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A DECOUPLING TWO-GRID METHOD FOR THE STEADY-STATE POISSON-NERNST-PLANCK EQUATIONS

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Journal of computational Mathematics 2019年第4期37卷 556-578页

作者： Ying Yang Benzhuo Lu Yan Xie School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin 541004 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing the National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck equations by coarse grid finite element approximations. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid algorithms for solving Poisson-Nernst-Planck equations.

关键词： Poisson-Nernst-Planck equations Two-grid finite element method Decoupling method Error analysis Gummel iteration

Higher-order rich-club phenomenon in collaborative research grant networks

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arXiv 2022年

作者： Nakajima, Kazuki Shudo, Kazuyuki Masuda, Naoki Department of Mathematical and Computing Science Tokyo Institute of Technology Meguro-ku Tokyo152-8552 Japan Department of Mathematics State University of New York at Buffalo Buffalo14260 United States Academic Center for Computing and Media Studies Kyoto University Sakyo-ku Kyoto606-8501 Japan Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo Buffalo14260 United States Faculty of Science and Engineering Waseda University Tokyo169-8555 Japan

Modern scientific work, including writing papers and submitting research grant proposals, increasingly involves researchers from different institutions. In grant collaborations, it is known that institutions involved in many collaborations tend to densely collaborate with each other, forming rich clubs. Here we investigate higher-order rich-club phenomena in networks of collaborative research grants among institutions and their associations with research impact. Using publicly available data from the National science Foundation in the US, we construct a bipartite network of institutions and collaborative grants, which distinguishes among the collaboration with different numbers of institutions. By extending the concept and algorithms of the rich club for dyadic networks to the case of bipartite networks, we find rich clubs both in the entire bipartite network and the bipartite subnetwork induced by the collaborative grants involving a given number of institutions up to five. We also find that the collaborative grants within rich clubs tend to be more productive in a per-dollar sense than the control. Our results highlight advantages of collaborative grants among the institutions in the rich clubs. Copyright © 2022, The Authors. All rights reserved.

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Leveraging VOSviewer approach for mapping, visualisation, and interpretation of crisis data for disaster management and decision-making

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International Journal of Information Management Data Insights 2025年第1期5卷

作者： Bukar, Umar Ali Sayeed, Md Shohel Amodu, Oluwatosin Ahmed Razak, Siti Fatimah Abdul Yogarayan, Sumendra Othman, Mohamed Centre for Intelligent Cloud Computing (CICC) Faculty of Information Science and Technology Multimedia University Jalan Ayer Keroh Lama Melaka Bukit Beruang 75450 Malaysia Department of Electronics Electrical and System Engineering Universiti Kebangsaan Malaysia Bangi 43600 Malaysia Department of Communication Technology and Network Universiti Putra Malaysia UPM Serdang Selangor 43400 Malaysia Laboratory of Computational Science and Mathematical Physics Institute for Mathematical Research Universiti Putra Malaysia UPM Serdang Selangor 43400 Malaysia

Analysing social media data is crucial for crisis management organisations to make timely decisions. Researchers in crisis informatics have devised various methods and systems to process and classify large volumes of crisis-related social media data for effective crisis response and recovery. However, the complexity of previous solutions hampers the timely processing of this data, its visualisation, and its interpretation, which is necessary for effective crisis response. Hence, this study addresses this challenge by employing visualisation of similarities to analyse and visualise crisis datasets to aid crisis management and decision-making. The results reveal a "nine-cluster community” of relevant keywords comprising “Green, Brown, Red, Blue, Pink, Purple, Yellow, Orange, and Cyan” colours, in both binary and full count. Specifically, the findings reveal various keywords such as the needs for food, water, shelter, medicine, and electricity. Thereafter, the study discusses the implications of VOSviewer for analysing crisis data theoretically and practically. © 2024

关键词： Co-occurrence networks Data analysis Decision-making Disaster management Social media Visualisation VOSviewer

COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

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Computers, Materials & Continua 2021年第7期68卷 391-407页

作者： Aqib Ali Wali Khan Mashwani Samreen Naeem Muhammad Irfan Uddin Wiyada Kumam Poom Kumam Hussam Alrabaiah Farrukh Jamal Christophe Chesneau Department of Computer Science Concordia College BahawalpurBahawalpur63100Pakistan Department of Computer Science&IT Glim Institute of Modern StudiesBahawalpur63100Pakistan Institute of Numerical Sciences Kohat University of Science&TechnologyKohat26000Pakistan Institute of Computing Kohat University of Science and TechnologyKohat26000Pakistan Program in Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiThanyaburi12110Thailand Departments of Mathematics Faculty of ScienceCenter of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research LaboratoryRoom SCL 802 Fixed Point LaboratoryScience Laboratory BuildingKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand Department of Medical Research China Medical University HospitalTaichung40402Taiwan College of Engineering Al Ain UniversityAl Ain64141United Arab Emirates Department of Mathematics Tafila Technical UniversityTafila66110Jordan Department of Statistics The Islamia University of BahawalpurBahawalpur63100Pakistan 11Department of MathematicsUniversitéde CaenLMNOCaen14032France

The purpose of this research is the segmentation of lungs computed tomography(CT)scan for the diagnosis of COVID-19 by using machine learning *** dataset contains data from patients who are prone to the *** contains three types of lungs CT images(Normal,Pneumonia,and COVID-19)collected from two different sources;the first one is the Radiology Department of Nishtar Hospital Multan and Civil Hospital Bahawalpur,Pakistan,and the second one is a publicly free available medical imaging database known as *** the preprocessing,a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest(ROIs)and acquire 52 hybrid statistical features for each ***,12 optimized statistical features are selected via the chi-square feature reduction *** the classification,five machine learning classifiers named as deep learning J4,multilayer perceptron,support vector machine,random forest,and naive Bayes are deployed to optimize the hybrid statistical features *** is observed that the deep learning J4 has promising results(sensitivity and specificity:0.987;accuracy:98.67%)among all the deployed *** a complementary study,a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.

关键词： COVID-19 machine learning fuzzy c-mean deep learning J4

Discrete energy analysis of the third-order variable-step BDF time-stepping for diffusion equations

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arXiv 2022年

作者： Liao, Hong-Lin Tang, Tao Zhou, Tao School of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China MIIT Nanjing211106 China Division of Science and Technology BNU-HKBU United International College Guangdong Province Zhuhai China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

This is one of our series works on discrete energy analysis of the variable-step BDF schemes. In this part, we present stability and convergence analysis of the third-order BDF (BDF3) schemes with variable steps for linear diffusion equations, see e.g. [SIAM J. Numer. Anal., 58:2294-2314] and [Math. Comp., 90: 1207-1226] for our previous works on the BDF2 scheme. To this aim, we first build up a discrete gradient structure of the variable-step BDF3 formula under the condition that the adjacent step ratios are less than 1.4877, by which we can establish a discrete energy dissipation law. Mesh-robust stability and convergence analysis in the L2 norm are then obtained. Here the mesh robustness means that the solution errors are well controlled by the maximum time-step size but independent of the adjacent time-step ratios. We also present numerical tests to support our theoretical *** Codes 65M06, 65M12 © 2022, CC BY-NC-SA.

关键词： Partial differential equations

Deep-Motion-Net: GNN-based volumetric organ shape reconstruction from single-view 2D projections

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arXiv 2024年

作者： Wijesinghe, Isuru Nix, Michael Zakeri, Arezoo Hokmabadi, Alireza Al-Qaisieh, Bashar Gooya, Ali Taylor, Zeike A. Centre for Computational Imaging and Simulation Technologies in Biomedicine School of Mechanical Engineering University of Leeds Leeds United Kingdom Institute of Medical and Biological Engineering School of Mechanical Engineering University of Leeds Leeds United Kingdom Department of Medical Physics and Engineering St James’s University Hospital Leeds Teaching Hospitals NHS Trust Leeds United Kingdom Division of Informatics Imaging and Data Sciences Faculty of Biology Medicine and Health University of Manchester Manchester United Kingdom School of Medicine and Population Health University of Sheffield Sheffield United Kingdom School of Computing Science University of Glasgow Glasgow United Kingdom

We propose Deep-Motion-Net: an end-to-end graph neural network (GNN) architecture that enables 3D (volumetric) organ shape reconstruction from a single in-treatment kV planar X-ray image acquired at any arbitrary projection angle. Estimating and compensating for true anatomical motion during radiotherapy is essential for improving the delivery of planned radiation dose to target volumes while sparing organs-at-risk, and thereby improving the therapeutic ratio. Achieving this using only limited imaging available during irradiation and without the use of surrogate signals or invasive fiducial markers is attractive. The proposed model learns the mesh regression from a patient-specific template and deep features extracted from kV images at arbitrary projection angles. A 2D-CNN encoder extracts image features, and four feature pooling networks fuse these features to the 3D template organ mesh. A ResNet-based graph attention network then deforms the feature-encoded mesh. The model is trained using synthetically generated organ motion instances and corresponding kV images. The latter is generated by deforming a reference CT volume aligned with the template mesh, creating digitally reconstructed radiographs (DRRs) at required projection angles, and DRR-to-kV style transferring with a conditional CycleGAN model. The overall framework was tested quantitatively on synthetic respiratory motion scenarios and qualitatively on in-treatment images acquired over full scan series for liver cancer patients. Overall mean prediction errors for synthetic motion test datasets were 0.16±0.13 mm, 0.18±0.19 mm, 0.22±0.34 mm, and 0.12±0.11 mm. Mean peak prediction errors were 1.39 mm, 1.99 mm, 3.29 mm, and 1.16 mm. © 2024, CC BY-SA.

关键词： Radiotherapy

Foundation Models for Atomistic Simulation of Chemistry and Materials

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arXiv 2025年

作者： Yuan, Eric C.-Y. Liu, Yunsheng Chen, Junmin Zhong, Peichen Raja, Sanjeev Kreiman, Tobias Vargas, Santiago Xu, Wenbin Head-Gordon, Martin Yang, Chao Blau, Samuel M. Cheng, Bingqing Krishnapriyan, Aditi Head-Gordon, Teresa Kenneth S. Pitzer Theory Center Department of Chemistry United States Department of Chemical and Biomolecular Engineering United States Electrical Engineering and Computer Science United States Bakar Institute of Digital Materials for the Planet University of California BerkeleyCA94720 United States Chemical Sciences Division United States Applied Mathematics and Computational Research Division United States Energy Technologies Area United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

Given the power of large language and large vision models, it is of profound and fundamental interest to ask if a foundational model based on data and parameter scaling laws and pre-training strategies is possible for learned simulations of chemistry and materials. The scaling of large and diverse datasets and highly expressive architectures for chemical and materials sciences should result in a foundation model that is more efficient and broadly transferable, robust to out-of-distribution challenges, and easily fine-tuned to a variety of downstream observables, when compared to specific training from scratch on targeted applications in atomistic simulation. In this Perspective we aim to cover the rapidly advancing field of machine learned interatomic potentials (MLIP), and to illustrate a path to create chemistry and materials MLIP foundation models at larger scale. © 2025, CC BY-SA.

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Accelerating Matrix Diagonalization through Decision Transformers with Epsilon-Greedy Optimization

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arXiv 2024年

作者： Bhatta, Kshitij Zollicoffer, Geigh Bhattarai, Manish Romero, Phil Negre, Christian F.A. Niklasson, Anders M.N. Adedoyin, Adetokunbo Department of Mechanical and Aerospace Engineering University of Virginia CharlottesvilleVA22904 United States School of Mathematics Georgia Institute of Technology AtlantaGA30332 United States High Performance Computing Division Los Alamos National Laboratory NM87545 United States Theoretical Division Los Alamos National Laboratory NM87545 United States Computational Science Division Los Alamos National Laboratory NM87545 United States

This paper introduces a novel framework for matrix diagonalization, recasting it as a sequential decision-making problem and applying the power of Decision Transformers (DTs). Our approach determines optimal pivot selection during diagonalization with the Jacobi algorithm, leading to significant speedups compared to the traditional max-element Jacobi method. To bolster robustness, we integrate an epsilon-greedy strategy, enabling success in scenarios where deterministic approaches fail. This work demonstrates the effectiveness of DTs in complex computational tasks and highlights the potential of reimagining mathematical operations through a machine learning lens. Furthermore, we establish the generalizability of our method by using transfer learning to diagonalize matrices of smaller sizes than those trained. Copyright © 2024, The Authors. All rights reserved.

关键词： Reinforcement learning

A FOURTH-ORDER UNFITTED CHARACTERISTIC FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATION ON TIME-VARYING DOMAINS

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arXiv 2021年

作者： Ma, Chuwen Zhang, Qinghai Zheng, Weiying School of Mathematical Science University of Chinese Academy of Sciences China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences Zhejiang University 38 Zheda Road Zhejiang Province Hangzhou310027 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for interface tracking, the fourth-order backward differentiation formula for temporal integration, and an unfitted finite element method for spatial discretization. Our convergence analysis includes errors of discretely representing the moving boundary, tracing boundary markers, and the spatial discretization and the temporal integration of the governing equation. Numerical experiments are performed on a rotating domain and a severely deformed domain to verify our theoretical results and to demonstrate the optimal convergence of the proposed method. Copyright © 2021, The Authors. All rights reserved.

关键词： Finite element method