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The q-gradient method for continuous global optimization

AIP Conference Proceedings 2013年第1期1558卷 2389-2393页

作者： Aline C. Soterroni Roberto L. Galski Fernando M. Ramos Applied Computing Program National Institute for Space Research São José dos Campos Brazil Satellite Control Centre National Institute for Space Research São José dos Campos Brazil Laboratory of Computing and Applied Mathematics National Institute for Space Research São José dos Campos Brazil

Here, we present an extension of the classical steepest descent method for solving global continuous optimization problems. To this end, we apply the concept of Jackson's derivative to compute the negative of the q-gradient of the objective function, used as the search direction. The use of Jackson's derivative has shown to be an effective mechanism for escaping from local minima. The q-gradient algorithm is complemented with strategies for selecting the parameter q and to compute the step length. These strategies are implemented in a way such that the search process gradually shifts from global in the beginning to local as the algorithm converges. For testing this new approach, we considered a set of multimodal test functions and compared our results with those obtained by Evolutionary Algorithms (EAs) widely used in optimizing multidimensional and multimodal functions. Overall, the q-gradient method performs well against the EAs arriving in forth position in a direct comparison with them, for the dimensions 10 and 30.

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Methods for Evaluating Medical Tests and Biomarkers

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Diagnostic and Prognostic Research 2017年第1期1卷 1-34页

作者： Gowri Gopalakrishna Miranda Langendam Patrick Bossuyt Mariska Leeflang Rob Scholten Anna Noel-Storr James Thomas Iain Marshall Byron Wallace Penny Whiting Clare Davenport Gowri GopalaKrishna Isabel de Salis Sue Mallett Robert Wolff Marie Westwood Jos Kleinen Richard Riley Gary Collins Hans Reitsma Karel Moons Antonia Zapf Katharina Kramer Annika Hoyer Oliver Kuss J. Ensor R. D. Riley J. J. Deeks E. C. Martin Gerta Rücker Martin Schumacher Susanne Steinhauser Joie Ensor Kym Snell Brian Willis Jon Deeks Thomas Debray Lavinia Ferrante di Ruffano Sian Taylor-Phillips Chris Hyde Stuart A. Taylor Gauraang Batnagar Lavinia Ferrante Di Ruffano Farah Seedat Aileen Clarke Sarah Byron Frances Nixon Rebecca Albrow Thomas Walker Carla Deakin Zhivko Zhelev Harriet Hunt Yaling Yang Lucy Abel James Buchanan Thomas Fanshawe Bethany Shinkins Laure Wynants Sabine Van Huffel Jan Verbakel Dirk Timmerman Ben Van Calster Aeliko Zwinderman Jason Oke Jack O’Sullivan Rafael Perera Brian Nicholson Hannah L. Bromley Tracy E. Roberts Adele Francis Denniis Petrie G. Bruce Mann Kinga Malottki Holly Smith Lucinda Billingham Alice Sitch Oke Gerke Mie Holm-Vilstrup Eivind Antonsen Segtnan Ulrich Halekoh Poul Flemming Høilund-Carlsen Bernard G. Francq Jac Dinnes Julie Parkes Walter Gregory Jenny Hewison Peter Selby Doug Altman William Rosenberg Julien Asselineau Paul Perez Aïssatou Paye Emilie Bessede Cécile Proust-Lima Christiana Naaktgeboren Joris de Groot Johannes Reitsma Anne Rutjes Emmanuel Ogundimu Jonathan Cook Yannick Le Manach Yvonne Vergouwe Romin Pajouheshnia Rolf Groenwold Karen Moons Linda Peelen Bavo De Cock Daan Nieboer Ewout W. Steyerberg Micael J. Pencina Jennifer Cooper Nick Parsons Chris Stinton Steve Smith Andy Dickens Rachel Jordan Alexandra Enocson David Fitzmaurice Peymane Adab Charles Boachie Gaj Vidmar Karoline Freeman Martin Connock Rachel Court Carl Moons Jessica Harris Zoe Plummer Barnaby Reeves Chris Rogers Andrew Mumford Kurtis Lee Veerle Verheyden Gianni D. Angelini Gavin J. Murphy Jeremy Huddy Melody Ni George Hanna Department of Clinical Epidemiology Biostatistics & Bioinformatics Academic Medical Center University of Amsterdam Amsterdam The Netherlands Department of Clinical Epidemiology and Biostatistics Academic Medical Center University of Amsterdam Amsterdam Netherlands Cochrane Netherlands Julius Center for Health Sciences and Primary Care University Medical Center Utrecht Utrecht Netherlands Cochrane Dementia and Cognitive Improvement Group University of Oxford Oxford UK EPPI-Centre Department of Social Science University College London London UK Division of Health and Social Care Research King’s College London London UK College of Computer and Information Science Northeastern University Boston USA University Hospitals Bristol NHS Foundation Trust School of Social and Community Medicine Bristol UK Institute of Applied Health Research University of Birmingham Birmingham UK School of Social and Community Medicine University of Bristol Bristol UK Kleijnen Systematic Reviews Ltd York UK Research Institute for Primary Care and Health Sciences Keele University Keele UK Centre for Statistics in Medicine Nuffield Department of Orthopaedics Rheumatology and Musculoskeletal Sciences University of Oxford Oxford UK Julius Center for Health Sciences and Primary Care University Medical Center Utrecht Utrecht The Netherlands Cochrane Netherlands University Medical Center Utrecht Utrecht The Netherlands Julius Center for Health Sciences and Primary Care University Medical Center Utrecht 3584 CG Utrecht Netherlands Department of Medical Statistics University Medical Center Göttingen Göttingen Germany Institute for Biometry and Epidemiology German Diabetes Center Leibniz Institute for Diabetes Research at Heinrich Heine University Düsseldorf Germany Manchester Pharmacy School University of Manchester Manchester UK Institute for Medical Biometry and Statistics Faculty of Medicine and Medical Center – University of Freiburg Stefan-Meier-Str. 26 79104 Freiburg Germany

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Efficient linear programming algorithm to generate the densest lattice sphere packings

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Physical Review E 2013年第6期87卷 063303-063303页

作者： Étienne Marcotte Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Institute of the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

Finding the densest sphere packing in d-dimensional Euclidean space Rd is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding theory, discrete geometry, number theory, and biological systems. Numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations, even for the restricted problem of finding the densest lattice sphere packings. In this paper we apply the Torquato-Jiao packing algorithm, which is a method based on solving a sequence of linear programs, to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19. We show that the TJ algorithm is appreciably more efficient at solving these problems than previously published methods. Indeed, in some dimensions, the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones. We also study the suboptimal local density-maxima solutions (inherent structures or “extreme” lattices) to gain insight about the nature of the topography of the “density” landscape.

关键词： Spheres

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Correlation and relativistic effects in U metal and U-Zr alloy: Validation of ab initio approaches

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Physical Review B 2013年第23期88卷 235128-235128页

作者： Wei Xie (谢玮) Wei Xiong Chris A. Marianetti Dane Morgan Materials Science Program University of Wisconsin-Madison Madison Wisconsin 53706 USA Department of Materials Science and Engineering University of Wisconsin-Madison Madison Wisconsin 53706 USA Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 USA Department of Engineering Physics University of Wisconsin-Madison Madison Wisconsin 53706 USA

Ab initio calculations have been performed on all solid phases of U metal and U-Zr alloy, the basis of a promising metallic fuel for fast nuclear reactors. Based on generalized gradient approximation, both density functional theory (DFT) in its standard form and the so-called DFT plus Hubbard U (DFT+U) modification are evaluated. The evolution of calculated energetics, volume, magnetic moments, electronic structure, and f-orbital occupation as functions of the effective Hubbard U parameter, Ueff, is carefully examined at Ueff from 0 to 4 eV. DFT is found to overestimate energetics, underestimate volume, downward shift some f bands near Fermi level and overestimate f-orbital occupation against existing experimental and/or computational data. The error is ∼0.07 eV/atom in terms of enthalpy, which affects phase stability modeling for δ(U,Zr) and γ(U,Zr). DFT+U at Ueff=1−1.5 eV offers clear improvement on these calculated properties (∼0.05 eV/atom in terms of enthalpy) and in general still neither promotes ordered magnetic moments nor opens unphysical band gaps, which occur at higher Ueff values. The empirical Ueff values of 1–1.5 eV are close to but smaller than the theoretical estimations of 1.9–2.3 eV that we obtain from the linear response approach. Ueff is found to vary only slightly (≤0.24 eV) between different phases and at different compositions of U and U-Zr; thus, a single Ueff=1.24 eV, which is the statistical optimal from energetic fitting, is suggested for both U and U-Zr. Besides correlation, the relativistic effect of spin-orbit coupling (SOC) is also systematically explored. SOC is found to lower energy, increase volume, and split the 5f shell above Fermi level and reduce f-orbital occupation. The effect predominates in the unoccupied states and is very small on all these calculated ground state properties (∼0.02 eV/atom in terms of enthalpy).

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Radiative transport produced by oblique illumination of turbid media with collimated beams

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Physical Review E 2013年第6期87卷 063308-063308页

作者： Adam R. Gardner Arnold D. Kim Vasan Venugopalan Department of Chemical Engineering and Materials Science University of California Irvine Irvine California 92697 USA Laser Microbeam and Medical Program Beckman Laser Institute University of California Irvine Irvine California 92697 USA Applied Mathematics Unit School of Natural Sciences University of California Merced 5200 North Lake Road Merced California 95343 USA

We examine the general problem of light transport initiated by oblique illumination of a turbid medium with a collimated beam. This situation has direct relevance to the analysis of cloudy atmospheres, terrestrial surfaces, soft condensed matter, and biological tissues. We introduce a solution approach to the equation of radiative transfer that governs this problem, and develop a comprehensive spherical harmonics expansion method utilizing Fourier decomposition (SHEFN). The SHEFN approach enables the solution of problems lacking azimuthal symmetry and provides both the spatial and directional dependence of the radiance. We also introduce the method of sequential-order smoothing that enables the calculation of accurate solutions from the results of two sequential low-order approximations. We apply the SHEFN approach to determine the spatial and angular dependence of both internal and boundary radiances from strongly and weakly scattering turbid media. These solutions are validated using more costly Monte Carlo simulations and reveal important insights regarding the evolution of the radiant field generated by oblique collimated beams spanning ballistic and diffusely scattering regimes.

关键词： Monte Carlo methods

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Author Correction: Study of 300,486 individuals identifies 148 independent genetic loci influencing general cognitive function

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Nature communications 2019年第1期10卷 2068页

作者： Gail Davies Max Lam Sarah E Harris Joey W Trampush Michelle Luciano W David Hill Saskia P Hagenaars Stuart J Ritchie Riccardo E Marioni Chloe Fawns-Ritchie David C M Liewald Judith A Okely Ari V Ahola-Olli Catriona L K Barnes Lars Bertram Joshua C Bis Katherine E Burdick Andrea Christoforou Pamela DeRosse Srdjan Djurovic Thomas Espeseth Stella Giakoumaki Sudheer Giddaluru Daniel E Gustavson Caroline Hayward Edith Hofer M Arfan Ikram Robert Karlsson Emma Knowles Jari Lahti Markus Leber Shuo Li Karen A Mather Ingrid Melle Derek Morris Christopher Oldmeadow Teemu Palviainen Antony Payton Raha Pazoki Katja Petrovic Chandra A Reynolds Muralidharan Sargurupremraj Markus Scholz Jennifer A Smith Albert V Smith Natalie Terzikhan Anbupalam Thalamuthu Stella Trompet Sven J van der Lee Erin B Ware B Gwen Windham Margaret J Wright Jingyun Yang Jin Yu David Ames Najaf Amin Philippe Amouyel Ole A Andreassen Nicola J Armstrong Amelia A Assareh John R Attia Deborah Attix Dimitrios Avramopoulos David A Bennett Anne C Böhmer Patricia A Boyle Henry Brodaty Harry Campbell Tyrone D Cannon Elizabeth T Cirulli Eliza Congdon Emily Drabant Conley Janie Corley Simon R Cox Anders M Dale Abbas Dehghan Danielle Dick Dwight Dickinson Johan G Eriksson Evangelos Evangelou Jessica D Faul Ian Ford Nelson A Freimer He Gao Ina Giegling Nathan A Gillespie Scott D Gordon Rebecca F Gottesman Michael E Griswold Vilmundur Gudnason Tamara B Harris Annette M Hartmann Alex Hatzimanolis Gerardo Heiss Elizabeth G Holliday Peter K Joshi Mika Kähönen Sharon L R Kardia Ida Karlsson Luca Kleineidam David S Knopman Nicole A Kochan Bettina Konte John B Kwok Stephanie Le Hellard Teresa Lee Terho Lehtimäki Shu-Chen Li Christina M Lill Tian Liu Marisa Koini Edythe London Will T Longstreth Oscar L Lopez Anu Loukola Tobias Luck Astri J Lundervold Anders Lundquist Leo-Pekka Lyytikäinen Nicholas G Martin Grant W Montgomery Alison D Murray Anna C Need Raymond Noordam Lars Nyberg William Ollier Goran Papenberg Alison Pattie Ozren Polasek Russell A Poldrack Bruce M Psaty Sim Centre for Cognitive Ageing and Cognitive Epidemiology Department of Psychology School of Philosophy Psychology and Language Sciences The University of Edinburgh Edinburgh EH8 9JZ UK. Institute of Mental Health Singapore 539747 Singapore. Medical Genetics Section Centre for Genomic & Experimental Medicine MRC Institute of Genetics & Molecular Medicine University of Edinburgh Western General Hospital Edinburgh EH4 2XU UK. BrainWorkup LLC Los Angeles 90033 CA USA. Department of Psychiatry and Behavioral Sciences Keck School of Medicine University of Southern California Los Angeles 90033 CA USA. Social Genetic and Developmental Psychiatry Centre Institute of Psychiatry Psychology & Neuroscience King's College London De Crespigny Park Denmark Hill London SE5 8AF UK. Research Centre of Applied and Preventive Cardiovascular Medicine University of Turku Turku 20520 Finland. Department of Internal Medicine Satakunta Central Hospital Pori 28100 Finland. Centre for Global Health Research Usher Institute of Population Health Sciences and Informatics University of Edinburgh Teviot Place Edinburgh EH8 9AG Scotland. Max Planck Institute for Molecular Genetics Berlin 14195 Germany. Cardiovascular Health Research Unit Department of Medicine University of Washington Seattle 98101 Washington USA. Department of Psychiatry Icahn School of Medicine at Mount Sinai New York 10029 NY USA. Mental Illness Research Education and Clinical Center (VISN 3) James J. Peters VA Medical Center Bronx 10468 NY USA. Department of Psychiatry Brigham and Women's Hospital Harvard Medical School Boston 02115 MA USA. NORMENT K.G. Jebsen Centre for Psychosis Research Department of Clinical Science University of Bergen Bergen 5021 Norway. Dr. Einar Martens Research Group for Biological Psychiatry Center for Medical Genetics and Molecular Medicine Haukeland University Hospital Bergen 5020 Norway. Center for Psychiatric Neuroscience Feinstein Institute for Medical Resea

Christina M. Lill, who contributed to analysis of data, was inadvertently omitted from the author list in the originally published version of this article. This has now been corrected in both the PDF and HTML versions...

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Nearly hyperuniform network models of amorphous silicon

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Physical Review B 2013年第24期87卷 245204-245204页

作者： Miroslav Hejna Paul J. Steinhardt Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We introduce the concept of nearly hyperuniform network (NHN) structures as alternatives to the conventional continuous random network (CRN) models for amorphous tetrahedrally coordinated solids, such as amorphous silicon (a-Si). A hyperuniform solid has a structure factor S(k) that approaches zero as the wavenumber k→0. We define a NHN as an amorphous network whose structure factor S(k→0) is smaller than the liquid value at the melting temperature. Using a novel implementation of the Stillinger-Weber potential for the interatomic interactions, we show that the energy landscape for a spectrum of NHNs includes a sequence of local minima with an increasing degree of hyperuniformity [smaller S(k→0)] that is significantly below the frozen-liquid value and that correlates with other measurable features in S(k) at intermediate and large k and with the width of the electronic band gap.

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Designer spin systems via inverse statistical mechanics

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Physical Review B 2013年第13期88卷 134104-134104页

作者： Robert A. DiStasio, Jr. Étienne Marcotte Roberto Car Frank H. Stillinger Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In this work, we extend recent inverse statistical-mechanical methods developed for many-particle systems to the case of spin systems. For simplicity, we focus in this initial study on the two-state Ising model with radial spin-spin interactions of finite range (i.e., extending beyond nearest-neighbor sites) on the square lattice under periodic boundary conditions. Our interest herein is to find the optimal set of shortest-range pair interactions within this family of Hamiltonians, whose corresponding ground state is a targeted spin configuration such that the difference in energies between the energetically closest competitor and the target is maximized. For an exhaustive list of competitors, this optimization problem is solved exactly using linear programming. The possible outcomes for a given target configuration can be organized into the following three solution classes: unique (nondegenerate) ground state (class I), degenerate ground states (class II), and solutions not contained in the previous two classes (class III). We have chosen to study a general family of striped-phase spin configurations comprised of alternating parallel bands of up and down spins of varying thicknesses and a general family of rectangular block checkerboard spin configurations with variable block size, which is a generalization of the classic antiferromagnetic Ising model. Our findings demonstrate that the structurally anisotropic striped phases, in which the thicknesses of up- and down-spin bands are equal, are unique ground states for isotropic short-ranged interactions. By contrast, virtually all of the block checkerboard targets are either degenerate or fall within class III solutions. The degenerate class II spin configurations are identified up to a certain block size. We also consider other target spin configurations with different degrees of global symmetries and order. Our investigation reveals that the solution class to which a target belongs depends sensitively on the nature

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Designer spin systems via inverse statistical mechanics. II. Ground-state enumeration and classification

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Physical Review B 2013年第18期88卷 184432-184432页

作者： Étienne Marcotte Robert A. DiStasio, Jr. Frank H. Stillinger Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In the first paper of this series [DiStasio, Jr., Marcotte, Car, Stillinger, and Torquato, Phys. Rev. B 88, 134104 (2013)], we applied inverse statistical-mechanical techniques to study the extent to which targeted spin configurations on the square lattice can be ground states of finite-ranged radial spin-spin interactions. In this sequel, we enumerate all of the spin configurations within a unit cell on the one-dimensional integer lattice and the two-dimensional square lattice up to some modest size under periodic boundary conditions. We then classify these spin configurations into those that can or cannot be unique classical ground states of the aforementioned radial pair spin interactions and found the relative occurrences of these ground-state solution classes for different system sizes. As a result, we also determined the minimal radial extent of the spin-spin interaction potentials required to stabilize those configurations whose ground states are either unique or degenerate (i.e., those sharing the same radial spin-spin correlation function). This enumeration study has established that unique ground states are not limited to simple target configurations. However, we also found that many simple target spin configurations cannot be unique ground states.

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A multi-start procedure for the minimum latency problem

A multi-start procedure for the minimum latency problem

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7th IFAC Conference on Manufacturing Modelling, Management, and Control, MIM 2013

作者： Angel-Bello, Francisco Alvarez, Ada García, Irma Tecnológico de Monterrey Campus Monterrey Department of Industrial and Systems Engineering Ave. Eugenio Garza Sada 2501 Monterrey Nuevo León CP 64849 Mexico Universidad Autónoma de Nuevo León Graduate Program in Systems Engineering Ave. Universidad s/n San Nicolás Nuevo León CP 66451 Mexico Universidad Autónoma de Coahuila Research Center on Applied Mathematics Edif. S Campo Redondo Saltillo Coahuila CP 25280 Mexico

ISBN: (纸本)9783902823359

In this paper we address a minimum latency problem and propose a multi-start strategy for solving it. For constructing initial solutions two procedures are designed, which are based on metaheuristic GRASP. We also develop a post-processing procedure based on Path Relinking to improve the obtained solutions. We carry up an extensive experimentation with 225 symmetrical instances to evaluate our procedures. In addition, using instances from literature, we compare our best procedure with previously reported methods, showing that the proposed procedure outperforms them in terms of solution quality and in elapsed CPU time to reach the solution. © IFAC.

关键词： Supply chains

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