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CEMRACS 2017: numerical probabilistic approach to MFG

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arXiv 2018年

作者： Angiuli, Andrea Graves, Christy V. Li, Houzhi Chassagneux, Jean-François Delarue, François Carmona, René Department of Statistics and Applied Probability University of California Santa Barbara Program in Applied and Computational Mathematics Princeton University Laboratoire de Probabilités Modélisation et Statistiques Université Paris Diderot Laboratoire Jean-Alexandre Dieudonné Université de Nice Sophia-Antipolis Operations Research and Financial Engineering Bendheim Center for Finance Princeton University

This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [27], and by Huang, Caines, and Malhamé, see [24]. Generally speaking, the purpose is to understand the continuum limit of optimizers or of equilibria (say in Nash sense) as the number of underlying players tends to infinity. When approached from the probabilistic viewpoint, solutions to these control problems (or games) can be described by coupled mean field FBSDEs, meaning that the coefficients depend upon the own marginal laws of the solution. In this note, we detail two methods for solving such FBSDEs which we implement and apply to five benchmark problems. The first method uses a tree structure to represent the pathwise laws of the solution, whereas the second method uses a grid discretization to represent the time marginal laws of the solutions. Both are based on a Picard scheme;importantly, we combine each of them with a generic continuation method that permits to extend the time horizon (or equivalently the coupling strength between the two equations) for which the Picard iteration converges. Copyright © 2018, The Authors. All rights reserved.

关键词： Numerical methods

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

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arXiv 2022年

作者： Aubry, Jean-Francois Bates, Oscar Boehm, Christian Pauly, Kim Butts Christensen, Douglas Cueto, Carlos Gélat, Pierre Guasch, Lluis Jaros, Jiri Jing, Yun Jones, Rebecca Li, Ningrui Marty, Patrick Montanaro, Hazael Neufeld, Esra Pichardo, Samuel Pinton, Gianmarco Pulkkinen, Aki Stanziola, Antonio Thielscher, Axel Treeby, Bradley Van't Wout, Elwin Physics for Medicine Paris INSERM U1273 ESPCI Paris PSL University CNRS UMR 8063 France Department of Bioengineering Imperial College London Exhibition Road LondonSW7 2AZ United Kingdom Institute of Geophysics ETH Zürich Sonneggstrasse 5 Zürich8092 Switzerland Department of Radiology Stanford University StanfordCA United States Department of Biomedical Engineering Department of Electrical and Computer Engineering University of Utah United States Department of Surgical Biotechnology Division of Surgery and Interventional Science University College London LondonNW3 2PF United Kingdom Earth Science and Engineering Department Imperial College London London United Kingdom Centre of Excellence IT4Innovations Faculty of Information Technology Brno University of Technology Bozetechova 2 Brno612 00 Czech Republic Graduate Program in Acoustics The Pennsylvania State University University Park PA16802 United States Joint Department of Biomedical Engineering University of North Carolina at Chapel Hill North Carolina State University NC United States Department of Electrical Engineering Stanford University StanfordCA United States Zurich Switzerland Laboratory for Acoustics / Noise control Empa Swiss Federal Laboratories for Materials Science and Technology Dubendorf Switzerland Zurich Switzerland Radiology and Clinical Neurosciences Departments Cumming School of Medicine University of Calgary Canada Department of Applied Physics University of Eastern Finland Kuopio70211 Finland Department of Medical Physics and Biomedical Engineering University College London Gower Street LondonWC1E 6BT United Kingdom Technical University of Denmark Denmark Danish Research Center for Magnetic Resonance Copenhagen University Hospital Hvidovre Denmark Institute for Mathematical and Computational Engineering School of Engineering and Faculty of Mathematics Pontificia Universidad Catolica de Chile Santiago Chile

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular-spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons. Copyright © 2022, The Authors. All rights reserved.

关键词： Bone

Effect of imperfections on the hyperuniformity of many-body systems

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Physical Review B 2018年第5期97卷 054105-054105页

作者： Jaeuk Kim Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

A hyperuniform many-body system is characterized by a structure factor Sk that vanishes in the small-wave-number limit or equivalently by a local number variance σN2R associated with a spherical window of radius R that grows more slowly than Rd in the large-R limit. Thus, the hyperuniformity implies anomalous suppression of long-wavelength density fluctuations relative to those in typical disordered systems, i.e., σN2R∼Rd as R→∞. Hyperuniform systems include perfect crystals, quasicrystals, and special disordered systems. Disordered hyperuniform systems are amorphous states of matter that lie between a liquid and crystal [S. Torquato et al., Phys. Rev. X 5, 021020 (2015)], and have been the subject of many recent investigations due to their novel properties. In the same way that there is no perfect crystal in practice due to the inevitable presence of imperfections, such as vacancies and dislocations, there is no “perfect” hyperuniform system, whether it is ordered or not. Thus, it is practically and theoretically important to quantitatively understand the extent to which imperfections introduced in a perfectly hyperuniform system can degrade or destroy its hyperuniformity and corresponding physical properties. This paper begins such a program by deriving explicit formulas for Sk in the small-wave-number regime for three types of imperfections: (1) uncorrelated point defects, including vacancies and interstitials, (2) stochastic particle displacements, and (3) thermal excitations in the classical harmonic regime. We demonstrate that our results are in excellent agreement with numerical simulations. We find that “uncorrelated” vacancies or interstitials destroy hyperuniformity in proportion to the defect concentration p. We show that “uncorrelated” stochastic displacements in perfect lattices can never destroy the hyperuniformity but it can be degraded such that the perturbed lattices fall into class III hyperuniform systems, where σN2R∼Rd−α as R→∞ and 0<α<1. By cont

关键词： Interstitials Structural properties Vacancies

Community Detection and Stochastic Block Models

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arXiv 2017年

作者： Abbe, Emmanuel Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University Princeton United States

The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study the information-theoretic and computational tradeoffs that arise in combinatorial statistics and more generally data science. This monograph surveys the recent developments that establish the fundamental limits for community detection in the SBM, both with respect to information-theoretic and computational tradeoffs, and for various recovery requirements such as exact, partial and weak recovery. The main results discussed are the phase transitions for exact recovery at the Chernoff-Hellinger threshold, the phase transition for weak recovery at the Kesten-Stigum threshold, the optimal SNR-mutual information tradeoff for partial recovery, and the gap between information-theoretic and computational thresholds. The monograph gives a principled derivation of the main algorithms developed in the quest of achieving the limits, in particular two-round algorithms via graph-splitting, semi-definite programming, (linearized) belief propagation, classical/nonbacktracking spectral methods and graph powering. Extensions to other block models, such as geometric block models, and a few open problems are also discussed. Copyright © 2017, The Authors. All rights reserved.

关键词： Recovery

Efficient algorithms for T-distributed stochastic neighborhood embedding

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arXiv 2017年

作者： Linderman, George C. Rachh, Manas Hoskins, Jeremy G. Steinerberger, Stefan Kluger, Yuval Applied Mathematics Program Yale University New HavenCT06511 United States Department of Mathematics Yale University New HavenCT06511 United States Department of Pathology and Applied Mathematics Program Yale University School of Medicine New HavenCT06511 United States

t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. We present Fast Fourier Transform-accelerated Interpolation-based t-SNE (FIt-SNE), which dramatically accelerates the computation of t-SNE. The most time-consuming step of t-SNE is a convolution that we accelerate by interpolating onto an equispaced grid and subsequently using the fast Fourier transform to perform the convolution. We also optimize the computation of input similarities in high dimensions using multi-threaded approximate nearest neighbors. We further present a modification to t-SNE called "late exaggeration," which allows for easier identification of clusters in t-SNE embeddings. Finally, for datasets that cannot be loaded into the memory, we present out-of-core randomized principal component analysis (oocPCA), so that the top principal components of a dataset can be computed without ever fully loading the matrix, hence allowing for t-SNE of large datasets to be computed on resource-limited machines. Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

Nonbacktracking bounds on the influence in independent cascade models

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arXiv 2017年

作者： Abbe, Emmanuel Kulkarni, Sanjeev Lee, Eun Jee Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University Princeton United States Department of Electrical Engineering Princeton University Princeton United States Program in Applied and Computational Mathematics Princeton University Princeton United States

This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin–Kasteleyn–Ginibre (FKG) type inequalities, and are computed by message passing implementation. Nonbacktracking walks have recently allowed for headways in community detection, and this paper shows that their use can also impact the influence computation. Further, we provide a knob to control the trade-off between the efficiency and the accuracy of the bounds. Finally, the tightness of the bounds is illustrated with simulations on various network models. Copyright © 2017, The Authors. All rights reserved.

关键词： Economic and social effects

Corrigendum to "Synergetic effect of bismuth vanadate over copolymerized carbon nitride composites for highly efficient photocatalytic H2 and O2 generation" [J. Colloid Interface Sci. 627 (2022) 621-629]

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Journal of colloid and interface science 2022年第PT A期628卷 366-367页

作者： Asif Hayat Muhammad Sohail T A Taha Sunil Kumar Baburao Mane Abdullah G Al-Sehemi Ahmed A Al-Ghamdi W I Nawawi Arkom Palamanit Mohammed A Amin Ahmed M Fallatah Zeeshan Ajmal Hamid Ali Wasim Ullah Khan Muhammad Wajid Shah Javid Khan S Wageh State Key Laboratory of Photocatalysis on Energy and Environment College of Chemistry Fuzhou University Fuzhou 350116 China. Yangtze Delta Region Institute (Huzhou) University of Electronic Science and Technology of China Huzhou 313001 China. Physics Department College of Science Jouf University P.O. Box: 2014 Sakaka Saudi Arabia Physics and Engineering Mathematics Department Faculty of Electronic Engineering Menoufia University Menouf 32952 Egypt. Department of Chemistry Khaja Bandanawaz University Kalaburagi Karnataka 585104 India. Research Center for Advanced Materials Science (RCAMS) King Khalid University P.O. Box 9004 Abha 61413 Saudi Arabia Department of Chemistry College of Science King Khalid University P.O. Box 9004 Abha 61413 Saudi Arabia. Department of Physics Faculty of Science King Abdulaziz University Jeddah 21589 Saudi Arabia. Faculty of Applied Sciences Universiti Teknologi MARA Cawangan Perlis Arau Perlis 02600 Malaysia. Energy Technology Program Department of Specialized Engineering Faculty of Engineering Prince of Songkla University 15 Karnjanavanich Rd. Hat Yai Songkhla 90110 Thailand. Department of Chemistry College of Science Taif University P.O. Box 11099 Taif 21944 Saudi Arabia. School of Chemistry and Chemical Engineering Northwestern Polytechnical University Xian 710072 China. Multiscale Computational Materials Facility Key Laboratory of Eco-Materials Advanced Technology College of Materials Science and Engineering Fuzhou University Fuzhou 350100 China. State Key Laboratory of Optoelectronic Materials and Technologies School of Materials Science and Engineering Sun Yat-sen University Guangzhou 510275 China. Electronic address: wasimullah89@***. School Of Chemistry Sun Yat-sen University Guangzhou 510275 China. Electronic address: m.wajidshah@***. College of Materials Science and Engineering Hunan University Changsha Hunan 410082 China. Electronic address: javidchemist@yahoo.com.

Local and global strong solutions for SQG in bounded domains

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arXiv 2017年

作者： Constantin, Peter Nguyen, Huy Quang DEPARTMENT OF MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States PROGRAM IN APPLIED AND COMPUTATIONAL MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States

We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of R2. When fractional Dirichlet Laplacian dissipation is added, global existence of strong solutions is obtained for small data for critical and supercritical cases. Global existence of strong solutions with arbitrary data is obtained in the subcritical *** Codes 35Q35, 35Q86 Copyright © 2017, The Authors. All rights reserved.

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Correction to: European first-year university students accept evolution but lack substantial knowledge about it: a standardized European cross-country assessment

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Evolution: Education and Outreach 2022年第1期15卷 1-2页

作者： Paul Kuschmierz Dittmar Graf Anna Beniermann Alexander Bergmann Rianne Pinxten Tuomas Aivelo Justyna Berniak-Woźny Gustav Bohlin Anxela Bugallo-Rodriguez Lucia Vazquez-Ben Pedro Cardia Bento Filipe Barreiras Pinto Cavadas Umran Betul Cebesoy Lütfullah Türkmen Dragana D. Cvetković Emilie Demarsy Mirko S. Đorđević Uroš B. Savković Szymon M. Drobniak Liudmyla Dubchak Radka M. Dvořáková Jana Fančovičová Corinne Fortin Momir Futo Nicoleta Adriana Geamănă Niklas Gericke Donato A. Grasso Ádám Z. Lendvai Zoltán Németh Evangelia Mavrikaki Andra Meneganzin Telmo Pievani Athanasios Mogias Andrea Möller Paulo G. Mota Yamama Naciri Katarzyna Ożańska-Ponikwia Silvia Paolucci Péter László Pap Maria Petersson Barbara Pietrzak Alma Pobric Juris Porozovs Giulia Realdon Xana Sá-Pinto Mathieu Sicard Mircea T. Sofonea Andrej Sorgo Alexandru N. Stermin Ioan Tăușan Gregor Torkar Slavica Tutnjević Anna E. Uitto Máté Varga Mirna Varga Konstantinos Korfiatis Enrique Viguera Lisa Christine Virtbauer Albena Vutsova Inmaculada Yruela Jelle Zandveld Institute for Didactics of Biology Justus-Liebig-University Giessen Giessen Germany Institute for Biology Teaching and Learning Research in Biology Education Humboldt-Universität Zu Berlin Berlin Germany Faculty of Life Science Department of Biology University of Leipzig Leipzig Germany Didactica Research Unit Faculty of Social Sciences & Behavioural Ecology & Ecophysiology Group Department of Biology University of Antwerp Antwerp Belgium Organismal and Evolutionary Biology Research Program University of Helsinki Helsinki Finland University of Information Technology and Management in Rzeszów Rzeszów Poland Public & Science (VA) Stockholm Sweden Department of Pedagogy and Didactics University of A Coruña A Coruña Spain Escola Superior de Educação Politécnico Do Porto Porto Portugal Department of Science and Mathematics Polytechnic Institute of Santarém/School of Education Santarém Portugal Faculty of Education/Department of Mathematics and Science Education Usak University Uşak Turkey Chair of Genetics and Evolution Faculty of Biology University of Belgrade Belgrade Serbia Department of Botany and Plant Biology University of Geneva Geneva Switzerland Department of Evolutionary Biology Institute for Biological Research Siniša Stanković”—National Institute of Republic of Serbia University of Belgrade Belgrade Serbia Institute of Environmental Sciences Jagiellonian University Kraków Poland Department of Parliamentarism and Political Management National Academy for Public Administration Under the President of Ukraine Kiev Ukraine Department of Teaching and Didactics of Biology Charles University Prague Czech Republic Department of Biology Faculty of Education Trnava University Trnava Slovakia Laboratory of Didactic André Revuz University of Paris Paris France Institut Ruđer Bošković/Division of Molecular Biology Zagreb Croatia Department/Research Center in Systems Ecology and Sustainability University of Bucharest Bucharest Romania Department of Enviro