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HTL-WASI preconditioner for finite element discretization of complex ADR equation and its application

Journal of computational and Applied mathematics 2025年 470卷

作者： Yang, Ronghua Wang, Junxian Shu, Shi School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China

The convection diffusion reaction (ADR) equation is widely used in engineering applications. In this paper, we focus on a complex ADR equation arising from Helmholtz equation with impedance boundary conditions, prove the coerceiveness and boundedness of the sesquilinear functional and discuss the fast solver of the discretization. Firstly, we design a Weighted Additive Schwarz with Impedance (WASI) preconditioner, in order to overcome the dependence of the WASI preconditioner on the number of subdomains and the overlapping width, an ideal coarse space is designed. Although it can be proved that the corresponding hybrid two-level preconditioner is the exact inverse of the ADR coefficient matrix, the dimension of this coarse space is too big. In order to overcome this deficiency, a smaller dimensional coarse space was constructed by introducing local generalized eigenvalue problems (GEP) on each subdomain, and the descent rate of the corresponding two-level preconditioned GMRES method was rigorously analyzed which does not depend on mesh size, overlapping width, wave number k, and the absorption parameter. Since the size of the coarse space is sensitive to k and the GEP on each subdomain needs to be solved, the computational cost is too high. Therefore, we design an iterative method based on an economical two-level preconditioner, and establish a heuristic convergence theory that is supported by numerical results. Numerical experiments show the robustness of GMRES with the corresponding economical two-level preconditioner(HTLE-WASI-GMRES). Finally, for the Helmholtz finite element discretization, by using the Shifted Laplace technique and ADR equation, we design a novel fast solver combining with HTLE-WASI-GMRES for ADR equation. Numerical experiments have demonstrated the effectiveness of the algorithm. © 2025

关键词： Convergence of numerical methods

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CLEARING SECTIONS OF LATTICE LIABILITY NETWORKS

arXiv

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arXiv 2025年

作者： Ghrist, Robert Gould, Julian Lopez, Miguel Riess, Hans Department of Mathematics and Electrical & Systems Engineering University of Pennsylvania Philadelphia PA Department of Mathematics University of Pennsylvania Philadelphia PA Applied Mathematics & Computational Science University of Pennsylvania Philadelphia PA School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA

Modern financial networks involve complex obligations that transcend simple monetary debts: multiple currencies, prioritized claims, supply chain dependencies, and more. We present a mathematical framework that unifies and extends these scenarios by recasting the classical Eisenberg-Noe model of financial clearing in terms of lattice liability networks. Each node in the network carries a complete lattice of possible states, while edges encode nominal liabilities. Our framework generalizes the scalar-valued clearing vectors of the classical model to lattice-valued clearing sections, preserving the elegant fixed-point structure while dramatically expanding its descriptive power. Our main theorem establishes that such networks possess clearing sections that themselves form a complete lattice under the product order. This structure theorem enables tractable analysis of equilibria in diverse domains, including multi-currency financial systems, decentralized finance with automated market makers, supply chains with resource transformation, and permission networks with complex authorization structures. We further extend our framework to chain-complete lattices for term structure models and multivalued mappings for complex negotiation systems. Our results demonstrate how lattice theory provides a natural language for understanding complex network dynamics across multiple domains, creating a unified mathematical foundation for analyzing systemic risk, resource allocation, and network *** Codes 91G40, 06B23, 91D30, 68Q85 Copyright © 2025, The Authors. All rights reserved.

关键词： Lattice theory

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A novel deep high-level concept-mining jointing hashing model for unsupervised cross-modal retrieval

High-Confidence Computing

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High-Confidence computing 2025年第2期5卷

作者： Dong, Chun-Ru Zhang, Jun-Yan Zhang, Feng Hua, Qiang Xu, Dachuan Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding071002 China Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing100124 China

Unsupervised cross-modal hashing has achieved great success in various information retrieval applications owing to its efficient storage usage and fast retrieval speed. Recent studies have primarily focused on training the hash-encoded networks by calculating a sample-based similarity matrix to improve the retrieval performance. However, there are two issues remain to solve: (1) The current sample-based similarity matrix only considers the similarity between image-text pairs, ignoring the different information densities of each modality, which may introduce additional noise and fail to mine key information for retrieval;(2) Most existing unsupervised cross-modal hashing methods only consider alignment between different modalities, while ignoring consistency between each modality, resulting in semantic conflicts. To tackle these challenges, a novel Deep High-level Concept-mining Jointing Hashing (DHCJH) model for unsupervised cross-modal retrieval is proposed in this study. DHCJH is able to capture the essential high-level semantic information from image modalities and integrate into the text modalities to improve the accuracy of guidance information. Additionally, a new hashing loss with a regularization term is introduced to avoid the cross-modal semantic collision and false positive pairs problems. To validate the proposed method, extensive comparison experiments on benchmark datasets are conducted. Experimental findings reveal that DHCJH achieves superior performance in both accuracy and efficiency. The code of DHCJH is available at Github. © 2024 The Author(s)

关键词： Online searching

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Design of Approximate Multiplier Using Highly Compressed 5_2 Counter

Design of Approximate Multiplier Using Highly Compressed 5_2...

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Mobile computing and Sustainable Informatics (ICMCSI), International Conference on

作者： Bathlin Nelmin N R S Shaji Hariprasad S Sudeshna Shettygari Vasan J K Vijayan V Department of Electronics and Communication Engineering University College of Engineering Nagercoil India Department of Computer Science and Engineering St. Xavier's Catholic College of Engineering Nagercoil India Department of Computational Intelligence School of Computing SRM Institute of Science and Technology Chennai India Department of Electronics and Communication Engineering SRM Institute of Science and Technology Chennai India

ISBN: (数字)9798331522667

ISBN: (纸本)9798331522674

Approximate computing effectively impacts low-power VLSI circuits by reducing circuit overhead. It introduces minimal error in the output, which does not significantly affect the application. This paper proposes an approximate multiplier constructed using 5_3 and 5_2 counters. The proposed 5_2 counter delivers two outputs instead of three, thereby achieving 60% compression. The overhead of the 5_2 counter circuit is reduced, achieving a power delay product (PDP) improvement of 18%. This reduction comes with an addition of an 6% error rate. The newly designed multiplier has less delay, where the Mean error distance (MED) is kept as low as possible. The complexity of the 5_2 counter is also reduced since the counter uses only a full adder and three gates. This is achieved by applying various error optimization mechanisms. The error parameters, (i) Error Distance (ED), and (ii) Mean Error Distance (MED) are analyzed and compared with existing works. The proposed multipliers are involved in image contrast application with better Peak Signal to Noise Ratio (PSNR) value.

关键词： Measurement PSNR Image coding Error compensation Very large scale integration Logic gates Delays Standards Optimization Mobile computing

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Structure function of helicity in compressible homogeneous isotropic turbulence

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Physical Review Fluids 2025年第3期10卷 034610-034610页

作者： Running Hu Zheng Yan Runyuan Gan Xinliang Li Changping Yu State Key Laboratory of High Temperature Gas Dynamics Institute of Mechanics Chinese Academy of Sciences Beijing 100190 China School of Engineering Science University of Chinese Academy of Sciences Beijing 100049 China Institute of Applied Physics and Computational Mathematics Beijing 100094 China

Helicity plays an essential role in the interscale dynamics of turbulence. This paper focuses on the compressible effects on helicity cascades via structure functions. We first investigate the spatial-local dynamics of helicity, revealing that helicity is enhanced by pressure gradients along vorticity lines. Then, structure functions are used to describe the multiscale dynamics. The scaling law r2/3 for helicity remains valid in compressible turbulence, as helicity is independent of the compressive components. Additional pressure and divergence terms are introduced in the new third-order relation for helicity in compressible turbulence. The pressure term is related to the pressure gradients along the vorticity lines and plays a dominant role in the dissipative range. The divergence term is mainly induced by the mixed structure function of divergence and helicity, significantly contributing to inverse helicity cascades in the inertial range.

关键词： Vorticity

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Conformal Graph-level Out-of-distribution Detection with Adaptive Data Augmentation 34

Conformal Graph-level Out-of-distribution Detection with Ada...

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34th ACM Web Conference, WWW 2025

作者： Lin, Xixun Cao, Yanan Sun, Nan Zou, Lixin Zhou, Chuan Zhang, Peng Zhang, Shuai Zhang, Ge Wu, Jia Institute of Information Engineering Chinese Academy of Sciences Beijing China Institute of Information Engineering Chinese Academy of Sciences School of Cyber Security University of Chinese Academy of Sciences Beijing China School of Cyber Science and Engineering Wuhan University Wuhan China Academy of Mathematics and Systems Science CAS School of Cyber Security University of Chinese Academy of Sciences Beijing China Cyberspace Institute of Advanced Technology Guangzhou University Guangzhou China Academy of Mathematics and Systems Science CAS Beijing China School of Computer Science and Technology Donghua University Shanghai China Department of Computing Macquarie University Sydney Australia

ISBN: (纸本)9798400712746

Graph-level out-of-distribution (OOD) detection, which attempts to identify OOD graphs originated from an unknown distribution, is a vital building block for safety-critical applications in Web and society. Current approaches concentrate on how to learn better graph representations, but fail to provide any statistically guarantee on detection results, therefore impeding their deployments in the scenario where detection errors would result in serious consequences. To overcome this critical issue, we propose the Conformal Graph-level Out-of-distribution Detection (CGOD), extending the theory of conformal prediction to graph-level OOD detection with a rigorous control over the false positive rate. In CGOD, we develop a new aggregated non-conformity score function based on the proposed adaptive data augmentation. Through the guidance from two designed metrics, i.e., score consistency and representation diversity, our augmentation strategy can generate multiple non-conformity scores, and aggregating these generated non-conformity scores together is robust to the misleading information. Meanwhile, our score function can perceive the subsequent process of conformal inference, enabling the aggregated non-conformity score to be adaptive to different input graphs and deriving a more accurate score estimation. We conduct experiments on multiple real-world datasets with different empirical settings. Extensive results and model analyses demonstrate the superior performance of our approach over several competitive baselines. © 2025 Copyright held by the owner/author(s).

关键词： conformal prediction graph neural networks Graph-level out-of-distribution detection

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Convolutional autoencoder-based deep learning for intracerebral hemorrhage classification using brain CT images

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Cognitive Neurodynamics 2025年第1期19卷 1-13页

作者： Nageswara Rao, B. Acharya, U. Rajendra Tan, Ru-San Dash, Pratyusa Mohapatra, Manoranjan Sabut, Sukanta Sensing and Computing Lab School of Electronics Engineering Kalinga Institute of Industrial Technology Bhubaneswar India School of Mathematics Physics and Computing University of Southern Queensland Springfield Central QLD Australia National Heart Centre Singapore Singapore Singapore Duke-NUS Medical School Singapore Singapore Department of Computer Science and Engineering Heritage Institute of Technology Kolkata India Department of Radio-Diagnosis Kalinga Institute of Medical Science Bhubaneswar India

Intracerebral haemorrhage (ICH) is a common form of stroke that affects millions of people worldwide. The incidence is associated with a high rate of mortality and morbidity. Accurate diagnosis using brain non-contrast computed tomography (NCCT) is crucial for decision-making on potentially life-saving surgery. Limited access to expert readers and inter-observer variability imposes barriers to timeous and accurate ICH diagnosis. We proposed a hybrid deep learning model for automated ICH diagnosis using NCCT images, which comprises a convolutional autoencoder (CAE) to extract features with reduced data dimensionality and a dense neural network (DNN) for classification. In order to ensure that the model generalizes to new data, we trained it using tenfold cross-validation and holdout methods. Principal component analysis (PCA) based dimensionality reduction and classification is systematically implemented for comparison. The study dataset comprises 1645 (“ICH” class) and 1648 (“Normal” class belongs to patients with non-hemorrhagic stroke) labelled images obtained from 108 patients, who had undergone CT examination on a 64-slice computed tomography scanner at Kalinga institute of Medical sciences between 2020 and 2023. Our developed CAE-DNN hybrid model attained 99.84% accuracy, 99.69% sensitivity, 100% specificity, 100% precision, and 99.84% F1-score, which outperformed the comparator PCA-DNN model as well as the published results in the literature. In addition, using saliency maps, our CAE-DNN model can highlight areas on the images that are closely correlated with regions of ICH, which have been manually contoured by expert readers. The CAE-DNN model demonstrates the proof-of-concept for accurate ICH detection and localization, which can potentially be implemented to prioritize the treatment using NCCT images in clinical settings. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.

关键词： Autoencoder CAE-DNN Deep learning ICH detection Intracerebral hemorrhage (ICH) Non-contrast CT

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Advancing Carriers Mobility in MnSb2Te4 Thermoelectrics via Tailored Textures and Vacancy Modification

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Advanced Energy Materials 2025年第0期

作者： Xu, Xiao Mao, Dasha Liedke, Maciej Oskar Butterling, Maik Cui, Juan Wang, Jinghan Luo, Yiyuan Ge, Zhenhua Hirschmann, Eric Wagner, Andreas He, Jiaqing Nielsch, Kornelius He, Ran Institute for Metallic Materials Leibniz Institute for Solid State and Materials Research Dresden01069 Germany Department of Physics Southern University of Science and Technology Shenzhen518055 China Institute of Radiation Physics Helmholtz-Zentrum Dresden-Rossendorf Dresden01328 Germany Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China Faculty of Materials Science and Engineering Kunming University of Science and Technology Kunming650093 China

Enhancing carrier mobility plays a crucial role in significantly improving thermoelectric performance. However, due to the lack of a systematic strategy, achieving high mobility remains an elusive goal for most compounds. In this study, the hot-forging method is applied to polycrystalline MnSb₂Te₄, achieving a remarkable 300% improvement in carrier mobility. Through electron backscattering diffraction microstructural analysis, it is demonstrated how optimizing textures can accelerate carrier movement in MnSb₂Te₄ bulk materials. Moreover, theoretical calculations, combined with experimental positron annihilation spectroscopy, reveal that Te vacancies help counteract intrinsic cation defects, leading to a simultaneous increase in carrier mobility. As a result, the hot-forged MnSb₂Te₄ specimen, with a diameter of 15 mm, reaches a record-high maximum figure of merit (ZT) value of 1.3 at 773 K and an impressive average ZT of 0.7 between 323 and 773 K. The experimental output efficiency of 4.6%, observed at 773 K on the MnSb₂Te₄-based single-leg module, further confirms that the improved transport properties are due to the enhanced carrier mobility. This comprehensive study offers valuable insights into mobility enhancement in MnSb₂Te₄ and provides a promising direction for exploring similar improvements in other thermoelectric materials. © 2025 The Author(s). Advanced Energy Materials published by Wiley-VCH GmbH.

关键词： Positron annihilation

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Optimization of Crop Yields in Sustainable Agriculture: Application of Big Data Analytics and Artificial Intelligence

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Remote Sensing in Earth Systems sciences 2025年第2期8卷 375-386页

作者： Nimma, Divya Dhanke, Jyoti A. Murthy, G.S.N. Khandekar, Sachin Dadu Hymavathi, J. Jangir, Pradeep Singh, Mahesh Department of Computational Science University of Southern Mississippi Hattiesburg 39406 MS United States Department of Engineering Science (Mathematics) Bharati Vidyapeeth’s College of Engineering Lavale Maharashtra Pune India Department of CSE Aditya University Surampalem India Department of Civil Engineering Sinhgad College of Engineering Maharashtra Pune India Department of CSE Koneru Lakshmaiah Education Foundation Andhra Pradesh Vaddeswaram India Department of Biosciences Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Chennai India Hourani Center for Applied Scientific Research Al-Ahliyya Amman University Amman 19328 Jordan Department of Robotics and Automation Symbiosis Institute of Technology Pune Campus Symbiosis International (Deemed University) Pune India

Making informed economic decisions based on agricultural data is challenging without proper crop management. Data has become the single most important part of modern farming, and its rapid evolution is a major contributor to the rise of “smart farming.” Using sensors to gather objective data with the end aim of increasing productivity and sustainability has several advantages. Information that might boost productivity while decreasing resource waste and pollution levels is essential for managed farms. The cornerstone of future sustainable farming will be data-driven agriculture using robotic solutions based on AI-based techniques. This paper examines the current state of advanced farm management systems, discussing topics like data acquisition in crop fields and variable rate applications, to assist farmers in saving money, protecting the environment, and transforming food production so that it can sustainably keep up with the expected increase in population. The advent of machine learning, big data technologies, and high-performance computers has opened up new avenues for data-intensive research in the interdisciplinary subject of agro technology. These avenues of exploration have been aided by the development of more capable computers. A comprehensive literature review on the issue of the applications of machine learning in agricultural manufacturing is provided in this research. Machine learning has shown its utility in agriculture via two applications: filtering and categorizing products. The use of machine learning on sensor data is transforming conventional farm management systems into AI-enabled programs. These services provide farmers instantaneous, complete access to ideas and insights that may guide their decisions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

关键词： Artificial intelligence Big data analytics Optimize crop yields Sustainable agriculture

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Cognitive Large Language Model in Social Media with Local Memory

Cognitive Large Language Model in Social Media with Local Me...

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Data science, Agents & Artificial Intelligence (ICDSAAI), International Conference on

作者： Vigneshwaran N A. Vijayaraj V. P. Murugan R. Jebakumar N. Mageshkumar R. Megavannan Department of IT R.M.K. Engineering College Chennai Department of Mathematics Panimalar Engineering College Chennai Department of Computing Technologies SRM Institute of Science and Technology Chennai Department of Computer Science and Technology Madanapalle Institute of Technology & Science Andhra Pradesh Faculty of Management SRM Institute of Science and Technology

ISBN: (数字)9798331537555

ISBN: (纸本)9798331537562

Enter the era of social media reimagined! This research taps into an interesting combination of advanced Artificial Intelligence, with large language models such as ChatGPT and GEMINI your favorite social platform. Personal information of each user is armed with voice commands and LLM. But this is the first. LLM talk to each other, exchange information. face recognition adds an extra layer in the mass layer the excitement of your Chatbot sharing only the right information Your account security level private, reserved or public. When it comes to security. We got you covered Choose between playing low key or just sharing just the right number of juicy details. Plus, all the classic features It's still fun, like scrolls and scrolls.

关键词： Social networking (online) Large language models Face recognition Oral communication Chatbots Security

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