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Eigenvalues of The Neumann-Poincare Operator In Dimension 3: Weyl’S Law and Geometry

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arXiv 2018年

作者： Miyanishi, Yoshihisa Rozenblum, Grigori Center for Mathematical Modeling and Data Science Osaka University Japan Chalmers University of Technology University of Gothenburg Sweden St.Petersburg State University Dept. Math. Physics St.Petersburg Russia

We consider the asymptotic properties of the eigenvalues of the Neumann-Poincare (NP) operator in three dimensions. The region Ω ⊂ R3 is bounded by a compact surface Γ = ∂Ω, with certain smoothness conditions imposed. The NP operator KΓ, called often ‘the direct value of the double layer potential’, acting in L2(Γ), is defined by (Formula inserted) where dSy is the surface element and n(y) is the outer unit normal vector on Γ. The first-named author proved in [26] that the singular numbers sj(KΓ) of KΓ and the ordered moduli of its eigenvalues λj(KΓ) satisfy the Weyl law (Formula inserted) , under the condition that Γ belongs to the class C2,α with α > 0, where W (Γ) and χ(Γ) denote, respectively, the Willmore energy and the Euler characteristic of the boundary surface Γ. Although the NP operator is not self-adjoint (and therefore no general relations between eigenvalues and singular number exist), the ordered moduli of the eigenvalues of KΓ satisfy the same asymptotic relation. Our main purpose here is to investigate the asymptotic behavior of positive and negative eigenvalues separately under the condition of infinite smoothness of the boundary Γ. These formulas are used, in particular, to obtain certain answers to the long-standing problem of the existence or finiteness of negative eigenvalues of KΓ. A more sophisticated estimation allows us to give a natural extension of the Weyl’s law for the case of a smooth boundary. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

From FAIR to CURE: Guidelines for Computational Models of Biological Systems

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arXiv 2025年

作者： Sauro, Herbert M. Agmon, Eran Blinov, Michael L. Gennari, John H. Hellerstein, Joe Heydarabadipour, Adel Hunter, Peter Jardine, Bartholomew E. May, Elebeoba Nickerson, David P. Smith, Lucian P. Bader, Gary D. Bergmann, Frank Boyle, Patrick M. Dräger, Andreas Faeder, James R. Feng, Song Freire, Juliana Fröhlich, Fabian Glazier, James A. Gorochowski, Thomas E. Helikar, Tomas Hoops, Stefan Imoukhuede, Princess Keating, Sarah M. Konig, Matthias Laubenbacher, Reinhard Loew, Leslie M. Lopez, Carlos F. Lytton, William W. McCulloch, Andrew Mendes, Pedro Myers, Chris J. Myers, Jerry G. Mulugeta, Lealem Niarakis, Anna van Niekerk, David D. Olivier, Brett G. Patrie, Alexander A. Quardokus, Ellen M. Radde, Nicole Rohwer, Johann M. Sahle, Sven Schaff, James C. Sego, T.J. Shin, Janis Snoep, Jacky L. Vadigepalli, Rajanikanth Wiley, H. Steve Waltemath, Dagmar Moraru, Ion Department of Bioengineering University of Washington SeattleWA98195-5061 United States Intelligent Systems Engineering and Biocomplexity Institute Indiana University Street BloomingtonIN47408 United States Center for Cardiovascular Biology University of Washington SeattleWA98195-5061 United States eScience Institute University of Washington SeattleWA98195-5061 United States Institute for Stem Cell and Regenerative Medicine University of Washington SeattleWA98195-5061 United States School of Biological Sciences University of Bristol 24 Tyndall Avenue BristolBS8 1TQ United Kingdom Departments of Physiology & Pharmacology Neurology Downstate Health Science University BrooklynNY11203 United States Department of Neurology Kings County Hospital BrooklynNY11203 United States NASA-John H. Glenn Research Center MS 110-3 21000 Brookpark Road ClevelandOH44135 United States Center for Cell Analysis and Modeling UConn Health 263 Farmington Avenue FarmingtonCT06030-6406 United States Amsterdam Institute for Life and Environment Vrije Universiteit Amsterdam De Boelelaan 1108 Amsterdam1081 HZ Netherlands Department of Pathology and Genomic Medicine Thomas Jefferson University 1020 Locust St PhiladelphiaPA19107 United States Biological Sciences Division Pacific Northwest National Laboratory 902 Battelle Blvd RichlandWA99354 United States Auckland Bioengineering Institute University of Auckland Auckland1010 New Zealand Center of Integrative Biology University of Toulouse III-Paul Sabatier 165 Rue Marianne Grunberg-Manago Toulouse31400 France Lifeware Group Inria Building Alan Turing 1 Rue Honoré d’Estienne d’Orves Palaiseau91120 France Multiscale Modeling Group Altos Labs Redwood CityCA94065 United States partner site Tübingen Tübingen Germany Ottfried-Müller-Str. 37 Tübingen72076 Germany 06120 Germany Department of Computer Science Center for Data Science New York University New YorkNY11201 United States Department of Bi

Guidelines for managing scientific data have been established under the FAIR principles requiring that data be Findable, Accessible, Interoperable, and Reusable. In many scientific disciplines, especially computational biology, both data and models are key to progress. For this reason, and recognizing that such models are a very special type of "data", we argue that computational models, especially mechanistic models prevalent in medicine, physiology and systems biology, deserve a complementary set of guidelines. We propose the CURE principles, emphasizing that models should be Credible, Understandable, Reproducible, and Extensible. We delve into each principle, discussing verification, validation, and uncertainty quantification for model credibility;the clarity of model descriptions and annotations for understandability;adherence to standards and open science practices for reproducibility;and the use of open standards and modular code for extensibility and reuse. We outline recommended and baseline requirements for each aspect of CURE, aiming to enhance the impact and trustworthiness of computational models, particularly in biomedical applications where credibility is paramount. Our perspective underscores the need for a more disciplined approach to modeling, aligning with emerging trends such as Digital Twins and emphasizing the importance of data and modeling standards for interoperability and reuse. Finally, we emphasize that given the non-trivial effort required to implement the guidelines, the community moves to automate as many of the guidelines as possible. © 2025, CC BY.

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Spectral structure of the Neumann–Poincaré operator on tori

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arXiv 2018年

作者： Ando, Kazunori Ji, Yong-Gwan Kang, Hyeonbae Kawagoe, Daisuke Miyanishi, Yoshihisa Department of Electrical and Electronic Engineering and Computer Science Ehime University Ehime790-8577 Japan Department of Mathematics Institute of Applied Mathematics Inha University Incheon22212 Korea Republic of Center for Mathematical Modeling and Data Science Osaka University Osaka560-8531 Japan

We address the question whether there is a three-dimensional bounded domain such that the Neumann–Poincaré operator defined on its boundary has infinitely many negative eigenvalues. It is proved in this paper that tori have such a property. It is done by decomposing the Neumann–Poincaré operator on tori into infinitely many self-adjoint compact operators on a Hilbert space defined on the circle using the toroidal coordinate system and the Fourier basis, and then by proving that the numerical range of infinitely many operators in the decomposition has both positive and negative values.47A45, 31B25 Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

data driven time scale in Gaussian quasi-likelihood inference

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arXiv 2018年

作者： Eguchi, Shoichi Masuda, Hiroki Center for Mathematical Modeling and Data Science Osaka University 1-3 Machikaneyama-cho Toyonaka City Osaka560-8531 Japan Faculty of Mathematics Kyushu University 744 Motooka Nishi-ku Fukuoka819-0395 Japan

We study parametric estimation of ergodic diffusions observed at high frequency. Different from the previous studies, we suppose that sampling stepsize is unknown, thereby making the conventional Gaussian quasi-likelihood not directly applicable. In this situation, we construct estimators of both model parameters and sampling stepsize in a fully explicit way, and prove that they are jointly asymptotically normally distributed. High order uniform integrability of the obtained estimator is also derived. Further, we propose the Schwarz (BIC) type statistics for model selection and show its model-selection consistency. We conducted some numerical experiments and found that the observed finite-sample performance well supports our theoretical findings. Also provided is a real data example. Copyright © 2018, The Authors. All rights reserved.

关键词： Gaussian distribution

Classification of protein crystallization X-ray images using major convolutional neural network architectures

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arXiv 2018年

作者： Ghafurian, Soheil Orth, Peter Strickland, Corey Su, Hua Patel, Sangita Soisson, Steven Dogdas, Belma Applied Mathematics and Modeling Global Data Science Center Merck & Co. Inc. RahwayNJ07065 United States Department of Biochemical Engineering and Structure MRL Merck & Co. Inc. KenilworthNJ07033 United States

The generation of protein crystals is necessary for the study of protein molecular function and structure. This is done empirically by processing large numbers of crystallization trials and inspecting them regularly in search of those with forming crystals. To avoid missing the hard-gained crystals, this visual inspection of the trial X-ray images is done manually as opposed to the existing less accurate machine learning methods. To achieve higher accuracy for automation, we applied some of the most successful convolutional neural networks (ResNet, Inception, VGG, and AlexNet) for 10-way classification of the X-ray images. We showed that substantial classification accuracy is gained by using such networks compared to two simpler ones previously proposed for this purpose. The best accuracy was obtained from ResNet (81.43%), which corresponds to a missed crystal rate of 5.9%. This rate could be lowered to less than 0.1% by using a top-3 classification strategy. Our dataset consisted of 486,000 internally annotated images, which was augmented to more than a million to address class imbalance. We also provide a label-wise analysis of the results, identifying the main sources of error and inaccuracy. Copyright © 2018, The Authors. All rights reserved.

关键词： Convolution

Parameter and uncertainty estimation for dynamical systems using surrogate stochastic processes

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arXiv 2018年

作者： Chung, Matthias Binois, Mickaël Gramacy, Robert B. Moquin, David J. Smithk, Amanda P. Smith, Amber M. Department of Mathematics Computational Modeling and Data Analytics Devision Academy of Integrated Science Virginia Tech BlacksburgVA Booth School of Business University of Chicago ChicagoIL Department of Statistics Virginia Tech BlacksburgVA Department of Internal Medicine University of Tennessee Health Science Center MemphisTN Department of Pediatrics University of Tennessee Health Science Center MemphisTN

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future experiments. Merging mathematical theory with empirical measurements in a statistically coherent way is critical and challenges abound, e.g.,: illposedness of the parameter estimation problem, proper regularization and incorporation of prior knowledge, and computational limitations on full uncertainty qualification. To address these issues, we propose a new method for learning parameterized dynamical systems from data. In many ways, our proposal turns the canonical framework on its head. We first fit a surrogate stochastic process to observational data, enforcing prior knowledge (e.g., smoothness), and coping with challenging data features like heteroskedasticity, heavy tails and censoring. Then, samples of the stochastic process are used as "surrogate data" and point estimates are computed via ordinary point estimation methods in a modular fashion. An attractive feature of this approach is that it is fully Bayesian and simultaneously parallelizable. We demonstrate the advantages of our new approach on a predator prey simulation study and on a real world application involving within-host influenza virus infection data paired with a viral kinetic *** Codes 60G15, 62F10, 62F15, 65L09, 65L05, 92-08 Copyright © 2018, The Authors. All rights reserved.

关键词： Parameter estimation

Beyond Low Earth Orbit: Biomonitoring, Artificial Intelligence, and Precision Space Health

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arXiv 2021年

作者： Scott, Ryan T. Antonsen, Erik L. Sanders, Lauren M. Hastings, Jaden J.A. Park, Seung-Min Mackintosh, Graham Reynolds, Robert J. Hoarfrost, Adrienne L. Sawyer, Aenor Greene, Casey S. Glicksberg, Benjamin S. Theriot, Corey A. Berrios, Daniel C. Miller, Jack Babdor, Joel Barker, Richard Baranzini, Sergio E. Beheshti, Afshin Chalk, Stuart Delgado-Aparicio, Guillermo M. Haendel, Melissa Hamid, Arif A. Heller, Philip Jamieson, Daniel Jarvis, Katelyn J. Kalantari, John Khezeli, Kia Komarova, Svetlana V. Komorowski, Matthieu Kothiyal, Prachi Mahabal, Ashish Manor, Uri Martin, Hector Garcia Mason, Christopher E. Matar, Mona Mias, George I. Myers, Jerry G. Nelson, Charlotte Oribello, Jonathan Parsons-Wingerter, Patricia Prabhu, R.K. Qutub, Amina Ann Rask, Jon Saravia-Butler, Amanda Saria, Suchi Singh, Nitin Kumar Soboczenski, Frank Snyder, Michael Soman, Karthik van Valen, David Venkateswaran, Kasthuri Warren, Liz Worthey, Liz Yang, Jason H. Zitnik, Marinka Costes, Sylvain V. KBR Space Biosciences Division NASA Ames Research Center Moffett FieldCA94035 United States Department of Emergency Medicine Center for Space Medicine Baylor College of Medicine HoustonTX77030 United States Blue Marble Space Institute of Science Space Biosciences Division NASA Ames Research Center Moffett FieldCA94035 United States Department of Physiology and Biophysics Weill Cornell Medicine New YorkNY10065 United States Department of Urology Department of Radiology Stanford University School of Medicine StanfordCA94305 United States Bay Area Environmental Research Institute NASA Ames Research Center Moffett FieldCA94035 United States Mortality Research & Consulting Inc. HoustonTX77058 United States Space Biosciences Division NASA Ames Research Center Moffett FieldCA94035 United States UC Space Health Department of Orthopaedic Surgery University of California San Francisco San FranciscoCA94143 United States Center for Health AI Department of Biochemistry and Molecular Genetics University of Colorado School of Medicine Anschutz Medical Campus AuroraCO80045 United States Hasso Plattner Institute for Digital Health at Mount Sinai Department of Genetics and Genomic Sciences Icahn School of Medicine at Mount Sinai New YorkNY10065 United States Department of Preventive Medicine and Community Health UTMB GalvestonTX77551 United States Human Health and Performance Directorate NASA Johnson Space Center HoustonTX77058 United States Department of Microbiology and Immunology Department of Otolaryngology Head and Neck Surgery University of California San Francisco San FranciscoCA94143 United States The Gilroy AstroBiology Research Group The University of Wisconsin Madison MadisonWI53706 United States Weill Institute for Neurosciences Department of Neurology University of California San Francisco San FranciscoCA94158 United States Department of Chemistry University of North Florida JacksonvilleFL32224 United States Data Scienc

Human space exploration beyond low Earth orbit will involve missions of significant distance and duration. To effectively mitigate myriad space health hazards, paradigm shifts in data and space health systems are necessary to enable Earth-independence, rather than Earth-reliance. Promising developments in the fields of artificial intelligence and machine learning for biology and health can address these needs. We propose an appropriately autonomous and intelligent Precision Space Health system that will monitor, aggregate, and assess biomedical statuses;analyze and predict personalized adverse health outcomes;adapt and respond to newly accumulated data;and provide preventive, actionable, and timely insights to individual deep space crew members and iterative decision support to their crew medical officer. Here we present a summary of recommendations from a workshop organized by the National Aeronautics and Space Administration, on future applications of artificial intelligence in space biology and health. In the next decade, biomonitoring technology, biomarker science, spacecraft hardware, intelligent software, and streamlined data management must mature and be woven together into a Precision Space Health system to enable humanity to thrive in deep space. © 2021, CC BY.

关键词： Earth (planet)

Beyond Low Earth Orbit: Biological Research, Artificial Intelligence, and Self-Driving Labs

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arXiv 2021年

作者： Sanders, Lauren M. Yang, Jason H. Scott, Ryan T. Qutub, Amina Ann Martin, Hector Garcia Berrios, Daniel C. Hastings, Jaden J.A. Rask, Jon Mackintosh, Graham Hoarfrost, Adrienne L. Chalk, Stuart Kalantari, John Khezeli, Kia Antonsen, Erik L. Babdor, Joel Barker, Richard Baranzini, Sergio E. Beheshti, Afshin Delgado-Aparicio, Guillermo M. Glicksberg, Benjamin S. Greene, Casey S. Haendel, Melissa Hamid, Arif A. Heller, Philip Jamieson, Daniel Jarvis, Katelyn J. Komarova, Svetlana V. Komorowski, Matthieu Kothiyal, Prachi Mahabal, Ashish Manor, Uri Mason, Christopher E. Matar, Mona Mias, George I. Miller, Jack Myers, Jerry G. Nelson, Charlotte Oribello, Jonathan Park, Seung-Min Parsons-Wingerter, Patricia Prabhu, R.K. Reynolds, Robert J. Saravia-Butler, Amanda Saria, Suchi Sawyer, Aenor Singh, Nitin Kumar Soboczenski, Frank Snyder, Michael Soman, Karthik Theriot, Corey A. van Valen, David Venkateswaran, Kasthuri Warren, Liz Worthey, Liz Zitnik, Marinka Costes, Sylvain V. Blue Marble Space Institute of Science Space Biosciences Division NASA Ames Research Center Moffett Field CA94035 United States Center for Emerging and Re-Emerging Pathogens Department of Microbiology Biochemistry and Molecular Genetics Rutgers New Jersey Medical School NewarkNJ07103 United States KBR Space Biosciences Division NASA Ames Research Center Moffett Field CA94035 United States AI MATRIX Consortium Department of Biomedical Engineering University of Texas San Antonio and UT Health Sciences San AntonioTX78249 United States Biological Systems and Engineering Division Lawrence Berkeley National Lab. BerkeleyCA94608 United States DOE Agile BioFoundry EmeryvilleCA94608 United States Joint BioEnergy Institute EmeryvilleCA94608 United States Department of Physiology and Biophysics Weill Cornell Medicine New YorkNY10065 United States Office of the Center Director NASA Ames Research Center Moffett Field CA94035 United States Bay Area Environmental Research Institute NASA Ames Research Center Moffett Field CA94035 United States Space Biosciences Division NASA Ames Research Center Moffett Field CA94035 United States Department of Chemistry University of North Florida JacksonvilleFL32224 United States Center for Individualized Medicine Department of Surgery Department of Quantitative Health Sciences Mayo Clinic RochesterMN55905 United States Department of Emergency Medicine Center for Space Medicine Baylor College of Medicine HoustonTX77030 United States Department of Microbiology and Immunology Department of Otolaryngology Head and Neck Surgery University of California San Francisco San FranciscoCA94143 United States The Gilroy AstroBiology Research Group The University of Wisconsin - Madison MadisonWI53706 United States Weill Institute for Neurosciences Department of Neurology University of California San Francisco San FranciscoCA94158 United States Data Science Analytics Georgia Institute of Technology Lima15024

Space biology research aims to understand fundamental effects of spaceflight on organisms, develop foundational knowledge to support deep space exploration, and ultimately bioengineer spacecraft and habitats to stabilize the ecosystem of plants, crops, microbes, animals, and humans for sustained multi-planetary life. To advance these aims, the field leverages experiments, platforms, data, and model organisms from both spaceborne and ground-analog studies. As research is extended beyond low Earth orbit, experiments and platforms must be maximally autonomous, light, agile, and intelligent to expedite knowledge discovery. Here we present a summary of recommendations from a workshop organized by the National Aeronautics and Space Administration on artificial intelligence, machine learning, and modeling applications which offer key solutions toward these space biology challenges. In the next decade, the synthesis of artificial intelligence into the field of space biology will deepen the biological understanding of spaceflight effects, facilitate predictive modeling and analytics, support maximally autonomous and reproducible experiments, and efficiently manage spaceborne data and metadata, all with the goal to enable life to thrive in deep space. © 2021, CC BY.

关键词： Predictive analytics

Sampled Tikhonov regularization for large linear inverse problems

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arXiv 2018年

作者： Tanner Slagel, J. Chung, Julianne Chung, Matthias Kozak, David Tenorio, Luis Department of Mathematics Virginia Tech BlacksburgVA United States Department of Mathematics Computational Modeling and Data Analytics Division Academy of Integrated Science Virginia Tech BlacksburgVA United States Applied Mathematics and Statistics Colorado School of Mines GoldenCO United States

In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once (e.g., for problems with streaming or massive datasets). Row-access methods provide an ideal framework for solving such problems, since they only require access to "blocks" of the data at any given time. However, when using these iterative sampling methods to solve inverse problems, the main challenges include a proper choice of the regularization parameter, appropriate sampling strategies, and a convergence analysis. To address these challenges, we first describe a family of sampled iterative methods that can incorporate data as they become available (e.g., randomly sampled). We consider two sampled iterative methods, where the iterates can be characterized as solutions to a sequence of approximate Tikhonov problems. The first method requires the regularization parameter to be fixed a priori and converges asymptotically to an unregularized solution for randomly sampled data. This is undesirable for inverse problems. Thus, we focus on the second method where the main benefits are that the regularization parameter can be updated during the iterative process and the iterates converge asymptotically to a Tikhonov-regularized solution. We describe adaptive approaches to update the regularization parameter that are based on sampled residuals, and we describe a limited-memory variant for larger problems. Numerical examples, including a large-scale super-resolution imaging example, demonstrate the potential for these *** Codes 65F22, 65F10, 15A29 Copyright © 2018, The Authors. All rights reserved.

关键词： Iterative methods