检索结果-内蒙古大学图书馆

On the uniqueness of FROG methods

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Bendory, Tamir Sidorenko, Pavel Eldar, Yonina C. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Physics and Solid State Institute Technion-Israel Institute of Technology Haifa Israel Department of Electrical Engineering Technion-Israel Institute of Technology Haifa Israel

The problem of recovering a signal from its power spectrum, called phase retrieval, arises in many scientific fields. One of many examples is ultra-short laser pulse characterization in which the electromagnetic field is oscillating with ∼ 1015 Hz and phase information cannot be measured directly due to limitations of the electronic sensors. Phase retrieval is ill-posed in most cases as there are many different signals with the same Fourier transform magnitude. To overcome this fundamental ill-posedness, several measurement techniques are used in practice. One of the most popular methods for complete characterization of ultra-short laser pulses is the Frequency-Resolved Optical Gating (FROG). In FROG, the acquired data is the power spectrum of the product of the unknown pulse with its delayed replica. Therefore the measured signal is a quartic function of the unknown pulse. A generalized version of FROG, where the delayed replica is replaced by a second unknown pulse, is called blind FROG. In this case, the measured signal is quadratic with respect to both pulses. In this letter we introduce and formulate FROG-type techniques. We then show that almost all band-limited signals are determined uniquely, up to trivial ambiguities, by blind FROG measurements (and thus also by FROG), if in addition we have access to the signals power spectrum. Copyright © 2017, The Authors. All rights reserved.

关键词： Power spectrum

On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Weinan, E. Hutzenthaler, Martin Jentzen, Arnulf Kruse, Thomas Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544-1000 United States BICMR and School of Mathematical Sciences Peking University Beijing100870 China Faculty of Mathematics University of Duisburg-Essen Essen45117 Germany Seminar für Angewandte Mathematik ETH Zurich Zürich8092 Switzerland

Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) are key ingredients in a number of models in physics and financial engineering. In particular, parabolic PDEs and BSDEs are fundamental tools in the state-of-the-art pricing and hedging of financial derivatives. The PDEs and BSDEs appearing in such applications are often high-dimensional and nonlinear. Since explicit solutions of such PDEs and BSDEs are typically not available, it is a very active topic of research to solve such PDEs and BSDEs approximately. In the recent article [E, W., Hutzenthaler, M., Jentzen, A., & Kruse, T. Linear scaling algorithms for solving high-dimensional nonlinear parabolic differential equations. arXiv:1607.03295 (2017)] we proposed a family of approximation methods based on Picard approximations and multilevel Monte Carlo methods and showed under suitable regularity assumptions on the exact solution for semilinear heat equations that the computational complexity is bounded by O(d ϵ-(4+δ)) for any δ 2 (0,∞), where d is the dimensionality of the problem and ϵ ∈ (0,∞) is the prescribed accuracy. In this paper, we test the applicability of this algorithm on a variety of 100-dimensional nonlinear PDEs that arise in physics and finance by means of numerical simulations presenting approximation accuracy against runtime. The simulation results for these 100-dimensional example PDEs are very satisfactory in terms of accuracy and speed. In addition, we also provide a review of other approximation methods for nonlinear PDEs and BSDEs from the literature. Copyright © 2017, The Authors. All rights reserved.

关键词： Monte Carlo methods

Correction to: Optimal deterministic algorithm generation

学校读者我要写书评

暂无评论

Journal of Global Optimization 2018年第2期73卷 465-465页

作者： Mitsos, Alexander Najman, Jaromił Kevrekidis, Ioannis G. AVT Process Systems Engineering (SVT) RWTH Aachen University Aachen Germany Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics Princeton University Princeton USA IAS-TUM Garching and Zuse Institut FU Berlin Berlin Germany Departments of Chemical and Biomolecular Engineering Applied Mathematics and Statistics and Urology Johns Hopkins University Baltimore USA

Unfortunately, the copyright information of the article in Springerlink appears as “©  Springer Science+Business Media, LLC, part of Springer Nature 2018” this has been corrected to “©  ...

Unfortunately, the copyright information of the article in Springerlink appears as “© Springer Science+Business Media, LLC, part of Springer Nature 2018” this has been corrected to “© The Author(s) 2018.”

关键词：

Limited angle acousto-electrical tomography

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Hubmer, Simon Knudsen, Kim Li, Changyou Sherina, Ekaterina Johannes Kepler University Linz Doctoral Program Computational Mathematics Altenbergerstraße 69 LinzA-4040 Austria Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark School of Electronics and Information Northwestern Polytechnical University Xian China Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark

This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from different prescribed boundary conditions. Particular emphasis is placed on the limited angle scenario, in which the boundary conditions are supported only on a part of the boundary. The reconstruction problem is formulated as an optimization problem in a Hilbert space setting and solved using Landweber iteration. The resulting algorithm is implemented numerically in two spatial dimensions and tested on simulated data. The results quantify the intuition that features close to the measurement boundary are stably reconstructed and features further away are less well reconstructed. Finally, the ill-posedness of the limited angle problem is quantified numerically using the singular value decomposition of the corresponding linearized problem.65J22, 35R30, 65M32 Copyright © 2017, The Authors. All rights reserved.

关键词： Boundary conditions

Reduced modeling of porous media convection in a minimal flow unit at large Rayleigh number

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Wen, Baole Chini, Gregory P. Department of Geological Sciences Jackson School of Geosciences University of Texas at Austin AustinTX78712 United States Institute of Computational Engineering and Sciences University of Texas at Austin AustinTX78712 United States Program in Integrated Applied Mathematics University of New Hampshire W113 Kingsbury Hall 33 Academic Way DurhamNH03824 United States Center for Fluid Physics University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States

Direct numerical simulations (DNS) indicate that at large values of the Rayleigh number (Ra) convection in porous media self-organizes into narrowly-spaced columnar flows, with more complex spatiotemporal features being confined to boundary layers near the top and bottom walls. In this investigation of high-Ra porous media convection in a minimal flow unit, two reduced modeling strategies are proposed that exploit these specific flow characteristics. Both approaches utilize the idea of decomposition since the flow exhibits different dynamics in different regions of the domain: small-scale cellular motions generally are localized within the thermal and vorticity boundary layers near the upper and lower walls, while in the interior, the flow exhibits persistent large-scale structures and only a few low (horizontal) wavenumber Fourier modes are active. Accordingly, in the first strategy, the domain is decomposed into two near-wall regions and one interior region. Our results confirm that suppressing the interior high-wavenumber modes has negligible impact on the essential structural features and transport properties of the flow. In the second strategy, a hybrid reduced model is constructed by using Galerkin projection onto a fully a priori eigenbasis drawn from energy stability and upper bound theory, thereby extending the model reduction strategy developed by Chini et al. (Physica D, vol. 240, 2011, pp. 241-248) to large Ra. The results indicate that the near-wall upper-bound eigenmodes can economically represent the small-scale rolls within the exquisitely-thin thermal boundary layers. Relative to DNS, the hybrid algorithm enables over an order-of-magnitude increase in computational efficiency with only a modest loss of accuracy. Copyright © 2018, The Authors. All rights reserved.

关键词： Porous materials

Ordered magnetic fields around the 3C 84 central black hole

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Paraschos, Georgios Filippos Kim, J.-Y. Wielgus, M. Röder, J. Krichbaum, T.P. Ros, E. Agudo, I. Myserlis, I. Moscibrodzka, M. Traianou, E. Zensus, J.A. Blackburn, L. Chan, C.-K. Issaoun, S. Janssen, M. Johnson, M.D. Fish, V.L. Akiyama, K. Alberdi, A. Alef, W. Algaba, J.C. Anantua, R. Asada, K. Azulay, R. Bach, U. Baczko, A.-K. Ball, D. Baloković, M. Barrett, J. Bauböck, M. Benson, B.A. Bintley, D. Blundell, R. Bouman, K.L. Bower, G.C. Boyce, H. Bremer, M. Brinkerink, C.D. Brissenden, R. Britzen, S. Broderick, A.E. Broguiere, D. Bronzwaer, T. Bustamante, S. Byun, D.-Y. Carlstrom, J.E. Ceccobello, C. Chael, A. Chang, D.O. Chatterjee, K. Chatterjee, S. Chen, M.T. Chen, Y. Cheng, X. Cho, I. Christian, P. Conroy, N.S. Conway, J.E. Cordes, J.M. Crawford, T.M. Crew, G.B. Cruz-Osorio, A. Cui, Y. Dahale, R. Davelaar, J. De Laurentis, M. Deane, R. Dempsey, J. Desvignes, G. Dexter, J. Dhruv, V. Doeleman, S.S. Dougal, S. Dzib, S.A. Eatough, R.P. Emami, R. Falcke, H. Farah, J. Fomalont, E. Ford, H.A. Foschi, M. Fraga-Encinas, R. Freeman, W.T. Friberg, P. Fromm, C.M. Fuentes, A. Galison, P. Gammie, C.F. García, R. Gentaz, O. Georgiev, B. Goddi, C. Gold, R. Gómez-Ruiz, A.I. Gómez, J.L. Gu, M. Gurwell, M. Hada, K. Haggard, D. Haworth, K. Hecht, M.H. Hesper, R. Heumann, D. Ho, L.C. Ho, P. Honma, M. Huang, C.L. Huang, L. Hughes, D.H. Ikeda, S. Impellizzeri, C.M.V. Inoue, M. James, D.J. Jannuzi, B.T. Jeter, B. Jaing, W. Jiménez-Rosales, A. Jorstad, S. Joshi, A.V. Jung, T. Karami, M. Karuppusamy, R. Kawashima, T. Keating, G.K. Kettenis, M. Kim, D.-J. Kim, J. Kim, J. Kino, M. Koay, J.Y. Kocherlakota, P. Kofuji, Y. Koch, P.M. Koyama, S. Kramer, C. Kramer, J.A. Kramer, M. Kuo, C.-Y. La Bella, N. Lauer, T.R. Lee, D. Lee, S.-S. Leung, P.K. Levis, A. Li, Z. Lico, R. Lindahl, G. Lindqvist, M. Lisakov, M. Liu, J. Liu, K. Liuzzo, E. Lo, W.-P. Lobanov, A.P. Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Department of Astronomy and Atmospheric Sciences Kyungpook National University Daegu702-701 Korea Republic of Institute of Physics Silesian University in Opava Bezručovo nám. 13 OpavaCZ-746 01 Czech Republic Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Avenida Divina Pastora 7 Local 20 GranadaE-18012 Spain Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Black Hole Initiative Harvard University 20 Garden Street CambridgeMA02138 United States Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave. TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Ave. TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 N. Santa Rita TucsonAZ85721 United States NASA Hubble Fellowship Program Einstein Fellow United States Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Department of Physics Faculty of Science Universiti Malaya Kuala Lumpur50603 Malaysia Department of Physics & Astronomy The University of Texas at San Antonio One UTSA Circle San AntonioTX78249 United States Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd. Taipei10617 Taiwan Departament d’Astronomia i Astrofísica Universitat de València C. Dr. Moliner 50 Burjassot ValènciaE-46100 Spain Observatori Astronòmic Universitat de València C. Catedrático José Beltrán 2 València PaternaE-46980 Spain Department of Space Earth and Environment Chalmers University of Technology Onsala Space Observatory OnsalaSE-43992 Sweden Yale C

Context. 3C 84 is a nearby radio source with a complex total intensity structure, showing linear polarisation and spectral patterns. A detailed investigation of the central engine region necessitates the use of very-long-baseline interferometry (VLBI) above the hitherto available maximum frequency of 86 GHz. Aims. Using ultrahigh resolution VLBI observations at the currently highest available frequency of 228 GHz, we aim to perform a direct detection of compact structures and understand the physical conditions in the compact region of 3C 84. Methods. We used Event Horizon Telescope (EHT) 228 GHz observations and, given the limited (u, v)-coverage, applied geometric model fitting to the data. Furthermore, we employed quasi-simultaneously observed, ancillary multi-frequency VLBI data for the source in order to carry out a comprehensive analysis of the core structure. Results. We report the detection of a highly ordered, strong magnetic field around the central, supermassive black hole of 3C 84. The brightness temperature analysis suggests that the system is in equipartition. We also determined a turnover frequency of νm = (113 ± 4) GHz, a corresponding synchrotron self-absorbed magnetic field of BSSA = (2.9 ± 1.6) G, and an equipartition magnetic field of Beq = (5.2 ± 0.6) G. Three components are resolved with the highest fractional polarisation detected for this object (mnet = (17.0 ± 3.9)%). The positions of the components are compatible with those seen in low-frequency VLBI observations since 2017-2018. We report a steeply negative slope of the spectrum at 228 GHz. We used these findings to test existing models of jet formation, propagation, and Faraday rotation in 3C 84. Conclusions. The findings of our investigation into different flow geometries and black hole spins support an advection-dominated accretion flow in a magnetically arrested state around a rapidly rotating supermassive black hole as a model of the jet-launching system in the core of 3C 84. However,

关键词： Magnetic fields

Detecting community structures in Hi-C genomic data

学校读者我要写书评

暂无评论

Detecting community structures in Hi-C genomic data

Annual Conference on Information Sciences and Systems (CISS)

作者： Irineo Cabreros Emmanuel Abbe Aristotelis Tsirigos Program in Applied and Computational Mathematics Princeton University Program in Applied and Computational Mathematics and Department of Electrical Engineering Princeton University Department of Pathology NYU Langone Medical Center

Community detection (CD) algorithms are applied to Hi-C data to discover new communities of loci in the 3D conformation of human and mouse DNA. We find that CD has some distinct advantages over pre-existing methods: (1) it is capable of finding a variable number of communities, (2) it can detect communities of DNA loci either adjacent or distant in the 1D sequence, and (3) it allows us to obtain a principled value of k, the number of communities present. Forcing k = 2, our method recovers earlier findings of Lieberman-Aiden, et al. (2009), but letting k be a parameter, our method obtains as optimal value k* = 6, discovering new candidate communities. In addition to discovering large communities that partition entire chromosomes, we also show that CD can detect small-scale topologically associating domains (TADs) such as those found in Dixon, et al. (2012). CD thus provides a natural and flexible statistical framework for understanding the folding structure of DNA at multiple scales in Hi-C data.

关键词： DNA Biological cells Three-dimensional displays Hidden Markov models Principal component analysis Algorithm design and analysis Genomics

Optimal Learning for Sequential Decision Making for Expensive Cost Functions with Stochastic Binary Feedbacks

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Wang, Yingfei Wang, Chu Powell, Warren Department of Computer Science Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08544 United States

We consider the problem of sequentially making decisions that are rewarded by "successes" and "failures" which can be predicted through an unknown relationship that depends on a partially controllable vector of attributes for each instance. The learner takes an active role in selecting samples from the instance pool. The goal is to maximize the probability of success in either offline (training) or online (testing) phases. Our problem is motivated by real-world applications where observations are time consuming and/or expensive. We develop a knowledge gradient policy using an online Bayesian linear classifier to guide the experiment by maximizing the expected value of information of labeling each alternative. We provide a finite-time analysis of the estimated error and show that the maximum likelihood estimator based produced by the KG policy is consistent and asymptotically normal. We also show that the knowledge gradient policy is asymptotically optimal in an offline setting. This work further extends the knowledge gradient to the setting of contextual bandits. We report the results of a series of experiments that demonstrate its efficiency. Copyright © 2017, The Authors. All rights reserved.

关键词： Maximum likelihood estimation

Correction to: Genes associated with survival of female bovine blastocysts produced in vivo

学校读者我要写书评

暂无评论

Cell and tissue research 2020年第3期382卷 679页

作者： A M Zolini J Block M B Rabaglino G Rincon M Hoelker J J Bromfield D Salilew-Wondim P J Hansen Department of Animal Sciences D.H. Barron Reproductive and Perinatal Biology Research Program and Genetics Institute University of Florida PO Box 110910 Gainesville FL 32611-0910 USA. Zoetis Inc. Kalamazoo MI 49007 USA. Instituto de Investigación en Ciencias de La Salud CONICET Córdoba Argentina. Quantitative Genetics Bioinformatics and Computational Biology Group Department of Applied Mathematics and Computer Science Technical University of Denmark Kemitorvet 2800 Kgs. Lyngby Denmark. Institute of Animal Science Animal Breeding and Husbandry University of Bonn Bonn Germany. Teaching and Research Station Frankenforst Faculty of Agriculture University of Bonn Königswinter Germany. Center of Integrated Dairy Research University of Bonn Bonn Germany. Department of Animal Sciences D.H. Barron Reproductive and Perinatal Biology Research Program and Genetics Institute University of Florida PO Box 110910 Gainesville FL 32611-0910 USA. pjhansen@ufl.edu.

The first error is on page 5. A sentence lists two genes as SCNA1A and SCNA2A but they should be SCN1A and SCN2A.

关键词：