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arXiv 2021年

作者： Davis, Samantha I. Mueller, Andrew Valivarthi, Raju Lauk, Nikolai Narvaez, Lautaro Korzh, Boris Beyer, Andrew D. Cerri, Olmo Colangelo, Marco Berggren, Karl K. Shaw, Matthew D. Xie, Si Sinclair, Neil Spiropulu, Maria Division of Physics Mathematics and Astronomy California Institute of Technology 1200 E California Blvd. PasadenaCA91125 United States California Institute of Technology 1200 E California Blvd. PasadenaCA91125 United States Division of Engineering and Applied Science California Institute of Technology 1200 E California Blvd. PasadenaCA91125 United States Jet Propulsion Laboratory California Institute of Technology 4800 Oak Grove Dr. PasadenaCA91109 United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology 50 Vassar St. CambridgeMA02139 United States Fermi National Accelerator Laboratory P.O. Box 500 BataviaIL60510 United States John A. Paulson School of Engineering and Applied Sciences Harvard University 29 Oxford St. CambridgeMA02138 United States

Deterministic generation of single photons is essential for many quantum information technologies. A bulk optical nonlinearity emitting a photon pair, where the measurement of one of the photons heralds the presence of the other, is commonly used with the caveat that the single-photon emission rate is constrained due a tradeoff between multi-photon events and pair emission rate. Using an efficient and low noise photon-number-resolving superconducting nanowire detector we herald, in real time, a single photon at telecommunication wavelength. We perform a second-order photon correlation g2(0) measurement of the signal mode conditioned on the measured photon number of the idler mode for various pump powers and demonstrate an improvement of a heralded single photon source. We develop an analytical model using a phase space formalism that encompasses all multi-photon effects and relevant imperfections, such as loss and multiple Schmidt modes. We perform a maximum likelihood fit to test the agreement of the model to the data and extract the best-fit mean photon number µ of the pair source for each pump power. A maximum reduction of 0.118 ±0.012 in the photon g2(0) correlation function at µ = 0.327 ±0.007 is obtained, indicating a strong suppression of multi-photon emissions. For a fixed g2(0) = 7 × 10-3, we increase the single pair generation probability by 25%. Our experiment, built using fiber-coupled and off-the-shelf components, delineates a path to engineering ideal sources of single photons. Copyright © 2021, The Authors. All rights reserved.

关键词： Photons

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Dying ReLU and initialization: Theory and numerical examples

arXiv

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arXiv 2019年

作者： Lu, Lu Shin, Yeonjong Su, Yanhui Karniadakis, George Em Division of Applied Mathematics Brown University ProvidenceRI02912 United States College of Mathematics and Computer Science Fuzhou University Fuzhou Fujian350116 China Pacific North National Laboratory RichlandWA99354 United States

The dying ReLU refers to the problem when ReLU neurons become inactive and only output 0 for any input. There are many empirical and heuristic explanations of why ReLU neurons die. However, little is known about its theoretical analysis. In this paper, we rigorously prove that a deep ReLU network will eventually die in probability as the depth goes to infinite. Several methods have been proposed to alleviate the dying ReLU. Perhaps, one of the simplest treatments is to modify the initialization procedure. One common way of initializing weights and biases uses symmetric probability distributions, which suffers from the dying ReLU. We thus propose a new initialization procedure, namely, a randomized asymmetric initialization. We show that the new initialization can effectively prevent the dying ReLU. All parameters required for the new initialization are theoretically designed. Numerical examples are provided to demonstrate the effectiveness of the new initialization procedure. Copyright © 2019, The Authors. All rights reserved.

关键词： Probability distributions

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Shoaling on steep continental slopes: Relating transmission and reflection coefficients to green's law

arXiv

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arXiv 2019年

作者： George, Jithin Ketcheson, David I. Leveque, Randall J. Department of Engineering Sciences and Applied Mathematics Northwestern University Computer Electrical and Mathematical Sciences & Engineering Division King Abdullah University of Science and Technology 4700 KAUST Thuwal23955 Saudi Arabia Department of Applied Mathematics University of Washington SeattleWA98195-3925 United States

The propagation of long waves onto a continental shelf is of great interest in tsunami modeling and other applications where understanding the amplification of waves during shoaling is important. When the linearized shallow water equations are solved with the continental shelf modeled as a sharp discontinuity, the ratio of the amplitudes is given by the transmission coefficient. On the other hand, when the slope is very broad relative to the wavelength of the incoming wave, then amplification is governed by Green's Law, which predicts a larger amplification than the transmission coefficient, and a much smaller amplitude reflection than given by the reflection coefficient of a sharp interface. We explore the relation between these results and elucidate the behavior in the intermediate case of a very steep continental shelf. Copyright © 2019, The Authors. All rights reserved.

关键词： Amplification

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A path integral method for solution of the wave equation with continuously-varying coefficients

arXiv

引用

arXiv 2019年

作者： George, Jithin D. Ketcheson, David I. LeVeque, Randall J. Department of Engineering Sciences and Applied Mathematics Northwestern University Computer Electrical and Mathematical Sciences & Engineering Division King Abdullah University of Science and Technology 4700 KAUST Thuwal23955 Saudi Arabia Department of Applied Mathematics University of Washington SeattleWA98195-3925 United States

A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an infinite series of integrals, where the integrand involves only the initial data and the PDE coefficients. Each term in the series represents the influence of paths with a fixed number of turning points. We prove that the series converges and provide bounds for the truncation error. The effectiveness of the approximation is illustrated with examples. We illustrate an interesting combinatorial connection between the traditional reflection and transmission coefficients for a sharp interface, and Green’s coefficient for transmission through a smoothly-varying region. Copyright © 2019, The Authors. All rights reserved.

关键词： Wave equations

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Leveraging randomized compiling for the QITE algorithm

arXiv

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arXiv 2021年

作者： Ville, Jean-Loup Morvan, Alexis Hashim, Akel Naik, Ravi K. Lu, Marie Mitchell, Bradley Kreikebaum, John-Mark O’Brien, Kevin P. Wallman, Joel J. Hincks, Ian Emerson, Joseph Smith, Ethan Younis, Ed Iancu, Costin Santiago, David I. Siddiqi, Irfan Quantum Nanoelectronics Laboratory Dept. of Physics University of California at Berkeley BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States Inst. for Quantum Computing Dept. of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Quantum Benchmark Inc. KitchenerONN2H 5G5 Canada

The success of the current generation of Noisy Intermediate-Scale Quantum (NISQ) hardware shows that quantum hardware may be able to tackle complex problems even without error correction. One outstanding issue is that of coherent errors arising from the increased complexity of these devices. These errors can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like Quantum Imaginary Time Evolution are susceptible to these errors. This article presents the combination of both noise tailoring using Randomized Compiling and error mitigation with a purification. We also show that Cycle Benchmarking gives an estimate of the reliability of the purification. We apply this method to the Quantum Imaginary Time Evolution of a Transverse Field Ising Model and report an energy estimation and a ground state infidelity both below 1%. Our methodology is general and can be used for other algorithms and platforms. We show how combining noise tailoring and error mitigation will push forward the performance of NISQ devices. © 2021, CC BY.

关键词： Benchmarking

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A Low-rank solver for the stochastic unsteady navier-stokes problem

arXiv

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arXiv 2019年

作者： Elman, Howard Su, Tengfei Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics & Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

We study a low-rank iterative solver for the unsteady Navier–Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once formulation where the algebraic systems at all the time steps are collected and solved simultaneously. The problem is linearized with Picard’s method. To efficiently solve the linear systems at each step, we use low-rank tensor representations within the Krylov subspace method, which leads to significant reductions in storage requirements and computational costs. Combined with effective mean-based preconditioners and the idea of inexact solve, we show that only a small number of linear iterations are needed at each Picard step. The proposed algorithm is tested with a model of flow in a two-dimensional symmetric step domain with different settings to demonstrate the computational efficiency. Copyright © 2019, The Authors. All rights reserved.

关键词： Navier Stokes equations

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New approaches to evacuation modelling for fire safety engineering applications

New approaches to evacuation modelling for fire safety engin...

引用

作者： Ronchi, Enrico Corbetta, Alessandro Galea, Edwin R. Kinateder, Max Kuligowski, Erica McGrath, Denise Pel, Adam Shiban, Youssef Thompson, Peter Toschi, Federico Division of Fire Safety Engineering Lund University Sweden Department of Applied Physics Eindhoven University of Technology Netherlands Fire Safety Engineering Group University of Greenwich United Kingdom NRC Construction – Fire Safety National Research Council Canada Fire Research Division National Institute of Standards and Technology United States School of Public Health Physiotherapy and Sports Science University College Dublin Ireland Transport and Planning Delft University of Technology Netherlands Department of Psychology PFH Private University Göttingen Germany Generative Design Division Autodesk Inc. United States Department of Applied Physics and Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands

This paper presents the findings of the workshop "New approaches to evacuation modelling", which took place on the 11th of June 2017 in Lund (Sweden)within the Symposium of the International Association for Fire Safety science (IAFSS). The workshop gathered international experts in the field of fire evacuation modelling from 19 different countries and was designed to build a dialogue between the fire evacuation modelling world and experts in areas outside of fire safety engineering. The contribution to fire evacuation modelling of five topics within research disciplines outside fire safety engineering (FSE)have been discussed during the workshop, namely 1)Psychology/Human Factors, 2)Sociology, 3)applied mathematics, 4)Transportation, 5)Dynamic Simulation and Biomechanics. The benefits of exchanging information between these two groups are highlighted here in light of the topic areas discussed and the feedback received by the evacuation modelling community during the workshop. This included the feasibility of development/application of modelling methods based on fields other than FSE as well as a discussion on their implementation strengths and limitations. Each subject area is here briefly presented and its links to fire evacuation modelling are discussed. The feedback received during the workshop is discussed through a set of insights which might be useful for the future developments of evacuation models for fire safety engineering. © 2019

关键词： Smoke

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HCVMultiscaleFit: A Simulator For Parameter Estimation in Multiscale Models Of Hepatitis C Virus Dynamics

引用

AIP conference proceedings 2020年第1期2293卷 420028页

作者： Alexander Churkin Vladimir Reinharz Stephanie Lewkiewicz Harel Dahari Danny Barash Department of Software Engineering Sami Shamoon College of Engineering Beer-Sheva Israel. Center for Soft and Living Matter Institute for Basic Science Ulsan South Korea. Department of Mathematics University of California at Los Angeles Los Angeles California USA. The Program for Experimental and Theoretical Modeling Division of Hepatology Department of Medicine Stritch School of Medicine Loyola University Chicago Maywood Illinois USA. Department of Computer Science Ben-Gurion Universty Beer-Sheva Israel.

Callibration in mathematical models that are based on differential equations is known to be of fundamental importance. For sophisticated models such as age-structured models that simulate biological agents, parameter estimation or fitting (callibration) that solves all cases of data points available presents a formidable challenge, as efficiency considerations need to be employed in order for the method to become practical. In the case of multiscale models of hepatitis C virus dynamics that deal with partial differential equations (PDEs), a fully numerical parameter estimation method was developed that does not require an analytical approximation of the solution to the multiscale model equations, avoiding the necessity to derive the long-term approximation for each model. However, the method is considerably slow because of precision problems in estimating derivatives with respect to the parameters near their boundary values, making it almost impractical for general use. In order to overcome this limitation, two steps have been taken that significantly reduce the running time by orders of magnitude and thereby lead to a practical method. First, constrained optimization is used, letting the user add constraints relating to the boundary values of each parameter before the method is executed. Second, optimization is performed by derivative-free methods, eliminating the need to evaluate expensive numerical derviative approximations. These steps that were successful in significantly speeding up a highly non-efficient approach, rendering it practical, can also be adapted to multiscale models of other viruses and other sophisticated differential equation models. The newly efficient methods that were developed as a result of the above approach are described. Illustrations are provided using a user-friendly simulator that incorporates the efficient methods for multiscale models. We provide a simulator called HCVMultiscaleFit with a Graphical User Interface that applies these

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Interactive Protocols for Classically-Verifiable Quantum Advantage

arXiv

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arXiv 2021年

作者： Zhu, Daiwei Kahanamoku-Meyer, Gregory D. Lewis, Laura Noel, Crystal Katz, Or Harraz, Bahaa Wang, Qingfeng Risinger, Andrew Feng, Lei Biswas, Debopriyo Egan, Laird Gheorghiu, Alexandru Nam, Yunseong Vidick, Thomas Vazirani, Umesh Yao, Norman Y. Cetina, Marko Monroe, Christopher Joint Quantum Institute Departments of Physics and Electrical and Computer Engineering University of Maryland College ParkMD20742 United States Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD20742 United States Department of Physics University of California BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Computing and Mathematical Sciences California Institute of Technology CA91125 United States Division of Physics Mathematics and Astronomy California Institute of Technology CA91125-0001 United States Duke Quantum Center Department of Physics Duke University DurhamNC27708 United States Department of Electrical and Computer Engineering Duke University DurhamNC27708 United States IonQ Inc. College ParkMD20740 United States Institute for Theoretical Studies ETH Zürich CH 8001 Switzerland Chemical Physics Program Institute for Physical Science and Technology University of Maryland College ParkMD20742 United States Departments of Electrical and Computer Engineering University of Maryland College ParkMD20742 United States

Interaction is a powerful resource for quantum computation. It can be utilized in applications ranging from the verification of quantum algorithms all the way to verifying quantum mechanics itself. Here, we present the first implementation of interactive protocols for proofs of quantumness — which when suitably scaled promise the efficient verification of quantum computational advantage. The key feature that distinguishes these protocols from existing demonstrations of quantum advantage is that the classical verification is efficient and scales polynomially rather than exponentially with the number of qubits. The experimental implementation of such interactive protocols requires the ability to independently measure subsets of qubits in the middle of a quantum circuit and to continue coherent evolution afterwards. This is achieved by spatially isolating target qubits via shuttling, and opens the door to a range of quantum interactive protocols as well as new information processing architectures. Copyright © 2021, The Authors. All rights reserved.

关键词： Qubits

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Dimensional reduction using conditional entropy for incomplete information systems 1

引用

15th International Conference on Parallel Computing Technologies, PaCT 2019

作者： Deris, Mustafa Mat Senan, Norhalina Abdullah, Zailani Mamat, Rabiei Handaga, Bana Faculty of Computer Science and Information Technology Universiti Tun Hussein Onn Malaysia Parit Raja Malaysia Faculty of Entrepreneurship and Business Universiti Malaysia Kelantan Pengkalan Chepa Kota BharuKelantan16100 Malaysia Faculty of Informatics and Applied Mathematics University of Malaysia Terengganu Kuala TerengganuTerengganu21030 Malaysia Program Studi Informatika Universitas Muhammadiah Surakarta SurakartaCentral Java57162 Indonesia

ISBN: (数字)9783030256364

ISBN: (纸本)9783030256357

Dimension reduction approach is one of the main data reduction approaches in order to reduce the storage and processing time while maintaining the integrity of the original data. A wide range of dimension reduction approaches are based on classical approaches such as PCA and Bayer’s, and machine learning approaches such as clustering, and feature selection techniques. However, many of the approaches do not consider the incomplete information systems where some attribute values are missing or incomplete. Only few studies were proposed for the problem in incomplete information systems due to its complexities, specifically on attribute selection. The most popular approaches is based on probability theory to replace missing values with the most common values, or remove the missing objects from the information systems. However, it needs to know the probability distribution of data in advance. To overcome these issues, we propose a new approach based on conditional entropy to reduce dimensionality. The results show that the proposed approach achieves better data reduction with higher accuracy for objects and dimensionality reduction in incomplete information systems. © 2019, Springer Nature Switzerland AG.

关键词： Data reduction

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