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CONSTRUCTING COARSE-SCALE BIFURCATION DIAGRAMS FROM SPATIO-TEMPORAL OBSERVATIONS OF MICROSCOPIC SIMULATIONS: A PARSIMONIOUS MACHINE LEARNING APPROACH

arXiv

引用

arXiv 2022年

作者： Evangelos, Galaris Gianluca, Fabiani Ioannis, Gallos Ioannis, Kevrekidis Constantinos, Siettos Dipartimento di Matematica e Applicazioni "Renato Caccioppoli" Universitá degli Studi di Napoli Federico II Naples Italy Scuola Superiore Meridionale Universitá degli Studi di Napoli Federico II Naples Italy School of Applied Mathematical and Physical Sciences National Technical University of Athens Greece Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Department of Medicine Johns Hopkins University BaltimoreMD United States Dipartimento di Matematica e Applicazioni"Renato Caccioppoli" Scuola Superiore Meridionale Universitá degli Studi di Napoli Federico II Naples Italy

We address a three-tier data-driven approach to solve the inverse problem in complex systems modelling from spatio-temporal data produced by microscopic simulators using machine learning. In the first step, we exploit manifold learning and in particular parsimonious Diffusion Maps using leave-one-out cross-validation (LOOCV) to both identify the intrinsic dimension of the manifold where the emergent dynamics evolve and for feature selection over the parametric space. In the second step, based on the selected features, we learn the right-hand-side of the effective partial differential equations (PDEs) using two machine learning schemes, namely shallow Feedforward Neural Networks (FNNs) with two hidden layers and single-layer Random Projection Networks(RPNNs) which basis functions are constructed using an appropriate random sampling approach. Finally, based on the learned black-box PDE model, we construct the corresponding bifurcation diagram, thus exploiting the numerical bifurcation analysis toolkit. For our illustrations, we implemented the proposed method to construct the one-parameter bifurcation diagram of the 1D FitzHugh-Nagumo PDEs from data generated by D1Q3 Lattice Boltzmann simulations. The proposed method was quite effective in terms of numerical accuracy regarding the construction of the coarse-scale bifurcation diagram. Furthermore, the proposed RPNN scheme was ∼ 20 to 30 times less costly regarding the training phase than the traditional shallow FNNs, thus arising as a promising alternative to deep learning for solving the inverse problem for high-dimensional PDEs. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

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The Waiting-Time Paradox

arXiv

引用

arXiv 2020年

作者： Masuda, Naoki Porter, Mason A. Department of Mathematics State University of New York at Buffalo BuffaloNY United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY United States Department of Mathematics University of California Los Angeles Los AngelesCA United States

Suppose that you’re going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer — possibly much longer — than what the bus schedule suggests intuitively. This phenomenon, called the waiting-time paradox, has a purely mathematical origin. Different buses arrive with different intervals, leading to this paradox. In this article, we look at the waiting-time paradox, explain why it happens, and explore some of its implications (beyond the possibility of being late for school). Copyright © 2020, The Authors. All rights reserved.

关键词： Buses

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Single and Multi-Hop Question-Answering Datasets for Reticular Chemistry with GPT-4-Turbo

arXiv

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arXiv 2024年

作者： Rampal, Nakul Wang, Kaiyu Burigana, Matthew Hou, Lingxiang Al-Johani, Juri Sackmann, Anna Murayshid, Hanan S. Al-Sumari, Walaa Abdullah Al-Abdulkarim, Arwa M. Al-Hazmi, Nahla Eid Al-Awad, Majed O. Borgs, Christian Chayes, Jennifer T. Yaghi, Omar M. Department of Chemistry University of California BerkeleyCA94720 United States Kavli Energy Nanoscience Institute University of California BerkeleyCA94720 United States Bakar Institute of Digital Materials for the Planet College of Computing Data Science and Society University of California BerkeleyCA94720 United States Department of Electrical Engineering and Computer Sciences University of California BerkeleyCA94720 United States Data Services Librarian University of California Berkeley Library United States Department of Mathematics University of California BerkeleyCA94720 United States Department of Statistics University of California BerkeleyCA94720 United States Riyadh12354 Saudi Arabia Hydrogen Technologies Institute King Abdulaziz City for Science and Technology P.O. Box 6086 Riyadh11442 Saudi Arabia KACST−UC Berkeley Center of Excellence for Nanomaterials for Clean Energy Applications King Abdulaziz City for Science and Technology Riyadh11442 Saudi Arabia

The rapid advancement in artificial intelligence and natural language processing has led to the development of large-scale datasets aimed at benchmarking the performance of machine learning models. Herein, we introduce 'RetChemQA,' a comprehensive benchmark dataset designed to evaluate the capabilities of such models in the domain of reticular chemistry. This dataset includes both single-hop and multi-hop question-answer pairs, encompassing approximately 45,000 Q&As for each type. The questions have been extracted from an extensive corpus of literature containing about 2,530 research papers from publishers including NAS, ACS, RSC, Elsevier, and Nature Publishing Group, among others. The dataset has been generated using OpenAI's GPT-4 Turbo, a cutting-edge model known for its exceptional language understanding and generation capabilities. In addition to the Q&A dataset, we also release a dataset of synthesis conditions extracted from the corpus of literature used in this study. The aim of RetChemQA is to provide a robust platform for the development and evaluation of advanced machine learning algorithms, particularly for the reticular chemistry community. The dataset is structured to reflect the complexities and nuances of real-world scientific discourse, thereby enabling nuanced performance assessments across a variety of tasks. The dataset is available at the following link: https://***/nakulrampal/RetChemQA. © 2024, CC BY.

关键词： Machine learning

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Corrigendum to “Group theoretic approach to (4 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation” [Alex. Eng. J. 118 (2025) 449–465]

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Alexandria engineering Journal 2025年 121卷 18-18页

作者： Muhammad Usman Akhtar Hussain Magda Abd El-Rahman Jorge Herrera College of Electrical and Mechanical Engineering (CEME) National University of Sciences and Technology (NUST) H-12 Islamabad 44000 Pakistan Department of Mathematics and Statistics The University of Lahore Lahore Pakistan Department of Physics College of Science King Khalid University Abha 61413 Saudi Arabia Facultad de Ciencias Naturales e Ingenieria Universidad de Bogota Jorge Tadeo Lozano Bogota 110311 Colombia

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Analysis of Exertion with Relative Grading Mechanism in Academics Using Computational Technique

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IOP Conference Series: Materials Science and engineering 2021年第1期1099卷

作者： Nagaraju Dasari Mahendra Parihar Mohiddin Shaw Shaik Department of Mathematics and Statistics Manipal University Jaipur Jaipur-303007 India Mukesh Patel School of Technology Management and Engineering SVKM's NMIMS University Mumbai India Department of Mathematics Narasaraopeta Engineering College Narasaraopet-522601 India

Evaluation process is an integral part of academic system in order to monitor the performance of students from many perspectives. Since, recent past lots of methodological changes has been taken places in evaluation process from traditional one. Many experts from concerned domain claims the superiority of one method over other but still dilemma continue with reference to optimum or appropriate method. In this connection even very recently being used to a maximum extent in Indian context too is the 'Grade Method'. However, even 'Grade Method' is also not completely free from certain controversies. That is, though grades were initially meant to serve various pedagogical purposes, grading systems remain controversial and hotly debated when those doesn't give recompensing results. Some argued that grades are psychologically harmful. Thus, given certain limitations of existing methods in some respect, the current study has been undertaken in order to address few issues associated with minimum passing grade and cut-off mark for highest grade - resulting out of relative grading, Therefore, in this article, through mathematical computation we propose acceptable ranges for the parameters mean and standard deviation-respectively to have appropriate mechanism and hence can make evaluation process more effective and applicable in various conditions.

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Use your smartphone to observe sound phenomenon and understand the concepts

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AIP Conference Proceedings 2023年第1期2572卷

作者： Ade Yeti Nuryantini Rizki Zakwandi Muhamad Ari Ariayuda 11Department of Physics Education State Islamic University Sunan Gunung Djati Bandung Bandung Indonesia 2Master Program of Physics Education Faculty of Mathematics and Natural Sciences Universitas Negeri Yogyakarta Yogyakarta Indonesia 3Mechanical Engineering Department Faculty of Engineering Universitas Diponegoro Semarang Indonesia

Smartphone sensors have been widely researched and published in literature by experts to be used in physics learning. This paper presents the use of smartphone sensors and applications as a measuring instrument in the classical sound wave experiment adapted from physics textbooks at school or university. Tone generator, sound meter, and audio autocorrelation were used in the experiment to visualize sound as a propagating vibration, sound waves as mechanical waves, characteristics of sound waves (loud and soft or high-pitched or low-pitched), sound range, and sound power. The experimental results presented are expected to help students understand the concept of sound waves.

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Six-State Continuous Processing Model for a New Theory of Computing 2nd

Six-State Continuous Processing Model for a New Theory of Co...

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2nd SLAAI-International Conference on Artificial Intelligence, SLAAI-ICAI 2018

作者： Weerakoon, Chinthanie Karunananda, Asoka Dias, Naomal Department of Statistics & Computer Science University of Kelaniya KelaniyaDalugama Sri Lanka Department of Computational Mathematics University of Moratuwa MoratuwaKatubedda Sri Lanka Department of Computer Systems Engineering University of Kelaniya KelaniyaDalugama Sri Lanka

ISBN: (纸本)9789811391286

In contrast to the computation in Von-Neumann Architecture, the human mind executes processing in the brain by improving speed and accuracy over execution cycles. Further, it has been postulated that the memory is a result of continuous processing and is not separated from processing in the human mind. Similar to that mind model, a six-state continuous processing model with the states New, Ready, Running, Blocked, Sleep and Terminate, has been proposed to implement a special compiler which consists of conditionally evolving memory that aids in improving performance in conventional computation by exploiting 24-Casual Relations explained in Buddhist Theory of Mind. The experiments have been conducted to demonstrate how the proposed computing model increases the performance of execution of source codes and compilers. The result shows a clear increase of performance in computation by avoiding overloading the memory, and ensuring the execution of high quality code segments at the right time. © 2019, Springer Nature Singapore Pte Ltd.

关键词： Computation theory

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On Coupling Lemma and Stochastic Properties with Unbounded Observables for 1-d Expanding Maps

arXiv

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arXiv 2020年

作者： Chen, Jianyu Zhang, Hong-Kun Zhang, Yiwei School of Mathematical Sciences Center for Dynamical Systems and Differential Equations Soochow University SuzhouJiangsu215006 China Department of Mathematics and Statistics University of Massachusetts Amherst AmherstMA01003 United States School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Hua-Zhong University of Sciences and Technology Wuhan430074 China

In this paper, we establish a coupling lemma for standard families in the setting of piecewise expanding interval maps with countably many branches. Our method merely requires that the expanding map satisfies Chernov’s one-step expansion at q-scale and eventually covers a magnet interval. Therefore, our approach is particularly powerful for maps whose inverse Jacobian has low regularity and those who does not satisfy the big image property. The main ingredients of our coupling method are two crucial lemmas: the growth lemma in terms of the characteristic Z function and the covering ratio lemma over the magnet interval. We first prove the existence of an absolutely continuous invariant measure. What is more important, we further show that the growth lemma enables the liftablity of the Lebesgue measure to the associated Hofbauer tower, and the resulting invariant measure on the tower admits a decomposition of Pesin-Sinai type. Furthermore, we obtain the exponential decay of correlations and the almost sure invariance principle (which is a functional version of the central limit theorem). For the first time, we are able to make a direct relation between the mixing rates and the Z function, see (2.7). The novelty of our results relies on establishing the regularity of invariant density, as well as verifying the stochastic properties for a large class of unbounded observables. Finally, we verify our assumptions for several well known examples that were previously studied in the literature, and unify results to these examples in our framework. Copyright © 2020, The Authors. All rights reserved.

关键词： Inverse problems

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Leader-following Consensus of Linear Fractional-order Multi-agent Systems via Event-triggered Control Strategy

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IFAC-PapersOnLine 2020年第2期53卷 2909-2914页

作者： Bo Chen Jiangping Hu Yiyi Zhao Bijoy Kumar Ghosh School of Automation Engineering University of Electronic Science and Technology of China Chengdu 611731 China School of Business Administration Southwestern University of Finance and Economics Chengdu 611130 China Department of Mathematics and Statistics Texas Tech University Lubbock TX 79409-1042 USA

Many complex systems can be more accurately described by fractional-order models. In this paper, a leader-following consensus problem of fractional-order multi-agent systems (FOMASs) is firstly formulated and then an event-trigger consensus control is proposed for each agent. Under the assumption that the interconnection network topology has a spanning tree, consensus of the closed-loop FOMAS is analyzed with the help of the Mittag-Leffler functions and stability theory of fractional-order differential equations. It is shown that Zeno behavior can be avoided. Simulation results are presented to demonstrate the effectiveness of the theoretical results.

关键词： Leader-following consensus fractional-order multi-agent system distributed event-trigger control Zeno behavior Mittag-Leffler function

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Heat transfer and irreversibility analysis in porous vertical disk configuration with Navier slip, thermal jump and quadratic Radiation: Numerical study using Corcione's correlation

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Journal of Radiation Research and Applied Sciences 2025年第3期18卷

作者： Khadija Rafique Zafar Mahmood Hamiden Abd El-Wahed Khalifa Emad A.A. Ismail Fuad A. Awwad Abhinav Kumar Seham Sh Tantawy Department of Mathematics and Statistics Hazara University Mansehra Pakistan College of Mechanical and Vehicle Engineering Hunan University Changsha Hunan 410082 PR China Department of Operations and Management Research Faculty of Graduate Studies for Statistical Research Cairo University Giza 12613 Egypt Department of Quantitative Analysis College of Business Administration King Saud University P.O. Box 71115 Riyadh 11587 Saudi Arabia Department of Nuclear and Renewable Energy Ural Federal University Named after the First President of Russia Boris Yeltsin Ekaterinburg 620002 Russia Centre for Research Impact & Outcome Chitkara University Institute of Engineering and Technology Chitkara University Rajpura 140401 Punjab India Department of Mechanical Engineering and Renewable Energy Technical Engineering College The Islamic University Najaf Iraq Department of Mathematics Faculty of Education Ain Shams University Roxy Cairo Egypt

This study presents the Corcione correlation, emphasizing the effects of fluid temperature, particle volume fraction, and particle size on the improvement of nanofluid heat transfer rate. This study examines the stagnation point flow of a nanofluid consisting of A l 2 O 3 / H 2 O across a vertically extending or shrinking disk. The study is conducted for nanoparticle sizes of 28 , 30 , and 45 nm, with volume concentrations reaching up to 4 %. The Navier velocity slip and thermal slip conditions enhance the mathematical model. It also looks at the effects of magnetohydrodynamics, suction, porous media, Joule heating, quadratic thermal radiation, viscous dissipation, and the production of entropy. The bvp4c solver numerically solves the system of ordinary differential equations created by the similarity transformation of the partial differential equations. For both the stretching and shrinking scenarios, graphs and tables illustrate the effects of several relevant factors. In the event of stretching, the velocity profile exhibits a declining trend for the Navier slip parameter, porosity, magnetic field, and mass suction parameters; in the case of shrinking, however, the opposite behavior is seen. The temperature profile increases with the nanoparticle volume fraction, radiation, and temperature ratio factors in both scenarios. Both cases show an increase in entropy production for the brinkman number and a reduction in entropy generation for the temperature difference. Skin friction and Nusselt number are measured for dp = 28, 30, and 45 nm nanoparticle sizes. The Nusselt number is larger for dp = 45 nm than 28 nm and 30 nm, while skin friction is higher for 28 nm. There exists an almost perfect concordance (with a relative error of around 0 %) between the present and previous results.

关键词： Stagnation point flow Mixed convection Navier slip Quadratic radiation Entropy generation Corcione's correlation Numerical analysis

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