检索结果-内蒙古大学图书馆

作者： Bandeira, A.S. Scheinberg, K. Vicente, L.N. Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Industrial and Systems Engineering Lehigh University Harold S. Mohler Laboratory 200 West Packer Avenue Bethlehem PA 18015-1582 United States CMUC Department of Mathematics University of Coimbra 3001-501 Coimbra Portugal

Interpolation-based trust-region methods are an important class of algorithms forDerivative-Free Optimizationwhich rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations between variables are negligible, implying, in the smooth case, a sparse structure in the Hessian matrix. To be able to exploit Hessian sparsity, existing optimization approaches require the knowledge of the sparsity structure. The goal of this paper is to develop and analyze a method where the sparse models are constructed automatically. The sparse recovery theory developed recently in the field of compressed sensing characterizes conditions under which a sparse vector can be accurately recovered from few random measurements. Such a recovery is achieved by minimizing the l1-norm of a vector subject to the measurements constraints. We suggest an approach for building sparse quadratic polynomial interpolationmodels byminimizing the l1-norm of the entries of themodel Hessian subject to the interpolation conditions. We show that this procedure recovers accurate models when the function Hessian is sparse, using relatively few randomly selected sample points. Motivated by this result, we developed a practical interpolation-based trust-region method using deterministic sample sets and minimum l1-norm quadratic models. Our computational results show that the new approach exhibits a promising numerical performance both in the general case and in the sparse one. © Springer and Mathematical Optimization Society 2012.

关键词： Interpolation

来源：评论

学校读者我要写书评

暂无评论

Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation

引用

Journal of Dynamics and Differential Equations 1991年第2期3卷 179-197页

作者： Jolly, M.S. Kevrekidis, I.G. Titi, E.S. Program in Applied and Computational Mathematics Princeton University Princeton 08544 New Jersey United States Department of Mathematics Indiana University Bloomington 47405 Indiana United States Department of Chemical Engineering Princeton University Princeton 08544 New Jersey United States Mathematical Sciences Institute Cornell University Ithaca 14853 New York United States Department of Mathematics University of California Irvine 92717 California United States

It has been observed, in earlier computations of bifurcation diagrams for dissipative partial differential equations, that the use of certain explicit approximate inertial forms can give rise to numerical artifacts such as spurious turning points and inaccurate solution branches. These shortcomings were attributed to a lack of dissipation in the forms used. We show analytically and verify numerically that with an appropriate adjustment we can eliminate these numerical artifacts. The motivation for this adjustment is to enforce dissipation, while maintaining the same order of approximation. We demonstrate with computations that the most natural remedy, namely, preparation of the equation, can be highly sensitive to assumptions on the size of the absorbing ball. In addition, we show that certain implicit forms are dissipative without any adjustment. As an illustrative example we use here the Kuramoto-Sivashinsky equation. © 1991 Plenum Publishing Corporation.

关键词： dissipation Inertial manifold Kuramoto-Sivashinsky non-linear Galerkin method

来源：评论

学校读者我要写书评

暂无评论

Evaluation of depth‐of‐focus in photolithography at 193 and 248 nm for feature sizes of 0.25 μm and below

Journal of Vacuum Science & Technology B: Microelectronics a...

引用

Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena 1993年第6期11卷 2720-2724页

作者： M. Rothschild S. P. Doran E. Barouch U. Hollerbach S. A. Orszag Lincoln Laboratory Massachusetts Institute of Technology Lexington Massachusetts 02173‐9108 Program of Applied and Computational Mathematics Princeton University Princeton New Jersey 08544

The aerial image of alternative exposure systems was calculated in order to determine process latitude in photolithography at 0.25 μm and below. A fast software package was used for both simple and complex mask patterns. The depth‐of‐focus (DOF) was obtained with the aid of exposure–defocus plots at 193 and 248 nm. The numerical aperture and degree of spatial coherence were varied over a wide range. The effects of annular illumination were also studied. It was shown that for most geometries the DOF at 193 nm exceeds that of 248‐nm systems. Only for equal lines and spaces does a 248‐nm tool with annular illumination possess a DOF comparable to that of a conventionally illuminated 193‐nm system.

关键词：

来源：评论

学校读者我要写书评

暂无评论

Erratum to: Some Joys and Trials of Mathematical Neuroscience

引用

Journal of Nonlinear Science 2014年第2期24卷 243-244页

作者： Holmes, Philip Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton USA Princeton Neuroscience Institute Princeton University Princeton USA

来源：评论

学校读者我要写书评

暂无评论

Nucleation of Ordered Phases in Block Copolymers

引用

Physical Review Letters 2010年第14期104卷 148301-148301页

作者： Xiuyuan Cheng Ling Lin Weinan E Pingwen Zhang An-Chang Shi School of Mathematical Sciences and The Key Laboratory of Mathematics and Applied Mathematics Peking University Beijing 100871 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-1000 USA Department of Physics and Astronomy McMaster University Hamilton Ontario L8S 4M1 Canada

Nucleation of various ordered phases in block copolymers is studied by examining the free-energy landscape within the self-consistent field theory. The minimum energy path (MEP) connecting two ordered phases is computed using a recently developed string method. The shape, size, and free-energy barrier of critical nuclei are obtained from the MEP, providing information about the emergence of a stable ordered phase from a metastable phase. In particular, structural evolution of embryonic gyroid nucleus is predicted to follow two possible MEPs, revealing an interesting transition pathway with an intermediate perforated layered structure.

关键词： Nucleation

来源：评论

学校读者我要写书评

暂无评论

Empowering Optimal Control with Machine Learning: A Perspective from Model Predictive Control

引用

IFAC-PapersOnLine 2022年第30期55卷 121-126页

作者： E Weinan Jiequn Han Jihao Long AI for Science Institute Beijing Center for Machine Learning Research and School of Mathematical Sciences Peking University Beijing China Center for Computational Mathematics Flatiron Institute New York 10010 USA Program of Applied and Computational Mathematics Princeton University Princeton 08544 USA

Solving complex optimal control problems have confronted computational challenges for a long time. Recent advances in machine learning have provided us with new opportunities to address these challenges. This paper takes model predictive control, a popular optimal control method, as the primary example to survey recent progress that leverages machine learning techniques to empower optimal control solvers. We also discuss some of the main challenges encountered when applying machine learning to develop more robust optimal control algorithms.

关键词： Machine Learning Optimal Control Model Predictive Control

来源：评论

学校读者我要写书评

暂无评论

Instantaneous radar polarimetry with multiple dually-polarized antennas

Instantaneous radar polarimetry with multiple dually-polariz...

引用

40th Asilomar Conference on Signals, Systems, and Computers, ACSSC '06

作者： Calderbank, A.R. Howard, S.D. Moran, W. Pezeshki, A. Zoltowski, M. Program in Applied and Computational Mathematics Princeton University Princeton NJ United States Defence Science and Technology Organization Edinburgh Australia Electrical Engineering and Computer Science University of Melbourne Melbourne Australia Electrical and Computer Engineering Purdue University West Lafayette IN United States

ISBN: (纸本)1424407850

Fully Polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar transmitter and receiver on a pulse by pulse basis, and can improve the radar detection performance and suppress range sidelobes. In this paper, we extend the use of instantaneous radar polarimetry for radar systems with multiple dually-polarized transmit and receive antennas. Alamouti signal processing is used to coordinate transmission of Golay pairs of phase codes waveforms across polarizations and multiple antennas. The integration of multi-antenna signal processing with instantaneous radar polarimetry can further improve the detection performance, at a computational cost comparable to single channel matched filtering.

关键词： Polarimeters

来源：评论

学校读者我要写书评

暂无评论

The knowledge gradient for sequential decision making with stochastic binary feedbacks 33

The knowledge gradient for sequential decision making with s...

引用

33rd International Conference on Machine Learning, ICML 2016

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

ISBN: (纸本)9781510829008

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, either after the offline training phase or minimizing regret in online learning. Our problem is motivated by real-world applications where observations are time consuming and/or expensive. With the adaptation of an online Bayesian linear classifier, we develop a knowledge-gradient type policy to guide the experiment by maximizing the expected value of information of labeling each alternative, in order to reduce the number of expensive physical experiments. We provide a finite-time analysis of the estimated error and demonstrate the performance of the proposed algorithm on both synthetic problems and benchmark UCI datasets.

关键词： Benchmarking

来源：评论

学校读者我要写书评

暂无评论

The impact of cosmic ray feedback during the epoch of reionisation

arXiv

引用

arXiv 2025年

作者： Farcy, Marion Rosdahl, Joakim Dubois, Yohan Blaizot, Jérémy Martin-Alvarez, Sergio Haehnelt, Martin Kimm, Taysun Teyssier, Romain Institute for Physics Laboratory for Galaxy Evolution and Spectral Modelling EPFL Observatoire de Sauverny Chemin Pegasi 51 Versoix1290 Switzerland Centre de Recherche Astrophysique de Lyon CNRS UMR 5574 Univ. Lyon Ens de Lyon 9 avenue Charles André Saint-Genis-LavalF-69230 France Institut d’Astrophysique de Paris CNRS UMR 7095 Sorbonne Université 98 bis bd Arago Paris75014 France Stanford University StanfordCA94305 United States Kavli Institute for Cosmology Institute of Astronomy Madingley Road CambridgeCB3 0HA United Kingdom Department of Astronomy Yonsei University 50 Yonsei-ro Seodaemun-gu Seoul03722 Korea Republic of Department of Astrophysical Sciences Princeton University Peyton Hall PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road PrincetonNJ08544-1000 United States

Galaxies form and evolve via a multitude of complex physics. In this work, we investigate the role of cosmic ray (CR) feedback in galaxy evolution and reionisation, by examining its impact on the escape of ionising radiation from galaxies. For this purpose, we present two sphinx cosmological radiation-magneto-hydrodynamics simulations, allowing for the first time a study of the impact of CR feedback on thousands of resolved galaxies during the Epoch of Reionisation (EoR). The simulations differ in their feedback prescriptions: one adopts a calibrated strong supernova (SN) feedback, while the other simulation reduces the strength of SN feedback and includes CR feedback instead. We show that both comparably regulate star formation, reasonably match observations of high-redshift UV luminosity functions, and produce a similar amount of hydrogen ionising photons. In contrast to the model with strong SN feedback, the model with CRs lead to incomplete reionisation, which is in strong disagreement with observational estimates of the reionisation history. This is due to CR feedback shaping the ISM differently, filling with gas the low density cavities otherwise carved by SN explosions. As a result, this reduces the escape of ionising photons, at any halo mass, and primarily in the close vicinity of the stars. Our study indicates that CR feedback regulates galaxy growth during the EoR, but negatively affects reionisation, a tension which paves the way for further exploration and refinement of existing galaxy formation and feedback models. Such improvements are crucial in order to capture and understand the process of reionisation and the underlying evolution of galaxies through cosmic time. © 2025, CC BY.

关键词： Cosmic rays

来源：评论

学校读者我要写书评

暂无评论

Executive Summary of Dagstuhl Seminar on Structured Decompositions and Efficient Algorithms (08492)

Executive Summary of Dagstuhl Seminar on Structured Decompos...

引用

Structured Decompositions and Efficient Algorithms 2008

作者： Dahlke, Stephan Daubechies, Ingrid Elad, M. Kutyniok, Gitta Teschke, Gerd Philipps-Universität Marburg FB12 Mathematik und Informatik Hans-Meerwein Straße Lahnberge Marburg35032 Germany Princeton University Program in Applied and Computational Mathematics Fine Hall Washington Road PrincetonNJ08544-1000 United States Technion Computer Science Department Haifa Technion City32000 Israel Universität Osnabrück Institute of Mathematics Osnabrück49069 Germany Hochschule Neubrandenburg University of Applied Sciences Institute for Computational Mathematics in Science and Technology Brodaer Str. 2 Neubrandenburg17033 Germany

New emerging technologies such as high-precision sensors or new MRI machines drive us towards a challenging quest for new, more effective, and more daring mathematical models and algorithms. Therefore, in the last few years researchers have started to investigate different methods to efficiently represent or extract relevant information from complex, high dimensional and/or multimodal data. Efficiently in this context means a representation that is linked to the features or characteristics of interest, thereby typically providing a sparse expansion of such. Besides the construction of new and advanced ansatz systems the central question is how to design algorithms that are able to treat complex and high dimensional data and that efficiently perform a suitable approximation of the signal. One of the main challenges is to design new sparse approximation algorithms that would ideally combine, with an adjustable tradeoff, two properties: a provably good 'quality' of the resulting decomposition under mild assumptions on the analyzed sparse signal, and numerically efficient design. The topic is driven by applications as well as by theoretical questions. Therefore, the aim of this seminar was to bring together a good mixture of scientists with different backgrounds in order to discuss recent progress as well as new challenging perspectives. In particular, it was intended to strengthen the interaction of mathematicians and computer scientists. © 2009 Dagstuhl Seminar Proceedings. All Rights Reserved.

关键词： Clustering algorithms

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：