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Investigating institutional influence on graduate program admissions by modelling physics GRE cut-off scores

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arXiv 2020年

作者： Mikkelsen, Nils Johannes Young, Nicholas T. Caballero, Marcos D. Center for Computing in Science Education Department of Physics University of Oslo OsloN-0316 Norway Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States CREATE for STEM Institute Michigan State University East LansingMI48824 United States

Despite limiting access to applicants from underrepresented racial and ethnic groups, the practice of using hard or soft GRE cut-off scores in physics graduate program admissions is still a popular method for reducing the pool of applicants. The present study considers whether the undergraduate institutions of applicants have any influence on the admissions process by modelling a physics GRE cut-off score with application data from admissions offices of five universities. Two distinct approaches based on inferential and predictive modelling are conducted. While there is some disagreement regarding the relative importance between features, the two approaches largely agree that including institutional information significantly aids the analysis. Both models identify cases where the institutional effects are comparable to factors of known importance such as gender and undergraduate GPA. As the results are stable across many cut-off scores, we advocate against the practice of employing physics GRE cut-off scores in admissions. Copyright © 2020, The Authors. All rights reserved.

关键词： Supervised learning

Better approximations of high dimensional smooth functions by deep neural networks with rectified power units

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arXiv 2019年

作者： Li, Bo Tang, Shanshan Yu, Haijun NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China China Justice Big Data Institute Beijing100043 China

MSC Codes 65D15, 65M12, 65M15Deep neural networks with rectified linear units (ReLU) are getting more and more popular due to their universal representation power and successful applications. Some theoretical progress regarding the approximation power of deep ReLU network for functions in Sobolev space and Korobov space have recently been made by [D. Yarotsky, Neural Network, 94:103-114, 2017] and [H. Montanelli and Q. Du, SIAM J Math. Data Sci., 1:78-92, 2019], etc. In this paper, we show that deep networks with rectified power units (RePU) can give better approximations for smooth functions than deep ReLU networks. Our analysis bases on classical polynomial approximation theory and some efficient algorithms proposed in this paper to convert polynomials into deep RePU networks of optimal size with no approximation error. Comparing to the results on ReLU networks, the sizes of RePU networks required to approximate functions in Sobolev space and Korobov space with an error tolerance Ε, by our constructive proofs, are in general O(log1Ε ) times smaller than the sizes of corresponding ReLU networks constructed in most of the existing literature. Comparing to the classical results of Mhaskar [Mhaskar, Adv. Comput. Math. 1:61-80, 1993], our constructions use less number of activation functions and numerically more stable, they can be served as good initials of deep RePU networks and further trained to break the limit of linear approximation theory. The functions represented by RePU networks are smooth functions, so they naturally fit in the places where derivatives are involved in the loss function. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

An enhanced SDR based global algorithm for nonconvex complex quadratic programs with signal processing applications

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arXiv 2019年

作者： Lu, Cheng Liu, Ya-Feng Zhou, Jing School of Economics and Management North China Electric Power University Beijing102206 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Applied Mathematics College of Science Zhejiang University of Technology Hangzhou310023 China

In this paper, we consider a class of nonconvex complex quadratic programming (CQP) problems, which find a broad spectrum of signal processing applications. By using the polar coordinate representations of the complex variables, we first derive a new enhanced semidefinite relaxation (SDR) for problem (CQP). Based on the newly derived SDR, we further propose an efficient branch-and-bound algorithm for solving problem (CQP). Key features of our proposed algorithm are: (1) it is guaranteed to find the global solution of the problem (within any given error tolerance);(2) it is computationally efficient because it carefully utilizes the special structure of the problem. We apply our proposed algorithm to solve the multiinput multi-output (MIMO) detection problem, the unimodular radar code design problem, and the virtual beamforming design problem. Simulation results show that our proposed enhanced SDR, when applied to the above problems, is generally much tighter than the conventional SDR and our proposed global algorithm can efficiently solve these problems. In particular, our proposed algorithm significantly outperforms the state-of-the-art sphere decode algorithm for solving the MIMO detection problem in the hard cases (where the number of inputs and outputs is equal or the SNR is low) and a state-of-the-art general-purpose global optimization solver called Baron for solving the virtual beamforming design problem. Copyright © 2019, The Authors. All rights reserved.

关键词： Beamforming

Two-grid based adaptive proper orthogonal decomposition algorithm for time dependent partial differential equations

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arXiv 2019年

作者： Dai, Xiaoying Kuang, Xiong Xin, Jack Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Department of Mathematics University of California at Irvine IrvineCA92697 United States

In this article, we propose a two-grid based adaptive proper orthogonal decomposition(POD) algorithm to solve the time dependent partial differential equations. Based on the error obtained in the coarse grid, we propose an error indicator for the numerical solution obtained in the fine grid. Our new algorithm is cheap and easy to implement. We implement our new method to the solution of time-dependent advection-diffusion equations with Kolmogorov flow and ABC flow. The numerical results show that our method is more efficient than the existing POD algorithms. Copyright © 2019, The Authors. All rights reserved.

关键词： Principal component analysis

PowerNet: Efficient representations of polynomials and smooth functions by deep neural networks with rectified power units

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arXiv 2019年

作者： Li, Bo Tang, Shanshan Yu, Haijun Lsec Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 School OfMathematical Sciences University of Chinese Academy of Sciences Beijing100049 National Center ForMathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing100190 China

MSC Codes 65M12, 65M15, 65P40Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not continuous, which limit the usage of ReLU network to situations only when smoothness is not required. In this paper, we construct deep neural networks with rectified power units (RePU), which can give better approximations for smooth functions. Optimal algorithms are proposed to explicitly build neural networks with sparsely connected RePUs, which we call PowerNets, to represent polynomials with no approximation error. For general smooth functions, we first project the function to their polynomial approximations, then use the proposed algorithms to construct corresponding PowerNets. Thus, the error of best polynomial approximation provides an upper bound of the best RePU network approximation error. For smooth functions in higher dimensional Sobolev spaces, we use fast spectral transforms for tensor-product grid and sparse grid discretization to get polynomial approximations. Our constructive algorithms show clearly a close connection between spectral methods and deep neural networks: a PowerNet with n layers can exactly represent polynomials up to degree sn, where s is the power of RePUs. The proposed PowerNets have potential applications in the situations where high-accuracy is desired or smoothness is required. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

On the complexity of an augmented lagrangian method for nonconvex optimization

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arXiv 2019年

作者： Grapiglia, Geovani N. Yuan, Ya-Xiang Departamento de Matemática Universidade Federal do Paraná Centro Politécnico Cx. postal 19.081 Paraná Curitiba81531-980 Brazil State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China

In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of O(| log(ǫ)|) outer iterations for the referred algorithm to generate an ǫ-approximate KKT point, for ǫ ∈ (0, 1). When the penalty parameters are unbounded, we prove an outer iteration complexity bound of O (ǫ−2/(α−1)), where α > 1 controls the rate of increase of the penalty parameters. For linearly constrained problems, these bounds yield to evaluation complexity bounds of O(| log(ǫ)|2ǫ−2) and O ( ǫ− ( 2(2+ α−1 α) +2 )), respectively, when appropriate first-order methods (p = 1) are used to approximately solve the unconstrained subproblems at each iteration. In the case of problems having only linear equality constraints, the latter bounds are improved to O(| log(ǫ)|2ǫ−(p+1)/p) and O ( ǫ− ( α−4 1 + p+1 p )), respectively, when appropriate p-order methods (p ≥ 2) are used as inner solvers. Copyright © 2019, The Authors. All rights reserved.

关键词： Nonlinear programming

Understanding metric-related pitfalls in image analysis validation

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arXiv 2023年

作者： Reinke, Annika Tizabi, Minu D. Baumgartner, Michael Eisenmann, Matthias Heckmann-Nötzel, Doreen Kavur, A. Emre Rädsch, Tim Sudre, Carole H. Acion, Laura Antonelli, Michela Arbel, Tal Bakas, Spyridon Benis, Arriel Blaschko, Matthew B. Buettner, Florian Cardoso, M. Jorge Cheplygina, Veronika Chen, Jianxu Christodoulou, Evangelia Cimini, Beth A. Collins, Gary S. Farahani, Keyvan Ferrer, Luciana Galdran, Adrian van Ginneken, Bram Glocker, Ben Godau, Patrick Haase, Robert Hashimoto, Daniel A. Hoffman, Michael M. Huisman, Merel Isensee, Fabian Jannin, Pierre Kahn, Charles E. Kainmueller, Dagmar Kainz, Bernhard Karargyris, Alexandros Karthikesalingam, Alan Kenngott, Hannes Kleesiek, Jens Kofler, Florian Kooi, Thijs Kopp-Schneider, Annette Kozubek, Michal Kreshuk, Anna Kurc, Tahsin Landman, Bennett A. Litjens, Geert Madani, Amin Maier-Hein, Klaus Martel, Anne L. Mattson, Peter Meijering, Erik Menze, Bjoern Moons, Karel G.M. Müller, Henning Nichyporuk, Brennan Nickel, Felix Petersen, Jens Rafelski, Susanne M. Rajpoot, Nasir Reyes, Mauricio Riegler, Michael A. Rieke, Nicola Saez-Rodriguez, Julio Sánchez, Clara I. Shetty, Shravya Summers, Ronald M. Taha, Abdel A. Tiulpin, Aleksei Tsaftaris, Sotirios A. van Calster, Ben Varoquaux, Gaël Yaniv, Ziv R. Jäger, Paul F. Maier-Hein, Lena Faculty of Mathematics and Computer Science Heidelberg University Heidelberg Germany Heidelberg Division of Intelligent Medical Systems Germany NCT Heidelberg A Partnership Between DKFZ University Medical Center Heidelberg Germany Heidelberg Division of Medical Image Computing Germany Heidelberg Division of Intelligent Medical Systems Germany MRC Unit for Lifelong Health and Ageing UCL Centre for Medical Image Computing Department of Computer Science University College London London United Kingdom School of Biomedical Engineering and Imaging Science King’s College London London United Kingdom Instituto de Cálculo CONICET – Universidad de Buenos Aires Buenos Aires Argentina Centre for Medical Image Computing University College London London United Kingdom McGill University Montreal Canada Division of Computational Pathology Dept of Pathology & Laboratory Medicine Indiana University School of Medicine IU Health Information and Translational Sciences Building Indianapolis United States University of Pennsylvania Richards Medical Research Laboratories FL7 PhiladelphiaPA United States Department of Digital Medical Technologies Holon Institute of Technology Holon Israel European Federation for Medical Informatics Le Mont-sur-Lausanne Switzerland Center for Processing Speech and Images Department of Electrical Engineering KU Leuven Leuven Belgium partner site Frankfurt/Mainz a partnership between DKFZ and UCT Frankfurt Marburg Germany Heidelberg Germany Goethe University Frankfurt Department of Medicine Germany Goethe University Frankfurt Department of Informatics Germany and Frankfurt Cancer Insititute Germany Department of Computer Science IT University of Copenhagen Copenhagen Denmark Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V. Dortmund Germany Imaging Platform Broad Institute of MIT and Harvard CambridgeMA United States Centre for Statistics in Medicine University of Oxford Oxford United Kingdom Center for Biomedical In

Validation metrics are key for tracking scientific progress and bridging the current chasm between artificial intelligence (AI) research and its translation into practice. However, increasing evidence shows that particularly in image analysis, metrics are often chosen inadequately. While taking into account the individual strengths, weaknesses, and limitations of validation metrics is a critical prerequisite to making educated choices, the relevant knowledge is currently scattered and poorly accessible to individual researchers. Based on a multi-stage Delphi process conducted by a multidisciplinary expert consortium as well as extensive community feedback, the present work provides the first reliable and comprehensive common point of access to information on pitfalls related to validation metrics in image analysis. While focused on biomedical image analysis, the addressed pitfalls generalize across application domains and are categorized according to a newly created, domain-agnostic taxonomy. The work serves to enhance global comprehension of a key topic in image analysis validation. © 2023, CC BY.

关键词： Computer vision

Author Correction: The influence of natural variability on extreme monsoons in Pakistan

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npj Climate and Atmospheric Science 2023年第1期6卷 1页

作者： Moetasim Ashfaq Matthew F. Horan Salil Mahajan Katherine J. Evans Nathaniel Johnson Fred Kucharski Muhammad Adnan Abid Noah S. Diffenbaugh Deepti Singh Subimal Ghosh Auroop R. Ganguly Shafiqul Islam Computational Sciences and Engineering Division (CSED) Oak Ridge National Laboratory Oak Ridge TN USA Bredesen Center University of Tennessee Knoxville TN USA National Oceanic and Atmospheric Administration/Geophysical Fluid Dynamics Laboratory Princeton NJ USA Earth System Physics Abdus Salam International Centre for Theoretical Physics Trieste Italy Doerr School of Sustainability Stanford University Stanford CA USA School of the Environment Washington State University Vancouver WA USA Department of Civil Engineering Indian Institute of Technology Bombay Mumbai India Sustainability and Data Sciences Laboratory Civil and Environmental Engineering Northeastern University Boston MA USA Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory Richland WA USA Indian Institute of Technology Gandhinagar Gandhinagar GJ India Department of Civil and Environmental Engineering The Fletcher School of Law and Diplomacy Tufts University Medford MA USA

High-order partitioned spectral deferred correction solvers for multiphysics problems

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arXiv 2019年

作者： Huang, Daniel Z. Pazner, Will Persson, Per-Olof Zahr, Matthew J. Institute for Computational and Mathematical Engineering Stanford University United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Department of Mathematics University of California Berkeley United States Department of Aerospace and Mechanical Engineering University of Notre Dame United States

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1, 2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem;therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems including a simple linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design order of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1, 2] on this suite of test problems. The results suggest that the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves. Copyright © 2019, The Authors. All rights reserved.

关键词： Stability