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Lectures on the Error Analysis of Interpolation on Simplicial Triangulations without the Shape-Regularity Assumption, Part 2: Lagrange Interpolation on Tetrahedrons

arXiv

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arXiv 2021年

作者： Kobayashi, Kenta Tsuchiya, Takuya Graduate School of Bussiness Administration Hitotsubashi University Kunitachi Japan Center for Mathematical Modeling and Data Science Osaka University Toyonaka Japan

This is the second lecture note on the error analysis of interpolation on simplicial elements without the shape regularity assumption 1. In this manuscript, we explain the error analysis of Lagrange interpolation on (possibly anisotropic) tetrahedrons. This topic is hardly explained in standard textbooks of the mathematical theory of finite element methods. The authors hope that this manuscript will be merged into a new textbook in future. Therefore, this manuscript is not intended to be a research paper. Supposed readers are students and researchers who are familiar with the mathematical theory of the finite element methods. © 2021, CC BY-NC-ND.

关键词： Interpolation

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Securing the light escaping in a Li-Fi network environment

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Procedia Computer science 2022年 201卷 684-689页

作者： D.D. Diambeki R.E. Mandiya K. Kyamakya S.K. Kasereka University of Kinshasa Mathematics and Computer Science Department Kinshasa DR Congo Artificial intelligence Big data and modeLing simulation research center (ABIL) Kinshasa Democratic Republic of the Congo Alpen-Adria-Universitaet Klagenfurt Institute of Smart Systems Technologies Department of Mathematical Sciences Klagenfurt Austria

Nowadays, everyone knows Wi-Fi. The technology that ensures connection of computer equipment. It is now positioned as the easiest way to interconnect multiple end users because It allows user mobility in workspaces, avoids cable clutter within the network coverage, such as offices, homes and so on. Despite these advantages, several scientific studies have shown that this technology can raise security and safety issues and is dangerous to human health, and therefore not suitable for hospital networks. In an attempt to overcome these difficulties, Li-Fi technology based on visible light is beginning to interest researchers. This technology is considered more secure than Wi-Fi because the light can be contained in a physical space and waves can’t pass through walls and other objects. Unfortunately, when the physical environment contains spaces that can escape light to the outdoors, this can be a security risk for Li-Fi because it uses light sources to transmit data. That why, in this paper, the main differences between Wi-Fi and Li-Fi technologies are explained, and a Li-Fi architecture provided with an authentification captive portal and a data transfer security mechanism between end users based on the AES algorithm is proposed. The developed prototype and the architecture proposed guarantee the security of the Li-Fi network even if the physical environment is provided with multiple light escape spaces.

关键词： Li-Fi (Light-Fidelity) VLC (Visible Light Communication) LED (Light Emitting Diode) Photodetector LDR (Light Dependent Resistor) Arduino AES algorithm Captive portal

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Leveraging graph neural networks for supporting Automatic Triage of Patients

arXiv

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arXiv 2024年

作者： Defilippo, Annamaria Veltri, Pierangelo Lió, Pietro Guzzi, Pietro Hiram Dept. Medical and Surgical Sciences Data Analytics Research Center Magna Graecia University of Catanzaro Catanzaro Italy DIMES Department of Informatics Modeling Electronics and Systems UNICAL Rende Cosenza Italy Department of Computer Science and Technology Cambridge University Cambridge United Kingdom Dept. Medical and Surgical Sciences Magna Graecia University of Catanzaro Catanzaro Italy

Patient triage plays a crucial role in emergency departments, ensuring timely and appropriate care based on correctly evaluating the emergency grade of patient conditions. Triage methods are generally performed by human operator based on her own experience and information that are gathered from the patient management process. Thus, it is a process that can generate errors in emergency-level associations. Recently, Traditional triage methods heavily rely on human decisions, which can be subjective and prone to errors. Recently, a growing interest has been focused on leveraging artificial intelligence (AI) to develop algorithms able to maximize information gathering and minimize errors in patient triage processing. We define and implement an AI-based module to manage patients’ emergency code assignments in emergency departments. It uses emergency department historical data to train the medical decision process. data containing relevant patient information, such as vital signs, symptoms, and medical history, are used to accurately classify patients into triage categories. Experimental results demonstrate that the proposed algorithm achieved high accuracy outperforming traditional triage methods. By using the proposed method we claim that healthcare professionals can predict severity index to guide patient management processing and resource allocation. Copyright © 2024, The Authors. All rights reserved.

关键词： Errors

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Machine-learning Accelerated Descriptor Design for Catalyst Discovery: A CO2 to Methanol Conversion Case Study

arXiv

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arXiv 2024年

作者： Pisal, Prajwal Krejčí, Ondřej Rinke, Patrick Department of Applied Physics Aalto University P.O. Box 11000 AALTO FI-00076 Finland Department of Physics Technical University of Munich James-Franck-Strasse 1 Garching85748 Germany Atomistic Modeling Center Munich Data Science Institute Technical University of Munich Walther-Von-Dyck Str. 10 Garching85748 Germany

Transforming CO2 into methanol represents a crucial step towards closing the carbon cycle, with thermoreduction technology nearing industrial application. However, obtaining high methanol yields and ensuring the stability of heterocatalysts remain significant challenges. Herein, we present a sophisticated computational framework to accelerate the discovery of novel thermal heterogeneous catalysts, using machine-learned force fields. We propose a new catalytic descriptor, termed adsorption energy distribution, that aggregates the binding energies for different catalyst facets, binding sites, and adsorbates. The descriptor is versatile and can easily be adjusted to a specific reaction through careful choice of the key-step reactants and reaction intermediates. By applying unsupervised machine learning and statistical analysis to a dataset comprising nearly 160 metallic alloys, we offer a powerful tool for catalyst discovery. Finally, we propose new promising candidate materials such as ZnRh and ZnPt3, which to our knowledge, have not yet been tested, and discuss their possible advantage in terms of stability. © 2024, CC BY.

关键词： Methanol

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A PCA-based fuzzy tensor evaluation model for multiple-criteria group decision making

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Applied Soft Computing 2023年 132卷

作者： Singh, Meenu Pant, Millie Kong, Lingping Alijani, Zahra Snášel, Václav Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee Uttarakhand247667 India Mehta Family School of Data Science and Artificial Intelligence Indian Institute of Technology Roorkee Uttarakhand247667 India Faculty of Electrical Engineering and Computer Science VŠB-TU Ostrava Czech Republic Institute for Research and Applications of Fuzzy Modeling University of Ostrava 30. dubna 22 701 03 Ostrava Czech Republic

Multiple-criteria group decision-making (MCGDM) problems mainly consist of multiple factors and multiple Decision Makers (DMs) or Users, for which dimension extension is necessary when considering all the entries of DMs together. Tensor, a generalized form of a matrix, displays a multi-way array item, which is the most suitable and practical way to represent high-dimensional data without losing any information. In this paper, we first reduce the dimension through Principal Component Analysis (PCA), which helps consider the most-informative criteria. Then, we reintroduced the tensor as a fuzzy-form tensor for the MCGDM problem because of user information uncertainty. We choose Interval-valued Neutrosophic Fuzzy numbers (IVNFNs) as the basis for the tensor form because of their ability to distinguish between truth, indeterminacy, and falsity in the data. Lastly, a Generalized Interval-valued Neutrosophic Fuzzy Weighted Geometric (GIVNFWG) operator is defined. Moreover, a generalized framework for fuzzy-form tensors for high-dimensional MCGDM problems is proposed. The feasibility and efficiency of this proposed process is illustrated for a real-world MCGDM problem of ranking the most efficient Third Party Reverse Logistics Partners (3PRLPs), i.e., recycled fiber-based paper mills for the packaging industry. The obtained results are according to the experts and are validated using sensitivity analysis. This analysis facilitates in assessing the impact on the overall ranking performance of 3PRLPs by considering various combinations of environment and technological sub-criteria. © 2022 Elsevier B.V.

关键词： Principal component analysis

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Cohomology and Deformation Theory of O-Operators on Hom-Lie Conformal Algebras

SSRN

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SSRN 2024年

作者： Asif, Sania Wang, Yao Mosbahi, Bouzid Basdouri, Imed School of Mathematics and Statistics Nanjing University of Information Science and Technology Jiangsu Nanjing210044 China Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Jiangsu Nanjing210044 China University of Sfax Department of Mathematics Faculty of Sciences of Sfax BP 1171 Sfax3000 Tunisia University of Gafsa Faculty of Sciences of Gafsa Gafsa2112 Tunisia

In the present paper, we aim to introduce the cohomology of $\mathcal{O}$-operators defined on the Hom-Lie conformal algebra concerning the given representation. To obtain the desired results, we describe three different cochain complexes and discuss the interrelation of their coboundary operators. And show that differential maps on the graded Lie algebra can also be defined by using the Maurer-Cartan element. We further find out that, the $\mathcal{O}$-operator on the given Hom-Lie conformal algebra serves as a Maurer-Cartan element and it leads to acquiring the notion of a differential map in terms of $\mathcal{O}$-operator $\delta_\T$. Next, we provide the notion of Hom-pre-Lie conformal algebra, that induces a sub-adjacent Hom-Lie conformal algebra structure. The differential $\delta_{\b,\a}$ of this sub-adjacent Hom-Lie conformal algebra is related to the differential $\delta_\T$. Finally, we provide the deformation theory of $\mathcal{O}$-operators on the Hom-Lie conformal algebras as an application to the cohomology theory, where we discuss linear and formal deformations in detail. © 2024, The Authors. All rights reserved.

关键词： Algebra

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Time Changes in the VEGF-A Concentration Gradient Lead Neovasculature to Engage in Stair-Like Growth

Time Changes in the VEGF-A Concentration Gradient Lead Neova...

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International Symposium on Fusion of Mathematics and Biology, 2020

作者： Ito, Yukinobu Minerva, Dhisa Tasaki, Sohei Yoshida, Makoto Suzuki, Takashi Goto, Akiteru Department of Cellular and Organ Pathology Graduate School of Medicine Akita University 1-1-1 Hondo Akita Akita010-8543 Japan Center for Mathematical Modeling and Data Science Osaka University Osaka Japan Institute for the Advanced Study of Human Biology Kyoto University Kyoto Japan

ISBN: (纸本)9789811648656

Arteriovenous malformations consist of tangles of arteries and veins that are often connected by a fistula. The causes of and mechanisms underlying the development of these clinical entities are not fully understood. We previously reported a novel in vivo angiogenesis model as a useful disease model of arteriovenous malformation. With this model, the arterial graft was collected from the left carotid artery and sutured to the left jugular vein as a patchwork. The neovasculature extended from the branch of the subclavian artery toward the arterial graft. We measured the neovasculature, which had sprouted from arterioles, in the tissue samples. In the present study, we collected the arterial patch graft and adipose tissue surrounding the arterial graft and examined the distribution of the VEGF concentration by an enzyme-linked immunosorbent assay. At the area most distant from the arterial graft, the VEGF-A concentration changed over time in a sine wave pattern that gradually attenuated. A mathematical model was then constructed using the results, and a mathematical simulation of the neovasculature growth was performed. The new vessels grew in a stair-like pattern in this simulation, a result that matched those obtained through histological measurements. © 2021, Springer Nature Singapore Pte Ltd.

关键词： Tissue

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Stability of Vegetation Net Primary Productivity and Climate Impacts in China in the Following Century

全球变化数据仓储（中英文）

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全球变化数据仓储（中英文） 2023年第6期 1-3页

作者： CHEN Xing WANG Junbang HE Qifan WANG Chunyu YE Hui National Ecosystem Science Data Center Key Laboratory of Ecosystem Network Observation and ModelingInstitute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijing 100101China University of Chinese Academy of Sciences Beijing 100049China College of Tourism and Geography Jiujiang UniversityJiujiang 332005JiangxiChina Qilu Normal University Jinan 205200China

In order to investigate NPP and its stability at long time scales of nearly 100 years under future climate scenarios,the authors developed the dataset of Stability of Vegetation Net Primary Productivity and Climate Impacts in China in the Following Century using HadGEM2-ES data scenarios based on the Regional Climate Model RegCM4.6 and *** dataset includes:(1)mean NPP values and their trends from 2006 to 2099 under RCP4.5 and RCP8.5 scenarios;(2)multi-year mean NPP stability values for the full(2006-2099),early(2006-2035),mid(2036-2065)and late(2066-2099)*** spatial resolution of the data is 0.1°.The dataset is archived in 17 data files with data size of 15.0 MB(Compressed into one file with 4.26 MB).One of the research results based on this dataset was published in Acta Geographica Sinica,Vol.78,No.3,2023.

关键词：

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10m分辨率全球红树林空间分布制图与分析

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science Bulletin 2023年第12期68卷 1306-1316,M0004页

作者：贾明明王宗明毛德华任春颖宋开山赵传朋王超萧向明王野乔 International Research Center of Big Data for Sustainable Development Goals Beijing 100094China Key Laboratory of Wetland Ecology and Environment Northeast Institute of Geography and AgroecologyChinese Academy of SciencesChangchun 130102China Department of Natural Resources Science University of Rhode IslandKingston RI 02881USA State Key Laboratory of Information Engineering in Surveying Mapping and Remote SensingWuhan UniversityWuhan 430079China Department of Microbiology and Plant Biology Center for Earth Observation and ModelingUniversity of OklahomaNorman OK 02881USA

由于其独特的海陆过渡特性和极高的物质生产能力,红树林被列为国际湿地生态保护和生物多样性保护的重要对象.准确可靠的大尺度空间格局信息是红树林湿地保护与利用的重要基础.然而,现有大尺度数据集缺乏空间细节和合理的地理信息.在此,... 详细信息

由于其独特的海陆过渡特性和极高的物质生产能力,红树林被列为国际湿地生态保护和生物多样性保护的重要对象.准确可靠的大尺度空间格局信息是红树林湿地保护与利用的重要基础.然而,现有大尺度数据集缺乏空间细节和合理的地理信息.在此,本文使用面向对象的随机森林分类方法,结合专家后处理,创建了具有时空一致性的10 m分辨率全球红树林数据集,命名为“高分辨率全球红树林(HGMF2020)”.然后,从保护、威胁和抵御海洋灾害的角度分析了全球红树林的状况.结果表明:(1) 2020年全球红树林面积为145068 km^(2),其中亚洲红树林面积最大(39.2%);(2)南亚红树林的保护比例较高,斑块整体性较高,而东亚和东南亚红树林面临严峻的威胁;(3)近99%的红树林斑块宽度大于100 m,表明几乎所有的红树林在抵御热带风暴等海洋灾害方面均有一定作用.本文提供了高精度全球红树林空间分布数据集,并分析其斑块信息,研究结果和讨论可为全球红树林生态系统的保护和合理利用提供决策依据,对于我国履行国际湿地公约、进行环境外交具有积极意义.

关键词：物质生产能力红树林生态系统海洋灾害时空一致性国际湿地公约生物多样性保护过渡特性地理信息

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A Skew Normal Mixed Models with Noise Estimation and Anisotropic Spatial Information Constraints

SSRN

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SSRN 2022年

作者： Zhang, Kaili Ma, Lianhong Cao, Chunzheng Yang, Jianwei Zhang, Zhichao Chen, Yunjie School of Mathematics and Statistics Nanjing University of Information Science Nanjing210044 China Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China

Accurate image segmentation facilitates image analysis. Gaussian mixture models (GMMs) are widely used for image segmentation due to their low complexity and high accuracy. However, the model assumes that the intensity distributions of images are symmetric, which makes it hard to obtain ideal results for images with asymmetric distributions. In addition, the model dose not consider any noise, which makes it difficult to obtain ideal distribution fitting results when images contain severe noises. And the model does not use any spatial information, which makes it sensitive to noise. To address these issues, we model the noise using a normal distribution and couple it into a skew normal mixture model to reduce the model's sensitivity to asymmetric distributions and noise. To further reduce the effect of noise, we propose a new anisotropic spatial information constraint term that preserves detailed information while reducing the effect of noise. Finally, an improved EM algorithm is proposed to solve the parameters of the model. Experimental results on synthetic and natural images illustrate that our model outperforms other state-of-the-art segmentation methods. © 2022, The Authors. All rights reserved.

关键词： Image segmentation

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