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A spectral penalty method for two-sided fractional differential equations with general boundary conditions

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arXiv 2018年

作者： Wang, Nan Mao, Zhiping Huang, Chengming Karniadakis, George Em School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Division of Applied Mathematics Brown University ProvidenceRI02912 United States Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

We consider spectral approximations to the conservative form of the two-sided Riemann-Liouville (R-L) and Caputo fractional differential equations (FDEs) with nonhomogeneous Dirichlet (fractional and classical, respectively) and Neumann (fractional) boundary conditions. In particular, we develop a spectral penalty method (SPM) by using the Jacobi poly-fractonomial approximation for the conservative R-L FDEs while using the polynomial approximation for the conservative Caputo FDEs. We establish the well-posedness of the corresponding weak problems and analyze sufficient conditions for the coercivity of the SPM for different types of fractional boundary value problems. This analysis allows us to estimate the proper values of the penalty parameters at boundary points. We present several numerical examples to verify the theory and demonstrate the high accuracy of SPM, both for stationary and time dependent FDEs. Moreover, we compare the results against a Petrov-Galerkin spectral tau method (PGS-τ, an extension of [23]) and demonstrate the superior accuracy of SPM for all cases considered. Copyright © 2018, The Authors. All rights reserved.

关键词： Constrained optimization

Benchmarking the CoW with the TopCoW Challenge: Topology-Aware Anatomical Segmentation of the Circle of Willis for CTA and MRA

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arXiv 2023年

作者： Yang, Kaiyuan Musio, Fabio Ma, Yihui Juchler, Norman Paetzold, Johannes C. Al-Maskari, Rami Höher, Luciano Li, Hongwei Bran Hamamci, Ibrahim Ethem Sekuboyina, Anjany Shit, Suprosanna Huang, Houjing Prabhakar, Chinmay de la Rosa, Ezequiel Waldmannstetter, Diana Kofler, Florian Navarro, Fernando Menten, Martin Ezhov, Ivan Rueckert, Daniel Vos, Iris Ruigrok, Ynte Velthuis, Birgitta Kuijf, Hugo Hämmerli, Julien Wurster, Catherine Bijlenga, Philippe Westphal, Laura Bisschop, Jeroen Colombo, Elisa Baazaoui, Hakim Makmur, Andrew Hallinan, James Wiestler, Bene Kirschke, Jan S. Wiest, Roland Montagnon, Emmanuel Letourneau-Guillon, Laurent Galdran, Adrian Galati, Francesco Falcetta, Daniele Zuluaga, Maria A. Lin, Chaolong Zhao, Haoran Zhang, Zehan Ra, Sinyoung Hwang, Jongyun Park, Hyunjin Chen, Junqiang Wodzinski, Marek Müller, Henning Shi, Pengcheng Liu, Wei Ma, Ting Yalçin, Cansu Hamadache, Rachika E. Salvi, Joaquim Llado, Xavier Estrada, Uma Maria Lal-Trehan Abramova, Valeriia Giancardo, Luca Oliver, Arnau Liu, Jialu Huang, Haibin Cui, Yue Lin, Zehang Liu, Yusheng Zhu, Shunzhi Patel, Tatsat R. Tutino, Vincent M. Orouskhani, Maysam Wang, Huayu Mossa-Basha, Mahmud Zhu, Chengcheng Rokuss, Maximilian R. Kirchhoff, Yannick Disch, Nico Holzschuh, Julius Isensee, Fabian Maier-Hein, Klaus Sato, Yuki Hirsch, Sven Wegener, Susanne Menze, Bjoern Department of Quantitative Biomedicine University of Zurich Zurich Switzerland Center for Computational Health Zurich University of Applied Sciences Zurich Switzerland Department of Neuroradiology University Hospital of Zurich Zurich Switzerland Department of Neurosurgery Zhongnan Hospital of Wuhan University Wuhan China Department of Computing Imperial College London London United Kingdom Helmholtz Center Munich Germany Athinoula A. Martinos Center for Biomedical Imaging Harvard Medical School Boston United States School of Medicine Technical University of Munich Munich Germany Department of Informatics Technical University of Munich Munich Germany Helmholtz AI Helmholtz Munich Munich Germany Image Sciences Institute UMC Utrecht Utrecht Netherlands Department of Neurology UMC Utrecht Utrecht Netherlands Department of Radiology UMC Utrecht Utrecht Netherlands Department of Clinical Neurosciences Division of Neurosurgery Geneva University Hospitals Geneva Switzerland Department of Neurology University Hospital of Zurich Zurich Switzerland Department of Physiology University of Toronto Toronto Canada Department of Neurosurgery University Hospital of Zurich Zurich Switzerland Department of Diagnostic Imaging National University Hospital Singapore Department of Diagnostic and Interventional Neuroradiology University Hospital Berne University of Berne Berne Switzerland Montreal Canada Universitat Pompeu Fabra Barcelona Spain EURECOM Biot France Institute of Medical Technology Peking University Health Science Center Beijing China Hangzhou Genlight Medtech Co. Ltd. Hangzhou China Department of Artificial Intelligence Sungkyunkwan University Seoul Korea Republic of Department of Electrical and Computer Engineering Sungkyunkwan University Seoul Korea Republic of Shanghai MediWorks Precision Instruments Co. Ltd. Shanghai China Institute of Informatics HES-SO Valais-Wallis Switzerland Department of Measurement and Electronics AGH University

The Circle of Willis (CoW) is an important network of arteries connecting major circulations of the brain. Its vascular architecture is believed to affect the risk, severity, and clinical outcome of serious neuro-vascular diseases. However, characterizing the highly variable CoW anatomy is still a manual and time-consuming expert task. The CoW is usually imaged by two angiographic imaging modalities, magnetic resonance angiography (MRA) and computed tomography angiography (CTA), but there exist limited public datasets with annotations on CoW anatomy, especially for CTA. Therefore we organized the TopCoW Challenge in 2023 with the release of an annotated CoW dataset. The TopCoW dataset was the first public dataset with voxel-level annotations for thirteen possible CoW vessel components, enabled by virtual-reality (VR) technology. It was also the first large dataset with paired MRA and CTA from the same patients. TopCoW challenge formalized the CoW characterization problem as a multiclass anatomical segmentation task with an emphasis on topological metrics. We invited submissions worldwide for the CoW segmentation task, which attracted over 140 registered participants from four continents. The top performing teams managed to segment many CoW components to Dice scores around 90%, but with lower scores for communicating arteries and rare variants. There were also topological mistakes for predictions with high Dice scores. Additional topological analysis revealed further areas for improvement in detecting certain CoW components and matching CoW variant topology accurately. TopCoW represented a first attempt at benchmarking the CoW anatomical segmentation task for MRA and CTA, both morphologically and topologically. © 2023, CC BY-NC-ND.

关键词： Large datasets

Collective neutrino oscillations in three flavors on qubit and qutrit processors

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Physical Review D 2025年第10期111卷 103054-103054页

作者： Luca Spagnoli Noah Goss Alessandro Roggero Ermal Rrapaj Michael J. Cervia Amol V. Patwardhan Ravi K. Naik A. Baha Balantekin Ed Younis David I. Santiago Irfan Siddiqi Sheakha Aldaihan Physics Department University of Trento Via Sommarive 14 I-38123 Trento Italy INFN-TIFPA Trento Institute of Fundamental Physics and Applications Via Sommarive 14 I-38123 Trento Italy Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley Berkeley California 94720 USA Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA INFN-TIFPA Trento Institute of Fundamental Physics and Applications Trento Italy National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Physics University of California Berkeley California 94720 USA RIKEN iTHEMS Wako Saitama 351-0198 Japan Department of Physics University of Washington Seattle Washington 98195 USA School of Physics and Astronomy University of Minnesota Minneapolis Minnesota 55455 USA Department of Physics New York Institute of Technology New York New York 10023 USA Department of Physics University of Wisconsin Madison Wisconsin 53706 USA Department of Physics and Astronomy College of Science King Saud University Riyadh 11451 Saudi Arabia

Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions, which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and Advanced Quantum Testbed device at the Lawrence Berkeley National Laboratory for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. While hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphsycial qubit space, unlike the qubit setup.

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Tailoring magnetism in self-intercalated Cr1+δTe2 epitaxial films

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arXiv 2020年

作者： Fujisawa, Y. Pardo-Almanza, M. Garland, J. Yamagami, K. Zhu, X. Chen, X. Araki, K. Takeda, T. Kobayashi, M. Takeda, Y. Hsu, C.H. Chuang, F.C. Laskowski, R. Khoo, K.H. Soumyanarayanan, A. Okada, Yoshinori Okinawa904-0495 Japan Applied Physics & Mathematics Department Northeastern University BostonMA02115 United States Institute of Materials Research and Engineering Agency for Science Technology and Research Singapore138634 Singapore Department of Electrical Engineering and Information Systems University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Center for Spintronics Research Network University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Condensed Matter Science Division Quantum Beam Science Directorate Japan Atomic Energy Agency 1-1-1 Kouto Sayo-cho Sayo-gunHyogo679-5148 Japan Department of Physics National Sun Yat-sen University Kaohsiung80424 Taiwan Institute of High Performance Computing Agency for Science Technology and Research 138632 Singapore Department of Physics National University of Singapore 117551 Singapore

Magnetic transition metal dichalcogenide (TMD) films have recently emerged as promising candidates to host novel magnetic phases relevant to next-generation spintronic devices. However, systematic control of the magnetization orientation, or anisotropy, and its thermal stability, characterized by Curie temperature (Tc) – remains to be achieved in such films. Here we present self-intercalated epitaxial Cr1+δTe2 films as a platform for achieving systematic/smooth magnetic tailoring in TMD films. Using a molecular beam epitaxy (MBE) based technique, we have realized epitaxial Cr1+δTe2 films with smoothly tunable δ over a wide range (0.33-0.82), while maintaining NiAs-type crystal structure. With increasing δ, we found monotonic enhancement of Tc from 160 to 350 K, and the rotation of magnetic anisotropy from out-of-plane to in-plane easy axis configuration for fixed film thickness. Contributions from conventional dipolar and orbital moment terms are insufficient to explain the observed evolution of magnetic behavior with δ. Instead, ab initio calculations suggest that the emergence of antiferromagnetic interactions with δ, and its interplay with conventional ferromagnetism, may play a key role in the observed trends. To our knowledge, this constitutes the first demonstration of tunable Tc and magnetic anisotropy across room temperature in TMD films, and paves the way for engineering novel magnetic phases for spintronic applications. Copyright © 2020, The Authors. All rights reserved.

关键词： Transition metals

On the properties of the (p, ν)-extension of the Whittaker function M κ,μ (z)

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arXiv 2018年

作者： Dara, S.A. Parisb, R.B. Department of Applied Sciences and Humanities Faculty of Engineering and Technology Jamia Millia Islamia New Delhi110025 India Division of Computing and Mathematics Abertay University DundeeDD1 1HG United Kingdom

In this paper, we obtain a (p, ν)-extension of the Whittaker function M K μ(z) by using the extended confluent hypergeometric function of the first kind Φ pl(b;c;z) introduced in Parmar et al. [J. Classical Anal. 11 (2017) 81-106]. Also, we derive some of the main properties of this function, namely several integral representations, a summation formula, the analogue of Kummer 's transformation formula, an asymptotic representation, the Mellin transform, a differential formula and some inequalities. Copyright © 2018, The Authors. All rights reserved.

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Progress on Feynman Integrals for 2 → 3 scattering at NNLO

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Journal of Physics: Conference Series 2021年第1期2105卷

作者： D D Canko A Kardos C G Papadopoulos A V Smirnov N Syrrakos C Wever Institute of Nuclear and Particle Physics NCSR 'Demokritos' Agia Paraskevi 15310 Greece Department of Physics University of Athens Zographou 15784 Greece University of Debrecen Faculty of Science and Technology Department of Experimental Physics 4010 Debrecen PO Box 105 Hungary Research Computing Center Moscow State University 119991 Moscow Russia Moscow Center for Fundamental and Applied Mathematics 119992 Moscow Russia Physics Division National Technical University of Athens Athens 15780 Greece Physik-Department T31 Technische Universitat Munchen James-Franck Strasse 1 D-85748 Garching Germany

We present recent results on two-loop five-point Feynman Integrals with one off-shell leg that are relevant to the study of many 2 → 3 scattering processes of interest at the LHC, especially for the leading-colour W ...

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Predicting Spring Phenology in Deciduous Broadleaf Forests: Neon Phenology Forecasting Community Challenge

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SSRN

SSRN 2023年

作者： Wheeler, Kathryn I. Dietze, Michael C. LeBauer, David Peters, Jody Richardson, Andrew D. Ross, Arun A. Thomas, R. Quinn Zhu, Kai Bhat, Uttam Munch, Stephan Buzbee, Raphaela Floreani Chen, Min Goldstein, Benjamin Guo, Jessica Hao, Dalei Jones, Chris Kelly-Fair, Mira Liu, Haoran Malmborg, Charlotte Neupane, Naresh Pal, Debasmita Shirey, Vaughn Song, Yiluan Steen, McKalee Vance, Eric A. Woelmer, Whitney M. Wynne, Jacob Zachmann, Luke Department of Earth and Environment Boston University 685 Commonwealth Avenue BostonMA02215 United States Cooperative Programs for the Advancement of Earth System Science University Corporation for Atmospheric Research Foothills Laboratory Bldg 4 3300 Mitchell Lane BoulderCO80301 United States National Oceanic and Atmospheric Administration Foothills Laboratory Bldg 4 3300 Mitchell Lane BoulderCO80301 United States Department of Civil and Environmental Engineering Massachusetts Institute of Technology 15 Vassar St CambridgeMA02142 United States Arizona Experiment Station University of Arizona 1230 N Cherry Ave TucsonAZ85721 United States Department of Biological Sciences University of Notre Dame 100 Galvin Notre DameIN46556 United States School of Informatics Computing and Cyber Systems Northern Arizona University 1295 Knoles Dr. FlagstaffAZ86011 United States Center for Ecosystem Science and Society Northern Arizona University PO Box 5620 FlagstaffAZ86011 United States Department of Computer Science and Engineering Michigan State University 428 South Shaw Lane East LansingMI48824 United States Department of Forest Resources and Environmental Conservation Virginia Polytechnic Instit 310 West Campus Drive BlacksburgVA24061 United States Department of Biological Sciences Virginia Tech 926 West Campus Drive BlacksburgVA24061 United States Institute for Global Change Biology University of Michigan 440 Church Street Ann ArborMI48109 United States School for Environment and Sustainability University of Michigan 440 Church Street Ann ArborMI48109 United States Institute of Marine Sciences University of California Santa Cruz 1156 High Street Santa CruzCA95060 United States Department of Applied Mathematics University of California Santa Cruz 1156 High Street Santa CruzCA95060 United States Department of Environmental Science Policy and Management University of California Berkeley 4004 Valley Life Sciences Building Universi

Accurate models are important to predict how global climate change will continue to alter plant phenology and near-term ecological forecasts can be used to iteratively improve models and evaluate predictions that are made a priori. The Ecological Forecasting Initiative’s National Ecological Observatory Network (NEON) Forecasting Challenge, is an open challenge to the community to forecast daily greenness values, measured through digital images collected by the PhenoCam Network at NEON sites before the data are collected. For the first round of the challenge, which is presented here, we forecasted canopy greenness throughout the spring at eight deciduous broadleaf sites to investigate what factors impact current predictive skill of phenology forecasts. A total of 192,536 predictions were submitted, representing eighteen models, including a persistence and a day of year mean null models. We found that overall forecast skill was highest when forecasting earlier in the greenup curve compared to the end, for shorter lead times, for sites that greened up earlier, and when submitting forecasts during times other than near budburst. The models based on day of year historical mean had the highest predictive skill across the challenge period. In this first round of the challenge, by synthesizing across forecasts, we started to elucidate what factors affect the predictive skill of near-term phenology forecasts. © 2023, The Authors. All rights reserved.

关键词： Forecasting

Predicting Spring Phenology in Deciduous Broadleaf Forests: An Open Community Forecast Challenge

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SSRN

SSRN 2023年

作者： Wheeler, Kathryn I. Dietze, Michael C. LeBauer, David Peters, Jody Richardson, Andrew D. Thomas, R. Quinn Zhu, Kai Bhat, Uttam Munch, Stephan Buzbee, Raphaela Floreani Chenp, Min Goldstein, Benjamin Guo, Jessica S. Haoq, Dalei Jones, Chris Kelly-Fair, Mira Liup, Haoran Malmborg, Charlotte Neupane, Naresh Pal, Debasmita Ross, Arun A. Shirey, Vaughn Song, Yiluan Steen, McKalee Vance, Eric A. Woelmer, Whitney M. Wynne, Jacob Zachmann, Luke Department of Earth and Environment Boston University 685 Commonwealth Avenue BostonMA02215 United States Cooperative Programs for the Advancement of Earth System Science University Corporation for Atmospheric Research Foothills Laboratory Bldg 4 3300 Mitchell Lane BoulderCO80301 United States National Oceanic and Atmospheric Administration Foothills Laboratory Bldg 4 3300 Mitchell Lane BoulderCO80301 United States Department of Civil and Environmental Engineering Massachusetts Institute of Technology 15 Vassar St CambridgeMA02142 United States Arizona Experiment Station University of Arizona 1230 N Cherry Ave TucsonAZ85721 United States Department of Biological Sciences University of Notre Dame 100 Galvin Notre DameIN46556 United States School of Informatics Computing and Cyber Systems Northern Arizona University 1295 Knoles Dr. FlagstaffAZ86011 United States Center for Ecosystem Science and Society Northern Arizona University PO Box 5620 FlagstaffAZ86011 United States Department of Forest Resources and Environmental Conservation Virginia Polytechnic Institute State University 310 West Campus Drive BlacksburgVA24061 United States Department of Biological Sciences Virginia Polytechnic Institute State University 926 West Campus Drive BlacksburgVA24061 United States Institute for Global Change Biology University of Michigan 440 Church Street Ann ArborMI48109 United States School for Environment and Sustainability University of Michigan 440 Church Street Ann ArborMI48109 United States Institute of Marine Sciences University of California Santa Cruz 1156 High Street Santa CruzCA95060 United States Department of Applied Mathematics University of California Santa Cruz 1156 High Street Santa CruzCA95060 United States Department of Environmental Science Policy and Management University of California Berkeley 4004 Valley Life Sciences Building University of California Berkeley BerkeleyCA94720 United States Department of For

Accurate phenology models are important to predict how global climate change will continue to alter the timing of plant phenological events, such as spring greenup in deciduous broadleaf forests. While there is merit in long-term predictions, investigating how models can predict near-term (1– 35 days) canopy greenness throughout the spring allows us to validate performance and understanding now. The Ecological Forecasting Initiative’s NEON Forecasting Challenge, is an open challenge to the community to predict daily greenness values, measured through digital images collected by the PhenoCam Network at National Ecological Observatory Network (NEON) sites. For the first round of the challenge, which is presented here, teams were tasked to forecast phenology at eight deciduous broadleaf sites. A total of 192,536 predictions were submitted, representing eighteen models, including a persistence and a day of year mean null models. We found that forecast skill was highest when forecasting earlier in the greenup curve compared to the end, for shorter lead times, for sites that greened up earlier, and when submitting forecasts during times other than near budburst. The models based on day of year historical mean had the highest predictive skill across the challenge period. In this first round of the challenge, by synthesizing across forecasts, we started to elucidate what factors affect the predictive skill of near-term phenology forecasts, which future rounds will continue to investigate. © 2023, The Authors. All rights reserved.

关键词： Forecasting

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THE ARCTIC

Bulletin of the American Meteorological Society 2024年第8期105卷 S277-S330页

作者： Druckenmiller, M.L. Thoman, R.L. Moon, T.A. National Snow and Ice Data Center Cooperative Institute for Research in Environmental Sciences University of Colorado Boulder Boulder Colorado International Arctic Research Center University of Alaska Fairbanks Fairbanks Alaska National Snow and Ice Data Center Cooperative Institute for Research in Environmental Sciences University of Colorado Boulder Colorado Section for Glaciers Ice and Snow Norwegian Water Resources and Energy Directorate Oslo Norway School of Informatics Computing and Cyber Systems Northern Arizona University Flagstaff Arizona Biospherical Instruments Inc. San Diego California Geophysical Institute University of Alaska Fairbanks Fairbanks Alaska Plant Soils and Climate Department Utah State University Logan Utah Norwegian Institute for Nature Research Trondheim Norway FRAM – High North Research Centre for Climate and the Environment Tromsø Norway Geological Survey of Denmark and Greenland (GEUS) Copenhagen Denmark NOAA/NWS Alaska Region Anchorage Alaska Alaska Native Tribal Health Consortium Anchorage Alaska Geological Survey of Canada Natural Resources Canada Ottawa Canada NOAA Chemical Sciences Laboratory Boulder Colorado Arctic Geophysics Department University Centre in Svalbard Longyearbyen Norway Geology Department University Centre in Svalbard Longyearben Norway Centre National de Recherches Météorologiques Météo-France/CNRS Toulouse France Climate Research Division Environment and Climate Change Canada Toronto Canada Norwegian Polar Institute Fram Centre Tromsø Norway Danish Meteorological Institute Copenhagen Denmark Department of Physics University of Toronto Toronto Canada Department of Environmental Sciences University of Virginia Charlottesville Virginia Department of Geographical Sciences University of Maryland College Park Maryland University of Liège Liège Belgium Environment and Climate Change Canada Toronto Canada Northern Rocky Mountain Science Center U.S. Geological Survey Bozeman Montana Arctic C