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Euclid: Searches for strong gravitational lenses using convolutional neural nets in Early Release Observations of the Perseus field

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arXiv 2024年

作者： Pearce-Casey, R. Nagam, B.C. Wilde, J. Busillo, V. Ulivi, L. Andika, I.T. Manjón-García, A. Leuzzi, L. Matavulj, P. Serjeant, S. Walmsley, M. Barroso, J.A. Acevedo O’Riordan, C.M. Clément, B. Tortora, C. Collett, T.E. Courbin, F. Gavazzi, R. Metcalf, R.B. Cabanac, R. Courtois, H.M. Crook-Mansour, J. Delchambre, L. Despali, G. Ecker, L.R. Franco, A. Holloway, P. Jahnke, K. Mahler, G. Marchetti, L. Melo, A. Meneghetti, M. Müller, O. Nucita, A.A. Pearson, J. Rojas, K. Scarlata, C. Schuldt, S. Sluse, D. Suyu, S.H. Vaccari, M. Vegetti, S. Verma, A. Vernardos, G. Bolzonella, M. Kluge, M. Saifollahi, T. Schirmer, M. Stone, C. Paulino-Afonso, A. Bazzanini, L. Hogg, N.B. Koopmans, L.V.E. Kruk, S. Mannucci, F. Bromley, J.M. Díaz-Sánchez, A. Dickinson, H.J. Powell, D.M. Bouy, H. Laureijs, R. Altieri, B. Amara, A. Andreon, S. Baccigalupi, C. Baldi, M. Balestra, A. Bardelli, S. Battaglia, P. Bonino, D. Branchini, E. Brescia, M. Brinchmann, J. Caillat, A. Camera, S. Capobianco, V. Carbone, C. Carretero, J. Casas, S. Castellano, M. Castignani, G. Cavuoti, S. Cimatti, A. Colodro-Conde, C. Congedo, G. Conselice, C.J. Conversi, L. Copin, Y. Cropper, M. Da Silva, A. Degaudenzi, H. De Lucia, G. Di Giorgio, A.M. Dinis, J. Dubath, F. Dupac, X. Dusini, S. Farina, M. Farrens, S. Faustini, F. Ferriol, S. Frailis, M. Franceschi, E. Galeotta, S. George, K. Gillard, W. Gillis, B. Giocoli, C. Gómez-Alvarez, P. Grazian, A. Grupp, F. Haugan, S.V.H. Holmes, W. Hook, I. Hormuth, F. Hornstrup, A. Hudelot, P. Jhabvala, M. Joachimi, B. Keihänen, E. Kermiche, S. Kiessling, A. Kilbinger, M. Kubik, B. Kümmel, M. Kunz, M. Kurki-Suonio, H. Le Mignant, D. Ligori, S. Lilje, P.B. Lindholm, V. Lloro, I. Maiorano, E. Mansutti, O. Marggraf, O. Markovic, K. Martinelli, M. Martinet, N. Marulli, F. Massey, R. Medinaceli, E. Mei, S. Melchior, M. Mellier, Y. Merlin, E. Meylan, G. Moresco, M. Moscardini, L. Nakajima, R. School of Physical Sciences The Open University Milton KeynesMK7 6AA United Kingdom Kapteyn Astronomical Institute University of Groningen PO Box 800 Groningen9700 AV Netherlands INAF-Osservatorio Astronomico di Capodimonte Via Moiariello 16 Napoli80131 Italy Department of Physics "E. Pancini" University Federico II Via Cinthia 6 Napoli80126 Italy INFN section of Naples Via Cinthia 6 Napoli80126 Italy University of Trento Via Sommarive 14 TrentoI-38123 Italy Dipartimento di Fisica e Astronomia Università di Firenze via G. Sansone 1 Sesto Fiorentino Firenze50019 Italy INAF-Osservatorio Astrofisico di Arcetri Largo E. Fermi 5 Firenze50125 Italy Technical University of Munich TUM School of Natural Sciences Physics Department James-Franck-Str. 1 Garching85748 Germany Max-Planck-Institut für Astrophysik Karl-Schwarzschild-Str. 1 Garching85748 Germany Departamento Física Aplicada Universidad Politécnica de Cartagena Campus Muralla del Mar Murcia Cartagena30202 Spain Dipartimento di Fisica e Astronomia "Augusto Righi" Alma Mater Studiorum Università di Bologna via Piero Gobetti 93/2 Bologna40129 Italy INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna Via Piero Gobetti 93/3 Bologna40129 Italy University of Applied Sciences and Arts of Northwestern Switzerland School of Engineering Windisch5210 Switzerland Department of Astronomy & Astrophysics University of Toronto 50 St George Street TorontoONM5S 3H4 Canada Jodrell Bank Centre for Astrophysics Department of Physics and Astronomy University of Manchester Oxford Road ManchesterM13 9PL United Kingdom Observatoire de Sauverny Versoix1290 Switzerland Lausanne1015 Switzerland Institute of Cosmology and Gravitation University of Portsmouth PortsmouthPO1 3FX United Kingdom Martí i Franquès 1 Barcelona08028 Spain Passeig de Lluís Companys 23 Barcelona08010 Spain Aix-Marseille Université CNRS CNES LAM Marseille France Institut d’Astrophysique de Paris UMR 709

The Euclid Wide Survey (EWS) is predicted to find approximately 170 000 galaxy-galaxy strong lenses from its lifetime observation of 14 000 deg2 of the sky. Detecting this many lenses by visual inspection with professional astronomers and citizen scientists alone is infeasible. As a result, machine learning algorithms, particularly convolutional neural networks (CNNs), have been used as an automated method of detecting strong lenses, and have proven fruitful in finding galaxy-galaxy strong lens candidates, such that the usage of CNNs in lens identification has increased. We identify the major challenge to be the automatic detection of galaxy-galaxy strong lenses while simultaneously maintaining a low false positive rate, thus producing a pure and complete sample of strong lens candidates from Euclid with a limited need for visual inspection. One aim of this research is to have a quantified starting point on the achieved purity and completeness with our current version of CNN-based detection pipelines for the VIS images of EWS. This work is vital in preparing our CNN-based detection pipelines to be able to produce a pure sample of the > 100 000 strong gravitational lensing systems widely predicted for Euclid. We select all sources with VIS IE 5 lensing systems in Euclid, this implies 106 objects for human classification, which while very large is not in principle intractable and not without precedent. © 2024, CC BY.

关键词： Convolutional neural networks

Common Limitations of Image Processing Metrics: A Picture Story

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arXiv 2021年

作者： Reinke, Annika Tizabi, Minu D. Sudre, Carole H. Eisenmann, Matthias Rädsch, Tim Baumgartner, Michael Acion, Laura Antonelli, Michela Arbel, Tal Bakas, Spyridon Bankhead, Peter Benis, Arriel Blaschko, Matthew Buettner, Florian Cardoso, M. Jorge Chen, Jianxu Cheplygina, Veronika Christodoulou, Evangelia Cimini, Beth A. Collins, Gary S. Engelhardt, Sandy Farahani, Keyvan Ferrer, Luciana Galdran, Adrian van Ginneken, Bram Glocker, Ben Godau, Patrick Haase, Robert Hamprecht, Fred Hashimoto, Daniel A. Heckmann-Nötzel, Doreen Hirsch, Peter Hoffman, Michael M. Huisman, Merel Isensee, Fabian Jannin, Pierre Kahn, Charles E. Kainmueller, Dagmar Kainz, Bernhard Karargyris, Alexandros Karthikesalingam, Alan Kavur, A. Emre Kenngott, Hannes Kleesiek, Jens Kleppe, Andreas Koehler, Sven Kofler, Florian Kopp-Schneider, Annette Kooi, Thijs 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 Moher, David Moons, Karel G.M. Müller, Henning Nichyporuk, Brennan Nickel, Felix Noyan, M. Alican Petersen, Jens Polat, Gorkem Rafelski, Susanne M. Rajpoot, Nasir Reyes, Mauricio Rieke, Nicola Riegler, Michael A. Rivaz, Hassan Saez-Rodriguez, Julio Sánchez, Clara I. Schroeter, Julien Saha, Anindo Selver, M. Alper Sharan, Lalith Shetty, Shravya Smeden, Maarten V.A.N. Stieltjes, Bram Summers, Ronald M. Taha, Abdel A. Tiulpin, Aleksei Tsaftaris, Sotirios A. Calster, Ben V.A.N. Varoquaux, Gaël Wiesenfarth, Manuel Yaniv, Ziv R. Jäger, Paul Maier-Hein, Lena Division of Intelligent Medical Systems and HI Helmholtz Imaging Heidelberg Germany Faculty of Mathematics and Computer Science Heidelberg University Heidelberg Germany Division of Intelligent Medical Systems Heidelberg Germany NCT Heidelberg DKFZ University Medical Center Heidelberg 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 Division of Medical Image Computing Heidelberg Germany Instituto de Cálculo CONICET – Universidad de Buenos Aires Buenos Aires Argentina Centre for Medical Image Computing University College London London United Kingdom McGill University Montréal 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 Institute of Genetics and Cancer University of Edinburgh Edinburgh United Kingdom 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 Kasteelpark Arenberg 10 - box 2441 Leuven3001 Belgium Frankfurt/Mainz DKFZ UCT Frankfurt-Marburg Germany Heidelberg Germany Goethe University Frankfurt Department of Medicine Germany Goethe University Frankfurt Department of Informatics Germany Frankfurt Cancer Insititute Germany Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V. Dortmund Germany Department of Computer Science IT University of Copenhagen Copenhagen Denmark Imaging Platform Broad Institute of MIT and Harvard CambridgeMA United States Centre for St

While the importance of automatic image analysis is continuously increasing, recent meta-research revealed major flaws with respect to algorithm validation. Performance metrics are particularly key for meaningful, objective, and transparent performance assessment and validation of the used automatic algorithms, but relatively little attention has been given to the practical pitfalls when using specific metrics for a given image analysis task. These are typically related to (1) the disregard of inherent metric properties, such as the behaviour in the presence of class imbalance or small target structures, (2) the disregard of inherent data set properties, such as the non-independence of the test cases, and (3) the disregard of the actual biomedical domain interest that the metrics should reflect. This living dynamically document has the purpose to illustrate important limitations of performance metrics commonly applied in the field of image analysis. In this context, it focuses on biomedical image analysis problems that can be phrased as image-level classification, semantic segmentation, instance segmentation, or object detection task. The current version is based on a Delphi process on metrics conducted by an international consortium of image analysis experts from more than 60 institutions worldwide. © 2021, CC BY.

关键词： Medical imaging

A family of single-node second-order boundary schemes for the lattice Boltzmann method

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arXiv 2017年

作者： Zhao, Weifeng Yong, Wen-An Department of Applied Mathematics and Mechanics University of Science and Technology Beijing Beijing100083 China Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing100084 China Beijing Computational Science Research Center Beijing100193 China

In this work, we propose a family of single-node second-order boundary schemes for the lattice Boltzmann method with general collision terms. The construction of the schemes is quite universal and simple, it does not involve concrete lattice Boltzmann models and uses the half-way bounce-back rule as a central step. The constructed schemes are all second-order accurate if so is the bounce-back rule. In addition, the proposed schemes have good stability thanks to convex combinations. The accuracy and stability of several specific schemes are numerically validated for multiple-relaxation-time models in both 2D and 3D. Copyright © 2017, The Authors. All rights reserved.

关键词： Kinetic theory

Entropy production in thermal phase separation: a kinetic-theory approach

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arXiv 2018年

作者： Zhang, Yudong Xu, Aiguo Zhang, Guangcai Gan, Yanbiao Chen, Zhihua Succi, Sauro National Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P. O. Box 8009-26 Beijing China Key Laboratory of Transient Physics Nanjing University of Science and Technology Nanjing210094 China State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing100081 China Center for Applied Physics and Technology MOE Key Center for High Energy Density Physics Simulations College of Engineering Peking University Beijing100871 China North China Institute of Aerospace Engineering Langfang065000 China College of Mathematics and Informatics & FJKLMAA Fujian Normal University Fuzhou350007 China Center for Life Nano Science at La Sapienza Fondazione Istituto Italiano di Tecnologia Viale Regina Margherita 295 Roma00161 Italy Physics Department and Institute for Applied Computational Science John A. Paul-son School of Engineering and Applied Sciences Harvard University Oxford Street 29 CambridgeMA02138 United States

Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decrease during the domain growth stage, attaining its maximum at the crossover between the two. Such behaviour provides a natural criterion to identify and discriminate between the two regimes. Furthermore, the effects of heat conductivity, viscosity and surface tension on the entropy production rate are investigated by systematically probing the interplay between non-equilibrium energy and momentum fluxes. It is found that the entropy production rate due to energy fluxes is an increasing function of the Prandtl number, while the momentum fluxes exhibit an opposite trend. On the other hand, both contributions show an increasing trend with surface tension. The present analysis inscribes within the general framework of non-equilibrium thermodynamics and consequently it is expected to be relevant to a broad class of soft-flowing systems far from mechanical and thermal equilibrium. Copyright © 2018, The Authors. All rights reserved.

关键词： Momentum

Asymptotics of extreme statistics of escape time in 1,2 and 3-dimensional diffusions

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arXiv 2017年

作者： Basnayake, K. Guerrier, C. Schuss, Z. Holcman, D. Applied Mathematics & Computational Biology Ecole Normale Supérieure 46 rue d'Ulm Paris75005 France University of British Columbia Mathematics Department VancouverBCV6T 1Z2 Canada Department of Applied Mathematics Tel-Aviv University Tel-Aviv69978 Israel

The first of N identical independently distributed (i.i.d.) Brownian trajectories that arrives to a small target, sets the time scale of activation, which in general is much faster than the arrival to the target of only a single trajectory. Analytical asymptotic expressions for the minimal time is notoriously difficult to compute in general geometries. We derive here asymptotic laws for the probability density function of the first and second arrival times of a large number of i.i.d. Brownian trajectories to a small target in 1,2, and 3 dimensions and study their range of validity by stochastic simulations. The results are applied to activation of biochemical pathways in cellular transduction.60H30 60-08 82C41 Copyright © 2017, The Authors. All rights reserved.

关键词： Chemical activation

Encryption and decryption algorithm using algebraic matrix approach

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Journal of Physics: Conference Series 2018年第1期1000卷

作者： K Thiagarajan P Balasubramanian J Nagaraj J Padmashree Department of Mathematics P.S.N.A. College of Engineering and Technology Dindigul Tamilnadu India. Department of Mathematics Bharathiar University Coimbatore Tamilnadu India Department of Applied Mathematics & Computational Sciences PSG College of Technology Coimbatore Tamilnadu India. Department of Mathematics Research Scholar Bharathiar University Coimbatore Tamilnadu India.

Cryptographic algorithms provide security of data against attacks during encryption and decryption. However, they are computationally intensive process which consume large amount of CPU time and space at time of encryption and decryption. The goal of this paper is to study the encryption and decryption algorithm and to find space complexity of the encrypted and decrypted data by using of algorithm. In this paper, we encrypt and decrypt the message using key with the help of cyclic square matrix provides the approach applicable for any number of words having more number of characters and longest word. Also we discussed about the time complexity of the algorithm. The proposed algorithm is simple but difficult to break the process.

关键词：

Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to modeling uncertainty

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Physical Review D 2022年第2期105卷 023515-023515页

作者： L. F. Secco S. Samuroff E. Krause B. Jain J. Blazek M. Raveri A. Campos A. Amon A. Chen C. Doux A. Choi D. Gruen G. M. Bernstein C. Chang J. DeRose J. Myles A. Ferté P. Lemos D. Huterer J. Prat M. A. Troxel N. MacCrann A. R. Liddle T. Kacprzak X. Fang C. Sánchez S. Pandey S. Dodelson P. Chintalapati K. Hoffmann A. Alarcon O. Alves F. Andrade-Oliveira E. J. Baxter K. Bechtol M. R. Becker A. Brandao-Souza H. Camacho A. Carnero Rosell M. Carrasco Kind R. Cawthon J. P. Cordero M. Crocce C. Davis E. Di Valentino A. Drlica-Wagner K. Eckert T. F. Eifler M. Elidaiana F. Elsner J. Elvin-Poole S. Everett P. Fosalba O. Friedrich M. Gatti G. Giannini R. A. Gruendl I. Harrison W. G. Hartley K. Herner H. Huang E. M. Huff M. Jarvis N. Jeffrey N. Kuropatkin P.-F. Leget J. Muir J. Mccullough A. Navarro Alsina Y. Omori Y. Park A. Porredon R. Rollins A. Roodman R. Rosenfeld A. J. Ross E. S. Rykoff J. Sanchez I. Sevilla-Noarbe E. S. Sheldon T. Shin A. Troja I. Tutusaus T. N. Varga N. Weaverdyck R. H. Wechsler B. Yanny B. Yin Y. Zhang J. Zuntz T. M. C. Abbott M. Aguena S. Allam J. Annis D. Bacon E. Bertin S. Bhargava S. L. Bridle D. Brooks E. Buckley-Geer D. L. Burke J. Carretero M. Costanzi L. N. da Costa J. De Vicente H. T. Diehl J. P. Dietrich P. Doel I. Ferrero B. Flaugher J. Frieman J. García-Bellido E. Gaztanaga D. W. Gerdes T. Giannantonio J. Gschwend G. Gutierrez S. R. Hinton D. L. Hollowood K. Honscheid B. Hoyle D. J. James T. Jeltema K. Kuehn O. Lahav M. Lima H. Lin M. A. G. Maia J. L. Marshall P. Martini P. Melchior F. Menanteau R. Miquel J. J. Mohr R. Morgan R. L. C. Ogando A. Palmese F. Paz-Chinchón D. Petravick A. Pieres A. A. Plazas Malagón M. Rodriguez-Monroy A. K. Romer E. Sanchez V. Scarpine M. Schubnell D. Scolnic S. Serrano M. Smith M. Soares-Santos E. Suchyta M. E. C. Swanson G. Tarle D. Thomas C. To Kavli Institute for Cosmological Physics University of Chicago Chicago Illinois 60637 USA Department of Physics and Astronomy University of Pennsylvania Philadelphia Pennsylvania 19104 USA McWilliams Center for Cosmology Department of Physics Carnegie Mellon University Pittsburgh Pennsylvania 15213 USA Department of Physics Northeastern University Boston Massachusetts 02115 USA Department of Astronomy/Steward Observatory University of Arizona 933 North Cherry Avenue Tucson Arizona 85721-0065 USA Laboratory of Astrophysics École Polytechnique Fédérale de Lausanne (EPFL) 1290 Versoix Switzerland Kavli Institute for Particle Astrophysics and Cosmology P. O. Box 2450 Stanford University Stanford California 94305 USA Department of Physics University of Michigan Ann Arbor Michigan 48109 USA Center for Cosmology and Astro-Particle Physics The Ohio State University Columbus Ohio 43210 USA Department of Physics The Ohio State University Columbus Ohio 43210 USA Department of Physics Stanford University 382 Via Pueblo Mall Stanford California 94305 USA SLAC National Accelerator Laboratory Menlo Park California 94025 USA Berkeley Center for Cosmological Physics University of California Berkeley California 94720 USA Jet Propulsion Laboratory California Institute of Technology 4800 Oak Grove Dr. Pasadena California 91109 USA Department of Physics and Astronomy University College London Gower Street London WC1E 6BT United Kingdom Department of Physics Duke University Durham North Carolina 27708 USA Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge CB3 0WA United Kingdom Instituto de Astrofísica e Ciências do Espaço Faculdade de Ciências Universidade de Lisboa 1769-016 Lisboa Portugal Institute for Astronomy University of Edinburgh Edinburgh EH9 3HJ United Kingdom Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo Ontario N2L 2Y5 Canada Institute for Particle Physics and Astrophysic

This work and its companion paper, Amon et al. [Phys. Rev. D 105, 023514 (2022)], present cosmic shear measurements and cosmological constraints from over 100 million source galaxies in the Dark Energy Survey (DES) Year 3 data. We constrain the lensing amplitude parameter S8≡σ8Ωm/0.3 at the 3% level in ΛCDM: S8=0.759−0.023+0.025 (68% CL). Our constraint is at the 2% level when using angular scale cuts that are optimized for the ΛCDM analysis: S8=0.772−0.017+0.018 (68% CL). With cosmic shear alone, we find no statistically significant constraint on the dark energy equation-of-state parameter at our present statistical power. We carry out our analysis blind, and compare our measurement with constraints from two other contemporary weak lensing experiments: the Kilo-Degree Survey (KiDS) and Hyper-Suprime Camera Subaru Strategic program (HSC). We additionally quantify the agreement between our data and external constraints from the Cosmic Microwave Background (CMB). Our DES Y3 result under the assumption of ΛCDM is found to be in statistical agreement with Planck 2018, although favors a lower S8 than the CMB-inferred value by 2.3σ (a p-value of 0.02). This paper explores the robustness of these cosmic shear results to modeling of intrinsic alignments, the matter power spectrum and baryonic physics. We additionally explore the statistical preference of our data for intrinsic alignment models of different complexity. The fiducial cosmic shear model is tested using synthetic data, and we report no biases greater than 0.3σ in the plane of S8×Ωm caused by uncertainties in the theoretical models.

关键词： Cosmological parameters Gravitational lenses Sky surveys

Modeling binary time series using gaussian processes with application to predicting sleep states

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arXiv 2017年

作者： Gao, Xu Shahbaba, Babak Ombao, Hernando Department of Statistics University of California IrvineCA United States Department of Cognitive Sciences University of California IrvineCA United States Program on Applied Mathematics and Computational Science King Abdullah University of Science and Technology

Motivated by the problem of predicting sleep states, we develop a mixed effects model for binary time series with a stochastic component represented by a Gaussian process. The fixed component captures the effects of covariates on the binary-valued response. The Gaussian process captures the residual variations in the binary response that are not explained by covariates and past realizations. We develop a frequentist modeling framework that provides efficient inference and more accurate predictions. Results demonstrate the advantages of improved prediction rates over existing approaches such as logistic regression, generalized additive mixed model, models for ordinal data, gradient boosting, decision tree and random forest. Using our proposed model, we show that previous sleep state and heart rates are significant predictors for future sleep states. Simulation studies also show that our proposed method is promising and robust. To handle computational complexity, we utilize Laplace approximation, golden section search and successive parabolic interpolation. With this paper, we also submit an R-package (HIBITS) that implements the proposed procedure. Copyright © 2017, The Authors. All rights reserved.

关键词： Gaussian noise (electronic)

Ab-InitioComputations of Electronic, Transport, and Structural Properties of zinc-blendeBeryllium Selenide (zb-BeSe)

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Journal of Modern Physics 2017年第4期8卷 552-566页

作者： Richard Inakpenu Cheick Bamba Ifeanyi H. Nwigboji Lashounda Franklin Yuriy Malozovsky Guang-Lin Zhao Diola Bagayoko Department of Mathematics and Physics Southern University and A&M College Baton Rouge Louisiana USA Computational Science Program University of Texas at El Paso El Paso Texas USA

We report results from several ab-initio computations of electronic, transport and bulk properties of zinc-blende beryllium selenide (zb-BeSe). Our nonrelativistic calculations utilized a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). The key distinction of our calculations from other DFT calculations is the implementation of the Bagayoko, Zhao and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF), in the LCAO formalism. Our calculated, indirect band gap is 5.46 eV, from Γto a conduction band minimum between Г and X, for a room temperature lattice constant of 5.152 Å. Available, room temperature experimental band gaps of 5.5 (direct) and 4 - 4.5 (unspecified) point to the need for additional measurements of this gap. Our calculated bulk modulus of 92.35 GPa is in excellent agreement with experiment (92.2 ±?1.8 GPa). Our predicted equilibrium lattice constant and band gap, at zero temperature, are 5.0438 Åand 5.4 eV, respectively.

关键词： Density Functional Theory (DFT) LDA Ab-Initio Calculations Band Gap BZW-EF Method