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A path integral method for solution of the wave equation with continuously-varying coefficients

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arXiv 2019年

作者： George, Jithin D. Ketcheson, David I. LeVeque, Randall J. Department of Engineering Sciences and Applied Mathematics Northwestern University Computer Electrical and Mathematical Sciences & Engineering Division King Abdullah University of Science and Technology 4700 KAUST Thuwal23955 Saudi Arabia Department of Applied Mathematics University of Washington SeattleWA98195-3925 United States

A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an infinite series of integrals, where the integrand involves only the initial data and the PDE coefficients. Each term in the series represents the influence of paths with a fixed number of turning points. We prove that the series converges and provide bounds for the truncation error. The effectiveness of the approximation is illustrated with examples. We illustrate an interesting combinatorial connection between the traditional reflection and transmission coefficients for a sharp interface, and Green’s coefficient for transmission through a smoothly-varying region. Copyright © 2019, The Authors. All rights reserved.

关键词： Wave equations

Generalization in quantum machine learning from few training data

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arXiv 2021年

作者： Caro, Matthias C. Huang, Hsin-Yuan Cerezo, M. Sharma, Kunal Sornborger, Andrew Cincio, Lukasz Coles, Patrick J. Department of Mathematics Technical University of Munich Garching Germany Munich Germany Institute for Quantum Information and Matter Caltech PasadenaCA United States Department of Computing and Mathematical Sciences Caltech PasadenaCA United States Information Sciences Los Alamos National Laboratory Los AlamosNM87545 United States Center for Nonlinear Studies Los Alamos National Laboratory Los AlamosNM87545 United States Joint Center for Quantum Information and Computer Science University of Maryland College ParkMD20742 United States Quantum Science Center Oak RidgeTN37931 United States Theoretical Division Los Alamos National Laboratory Los AlamosNM87545 United States

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as √T/N. When only K T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to √K/N. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data. Copyright © 2021, The Authors. All rights reserved.

关键词： Machine learning

Simultaneous dimensionality and complexity model selection for spectral graph clustering

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arXiv 2019年

作者： Yang, Congyuan Priebe, Carey E. Park, Youngser Marchette, David J. Department of Electrical and Computer Engineering Johns Hopkins University Department of Applied Math and Statistics Johns Hopkins University Center for Imaging Science Johns Hopkins University Applied Mathematics and Data Analytics Group Naval Surface Warfare Center Dahlgren Division

Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement while often outperforming more traditional clustering algorithms. However, there are two inherent model selection problems in spectral clustering, namely estimating both the embedding dimension and number of clusters. This paper attempts to address the issue by establishing a novel model selection framework specifically for vertex clustering on graphs under a stochastic block model. The first contribution is a probabilistic model which approximates the distribution of the extended spectral embedding of a graph. The model is constructed based on a theoretical result of asymptotic normality of the informative part of the embedding, and on a simulation result providing a conjecture for the limiting behavior of the redundant part of the embedding. The second contribution is a simultaneous model selection framework. In contrast with the traditional approaches, our model selection procedure estimates embedding dimension and number of clusters simultaneously. Based on our conjectured distributional model, a theorem on the consistency of the estimates of model parameters is stated and proven. The theorem provides statistical support for the validity of our method. Heuristic algorithms via the simultaneous model selection framework for vertex clustering are proposed, with good performance shown in the experiment on synthetic data and on the real application of connectome analysis. Copyright © 2019, The Authors. All rights reserved.

关键词： Embeddings

Leveraging randomized compiling for the QITE algorithm

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arXiv 2021年

作者： Ville, Jean-Loup Morvan, Alexis Hashim, Akel Naik, Ravi K. Lu, Marie Mitchell, Bradley Kreikebaum, John-Mark O’Brien, Kevin P. Wallman, Joel J. Hincks, Ian Emerson, Joseph Smith, Ethan Younis, Ed Iancu, Costin Santiago, David I. Siddiqi, Irfan Quantum Nanoelectronics Laboratory Dept. of Physics University of California at Berkeley BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States Inst. for Quantum Computing Dept. of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Quantum Benchmark Inc. KitchenerONN2H 5G5 Canada

The success of the current generation of Noisy Intermediate-Scale Quantum (NISQ) hardware shows that quantum hardware may be able to tackle complex problems even without error correction. One outstanding issue is that of coherent errors arising from the increased complexity of these devices. These errors can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like Quantum Imaginary Time Evolution are susceptible to these errors. This article presents the combination of both noise tailoring using Randomized Compiling and error mitigation with a purification. We also show that Cycle Benchmarking gives an estimate of the reliability of the purification. We apply this method to the Quantum Imaginary Time Evolution of a Transverse Field Ising Model and report an energy estimation and a ground state infidelity both below 1%. Our methodology is general and can be used for other algorithms and platforms. We show how combining noise tailoring and error mitigation will push forward the performance of NISQ devices. © 2021, CC BY.

关键词： Benchmarking

Electroweak, QCD and flavour physics studies with ATLAS data from Run 2 of the LHC

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Physics Reports 2025年 1116卷 57-126页

作者： Aad, G. Aakvaag, E. Abbott, B. Abdelhameed, S. Abeling, K. Abicht, N.J. Abidi, S.H. Aboelela, M. Aboulhorma, A. Abramowicz, H. Abreu, H. Abulaiti, Y. Acharya, B.S. Ackermann, A. Adam Bourdarios, C. Adamczyk, L. Addepalli, S.V. Addison, M.J. Adelman, J. Adiguzel, A. Adye, T. Affolder, A.A. Afik, Y. Agaras, M.N. Agarwala, J. Aggarwal, A. Agheorghiesei, C. Ahmad, A. Ahmadov, F. Ahmed, W.S. Ahuja, S. Ai, X. Aielli, G. Aikot, A. Ait Tamlihat, M. Aitbenchikh, B. Akbiyik, M. Åkesson, T.P.A. Akimov, A.V. Akiyama, D. Akolkar, N.N. Aktas, S. Al Khoury, K. Alberghi, G.L. Albert, J. Albicocco, P. Albouy, G.L. Alderweireldt, S. Alegria, Z.L. Aleksa, M. Aleksandrov, I.N. Alexa, C. Alexopoulos, T. Alfonsi, F. Algren, M. Alhroob, M. Ali, B. Ali, H.M.J. Ali, S. Alibocus, S.W. Aliev, M. Alimonti, G. Alkakhi, W. Allaire, C. Allbrooke, B.M.M. Allen, J.F. Allendes Flores, C.A. Allport, P.P. Aloisio, A. Alonso, F. Alpigiani, C. Alsolami, Z.M.K. Alvarez Estevez, M. Alvarez Fernandez, A. Alves Cardoso, M. Alviggi, M.G. Aly, M. Amaral Coutinho, Y. Ambler, A. Amelung, C. Amerl, M. Ames, C.G. Amidei, D. Amirie, K.J. Amor Dos Santos, S.P. Amos, K.R. An, S. Ananiev, V. Anastopoulos, C. Andeen, T. Anders, J.K. Andrean, S.Y. Andreazza, A. Angelidakis, S. Angerami, A. Anisenkov, A.V. Annovi, A. Antel, C. Antipov, E. Antonelli, M. Anulli, F. Aoki, M. Aoki, T. Aparo, M.A. Aperio Bella, L. Appelt, C. Apyan, A. Arbiol Val, S.J. Arcangeletti, C. Arce, A.T.H. Arena, E. Arguin, J.-F. Argyropoulos, S. Arling, J.-H. Arnaez, O. Arnold, H. Artoni, G. Asada, H. Asai, K. Asai, S. Asbah, N.A. Ashby Pickering, R.A. Assamagan, K. Astalos, R. Astrand, K.S.V. Atashi, S. Atkin, R.J. Atkinson, M. Atmani, H. Atmasiddha, P.A. Augsten, K. Auricchio, S. Auriol, A.D. Austrup, V.A. Avolio, G. Axiotis, K. Azuelos, G. Babal, D. Bachacou, H. Bachas, K. Bachiu, A. Backman, F. Badea, A. Baer, T.M. Bagnaia, P. Bahmani, M. Bahner, D. Bai, K. Baines, J.T. Baines, L. Baker, O.K. Bakos, E. Bakshi Gupta, D. Balakrishnan, V. Balasubramanian, R. Baldin, E.M. Balek, P. Ballabene, E. CPPM Aix-Marseille Université CNRS IN2P3 Marseille France Department for Physics and Technology University of Bergen Bergen Norway Homer L. Dodge Department of Physics and Astronomy University of Oklahoma Norman OK United States New York University Abu Dhabi Abu Dhabi United Arab Emirates II. Physikalisches Institut Georg-August-Universität Göttingen Göttingen Germany Fakultät Physik Technische Universität Dortmund Dortmund Germany Physics Department Brookhaven National Laboratory Upton NY United States Physics Department Southern Methodist University Dallas TX United States Faculté des sciences Université Mohammed V Rabat Morocco Raymond and Beverly Sackler School of Physics and Astronomy Tel Aviv University Tel Aviv Israel Department of Physics Technion Israel Institute of Technology Haifa Israel Department of Physics New York University New York NY United States INFN Gruppo Collegato di Udine Sezione di Trieste Udine Italy ICTP Trieste Italy Department of Physics King's College London London United Kingdom Kirchhoff-Institut für Physik Ruprecht-Karls-Universität Heidelberg Heidelberg Germany LAPP Université Savoie Mont Blanc CNRS IN2P3 Annecy France AGH University of Krakow Faculty of Physics and Applied Computer Science Krakow Poland Department of Physics Brandeis University Waltham MA United States School of Physics and Astronomy University of Manchester Manchester United Kingdom Department of Physics Northern Illinois University DeKalb IL United States Department of Physics Istanbul University Istanbul Turkey Particle Physics Department Rutherford Appleton Laboratory Didcot United Kingdom Santa Cruz Institute for Particle Physics University of California Santa Cruz Santa Cruz CA United States Enrico Fermi Institute University of Chicago Chicago IL United States Institut de Física d'Altes Energies (IFAE) Barcelona Institute of Science and Technology Barcelona Spain INFN Sezione di Pavia Italy Dipartimento di Fisica Uni

A summary of precision measurements sensitive to electroweak, QCD and quark-flavour effects performed by the ATLAS Collaboration at the Large Hadron Collider is reported. The measurements are predominantly performed on proton–proton (pp) collision data recorded at a centre-of-mass energy of 13 TeV taken from 2015 to 2018, with an integrated luminosity of up to 140 fb⁻¹, with some results based on pp and Pb+Pb data recorded at lower nucleon centre-of-mass energies. The results cover a wide range of topics, from strong production of particles at low energies and the spectroscopy of hadrons to perturbative QCD with hadronic jets and electroweak and strong production of single and multiple vector bosons. They provide precise measurements of fundamental constants and stringent tests of the Standard Model with unprecedented precision and in energy ranges never explored before. They are also used to explore the proton structure and to perform model-independent searches for new physics. © 2024 CERN for the benefit of the ATLAS Collaboration

关键词：

One pathogen does not an epidemic make: A review of interacting contagions, diseases, beliefs, and stories

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arXiv 2025年

作者： Hébert-Dufresne, Laurent Ahn, Yong-Yeol Allard, Antoine Crothers, Jessica W. Dodds, Peter Sheridan Galesic, Mirta Ghanbarnejad, Fakhteh Gravel, Dominique Hammond, Ross A. Lerman, Kristina Lovato, Juniper Openshaw, John J. Redner, S. Scarpino, Samuel V. St-Onge, Guillaume Tangherlini, Timothy R. Young, Jean-Gabriel Vermont Complex Systems Institute University of Vermont BurlingtonVT United States Translational Global Infectious Disease Research Center University of Vermont BurlingtonVT United States Department of Computer Science University of Vermont BurlingtonVT United States Center for Complex Networks and Systems Research Luddy School of Informatics Computing and Engineering Indiana University BloomingtonIN United States Département de physique de génie physique et d’optique Université Laval QuébecQC Canada Department of Pathology and Laboratory Medicine Robert Larner M.D. College of Medicine University of Vermont BurlingtonVT United States Santa Fe Institute Santa FeNM United States Complexity Science Hub Vienna Austria School of Technology and Architecture SRH University of Applied Sciences Heidelberg Leipzig Germany Département de biologie Université de Sherbrooke SherbrookeQC Canada Brown School Washington University in St. Louis St. LouisMO United States The Brookings Institution WashingtonDC United States Information Sciences Institute University of Southern California United States Division of Infectious Diseases and Geographic Medicine Stanford University StanfordCA United States Institute for Experiential AI Northeastern University BostonMA United States Laboratory for the Modeling of Biological and Socio-technical Systems Northeastern University BostonMA United States The Roux Institute Northeastern University PortlandME United States Department of Scandinavian School of Information University of California Berkeley BerkeleyCA United States Department of Mathematics & Statistics University of Vermont BurlingtonVT United States

From pathogens and computer viruses to genes and memes, contagion models have found widespread utility across the natural and social sciences. Despite their success and breadth of adoption, the approach and structure of these models remain surprisingly siloed by field. Given the siloed nature of their development and widespread use, one persistent assumption is that a given contagion can be studied in isolation, independently from what else might be spreading in the population. In reality, countless contagions of biological and social nature interact within hosts (interacting with existing beliefs, or the immune system) and across hosts (interacting in the environment, or affecting transmission mechanisms). Additionally, from a modeling perspective, we know that relaxing these assumptions has profound effects on the physics and translational implications of the models. Here, we review mechanisms for interactions in social and biological contagions, as well as the models and frameworks developed to include these interactions in the study of the contagions. We highlight existing problems related to the inference of interactions and to the scalability of mathematical models and identify promising avenues of future inquiries. In doing so, we highlight the need for interdisciplinary efforts under a unified science of contagions and for removing a common dichotomy between social and biological contagions. Copyright © 2025, The Authors. All rights reserved.

关键词： Histology

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

Colloidal dynamics on a choreographic time crystal

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arXiv 2019年

作者： Libál, András Balázs, Tünde Reichhardt, C. Reichhardt, C.J.O. Theoretical Division and Center for Nonlinear Studies Los Alamos National Laboratory Los AlamosNM87545 United States Mathematics and Computer Science Department Babeş-Bolyai University Cluj400084 Romania

A choreographic time crystal is a dynamic lattice structure in which the points comprising the lattice move in a coordinated fashion. These structures were initially proposed for understanding the motion of synchronized satellite swarms. Using simulations we examine colloids interacting with a choreographic crystal consisting of traps that could be created optically. As a function of the trap strength, speed, and colloidal filling fraction, we identify a series of phases including states where the colloids organize into a dynamic chiral loop lattice as well as a frustrated induced liquid state and a choreographic lattice state. We show that transitions between these states can be understood in terms of vertex frustration effects that occur during a certain portion of the choreographic cycle. Our results can be generalized to a broader class of systems of particles coupled to choreographic structures, such as vortices, ions, cold atoms, and soft matter systems. Copyright © 2019, The Authors. All rights reserved.

关键词： Crystal atomic structure