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arXiv 2019年

作者： Kim, Jaeuk Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space Rd. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a "bounded-cell" condition, hard particles are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size in Rd are perfectly hyperuniform in the infinite-sample-size limit and the hyperuniformity of such packings is independent of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R2 and R3. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that pack

关键词： Cells

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Estimation in the group action channel

arXiv

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arXiv 2018年

作者： Abbe, Emmanuel Pereira, João M. Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Electrical Engineering Department Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States

MSC Codes 94A15, 62B10We analyze the problem of estimating a signal from multiple measurements on a group action channel that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel is motivated by applications such as multi-reference alignment and cryoelectron microscopy. We focus on the large noise regime prevalent in these applications. We give a lower bound on the mean square error (MSE) of any asymptotically unbiased estimator of the signal's orbit in terms of the signal's moment tensors, which implies that the MSE is bounded away from 0 when N=σ2dis bounded from above, where N is the number of observations, σ is the noise standard deviation, and d is the so-called moment order cutoff. In contrast, the maximum likelihood estimator is shown to be consistent if N=σ2ddiverges. Copyright © 2018, The Authors. All rights reserved.

关键词： Mean square error

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Communication-computation efficient gradient coding

arXiv

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arXiv 2018年

作者： Ye, Min Abbe, Emmanuel Department of Electrical Engineering Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University School of Mathematics Institute for Advanced Study PrincetonNJ08544 United States

This paper develops coding techniques to reduce the running time of distributed learning tasks. It characterizes the fundamental tradeoff to compute gradients (and more generally vector summations) in terms of three parameters: computation load, straggler tolerance and communication cost. It further gives an explicit coding scheme that achieves the optimal tradeoff based on recursive polynomial constructions, coding both across data subsets and vector components. As a result, the proposed scheme allows to minimize the running time for gradient computations. Implementations are made on Amazon EC2 clusters using Python with mpi4py package. Results show that the proposed scheme maintains the same generalization error while reducing the running time by 32% compared to uncoded schemes and 23% compared to prior coded schemes focusing only on stragglers (Tandon et al., ICML 2017). Copyright © 2018, The Authors. All rights reserved.

关键词： Python

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Numerical Analysis of QCW-Laser-Based Spot-Beam Crystallization of Si Films

Numerical Analysis of QCW-Laser-Based Spot-Beam Crystallizat...

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SID Symposium, Seminar, and Exhibition 2017, Display Week 2017

作者： Pann, Wenkai Song, Ruobing Suresh, Akhilesh K. Wong, Vernon K. Yu, Miao Choi, Insung Im, James S. Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University New YorkNY United States

ISBN: (纸本)9781510848757

We are in the process of developing a new laser annealing method referred to as Spot-Beam Crystallization (SBC). The SBC method, which is potentially well suited for manufacturing advanced ultra-high-resolution AMOLED displays, is most effectively implemented using ultra-high- frequency quasi-continuous-wave (QCW) pulsed lasers. Conceptually and physically, this QCW-laser-based SBC (Q- SBC) approach builds on a thermally additive utilization of multiple short-lived ultra-high-frequency pulses, achieved via overlapped scanning of a small spot beam to incrementally and gradually heat and melt the beam-irradiated region. Using an updated version of a previously developed numerical program, we have carried out a simulation-based investigation to quantitatively examine and evaluate the basic tenets of the approach relevant specifically to partial-melting-based "ELA- like" crystallization of small-columnar-grained polycrystalline Si films using the Q-SBC method. The results from the effort to date as reported in this paper (1) largely confirm and validate the viability of the Q-SBC approach, and (2) suggest some specific directions for optimal development of the Q-SBC equipment and process. © 2017 SID.

关键词： Continuous wave lasers

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Solving many-electron Schrödinger equation using deep neural networks

arXiv

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arXiv 2018年

作者： Han, Jiequn Zhang, Linfeng Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schrödinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical. The optimal trial wave-function is obtained through variational Monte Carlo and the computational cost scales quadratically with the number of electrons. The algorithm does not make use of any prior knowledge such as atomic orbitals. Yet it is able to represent accurately the ground-states of the tested systems, including He, H2, Be, B, LiH, and a chain of 10 hydrogen atoms. This opens up new possibilities for solving large-scale many-electron Schrödinger equation. Copyright © 2018, The Authors. All rights reserved.

关键词： Wave functions

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APPLE picker: Automatic particle picking, a low-effort cryo-EM framework

arXiv

引用

arXiv 2018年

作者： Heimowitz, Ayelet Andén, Joakim Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Center for Computational Biology Flatiron Institute New YorkNY United States Department of Mathematics Princeton University PrincetonNJ United States

Particle picking is a crucial first step in the computational pipeline of single-particle cryo-electron microscopy (cryo-EM). Selecting particles from the micrographs is difficult especially for small particles with low contrast. As high-resolution reconstruction typically requires hundreds of thousands of particles, manually picking that many particles is often too time-consuming. While semi-automated particle picking is currently a popular approach, it may suffer from introducing manual bias into the selection process. In addition, semi-automated particle picking is still somewhat time-consuming. This paper presents the APPLE (Automatic Particle Picking with Low user Effort) picker, a simple and novel approach for fast, accurate, and fully automatic particle picking. While our approach was inspired by template matching, it is completely template-free. This approach is evaluated on publicly available datasets containing micrographs of β-Galactosidase, T20S proteasome, 70S ribosome and keyhole limpet hemocyanin projections. Copyright © 2018, The Authors. All rights reserved.

关键词： Support vector machines

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Recovering Signals from their FROG Trace

Recovering Signals from their FROG Trace

引用

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Tamir Bendory Dan Edidin Yonina C. Eldar The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics University of Missouri Columbia Missouri USA The Andrew and Erna Viterbi Faculty of Electrical Engineering Technion - Israel Institute of Technology Haifa Israel

ISBN: (纸本)9781538646595

The problem of recovering a signal from its power spectrum is called phase retrieval. This problem appears in a variety of scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. However, the problem for one-dimensional signals is ill-posed as there is no one-to-one mapping between a one-dimensional signal and its power spectrum. In the field of ultra-short laser pulse characterization, it is common to overcome this ill-posedness by using a technique called Frequency-Resolved Optical Gating (FROG). In FROG, the measured data, referred to as FROG trace, is the Fourier magnitude of the product of the underlying signal with several translated versions of itself. Therefore, in order to recover a signal from its FROG trace, one needs to invert a system of phaseless quartic equations. In this paper, we explore the symmetries and uniqueness of the FROG mapping. Our main result states that a signal bandlimited to B is determined uniquely, up to symmetries, by only 3B FROG measurements.

关键词： phase retrieval phaseless quartic system of equations ultra-short laser pulse characterization FROG signals Ultrashort laser pulses power spectra frogs Amphibians RECOVERING Trace One dimensional quartic equations

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Development of a do-it-yourself (D.I.Y.) gel electrophoresis apparatus for Grade-12 STEM general biology students

引用

Journal of Physics: Conference Series 2021年第1期1835卷

作者： Janne Noelle L. Gamale Dharel P. Acut Karla Marie Frances P. Niere Gwen Stephany S. Silagan Ethel P. Curaraton Guadalupe C. Latonio Rhett Anthony C. Latonio Joy R. Magsayo High School Department Sotero B. Cabahug FORUM for Literacy Consolacion Cebu 6001 Philippines Applied Physics Program National Institute of Physics College of Science University of the Philippines – Diliman Roxas Ave. Diliman Quezon City 1101 Philippines Science Education Program Graduate School College of Teacher Education Cebu Normal University Osmeña Blvd. Cebu City Cebu 6000 Philippines Department of Science and Mathematics Education College of Education Mindanao State University – Iligan Institute of Technology Iligan City 9200 Philippines

A hurdle to effective science education in schools is often the lack of teaching materials. Teaching science education in the 21st century requires direct visualization and manipulation with effective use and implementation for meaningful learning to occur, thus, unleashing students' potential towards the lesson, boosting their engagement in learning, and applying the knowledge into skills. This study was carried out to develop a do-it-yourself gel electrophoresis apparatus. This study was conducted in Cebu Normal University, Philippines with nineteen (19) teachers from the Methods of Teaching Science and Instructional Trends and Issues Class who evaluated the apparatus in terms of usability and functionality. The respondents tested the Gel Electrophoresis apparatus by conducting the experiment and they evaluated the apparatus' functionality and usability by using an evaluation sheet which is composed of eleven (11) usability questions, four (4) functionality questions. Suggestions were also asked to improve the said apparatus. After gathering data, the suggestions made by the respondents were incorporated which resulted to the improved D.I.Y. Gel Electrophoresis Apparatus. A manual with the procedures was also designed to further guide students and teachers on how to build the apparatus. With the findings and results obtained in the study, the respondents recommended the usage of the developed do-it-yourself gel electrophoresis apparatus in their respective classes and agreed that it is a good source of learning the concept of gel electrophoresis as a 21st century biological technique. The apparatus was easy to set-up and is of low-cost. During experimentation, the apparatus yielded with a positive result – the separation of food dyes which follows the principle of gel electrophoresis. Moreover, the experiment encourages creativity and it helps with the understanding of the nature of DNA and the concept of gel electrophoresis as a 21st century biological skills.

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The Athena++ adaptive mesh refinement framework: Design and magnetohydrodynamic solvers

arXiv

引用

arXiv 2020年

作者： Stone, James M. Tomida, Kengo White, Christopher J. Felker, Kyle G. Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Earth and Space Science Osaka University Toyonaka Osaka560-0043 Japan Kavli Institute for Theoretical Physics University of California Santa Barbara Santa BarbaraCA93107 United States School of Natural Sciences Institute for Advanced Study PrincetonNJ08544 United States Astronomical Institute Tohoku University Sendai Miyagi980-8578 Japan Argonne National Laboratory LemontIL60439 United States

The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use for a wide variety of physics. The framework works with both uniform and nonuniform grids in Cartesian and curvilinear coordinate systems. It adopts a dynamic execution model based on a simple design called a "task list" that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation. We describe physics modules implemented in this framework for both non-relativistic and relativistic magnetohydrodynamics (MHD). These modules adopt mature and robust algorithms originally developed for the Athena MHD code and incorporate new extensions: support for curvilinear coordinates, higher-order time integrators, more realistic physics such as a general equation of state, and diffusion terms that can be integrated with super-time-stepping algorithms. The modules show excellent performance and scaling, with well over 80% parallel efficiency on over half a million threads. The source code has been made publicly available. Copyright © 2020, The Authors. All rights reserved.

关键词： Magnetohydrodynamics

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Unsupervised particle sorting for high-resolution single-particle cryo-EM

arXiv

引用

arXiv 2019年

作者： Zhou, Ye Moscovich, Amit Bendory, Tamir Bartesaghi, Alberto Department of Computer Science Duke University Durham United States Program in Applied and Computational Mathematics Princeton University United States School of Electrical Engineering Tel Aviv University Tel Aviv Israel Department of Biochemistry Duke University School of Medicine Durham United States Department of Electrical and Computer Engineering Duke University Durham United States

Single-particle cryo-Electron Microscopy (EM) has become a popular technique for determining the structure of challenging biomolecules that are inaccessible to other technologies. Recent advances in automation, both in data collection and data processing, have significantly lowered the barrier for non-expert users to successfully execute the structure determination workflow. Many critical data processing steps, however, still require expert user intervention in order to converge to the correct high-resolution structure. In particular, strategies to identify homogeneous populations of particles rely heavily on subjective criteria that are not always consistent or reproducible among different users. Here, we explore the use of unsupervised strategies for particle sorting that are compatible with the autonomous operation of the image processing pipeline. More specifically, we show that particles can be successfully sorted based on a simple statistical model for the distribution of scores assigned during refinement. This represents an important step towards the development of automated workflows for protein structure determination using single-particle *** Codes 62P10 Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems

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