检索结果-内蒙古大学图书馆

Multigoal-oriented optimal control problems with nonlinear PDE constraints

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Endtmayer, B. Langer, U. Neitzel, I. Wick, T. Wollner, W. Doctoral Program on Computational Mathematics Johannes Kepler University Altenbergerstr. 69 LinzA-4040 Austria Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstr. 69 LinzA-4040 Austria Institut für Numerische Simulation Endenicher Allee 19b Bonn53115 Germany Institut für Angewandte Mathematik Leibniz Universität Hannover Welfengarten 1 Hannover30167 Germany Leibniz Universität Hannover Germany Technische Universität Darmstadt Fachbereich Mathematik Dolivostr. 15 Darmstadt64293 Germany

In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized p-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is formulated. Based on the reduced approach, we then derive an a posteriori error representation and mesh adaptivity for multiple quantities of interest. All quantities are combined to one, and then the dual-weighted residual (DWR) method is applied to this combined functional. Furthermore, the estimator allows for balancing the discretization error and the nonlinear iteration error. These developments allow us to formulate an adaptive solution strategy, which is finally substantiated via several numerical examples. Copyright © 2019, The Authors. All rights reserved.

关键词： Optimal control systems

Comparing demographics of signatories to public letters on diversity in the mathematical sciences

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Topaz, Chad M. Cart, James Eaton, Carrie Diaz Shrout, Anelise Hanson Higdon, Jude A. İnce, Kenan Katz, Brian Lewis, Drew Libertini, Jessica Smith, Christian Michael Department of Mathematics and Statistics Williams College WilliamstownMA United States Institute for the Quantitative Study of Inclusion Diversity and Equity WilliamstownMA United States Office of Institutional Research Williams College WilliamstownMA United States Digital and Computational Studies Program Bates College LewistonME United States Department of Mathematics Westminster College Salt Lake CityUT United States Department of Mathematics and Statistics Smith College NorthamptonMA United States Department of Mathematics and Statistics University of South Alabama MobileAL United States Department of Applied Mathematics Virginia Military Institute LexingtonVA United States Department of Sociology University of Wisconsin-Madison MadisonWI United States

In its December 2019 edition, the Notices of the American Mathematical Society published an essay critical of the use of diversity statements in academic hiring. The publication of this essay prompted many responses, including three public letters circulated within the mathematical sciences community. Each letter was signed by hundreds of people and was published online, also by the American Mathematical Society. We report on a study of the signatories’ demographics, which we infer using a crowdsourcing approach. Letter A highlights diversity and social justice. The pool of signatories contains relatively more individuals inferred to be women and/or members of underrepresented ethnic groups. Moreover, this pool is diverse with respect to the levels of professional security and types of academic institutions represented. Letter B does not comment on diversity, but rather, asks for discussion and debate. This letter was signed by a strong majority of individuals inferred to be white men in professionally secure positions at highly research intensive universities. Letter C speaks out specifically against diversity statements, calling them "a mistake," and claiming that their usage during early stages of faculty hiring "diminishes mathematical achievement." Individuals who signed both Letters B and C, that is, signatories who both privilege debate and oppose diversity statements, are overwhelmingly inferred to be tenured white men at highly research intensive universities. Our empirical results are consistent with theories of power drawn from the social sciences. Copyright © 2019, The Authors. All rights reserved.

关键词： Population statistics

Towards Implementation of the Pressure-Regulated, Feedback-Modulated Model of Star Formation in Cosmological Simulations: Methods and Application to TNG

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Hassan, Sultan Ostriker, Eve C. Kim, Chang-Goo Bryan, Greg L. Burger, Jan D. Fielding, Drummond B. Forbes, John C. Genel, Shy Hernquist, Lars Jeffreson, Sarah M.R. Motwani, Bhawna Smith, Matthew C. Somerville, Rachel S. Steinwandel, Ulrich P. Teyssier, Romain Center for Cosmology and Particle Physics Department of Physics New York University 726 Broadway New YorkNY10003 United States Center for Computational Astrophysics Flatiron Institute 162 5th Ave New YorkNY10010 United States Department of Physics & Astronomy University of the Western Cape Cape Town7535 South Africa Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States Department of Astronomy Columbia University 550 W 120th Street New YorkNY10027 United States Max-Planck-Institut für Astrophysik Karl-Schwarzschild-Str. 1 GarchingD-85748 Germany Department of Astronomy Cornell University IthacaNY14853 United States School of Physical and Chemical Sciences-Te Kura Matū University of Canterbury Private Bag 4800 Christchurch8140 New Zealand Columbia Astrophysics Laboratory Columbia University 550 West 120th Street New YorkNY10027 United States Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA United States Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road PrincetonNJ08544-1000 United States

Traditional star formation subgrid models implemented in cosmological galaxy formation simulations, such as that of Springel & Hernquist (2003, hereafter SH03), employ adjustable parameters to satisfy constraints measured in the local Universe. In recent years, however, theory and spatially-resolved simulations of the turbulent, multiphase, star-forming ISM have begun to produce new first-principles models, which when fully developed can replace traditional subgrid prescriptions. This approach has advantages of being physically motivated and predictive rather than empirically tuned, and allowing for varying environmental conditions rather than being tied to local Universe conditions. As a prototype of this new approach, by combining calibrations from the TIGRESS numerical framework with the Pressure-Regulated Feedback-Modulated (PRFM) theory, simple formulae can be obtained for both the gas depletion time and an effective equation of state. Considering galaxies in TNG50, we compare the "native" simulation outputs with post-processed predictions from PRFM. At TNG50 resolution, the total midplane pressure is nearly equal to the total ISM weight, indicating that galaxies in TNG50 are close to satisfying vertical equilibrium. The measured gas scale height is also close to theoretical equilibrium predictions. The slopes of the effective equations of states are similar, but with effective velocity dispersion normalization from SH03 slightly larger than that from current TIGRESS simulations. Because of this and the decrease in PRFM feedback yield at high pressure, the PRFM model predicts shorter gas depletion times than the SH03 model at high densities and redshift. Our results represent a first step towards implementing new, numerically calibrated subgrid algorithms in cosmological galaxy formation simulations. Copyright © 2024, The Authors. All rights reserved.

关键词： Cosmology

Quality of internal representation shapes learning performance in feedback neural networks

学校读者我要写书评

暂无评论

Physical Review Research 2021年第1期3卷 013176-013176页

作者： Lee Susman Francesca Mastrogiuseppe Naama Brenner Omri Barak Interdisciplinary Program in Applied Mathematics Technion Israel Institute of Technology Haifa 32000 Israel Network Biology Research Laboratories Technion Israel Institute of Technology Haifa 32000 Israel Gatsby Computational Neuroscience Unit University College London London W1T 4JG United Kingdom Department of Chemical Engineering Technion Israel Institute of Technology Haifa 32000 Israel Rappaport Faculty of Medicine Technion Israel Institute of Technology Haifa 32000 Israel

A fundamental feature of complex biological systems is the ability to form feedback interactions with their environment. A prominent model for studying such interactions is reservoir computing, where learning acts on low-dimensional bottlenecks. Despite the simplicity of this learning scheme, the factors contributing to or hindering the success of training in reservoir networks are in general not well understood. In this work, we study nonlinear feedback networks trained to generate a sinusoidal signal, and analyze how learning performance is shaped by the interplay between internal network dynamics and target properties. By performing exact mathematical analysis of linearized networks, we predict that learning performance is maximized when the target is characterized by an optimal, intermediate frequency which monotonically decreases with the strength of the internal reservoir connectivity. At the optimal frequency, the reservoir representation of the target signal is high-dimensional, desynchronized, and thus maximally robust to noise. We show that our predictions successfully capture the qualitative behavior of performance in nonlinear networks. Moreover, we find that the relationship between internal representations and performance can be further exploited in trained nonlinear networks to explain behaviors which do not have a linear counterpart. Our results indicate that a major determinant of learning success is the quality of the internal representation of the target, which in turn is shaped by an interplay between parameters controlling the internal network and those defining the task.

关键词： Learning theory Artificial neural networks Dynamical systems Neuronal network models

Cross-system biological image quality enhancement based on the generative adversarial network as a foundation for establishing a multi-institute microscopy cooperative network

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Panek, Dominik Rząca, Carina Szczypior, Maksymilian Sorysz, Joanna Misztal, Krzysztof Baster, Zbigniew Rajfur, Zenon Doctoral School of Exact and Natural Sciences Jagiellonian University ul. Lojasiewicza 11 Kraków30-348 Poland Department of Molecular and Interfacial Biophysics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30‑348 Poland Undergraduate Program in Biophysics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30‑348 Poland Undergraduate program in Biomedical Engineering Faculty of Electrical Engineering Automatics Computer Science and Biomedical Engineering AGH University of Science and Technology Al. A. Mickiewicza 30 Building B-1 Kraków30-059 Poland Division of Computational Mathematics Faculty of Mathematics and Computer Science Jagiellonian University 6 Lojasiewicza St. Kraków Poland

High-quality fluorescence imaging of biological systems is limited by processes like photobleaching and phototoxicity, and also in many cases, by limited access to the latest generations of microscopes. Moreover, low temporal resolution can lead to a motion blur effect in living systems. Our work presents a deep learning (DL) generative-adversarial approach to the problem of obtaining high-quality (HQ) images based on their low-quality (LQ) equivalents. We propose a generative-adversarial network (GAN) for contrast transfer between two different separate microscopy systems: a confocal microscope (producing HQ images) and a wide-field fluorescence microscope (producing LQ images). Our model proves that such transfer is possible, allowing us to receive HQ-generated images characterized by low mean squared error (MSE) values, high structural similarity index (SSIM), and high peak signal-to-noise ratio (PSNR) values. For our best model in the case of comparing HQ-generated images and HQ-ground truth images, the median values of the metrics are 6·10-4, 0.9413, and 31.87, for MSE, SSIM, and PSNR, respectively. In contrast, in the case of comparison between LQ and HQ ground truth median values of the metrics are equal to 0.0071, 0.8304, and 21.48 for MSE, SSIM, and PSNR respectively. Therefore, we observe a significant increase ranging from 14% to 49% for SSIM and PSNR respectively. These results, together with other single-system cross-modality studies, provide proof of concept for further implementation of a cross-system biological image quality enhancement. © 2024, CC BY-SA.

关键词： Fluorescence imaging

On the effect of non-Gaussian lensing deflections on CMB lensing measurements

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Böhm, Vanessa Sherwin, Blake D. Liu, Jia Hill, J. Colin Schmittfull, Marcel Namikawa, Toshiya Berkeley Center for Cosmological Physics University of California BerkeleyCA94720 United States Lawrence Berkeley National Laboratory 1 Cyclotron Road BerkeleyCA93720 United States Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road CambridgeCB3 0WA United Kingdom Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States Center for Computational Astrophysics Flatiron Institute 162 5th Avenue 10010 New YorkNY United States Institute for Advanced Study Einstein Drive PrincetonNJ08540 United States Leung Center for Cosmology and Particle Astrophysics National Taiwan University Taipei10617 Taiwan

We investigate the impact of non-Gaussian lensing deflections on measurements of the CMB lensing power spectrum. We find that the false assumption of their Gaussianity significantly biases these measurements in current and future experiments at the percent level. The bias is detected by comparing CMB lensing reconstructions from simulated CMB data lensed with Gaussian deflection fields to reconstructions from simulations lensed with fully non-Gaussian deflection fields. The non-Gaussian deflections are produced by ray-tracing through snapshots of an N-body simulation and capture both the non-Gaussianity induced by non-linear structure formation and by multiple correlated deflections. We find that the amplitude of the measured bias is in agreement with analytical predictions by Böhm et al. 2016. The bias is largest in temperature-based measurements and we do not find evidence for it in measurements from a combination of polarization fields (EB,EB). We argue that the non-Gaussian bias should be even more important for measurements of cross-correlations of CMB lensing with low-redshift tracers of large-scale structure. Copyright © 2018, The Authors. All rights reserved.

关键词： Deflection (structures)

The Material Properties of Weakly Collisional, High-β Plasmas White Paper for Plasma 2020 Decadal Survey

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Kunz, Matthew Squire, Jonathan Balbus, Steven Bale, Stuart Chen, Christopher Churazov, Eugene Cowley, Steven Forest, Cary Gammie, Charles Quataert, Eliot Reynolds, Christopher Schekochihin, Alexander Sironi, Lorenzo Spitkovsky, Anatoly Stone, James Zhuravleva, Irina Zweibel, Ellen Dept. of Astrophysical Sciences Princeton University and Princeton Plasma Physics Laboratory Dept. of Physics University of Otago New Zealand Dept. of Physics University of Oxford New College Oxford United Kingdom Dept. of Physics University of California Berkeley United States Space Sciences Laboratory at University of California Berkeley United States School of Physics and Astronomy Queen Mary University of London Max Planck Institute for Astrophysics Garching Germany Moscow Russia Dept. of Astrophysical Sciences Princeton University Princeton Plasma Physics Laboratory Dept. of Physics University of Wisconsin-Madison Dept. of Astronomy University of Illinois at Urbana-Champaign Dept. of Physics University of Illinois at Urbana-Champaign Dept. of Astronomy University of California Berkeley United States Institute of Astronomy University of Cambridge Sidney Sussex College Cambridge United Kingdom Rudolf Peierls Centre for Theoretical Physics University of Oxford Merton College Oxford United Kingdom Dept. of Astronomy Columbia University Dept. of Astrophysical Sciences Princeton University Dept. of Applied and Computational Mathematics Princeton University Dept. of Astronomy and Astrophysics University of Chicago Dept. of Astronomy University of Wisconsin-Madison

A Model of Fluid-Structure and Biochemical Interactions for Applications to Subclinical Leaflet Thrombosis

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Barrett, Aaron Brown, Jordan A. Smith, Margaret Anne Woodward, Andrew Vavalle, John P. Kheradvar, Arash Griffith, Boyce E. Fogelson, Aaron L. Department of Mathematics University of Utah Salt Lake CityUT United States Department of Mathematics University of North Carolina Chapel HillNC United States Advanced Medical Imaging Lab University of North Carolina Medical Center Chapel HillNC United States University of North Carolina School of Medicine Chapel HillNC United States Division of Cardiology Department of Medicine University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of California Irvine IrvineCA United States Department of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States Department of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis in which they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction. © 2022, CC BY-SA.

关键词： Deposition

SRBench++: Principled Benchmarking of Symbolic Regression With Domain-Expert Interpretation

学校读者我要写书评

暂无评论

IEEE Transactions on Evolutionary Computation 2024年 1-1页

作者： de Franca, F.O. Virgolin, M. Kommenda, M. Majumder, M.S. Cranmer, M. Espada, G. Ingelse, L. Fonseca, A. Landajuela, M. Petersen, B. Glatt, R. Mundhenk, N. Lee, C.S. Hochhalter, J.D. Randall, D.L. Kamienny, P. Zhang, H. Dick, G. Simon, A. Burlacu, B. Kasak, Jaan Machado, Meera Wilstrup, Casper Cavaz, W.G.L. Federal University of ABC Santo Andre Brazil Evolutionary Intelligence group Centrum Wiskunde and Informatica Science Park Amsterdam Netherlands University of Applied Sciences Upper Austria Hagenberg Austria Computational Health Informatics Program Boston Children’s Hospital Harvard Medical School Boston USA Center for Computational Astrophysics Flatiron Institute and Department of Astrophysical Sciences of Princeton University USA LASIGE Faculdade de Ciências Universidade de Lisboa Lisboa Portugal Computational Engineering Division Lawrence Livermore National Laboratory Livermore USA Department of Mechanical Engineering University of Utah Utah USA Meta FAIR France Victoria University of Wellington School of Engineering and Computer Science New Zealand University of otago Department of Information Science New Zealand Institut für Angewandte Physik Universität TübingenMax Planck Institute for Intelligent Systems Tübingen Germany Abzu AI Orient Plads 1 Nordhavn Denmark

Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main promise of this approach is that it may return an interpretable model that can be insightful to users, while maintaining high accuracy. The current standard for benchmarking these algorithms is SRBench, which evaluates methods on hundreds of datasets that are a mix of real-world and simulated processes spanning multiple domains. At present, the ability of SRBench to evaluate interpretability is limited to measuring the size of expressions on real-world data, and the exactness of model forms on synthetic data. In practice, model size is only one of many factors used by subject experts to determine how interpretable a model truly is. Furthermore, SRBench does not characterize algorithm performance on specific, challenging sub-tasks of regression such as feature selection and evasion of local minima. In this work, we propose and evaluate an approach to benchmarking SR algorithms that addresses these limitations of SRBench by 1) incorporating expert evaluations of interpretability on a domain-specific task, and 2) evaluating algorithms over distinct properties of data science tasks. We evaluate 12 modern symbolic regression algorithms on these benchmarks and present an in-depth analysis of the results, discuss current challenges of symbolic regression algorithms and highlight possible improvements for the benchmark itself. Authors

关键词： Benchmarking