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Automated symbolic and numerical testing of DLMF formulae using computer algebra systems

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arXiv 2021年

作者： Cohl, Howard S. Greiner-Petter, André Schubotz, Moritz Applied and Computational Mathematics Division National Institute of Standards and Technology Mission ViejoCA United States Dept. of Computer and Information Science University of Konstanz Konstanz Germany

We have developed an automated procedure for symbolic and numerical testing of formulae extracted from the NIST Digital Library of Mathematical Functions (DLMF). For the NIST Digital Repository of Mathematical Formulae, we have developed conversion tools from semantic LATEX to the computer Algebra System (CAS) MAPLE which relies on Youssef’s part-of-math tagger. We convert a test data subset of 4,078 semantic LATEX DLMF formulae to the native CAS representation and then apply an automated scheme for symbolic and numerical testing and verification. Our framework is implemented using Java and MAPLE. We describe in detail the conversion process which is required so that the CAS can correctly interpret the mathematical representation of the formulae. We describe the improvement of the effectiveness of our automated scheme through incremental enhancement (making more precise) of the mathematical semantic markup for the formulae. © 2021, CC BY.

关键词： Automation

Mathematical modeling and simulation of magnetized bioconvective nanoliquid flow capturing Brownian motion, multiple slip, thermophoresis and gyrotactic microorganisms configured by rotating disk

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Partial Differential Equations in applied mathematics 2024年 12卷

作者： Garalleh, Hakim AL Khan, Sami Ullah Waqas, M. Zamri, Nurnadiah Abdullaeva, Barno Gupta, Manish Department of Mathematical Science College of Engineering University of Business and Technology Jeddah 21361 Saudi Arabia Department of Mathematics Namal University Mianwali 42250 Pakistan NUTECH School of Applied Sciences and Humanities National University of Technology Islamabad 44000 Pakistan Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Faculty of Informatics and Computing University Sultan Zainal Abidin Besut Campus Terengganu Besut 22200 Malaysia Department of Mathematics and Information Technologies Vice-Rector for Scientific Affairs Tashkent State Pedagogical University Tashkent Uzbekistan Division of Research and Development Lovely Professional University Phagwara India

This analysis describes the bioconvective flow of nanofluid due to rotation of disk. A uniform suspension of nanofluid between microorganisms is considered to analyze the applications of bioconvection. The nanofluid assumed to be electrically conducting with amplification of magnetic force. The problem is entertained in presence of different slip features including velocity, temperature, concentration and microorganisms. The formulation of problem in simplified form is attained via dimensionless variables. Shooting numerical scheme is used to compute the simulations. Physical interpretation and visualization of results is observed in view of parameters. The observations concluded that interaction of slip effects reduces the velocity profile but enhances nanofluid temperature and concentration profiles. The temperature profile increases with thermophoresis parameter. Current results comprise applications in cooling of electronics devices, thin film coating, gas turbines engine, energy systems etc. © 2024

关键词： Bioconvection Multiple slip effects Nanoparticles Numerical computations Rotating disks

Learning shared neural manifolds from multi-subject FMRI data

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arXiv 2021年

作者： Huang, Jessie Busch, Erica L. Wallenstein, Tom Gerasimiuk, Michal Benz, Andrew Lajoie, Guillaume Wolf, Guy Turk-Browne, Nicholas B. Krishnaswamy, Smita Department Of Computer Science Department Of Psychology Department Of Mathematics Department Of Genetics Program In Applied Mathematics Wu Tsai Institute Yale University United States Department Of Mathematics And Statistics Université De Montréal Canada Mila Quebec AI Institute Canada

Functional magnetic resonance imaging (fMRI) is a notoriously noisy measurement of brain activity because of the large variations between individuals, signals marred by environmental differences during collection, and spatiotemporal averaging required by the measurement resolution. In addition, the data is extremely high dimensional, with the space of the activity typically having much lower intrinsic dimension. In order to understand the connection between stimuli of interest and brain activity, and analyze differences and commonalities between subjects, it becomes important to learn a meaningful embedding of the data that denoises, and reveals its intrinsic structure. Specifically, we assume that while noise varies significantly between individuals, true responses to stimuli will share common, low-dimensional features between subjects which are jointly discoverable. Similar approaches have been exploited previously but they have mainly used linear methods such as PCA and shared response modeling (SRM). In contrast, we propose a neural network called MRMD-AE (manifold-regularized multiple decoder, autoencoder), that learns a common embedding from multiple subjects in an experiment while retaining the ability to decode to individual raw fMRI signals. We show that our learned common space represents an extensible manifold (where new points not seen during training can be mapped), improves the classification accuracy of stimulus features of unseen timepoints, as well as improves cross-subject translation of fMRI signals. We believe this framework can be used for many downstream applications such as guided brain-computer interface (BCI) training in the future. Copyright © 2021, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

Using Machine Learning for Early Prediction of Cardiogenic Shock in Patients With Acute Heart Failure

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Journal of the Society for Cardiovascular Angiography and Interventions 2022年第3期1卷 100308-100308页

作者： Rahman, Faisal Finkelstein, Noam Alyakin, Anton Gilotra, Nisha A. Trost, Jeff Schulman, Steven P. Saria, Suchi Department of Cardiology Baylor College of Medicine Houston TX United States Department of Computer Science Johns Hopkins University Baltimore MD United States Department of Applied Mathematics and Statistics Johns Hopkins University Baltimore MD United States Division of Cardiology Department of Medicine Johns Hopkins University School of Medicine Baltimore MD United States Departments of Computer Science Applied Mathematics and Statistics and Health Policy and Management Johns Hopkins University Baltimore MD United States

Background: Despite technological and treatment advancements over the past 2 decades, cardiogenic shock (CS) mortality has remained between 40% and 60%. Our objective was to develop an algorithm that can continuously monitor heart failure patients and partition them into cohorts of high and low risk for CS. Methods: We retrospectively studied 24,461 patients hospitalized with acute decompensated heart failure, 265 of whom developed CS, in the Johns Hopkins Health System. Our cohort identification approach is based on logistic regression and makes use of vital signs, lab values, and medication administrations recorded during the normal course of care. Results: Our algorithm identified patients at high risk of CS. Patients in the high-risk cohort had 10.2 times (95% confidence interval, 6.1-17.2) higher prevalence of CS than those in the low-risk cohort. Patients who experienced CS while in the high-risk cohort were first deemed high risk a median of 1.7 days (interquartile range, 0.8-4.6) before CS diagnosis was made by their clinical team. To evaluate actionability, we randomly selected 50 patients designated as high risk who did develop CS and 50 who did not. On review of true positive cases, from the time of model identification as high risk to the eventual diagnosis of CS, 12% of patients had possible inappropriate therapy, and for 50% of patients, more tailored therapy options existed. On review of the false positive cases, 44% of cases were considered at high risk of CS or end-stage cardiomyopathy by their clinical teams or went onto develop other types of shock. Conclusions: This risk model was able to predict patients at higher risk of CS in a time frame that allowed a change in clinical care. The actionability evaluation demonstrates a possible opportunity to intervene as part of a CS algorithm for escalation of care. © 2022 The Authors

关键词： Acute decompensated heart failure cardiogenic shock machine learning risk prediction

Numerical evidence against advantage with quantum fidelity kernels on classical data

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arXiv 2022年

作者： Slattery, Lucas Shaydulin, Ruslan Chakrabarti, Shouvanik Pistoia, Marco Khairy, Sami Wild, Stefan M. Department of Physics University of Illinois Urbana-Champaign ChampaignIL61820 United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States Global Technology Applied Research JPMorgan Chase New YorkNY10017 United States

Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well-aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential "flattening" of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well-approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data. Copyright © 2022, The Authors. All rights reserved.

关键词： Machine learning

Extended Fayans energy density functional: optimization and analysis

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arXiv 2024年

作者： Reinhard, Paul-Gerhard O'Neal, Jared Wild, Stefan M. Nazarewicz, Witold Institut für Theoretische Physik II Universität Erlangen-Nürnberg ErlangenD-91058 Germany Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Industrial Engineering and Management Sciences Northwestern University EvanstonIL60208 United States Facility for Rare Isotope Beams Michigan State University East LansingMI48824 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States

The Fayans energy density functional (EDF) has been very successful in describing global nuclear properties (binding energies, charge radii, and especially differences of radii) within nuclear density functional theory. In a recent study, supervised machine learning methods were used to calibrate the Fayans EDF. Building on this experience, in this work we explore the effect of adding isovector pairing terms, which are responsible for different proton and neutron pairing fields, by comparing a 13D model without the isovector pairing term against the extended 14D model. At the heart of the calibration is a carefully selected heterogeneous dataset of experimental observables representing ground-state properties of spherical even-even nuclei. To quantify the impact of the calibration dataset on model parameters and the importance of the new terms, we carry out advanced sensitivity and correlation analysis on both models. The extension to 14D improves the overall quality of the model by about 30%. The enhanced degrees of freedom of the 14D model reduce correlations between model parameters and enhance sensitivity. Copyright © 2024, The Authors. All rights reserved.

关键词： Density functional theory

Developing a medical artificial intelligence course for high school students

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Developing a medical artificial intelligence course for high...

International Forum on Medical Imaging in Asia 2021, IFMIA 2021

作者： Huang, Chao-Jung Wu, Tinghui Lu, Jui-Ting Lin, Beatrice Chang, Dawei Wang, Pochuan Wang, Mei-Chi Lee, Peijung Wang, Weichung National Taiwan University-Stanford Joint Program Office of AI in Biotechnology Ministry of Science and Technology Joint Research Center for Artificial Intelligence Technology and All Vista Healthcare Taipei Taiwan Institute of Applied Mathematical Sciences National Taiwan University Taipei Taiwan Department of Mathematics Ecole Normale Supérieure de Lyon Lyon France Department of Computer Science and Information Engineering National Taiwan University Taipei Taiwan Department of Electronic and Computer Engineering National Taiwan University of Science and Technology Taipei Taiwan Department of Mathematics National Taiwan University Taipei Taiwan

ISBN: (数字)9781510644212

ISBN: (纸本)9781510644205

Artificial intelligence (AI) training courses often require prerequisites such as calculus or statistics. It is hence challenging to design and develop an introductory AI course for students of secondary education. This research intends to develop a medical AI course, provide high school students with an overview of deep learning applications in medical image analysis, and inspire them to pursue careers in the field of medical AI. We designed a 20-hour course, including lectures and two hands-on projects based on medical image classification. The proposed courses provided medical AI disciplines and built up their knowledge from basic to advanced levels. During the ten-day online courses, all the students were fully engaged and gave us positive feedback. The students endeavored to complete the experimental study in training, testing, and hypothesis of medical images application in the course. Their performance exceeded all expectations, for they did further analysis by tuning different hyperparameters. We designed a course evaluation form, which suggested that the students found it essential and expected to interact with the instructors. The results indicate that combining lectures with hands-on sessions would lead to evidently better achievement in terms of high school students' medical AI knowledge and positive attitudes while addressing real-world problems in the projects. Through this innovative education model, high school students regained their enthusiasm and were encouraged to cultivate their medical AI skills through self-learning while finishing the project. We conclude that this course could be successfully applied to interdisciplinary education in high school. © 2021 SPIE.

关键词： Students

Sparse-grid Discontinuous Galerkin Methods for the Vlasov–Poisson–Lenard–Bernstein Model

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arXiv 2024年

作者： Schnake, Stefan Kendrick, Coleman Endeve, Eirik Stoyanov, Miroslav Hahn, Steven Hauck, Cory D. Green, David L. Snyder, Phil Canik, John Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Fusion Energy Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Physics and Astronomy University of Tennessee KnoxvilleTN37996 United States Department of Mathematics University of Tennessee KnoxvilleTN37996 United States Type One Energy Group Oak RidgeTN37830 United States Commonwealth Scientific and Industrial Research Organisation Mayfield WestNSW2304 Australia

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. We use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD. Copyright © 2024, The Authors. All rights reserved.

关键词： Integral equations

Comparative numerical study featuring magnetized nanofluids configured by elongating sheet with thermophoresis and Brownian motion

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Partial Differential Equations in applied mathematics 2024年 11卷

作者： Puchakayala, Srinivasa Rao Borra, Shashidar Reddy Kallu, Saritha Formanova, Shoira Khan, M. Ijaz Waqas, M. Ahmad, Furqan Gupta, Manish Department of Mathematics Malla Reddy Engineering College (Autonomous) Dhulapally Telangana Hyderabad 500100 India Department of Mathematics Sreenidhi Institute of Science and Technology Ghatkesar Telangana Hyderabad 501301 India Department of Humanities and Sciences (Mathematics) CVR College of Engineering Ibrahimpatnam Telangana Hyderabad 501510 India Department of Chemistry and Its Teaching Methods Tashkent State Pedagogical University Tashkent Uzbekistan Department of Mechanical Engineering College of Engineering Prince Mohammad Bin Fahd University Al-Khobar Saudi Arabia NUTECH School of Applied Science and Humanities National University of Technology Islamabad 44000 Pakistan Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Western Caspian University Baku Azerbaijan Division of Research and Development Lovely Professional University Phagwara India

This study investigates the heat and mass transfer characteristics of MHD rotating Fe₃O₄-Al₂O₃/H₂O hybrid nanofluid flow over a three-dimensional stretching surface. Comparative analysis was conducted among the base fluid H₂O, Al₂O₃-H₂O nanofluid, and Fe₃O₄-Al₂O₃/H₂O hybrid nanofluid, focusing on velocity, temperature, and concentration distributions influenced by thermophoresis, Brownian motion, Hall current, temperature ratio, magnetic parameter, rotation, and thermal radiation. The governing nonlinear partial differential equations were transformed into ordinary differential equations using similarity adaptations and solved numerically with the BVP-5C method in MATLAB. Results indicate that increasing the thermophoresis and Brownian motion parameters elevates the temperature profile while affecting the concentration distribution differently. The hybrid nanofluid exhibited a higher temperature distribution compared to the nanofluid and base fluid, whereas the base fluid showed a greater concentration gradient. © 2024 The Author(s)

关键词： Brownian motion Elongating sheet Hall current Hybrid nanofluid Joule heating Thermophoresis