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arXiv 2023年

作者： Soner, H. Mete Yan, Qinxin Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

Dynamic programming equations for mean field control problems with a separable structure are Eikonal type equations on the Wasserstein space. Standard differentiation using linear derivatives yield a direct extension of the classical viscosity theory. We use Fourier representation of the Sobolev norms on the space of measures, together with the standard techniques from the finite dimensional theory to prove a comparison result among semicontinuous sub and super solutions, obtaining a unique characterization of the value *** Codes 35D40, 35Q89, 49L12, 49L25, 60G99 © 2023, CC BY-NC-ND.

关键词： Viscosity

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Design and implementation of a fully integrated compressed-sensing signal acquisition system

Design and implementation of a fully integrated compressed-s...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Juhwan Yoo Stephen Becker Manuel Monge Matthew Loh Emmanuel Candès Azita Emami-Neyestanak Department of Electrical Engineering California Institute of Technology Pasadena CA USA Department of Applied and Computational Mathematics California Institute of Technology Pasadena CA USA Department of Statistics University of Stanford Stanford CA USA

Compressed sensing (CS) is a topic of tremendous interest because it provides theoretical guarantees and computationally tractable algorithms to fully recover signals sampled at a rate close to its information content. This paper presents the design of the first physically realized fully-integrated CS based Analog-to-Information (A2I) pre-processor known as the Random-Modulation Pre-Integrator (RMPI) [1]. The RMPI achieves 2GHz bandwidth while digitizing samples at a rate 12.5× lower than the Nyquist rate. The success of this implementation is due to a coherent theory/algorithm/hardware co-design approach. This paper addresses key aspects of the design, presents simulation and hardware measurements, and discusses limiting factors in performance.

关键词： Bandwidth Compressed sensing Harmonic analysis Noise Hardware Frequency estimation CMOS integrated circuits

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Convex Inversion of the Entrywise Product of Real Signals with Known Signs

Convex Inversion of the Entrywise Product of Real Signals wi...

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Asilomar Conference on Signals, Systems, and Computers

作者： Alireza Aghasi Ali Ahmed Paul Hand School of Business Georgia State University Atlanta School of Electrical and Computer Engineering Information Technology University Lahore Pakistan Department of Computational and Applied Mathematics Rice University Houston TX

We consider the bilinear inverse problem of recovering two vectors, x and w, in R~L from their entrywise product. For the case where the vectors have known signs and belong to known subspaces, we introduce the convex program BranchHull, which is posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved. Under the structural assumptions that x and w are the members of known K and N dimensional random subspaces, we prove that BranchHull recovers x and w up to the inherent scaling ambiguity with high probability, whenever L {approx.>} K + N. This problem is motivated by applications in the sweep distortion removal task in dielectric imaging, where one of the signals is a nonnegative reflectivity, and the other signal lives in a known wavelet subspace. Additional potential applications are blind deconvolution and self-calibration.

关键词： Deconvolution Electronic mail Signal processing Calibration Task analysis Imaging

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Dynamic Mode Decomposition and Sparse Measurements for Characterization and Monitoring of Power System Disturbances

arXiv

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arXiv 2019年

作者： Ramos, J. Jorge Kutz, J. Nathan Graduate Program in Electrical Engineering Cinvestav Unidad Guadalajara Guadalajaram Jal Mexico Department of Applied Mathematics University of Washington SeattleWA98195 United States

We introduce the dynamics mode decomposition for monitoring wide-area power grid networks from sparse measurement data. The mathematical framework fuses data from multiple sensors based on multivariate statistics, providing accurate full state estimation from limited measurements and generating data-driven forecasts for the state of the system. Our proposed data-driven strategy, which is based on energy metrics, can be used for the analysis of major disturbances in the network. The approach is tested and validated using time domain simulations in the IEEE 118 bus system under various disturbance scenarios and under different sparse observations of the system. In addition to state reconstruction, the minimal number of sensors required for monitoring disturbances can be evaluated. Visualization techniques are developed in order to aid in the analysis and characterization of the system after disturbance. Copyright © 2019, The Authors. All rights reserved.

关键词： Time domain analysis

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Sentiment Analysis of Snapchat Application's Reviews 2

Sentiment Analysis of Snapchat Application's Reviews

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2nd International Conference on Artificial Intelligence and Data Sciences, AiDAS 2021

作者： Wong, Weng Hao Ismail, Shuhaida Arifin, Muhammad Amirul Make, Siti Salwa Abdullah Wahab, Mohd Helmy Abd Shaharudin, Shazlyn Milleana Universiti Tun Hussein Onn Malaysia Faculty of Applied Sciences and Technology Pagoh Malaysia Kuliyyah of Science Universiti Islam Antarabangsa Malaysia Department of Computational and Theoretical Sciences Pahang Malaysia Universiti Tun Hussein Onn Malaysia Faculty of Electrical and Electronic Engineering Pagoh Malaysia Universiti Pendidikan Sultan Idris Faculty of Science and Mathematics Tanjong Malim Malaysia

ISBN: (纸本)9781665417266

Sentiment analysis is a process of extracting opinion and subjectivity knowledge from user generated text content without the need to monitor the reviews manually. It can help to obtain an overview on performance of a product or subject based on the reviews from users. The aim of this study is to classify the Snapchat application's reviews into different polarities which are positive, neutral or negative. Next, the most frequent words are identified. Furthermore, Multinomial Naïve Bayes and Random Forest classification algorithm are used to predict the user's rating. The performances of the classification models are evaluated using accuracy, precision, recall and F1-score. The results showed majority of the Snapchat users had a positive experience with the total of 6037 positive reviews. Based on the performance measures, Multinomial Naïve Bayes classification algorithm performed slightly better than the Random Forest classification algorithm in predicting the rating of Snapchat application. Overall, both of the classification algorithms have average performance in predicting user's rating for Snapchat application. © 2021 IEEE.

关键词： Sentiment analysis

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Symmetry classification and invariant geodesic equations characterization of two-dimensional

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12th Regional Conference on Mathematical Physics

作者： Kashif, A.R. Mahomed, F.M. Qadir, A. College of Electrical and Mechanical Engineering National University of Sciences and Technology Peshawar Road Rawalpindi Pakistan Centre of Differential Equations Continuum Mechanics and Applications School of Computational and Applied Mathematics University of Witwatersrand Wits 2050 Johannesberg South Africa Centre of Advanced Mathematics and Physics National University of Sciences and Technology Peshawar Road Rawalpindi Pakistan Department of Mathematical Sciences King Fahd University of Petroleum and Minerals Dhahran 30261 Saudi Arabia

ISBN: (纸本)9812705910

We present the point symmetry classification and invariant characterization of a system of two geodesic equations. Previously, Aminova and Aminovl attempted the point symmetry classification. However, they did not identify the Lie algebras nor did they provide an invariant characterization, in terms of coefficients, of the geodesic equations. In this paper we do both. Copyright © 2007 by World Scientific Publishing Co. Pvt. Ltd.

关键词： Geodesy

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

arXiv

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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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Quantum simulation of materials at micron scales and beyond

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Physical Review B 2008年第5期78卷 054118-054118页

作者： Qing Peng Xu Zhang Linda Hung Emily A. Carter Gang Lu Department of Physics and Astronomy California State University Northridge Northridge California USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey USA

We present a multiscale modeling approach that can simulate multimillion atoms effectively via density-functional theory. The method is based on the framework of the quasicontinuum (QC) approach with orbital-free density-functional theory (OFDFT) as its sole energetics formulation. The local QC part is formulated by the Cauchy-Born hypothesis with OFDFT calculations for strain energy and stress. The nonlocal QC part is treated by an OFDFT-based embedding approach, which couples OFDFT nonlocal atoms to local region atoms. The method—QCDFT—is applied to a nanoindentation study of an Al thin film, and the results are compared to a conventional QC approach. The results suggest that QCDFT represents a new direction for the quantum simulation of materials at length scales that are relevant to experiments.

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Density of States for a Specified Correlation Function and the Energy Landscape

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Physical Review Letters 2012年第8期108卷 080601-080601页

作者： C. J. Gommes Y. Jiao S. Torquato Department of Chemical Engineering University of Liège B-4000 Liège Belgium Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA

The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are explained in terms of the roughness of an energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered structures.

关键词： ENERGY levels (Quantum mechanics) CORRELATION (Statistics) MICROSTRUCTURE GROUND state (Quantum mechanics) MONTE Carlo method CONFIGURATION space QUANTITATIVE research

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Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation

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Physical Review B 2015年第4期91卷 045124-045124页

作者： Junchao Xia Emily A. Carter Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544-5263 USA Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

We present a comprehensive study of single-point kinetic energy density functionals (KEDFs) to be used in orbital-free density functional theory (DFT) calculations. We first propose a form of KEDFs based on a pointwise Kohn-Sham (KS) kinetic energy density (KED) and electron localization function (ELF) analysis. We find that the ELF and modified enhancement factor have a very strong and transferable correlation with the reduced density in various bulk metals. The non-self-consistent kinetic energy errors predicted by our KEDF models are decreased greatly compared to previously reported generalized gradient approximation (GGA) KEDFs. Second, we perform self-consistent calculations with various single-point KEDFs and investigate their numerical convergence behavior. We find striking numerical instabilities for previous GGA KEDFs; most of the GGA KEDFs fail to converge and show unphysical densities during the optimization. In contrast, our KEDFs demonstrate stable convergence, and their self-consistent results of various bulk properties agree reasonably well with KSDFT. A further detailed KED analysis reveals an interesting bifurcation phenomenon in defective metals and alloys, which may shed light on directions for future KEDF development.

关键词： KINETIC energy DENSITY functionals DENSITY functional theory ELECTRON research BIFURCATION theory

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