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Asymptotics of Elliptic and Parabolic PDEs 1

丛书名： applied Mathematical sciences

1000年

作者： David Holcman Zeev Schuss

ISBN: (数字)9783319768953

ISBN: (纸本)9783319768946;9783030083199

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences.;Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested inderiving solutions to real-world problems from first principles.

关键词： Partial Differential Equations Mathematical Applications in the Physical sciences Numerical and computational Physics, Simulation Mathematical and computational Biology Mathematical Methods in Physics Biological and Medical Physics, Biophysics

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Performance of a rack of liquid-cooled servers

Performance of a rack of liquid-cooled servers

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2007 Winter Meeting of the American Society of Heating, Refrigerating and Air-Conditioning Engineers

作者： Cader, Tahir McAllister, Herley Westra, Levi Regimbal, Kevin Marquez, Andres Government Computing Group Isothermal Systems Research Liberty Lake WA Applied Computer Science Department Computational Sciences and Mathematics Division Pacific North-west National Laboratory Richland WA

Electronics densification is continuing at an unrelenting pace at the server, rack, and facility level. With increasing facility density levels, airflow management has become a major challenge and concern. In an effort to deal with the resulting thermal management challenges, manufacturers are increasingly turning to liquid cooling as a practical solution. The majority of manufacturers have turned to liquid-cooled enclosed racks or rear-door heat exchangers, in which chilled water is delivered to the racks. Some manufacturers are now looking to cold plate cooling solutions that take the heat directly off problem components, such as the CPUs, to get it directly out of the facility. This paper describes work done at the Pacific Northwest National Labs (PNNL) under a Department of Energy-funded program titled "Energy Smart Data Center." An 8.2 kW (27,980 Btu/h) rack of HP rx2600 2U servers has been converted from air-cooling to liquid spray cooling (CPUs only). The rack has been integrated into PNNL's main cluster and subjected to a suite of acceptance tests. Under the testing, the spray-cooled CPUs ran an average of 10°C (18°F) cooler than the air-cooled CPUs. Other peripheral devices, such as the memory D1MMs, ran an average of 8°C (14.4°F) cooler, and the power pod board was measured at 15°C(27°F) cooler. Since installation in July 2005, the rack has been undergoing a one-year uptime and reliability investigation. As part of the investigation, the rack has been subjected to monthly robustness testing and ongoing performance evaluation while running applications such as High Performance Linpack, parts of the NASA NPB-2 Benchmark Suite, and NW Chem. The rack has undergone three months' worth of robustness testing with no major events. Including the robustness testing, the rack uptime is at 95.54% over 299 days. While undergoing application testing, no computational performance differences have been observed between the liquid-cooled and standard air-cooled racks. A sm

关键词： Electronic equipment

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Multiple Imputation with Neural Network Gaussian Process for High-dimensional Incomplete Data

arXiv

引用

arXiv 2022年

作者： Dai, Zongyu Bu, Zhiqi Long, Qi Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Division of Biostatistics University of Pennsylvania United States

Missing data are ubiquitous in real world applications and, if not adequately handled, may lead to the loss of information and biased findings in downstream analysis. Particularly, high-dimensional incomplete data with a moderate sample size, such as analysis of multi-omics data, present daunting challenges. Imputation is arguably the most popular method for handling missing data, though existing imputation methods have a number of limitations. Single imputation methods such as matrix completion methods do not adequately account for imputation uncertainty and hence would yield improper statistical inference. In contrast, multiple imputation (MI) methods allow for proper inference but existing methods do not perform well in high-dimensional settings. Our work aims to address these significant methodological gaps, leveraging recent advances in neural network Gaussian process (NNGP) from a Bayesian viewpoint. We propose two NNGP-based MI methods, namely MI-NNGP, that can apply multiple imputations for missing values from a joint (posterior predictive) distribution. The MI-NNGP methods are shown to significantly outperform existing state-of-the-art methods on synthetic and real datasets, in terms of imputation error, statistical inference, robustness to missing rates, and computation costs, under three missing data mechanisms, MCAR, MAR, and MNAR. Code is available in the GitHub repository https://***/bestadcarry/MI-NNGP. Copyright © 2022, The Authors. All rights reserved.

关键词： Gaussian noise (electronic)

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A Variational Spike-and-Slab Approach for group Variable Selection

arXiv

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arXiv 2023年

作者： Lin, Buyu Ge, Changhao Liu, Jun S. Department of Statistics Harvard University United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States

We introduce a class of generic spike-and-slab priors for high-dimensional linear regression with grouped variables and present a Coordinate-ascent Variational Inference (CAVI) algorithm for obtaining an optimal variational Bayes approximation. Using parameter expansion for a specific, yet comprehensive, family of slab distributions, we obtain a further gain in computational efficiency. The method can be easily extended to fitting additive models. Theoretically, we present general conditions on the generic spike-and-slab priors that enable us to derive the contraction rates for both the true posterior and the VB posterior for linear regression and additive models, of which some previous theoretical results can be viewed as special cases. Our simulation studies and real data application demonstrate that the proposed method is superior to existing methods in both variable selection and parameter estimation. Our algorithm is implemented in the R package GVSSB. Copyright © 2023, The Authors. All rights reserved.

关键词： computational efficiency

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Day-Ahead Forecasting of Solar Irradiance & PV Power Output Through Statistical Machine Learning Methods

Day-Ahead Forecasting of Solar Irradiance & PV Power Output ...

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2022 Saudi Arabia Smart Grid Conference, SASG 2022

作者： Kamarianakis, Yiannis Pantazis, Yannis Kalligiannaki, Evangelia Katsaounis, Theodoros D. Kotsovos, Konstantinos Gereige, Issam Abdullah, Marwan Jamal, Aqil Tzavaras, Athanasios Foundation for Research and Technology-Hellas Institute of Applied and Computational Mathematics Data Science Group Greece University of Crete Dept. of Mathematics and Applied Mathematics Greece Saudi Aramco RandD Center Carbon Management Division Dhahran Saudi Arabia Computer Electrical and Mathematical Sciences and Engineering Division Thuwal Saudi Arabia

ISBN: (纸本)9781665475891

Energy production from solar photovoltaic (PV) plants is unpredictable, mainly due to the stochastic formation and movement of clouds or aerosol - dust particles which scatter or disperse solar radiation. Accurate forecasts of PV output are essential to Distribution and Transportation System Operators as they assist efficient solar energy trading and management of electricity grids. This work evaluates an autoregressive, computationally-light KNN-regression scheme (TSFKNN) for hourly, day-ahead forecasts of solar irradiance and energy yield of various PV technologies. The model is being tested and validated using data measured in Thuwal, Saudi Arabia. The available measured records span a 60-month period. The developed forecasting models are designed for online systems and provide increased levels of accuracy and low computational cost. Several parametric and nonparametric specifications, coupled with conventional versus outlier-robust estimation procedures are tested, in order to derive an optimal month-specific daily profile (MDP). Current results demonstrate that including intraday variability to the monthly-based irradiance models achieve improved predictive accuracy between 10% and 25% on average. © 2022 IEEE.

关键词： Forecasting

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Accelerating the complex Hessenberg QR algorithm with the csx600 floating-point coprocessor

Accelerating the complex Hessenberg QR algorithm with the cs...

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19th IASTED International Conference on Parallel and Distributed Computing and Systems

作者： Yamamoto, Yusaku Miyata, Takafumi Nakamura, Yoshimasa Dept. of Computational Science and Engineering Graduate School of Engineering Nagoya University Nagoya 464-8603 Japan Dept. of Applied Mathematics and Physics Graduate School of Informatics Kyoto University/ JST SORST Kyoto 606-8501 Japan

ISBN: (纸本)9780889867048

In this paper, we show how to speed up the Hessenberg QR algorithm for computing the eigenvalues of a dense complex nonsymmetric matrix using the CSX600 floating-point coprocessor. Our approach is based on the small-bulge multishift QR algorithm proposed by Braman et al. This algorithm can perform a major part of the computation in the form of matrix multiplication and is therefore very suited to high performance architectures. However, to exploit the potential of the CSX600, the number of shifts must be increased to more than two hundred. In that case, the parts other than matrix multiplication begin to occupy a considerable percentage of the execution time, thereby limiting the speedup. To solve this problem, we focus on two most time-consuming parts in the algorithm except for matrix multiplication: accumulation of bulge-chasing transformations and solution of a decoupled small eigenproblem. We reconstruct the former as a recursive algorithm and apply a blocking technique to the latter. This enables these parts to be computed also using matrix multiplication. As a result of these optimizations, we obtained up to 3.8 times speedup with the CSX600 processor over a 3.2GHz Xeon processor when computing the eigenvalues of a 12,000 × 12,000 complex Hessenberg matrix.

关键词： Coprocessor

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Subsalt imaging with internal multiples 78

Subsalt imaging with internal multiples

引用

78th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2008

作者： Malcolm, Alison E. Ursin, Bjørn De Hoop, Maarten V. Department of Earth Atmospheric and Planetary Sciences MIT United States Department of Petroleum Engineering and Applied Geophysics Norwegian University of Science and Technology Norway Center for Computational and Applied Mathematics Geo-Mathematical Imaging Group Purdue University United States

ISBN: (纸本)9781605607856

If singly scattered seismic waves illuminate the entirety of a subsurface structure of interest, standard methods can be applied to image it. In many cases, subsalt imaging for example, a combination of restricted acquisition geometry and imperfect velocity models results in regions of the model that are not illuminated with singly scattered waves. We present an approach to use multiply scattered waves to illuminate such structures, and illustrate the method by creating images of the base of salt with an erroneous velocity model. This method builds upon past work in which methods to predict artifacts in imaging from multiply scattered waves have been developed and shares similarities with current techniques of imaging with surface-related multiples. Copyright © (2008) by the Society of Exploration Geophysicists All rights reserved.

关键词： Subsalt imaging

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Distributed linear regression by averaging

arXiv

引用

arXiv 2018年

作者： Dobriban, Edgar Sheng, Yue Wharton Statistics Department University of Pennsylvania United States Graduate Group in Applied Mathematics and Computational Science Department of Mathematics University of Pennsylvania United States

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck. In this paper, we study one-step and iterative weighted parameter averaging in statistical linear models under data parallelism. We do linear regression on each machine, send the results to a central server, and take a weighted average of the parameters. Optionally, we iterate, sending back the weighted average and doing local ridge regressions centered at it. How does this work compared to doing linear regression on the full data? Here we study the performance loss in estimation, test error, and confidence interval length in high dimensions, where the number of parameters is comparable to the training data size. We find the performance loss in one-step weighted averaging, and also give results for iterative averaging. We also find that different problems are affected differently by the distributed framework. Estimation error and confidence interval length increase a lot, while prediction error increases much less. We rely on recent results from random matrix theory, where we develop a new calculus of deterministic equivalents as a tool of broader interest. Copyright © 2018, The Authors. All rights reserved.

关键词： Linear regression

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Positron-Impact Excitation of Hydrogen Atoms in Debye Plasmas

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Chinese Physics Letters 2010年第1期27卷 111-114页

作者：张松斌祁月盈屈一至陈向军王建国 Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of China Hefei 230026 Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics PO Box 8009 Beijing 100088 School of Electrical Engineering Jiaxing University Jiaxing 314001 College of Material Sciences and Optoelectronic Technology Graduate School of the Chinese Academy of Sciences PO Box 4588 Beijing 100049

The positron-impact excitation of hydrogen atoms embedded in plasma environments is investigated using the close-coupling approximation from the low to intermediate energy region without including any positronium formation channel, and the excitation cross sections for 1s→2s, 1s→2p and 2s→2p processes are calculated in a wide Debye parameter range. The screening interactions, described by the Debye-Hückel model, decrease the coupling matrix elements, resulting in the reduction of the excitation cross sections from a few percent to one magnitude of ten. This will alter remarkably the spectroscopy of hydrogen in intensity and position, which should be considered in the simulation and diagnostics under some specific plasma conditions.

关键词： Chinese climate network complex systems small world community

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Solving optimal feedback control of Chinese population dynamics by viscosity solution approach

Solving optimal feedback control of Chinese population dynam...

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作者： Sun, Bing Guo, Bao-Zhu Institute of Systems Science Academy of Mathematics and System Sciences Beijing 100080 China Graduate School Chinese Academy of Sciences Beijing 100039 China School of Computational and Applied Mathematics University of the Witwatersrand Private 3 Wits 2050 Johannesburg South Africa

ISBN: (纸本)008045108X

in this paper, the optimal birth feedback control of a McKendrick type age-structured population dynamic system based on the Chinese population dynamics is considered. Adopt the dynamic programming approach, to obtain the Hamilton-Jacobi-Bellman equation and prove that the value function is its viscosity solution. By the derived classical verification theorem, the optimal birth feedback control is found explicitly. A finite difference scheme is designed to solving numerically the optimal birth feedback control. Under the same constraint, by comparing with different controls, the validity of the optimality of the obtained control is verified numerically. Copyright © 2005 IFAC.

关键词： Dynamic programming

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