective resolution of Lane–Emden equations, which are characterized as second-order boundary value problems incorporating a singularity at the origin. Utilizing a strategic selection of grid points through the rational approximation of optimal points, this method aims at minimizing local truncation errors, thereby enhancing the precision of solutions. Extensive numerical experimentation reveals that this approach, hereinafter referred to as the Rational Optimal Block Hybrid Method (ROBHM), offers improved accuracy and convergence rates over traditional methods. The analysis underscores the critical role of the rational approximation parameter (denoted as d) in optimizing both accuracy and computational efficiency. By maintaining a balance between computational demands and the quality of solutions, the Rational Optimal Block Hybrid Method opens new avenues for tackling complex differential equations, thus contributing to the advancement of numerical analysis of boundary value problems marked by singularities. © 2024 The Authors

关键词： Block hybrid method Lane–Emden equations Quasi-linearization method Rational approximation Second order boundary value problems

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Eliminating Crossings in Ordered Graphs 19

Eliminating Crossings in Ordered Graphs

引用

19th Scandinavian Symposium on Algorithm Theory, SWAT 2024

作者： Agrawal, Akanksha Cabello, Sergio Kaufmann, Michael Saurabh, Saket Sharma, Roohani Uno, Yushi Wolff, Alexander Indian Institute of Technology Madras Chennai India Faculty of Mathematics and Physics University of Ljubljana Slovenia Institute of Mathematics Physics and Mechanics Ljubljana Slovenia Department of Computer Science Tübingen University Germany Institute of Mathematical Sciences Chennai India University of Bergen Norway Graduate School of Informatics Osaka Metropolitan University Sakai Japan Universität Würzburg Germany

ISBN: (纸本)9783959773188

Drawing a graph in the plane with as few crossings as possible is one of the central problems in graph drawing and computational geometry. Another option is to remove the smallest number of vertices or edges such that the remaining graph can be drawn without crossings. We study both problems in a book-embedding setting for ordered graphs, that is, graphs with a fixed vertex order. In this setting, the vertices lie on a straight line, called the spine, in the given order, and each edge must be drawn on one of several pages of a book such that every edge has at most a fixed number of crossings. In book embeddings, there is another way to reduce or avoid crossings;namely by using more pages. The minimum number of pages needed to draw an ordered graph without any crossings is its (fixed-vertex-order) page number. We show that the page number of an ordered graph with n vertices and m edges can be computed in 2m · nO(1) time. An O(log n)-approximation of this number can be computed efficiently. We can decide in 2O(d√k log(d+k)) · nO(1) time whether it suffices to delete k edges of an ordered graph to obtain a d-planar layout (where every edge crosses at most d other edges) on one page. As an additional parameter, we consider the size h of a hitting set, that is, a set of points on the spine such that every edge, seen as an open interval, contains at least one of the points. For h = 1, we can efficiently compute the minimum number of edges whose deletion yields fixed-vertex-order page number p. For h > 1, we give an XP algorithm with respect to h + p. Finally, we consider spine+t-track drawings, where some but not all vertices lie on the spine. The vertex order on the spine is given;we must map every vertex that does not lie on the spine to one of t tracks, each of which is a straight line on a separate page, parallel to the spine. In this setting, we can minimize in 2n · nO(1) time either the number of crossings or, if we disallow crossings, the number of tracks. © Akanks

关键词： Computational geometry

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Enhanced Dai–Liao conjugate gradient methods for systems of monotone nonlinear equations

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SeMA Journal 2021年第1期78卷 15-51页

作者： Waziri, M.Y. Ahmed, K. Sabi’u, J. Halilu, A.S. Department of Mathematical Sciences Faculty of Science Bayero University Kano Kano Nigeria Department of Mathematics Faculty of Sciences Yusuf Maitama Sule University Kano Kano Nigeria Department of Mathematics and Computer Science Sule Lamido University Kafin Hausa Nigeria

In this paper, we propose two conjugate gradient methods for solving large-scale monotone nonlinear equations. The methods are developed by combining the hyperplane projection method by Solodov and Svaiter (Reformulation: nonsmooth, piecewise smooth, semismooth and smoothing methods. Springer, pp 355–369, 1998) and two modified search directions of the famous Dai and Liao (Appl Math Optim 43(1): 87–101, 2001) method. It is shown that the proposed schemes satisfy the sufficient descent condition. The global convergence of the methods are established under mild conditions, and computational experiments on some benchmark test problems show that the methods are promising. © 2020, Sociedad Española de Matemática Aplicada.

关键词： Eigenvalue analysis Global convergence Hyperplane projection Monotonicity property Nonlinear equations

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Contextualised Modelling for Effective Citation Function Classification 22

Contextualised Modelling for Effective Citation Function Cla...

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Proceedings of the 2022 6th International Conference on Natural Language Processing and Information Retrieval

作者： Xiaorui Jiang Chaoxiang Cai Wenwen Fan Tong Liu Jingqiang Chen Faculty Research Centre for Computational Sciences and Mathematical Modelling Coventry University United Kingdom School of Computer Science and Technology Nanjing University of Posts and Telecommunications China

ISBN: (纸本)9781450397629

Citation function classification is an important task in scientific text mining. The past two decades have witnessed many computerised algorithms working on various citation function datasets tailored to various annotation schemes. Recently, deep learning has pushed the state of the art by a large margin. Several pitfalls exist. Due to annotation difficulty, data sizes, especially the minority classes, are often not big enough for training effective deep learning models. Being less discussed, most state-of-the-art deep learning solutions in fact generate a feature representation for the citation sentence or context, instead of modelling individual in-text citations. This is conceptually flawed as it is common to see multiple in-text citations with different functions in the same citation sentence. In addition, existing deep learning studies have only explored a rather limited design space of encoding citation and its surrounding context. This paper explored a wide range of modelling options based on SciBERT, the popular cross-disciplinary pre-trained scientific language model, and their performances on citation function classification, for the purpose of determining the most effective way of modeling citation and its context. To deal with the data size issue, we created a large-scale citation function dataset by mapping, merging and re-annotating six publicly available datasets from the computational linguistics domain by adapting Teufel et al.’s 12-class scheme. The best F1 scores we achieved were around 66.16%, 71.39% and 73.56% on a 11-class annotation scheme slightly adapted from Teufel et al.’s 12-class scheme, a reduced 7-class scheme by merging comparison functions, and Jurgens et al.’s 6-class scheme respectively. A useful observation is that there is no single best model that is superior for all functions, therefore the trained model variants allow for applications which emphasise on a specific type of or a specific group of citation functions.

关键词： Citation function classification SciBERT citation context analysis citation intent identification deep learning

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Perceptions Toward Using Artificial Intelligence and Technology for Asthma Attack Risk Prediction: Qualitative Exploration of Maori Views

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JMIR Formative Research 2024年 8卷 e59811页

作者： Jayamini, Widana Kankanamge Darsha Mirza, Farhaan Bidois-Putt, Marie-Claire Naeem, M. Asif Chan, Amy Hai Yan Department of Computer Science School of Engineering Computer and Mathematical Sciences Auckland University of Technology Auckland New Zealand Department of Software Engineering Faculty of Computing and Technology University of Kelaniya Kelaniya Sri Lanka School of Pharmacy Faculty of Medical and Health Sciences University of Auckland Auckland New Zealand Department of Data Science & Artificial Intelligence National University of Computer and Emerging Sciences (NUCES) Islamabad Pakistan

Background: Asthma is a significant global health issue, impacting over 500,000 individuals in New Zealand and disproportionately affecting Maori communities in New Zealand, who experience worse asthma symptoms and attacks. Digital technologies, including artificial intelligence (AI) and machine learning (ML) models, are increasingly popular for asthma risk prediction. However, these AI models may underrepresent minority ethnic groups and introduce bias, potentially exacerbating disparities. Objective: This study aimed to explore the views and perceptions that Maori have toward using AI and ML technologies for asthma self-management, identify key considerations for developing asthma attack risk prediction models, and ensure Maori are represented in ML models without worsening existing health inequities. Methods: Semistructured interviews were conducted with 20 Maori participants with asthma, 3 male and 17 female, aged 18-76 years. All the interviews were conducted one-on-one, except for 1 interview, which was conducted with 2 participants. Altogether, 10 web-based interviews were conducted, while the rest were kanohi ki te kanohi (face-to-face). A thematic analysis was conducted to identify the themes. Further, sentiment analysis was carried out to identify the sentiments using a pretrained Bidirectional Encoder Representations from Transformers model. Results: We identified four key themes: (1) concerns about AI use, (2) interest in using technology to support asthma, (3) desired characteristics of AI-based systems, and (4) experience with asthma management and opportunities for technology to improve care. AI was relatively unfamiliar to many participants, and some of them expressed concerns about whether AI technology could be trusted, kanohi ki te kanohi interaction, and inadequate knowledge of AI and technology. These concerns are exacerbated by the Maori experience of colonization. Most of the participants were interested in using technology to support their as

关键词： artificial intelligence asthma risk prediction health system development machine learning maori perceptions mobile phone

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A hybrid correlation-based deep learning model for email spam classification using fuzzy inference system

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Decision Analytics Journal 2024年 10卷

作者： Ayo, Femi Emmanuel Ogundele, Lukman Adebayo Olakunle, Solanke Awotunde, Joseph Bamidele Kasali, Funmilayo A. Department of Mathematical Sciences Olabisi Onabanjo University Ogun State Ago-Iwoye 120107 Nigeria Department of Computer Science Faculty of Information and Communication Sciences University of Ilorin Ilorin 240003 Nigeria Department of Computer Science and Mathematics Mountain Top University Ogun State Nigeria

Spam emails are unwanted and unsolicited messages. The major problems in email spam detection methods are low detection rates and a high likelihood of false alarms. This study proposes a hybrid correlation-based deep learning model for email spam classification using a fuzzy inference system. Using a rule-based hybrid feature selection technique, we choose the most crucial features from a preprocessed spam-based dataset. The selected features are then loaded into a deep learning model for spam classification, and fuzzy logic is employed to categorize each spam class into its severity levels to decrease misclassification. Compared with other machine learning methods, the proposed method shows better F1-score results for both test set spambase and test set non-spambase of 96.5% and 96.4%, respectively. Similarly, the developed method shows better accuracy, error rate, and processing time of 94.0017%, 5.9983%, and 0.5 s, respectively. The proposed approach also shows a reduced misclassification based on the fuzzy inference system. © 2023 The Author(s)

关键词： Deep learning Email filtering Feature selection Fuzzy logic Neural networks Spam classification

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On weight and variance uncertainty in neural networks for regression tasks

arXiv

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arXiv 2025年

作者： Monemi, Moein Amini, Morteza Taheri, S. Mahmoud Arashi, Mohammad School of Engineering Science College of Engineering University of Tehran Tehran Iran Department of Statistics School of Mathematics Statistics and Computer Science College of Science University of Tehran Tehran Iran Department of Statistics Faculty of Mathematical Sciences Ferdowsi University of Mashhad Mashhad*** Iran

We consider the problem of weight uncertainty proposed by [Blundell et al. (2015). Weight uncertainty in neural network. In International conference on machine learning, 1613-1622, PMLR.] in neural networks (NNs) specialized for regression tasks. We further investigate the effect of variance uncertainty in their model. We show that including the variance uncertainty can improve the prediction performance of the Bayesian NN. Variance uncertainty enhances the generalization of the model by considering the posterior distribution over the variance parameter. We examine the generalization ability of the proposed model using a function approximation example and further illustrate it with the riboflavin genetic data set. We explore fully connected dense networks and dropout NNs with Gaussian and spike-and-slab priors, respectively, for the network weights. © 2025, CC BY.

关键词： Neural network models

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Ordered graph limits and their applications 12

Ordered graph limits and their applications

引用

12th Innovations in Theoretical computer science Conference, ITCS 2021

作者： Ben-Eliezer, Omri Fischer, Eldar Levi, Amit Yoshida, Yuichi Center of Mathematical Sciences and Applications Harvard University CambridgeMA United States Faculty of Computer Science Technion - Israel Institute of Technology Haifa Israel Cheriton School of Computer Science University of Waterloo Canada Tokyo Japan

ISBN: (纸本)9783959771771

The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in analytic language. We extend the theory of graph limits to the ordered setting, presenting a limit object for dense vertex-ordered graphs, which we call an orderon. As a special case, this yields limit objects for matrices whose rows and columns are ordered, and for dynamic graphs that expand (via vertex insertions) over time. Along the way, we devise an ordered locality-preserving variant of the cut distance between ordered graphs, showing that two graphs are close with respect to this distance if and only if they are similar in terms of their ordered subgraph frequencies. We show that the space of orderons is compact with respect to this distance notion, which is key to a successful analysis of combinatorial objects through their limits. For the proof we combine techniques used in the unordered setting with several new techniques specifically designed to overcome the challenges arising in the ordered setting. We derive several applications of the ordered limit theory in extremal combinatorics, sampling, and property testing in ordered graphs. In particular, we prove a new ordered analogue of the well-known result by Alon and Stav [RS&A’08] on the furthest graph from a hereditary property;this is the first known result of this type in the ordered setting. Unlike the unordered regime, here the Erdős–Rényi random graph G(n, p) with an ordering over the vertices is not always asymptotically the furthest from the property for some p. However, using our ordered limit theory, we show that random graphs generated by a stochastic block model, where the blocks are consecutive in the vertex ordering, are (approximately) the furthest. Additionally, we describe an alternative analytic proof of the ordered graph removal lemma [Alon et al., FOCS’17]

关键词： Stochastic systems

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POLYNOMIAL GROWTH AND PROPERTY RDp FOR ÉTALE GROUPOIDS WITH APPLICATIONS TO K-THEORY

arXiv

引用

arXiv 2023年

作者： Austad, Are Ortega, Eduard Palmstrøm, Mathias Department of Mathematics and Computer Science Faculty of Science SDU Odense University of Southern Denmark Odense Denmark Department of Mathematical Sciences Faculty of Information Technology and Electrical Engineering NTNU Norwegian University of Science and Technology Trondheim Norway

We investigate property RDp for étale groupoids and apply it to the computation of the K-theory of reduced groupoid L p-operator algebras. In particular, under the assumption of polynomial growth, we show that the K-theory groups for a reduced groupoid L p-operator algebra are independent of p ∈ (1, ∞). We apply the results to coarse groupoids and graph *** Codes 46L80, 47L10, 46L87 Copyright © 2023, The Authors. All rights reserved.

关键词： Computation theory

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The contact process with an asymptomatic state

arXiv

引用

arXiv 2023年

作者： Belhadji, Lamia Lanchier, Nicolas Mercer, Max Faculty of Exact Sciences and Computer Science University of Abdelhamid Ibn Badis Mostaganem Algeria School of Mathematical and Statistical Sciences Arizona State University TempeAZ85287 United States

In order to understand the cost of a potentially high infectiousness of symptomatic individuals or, on the contrary, the benefit of social distancing, quarantine, etc. in the course of an infectious disease, this paper considers a natural variant of the popular contact process that distinguishes between asymptomatic and symptomatic individuals. Infected individuals all recover at rate one but infect nearby individuals at a rate that depends on whether they show the symptoms of the disease or not. Newly infected individuals are always asymptomatic and may or may not show the symptoms before they recover. The analysis of the corresponding mean-field model reveals that, in the absence of local interactions, regardless of the rate at which asymptomatic individuals become symptomatic, there is an epidemic whenever at least one of the infection rates is sufficiently large. In contrast, our analysis of the interacting particle system shows that, when the rate at which asymptomatic individuals become symptomatic is small and the asymptomatic individuals are not infectious, there cannot be an epidemic even when the symptomatic individuals are highly *** Codes 60K35 © 2023, CC BY.

关键词： Mean field theory

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