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作者： Batson, Joshua Spielman, Daniel A. Srivastava, Nikhil Department of Mathematics MIT Cambridge MA 02139 United States Program in Applied Mathematics Department of Computer Science Yale University New Haven CT 06520 United States Department of Computer Science Yale University New Haven CT 06520 United States

We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be viewed as generalizations of expander graphs. In particular, we prove that for every d > 1 and every undirected, weighted graph G = (V, E,w) on n vertices, there exists a weighted graph H = (V, F, w˜) with at most d(n - 1)] edges such that for every x ∈ v, xT LGx ≤ xT LHx ≤ (d+1+2√d/d+1+2√d)· x T Lgx, where LG and LH are the Laplacian matrices of G and H, respectively. Thus, H approximates G spectrally at least as well as a Ramanujan expander with dn/2 edges approximates the complete graph. We give an elementary deterministic polynomial time algorithm for constructing H. Copyright © by SIAM.

关键词： Polynomial approximation

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On the interaction between acoustic pressure waves and the living cell

On the interaction between acoustic pressure waves and the l...

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19th International Congress on Sound and Vibration 2012, ICSV 2012

作者： Kimmel, Eitan Krasovitski, Boris Plaksin, Michael Assa, Michael Geva, Avner Shoham, Shy Department of Biomedical Engineering Technion Haifa 32000 Israel Russell Berrie Nanotechnology Institute Technion Haifa 32000 Israel Applied Mathematics Program Technion Haifa 32000 Israel

ISBN: (纸本)9781622764655

Non-invasive manipulation of cells in vivo by ultrasound for therapeutic purposes (e.g. opening the blood brain barrier for the introduction of drugs) is a field that has a great potential but is not fully understood. We have provided last year a comprehensive explanation for the generation of sub-cellular-level forces by an ultrasonic pressure wave. Using a physical model that incorporates molecular forces with bubble dynamics and gas diffusion, we predicted that ultrasound induces a pulsating bubble in the intra-membrane space between the two lipid leaflets;by periodically pulling the leaflets away from each other, while pockets of dissolved gas accumulate in the hydrophobic zone located between them. This model is extended here to the induction of action potential in a neuron cell- one of many potential applications of cell modulation;and to a simplified model for an artificial membrane that encloses a spherical liposome - where intra-membrane cavitation is similar to a gas filled microbubble. Basically, any abrupt pressure change affect cells, and this is demonstrated by a model for traumatic brain damage that is induced by a high energy explosion or by a violent mechanical impact such as in car accident. The main reason that such membrane response to ultrasound irradiation was not previously observed is that it involves both very tiny displacements of a few nanometers and very rapid movements of less than hundred microseconds. At this stage "intra-membrane cavitation" is not yet a common knowledge and investigations of membrane behavior under ultrasound are needed as well as direct experimental validation of the theory. Current optical methods (e.g., Fluorescence Resonance Energy Transfer - FRET) that are sensitive to nanometric displacements will be discussed, and compared with acoustic and dynamic methods.

关键词： Cavitation

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Approximating algebraic space curves by circular arcs 1

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7th International Conference on Curves and Surfaces, Curves and Surfaces 2010

作者： Béla, Szilvia Jüttler, Bert Doctoral Program in Computational Mathematics Johannes Kepler University 4040 Linz Austria Institute of Applied Geometry Johannes Kepler University Altenberger Str. 69 4040 Linz Austria

ISBN: (数字)9783642274138

ISBN: (纸本)9783642274121

We introduce a new method to approximate algebraic space curves. The algorithm combines a subdivision technique with local approximation of piecewise regular algebraic curve segments. The local technique computes pairs of polynomials with modified Taylor expansions and generates approximating circular arcs. We analyze the connection between the generated approximating arcs and the osculating circles of the algebraic curve. © 2012 Springer-Verlag.

关键词： Approximation algorithms

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Erratum to: Methods for evaluating medical tests and biomarkers

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Diagnostic and prognostic research 2017年第1期1卷 11页

作者： Gowri Gopalakrishna Miranda Langendam Rob Scholten Patrick Bossuyt Mariska Leeflang Anna Noel-Storr James Thomas Iain Marshall Byron Wallace Penny Whiting Clare Davenport Gowri GopalaKrishna Isabel de Salis Sue Mallett Robert Wolff Richard Riley Marie Westwood Jos Kleinen Gary Collins Hans Reitsma Karel Moons Antonia Zapf Annika Hoyer Katharina Kramer Oliver Kuss J Ensor J J Deeks E C Martin R D Riley Gerta Rücker Susanne Steinhauser Martin Schumacher Joie Ensor Kym Snell Brian Willis Thomas Debray Jon Deeks 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 Jan Verbakel Sabine Van Huffel 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 Doug Altman William Rosenberg Peter Selby Julien Asselineau Paul Perez Aïssatou Paye Emilie Bessede Cécile Proust-Lima Christiana Naaktgeboren Joris de Groot Anne Rutjes Johannes Reitsma Emmanuel Ogundimu Jonathan Cook Yannick Le Manach Yvonne Vergouwe Romin Pajouheshnia Rolf Groenwold Karen Moons Linda Peelen Daan Nieboer Bavo De Cock Micael J Pencina Ewout W Steyerberg 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 Andrew Mumford Zoe Plummer Kurtis Lee Barnaby Reeves Chris Rogers Veerle Verheyden Gianni D Angelini Gavin J Murphy Jeremy Huddy Melody Ni Katherine Good Graham Cooke 1Department of Clinical Epidemiology Biostatistics & Bioinformatics Academic Medical Center University of Amsterdam Amsterdam The Netherlands. 2Cochrane Netherlands Julius Center for Health Sciences and Primary Care University Medical Center Utrecht Utrecht Netherlands. 234Department of Clinical Epidemiology Biostatistics & Bioinformatics Academic Medical Center University of Amsterdam Amsterdam The Netherlands. 49Department of Clinical Epidemiology Biostatistics & Bioinformatics Academic Medical Center University of Amsterdam Amsterdam The Netherlands. 3Cochrane Dementia and Cognitive Improvement Group University of Oxford Oxford UK. 4EPPI-Centre Department of Social Science University College London London UK. 5Division of Health and Social Care Research King's College London London UK. 6College of Computer and Information Science Northeastern University Boston USA. 13University Hospitals Bristol NHS Foundation Trust School of Social and Community Medicine Bristol UK. 275Institute of Applied Health Research University of Birmingham Birmingham UK. 9Department of Clinical Epidemiology Biostatistics & Bioinformatics Academic Medical Center University of Amsterdam Amsterdam The Netherlands. 10School of Social and Community Medicine University of Bristol Bristol UK. 179Institute of Applied Health Research University of Birmingham Birmingham UK. 12Kleijnen Systematic Reviews Ltd York UK. 25Research Institute for Primary Care and Health Sciences Keele University Keele UK. 188Centre for Statistics in Medicine Nuffield Department of Orthopaedics Rheumatology and Musculoskeletal Sciences University of Oxford Oxford UK. 191Julius Center for Health Sciences and Primary Care University Medical Center Utrecht 3584 CG Utrecht Netherlands. 237Julius Center for Health Sciences and Primary Care University Medical Center Utrecht 3584 CG Utrecht Netherlands. 18Department of Medical Statistics University Medical Center Göttingen Göttingen Germany. 19Institute for B

[This corrects the article DOI: 10.1186/s41512-016-0001-y.].

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Heterogeneities of flow in stochastically generated porous media

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Physical Review E 2012年第5期86卷 056701-056701页

作者： Jeffrey D. Hyman Piotr K. Smolarkiewicz C. Larrabee Winter University of Arizona Program in Applied Mathematics Tucson Arizona 85721-0089 USA. jhyman@math.arizona.edu

Heterogeneous flows are observed to result from variations in the geometry and topology of pore structures within stochastically generated three dimensional porous media. A stochastic procedure generates media comprising complex networks of connected pores. Inside each pore space, the Navier-Stokes equations are numerically integrated until steady state velocity and pressure fields are attained. The intricate pore structures exert spatially variable resistance on the fluid, and resulting velocity fields have a wide range of magnitudes and directions. Spatially nonuniform fluid fluxes are observed, resulting in principal pathways of flow through the media. In some realizations, up to 25% of the flux occurs in 5% of the pore space depending on porosity. The degree of heterogeneity in the flow is quantified over a range of porosities by tracking particle trajectories and calculating their attributes including tortuosity, length, and first passage time. A representative elementary volume is first computed so the dependence of particle based attributes on the size of the domain through which they are followed is minimal. High correlations between the dimensionless quantities of porosity and tortuosity are calculated and a logarithmic relationship is proposed. As the porosity of a medium increases the flow field becomes more uniform.

关键词： Porosity

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Effect of film thickness variation on (100)-surface texturing of MPS processed polycrystalline Si films

Effect of film thickness variation on (100)-surface texturin...

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2012 MRS Spring Meeting

作者： Chahal, Monica Van Der Wilt, P.C. Van Gestel, D. Limanov, A.B. Chitu, A.M. Im, James S. Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University New York NY United States IMEC Solar Cell Tech. Group Leuven Belgium Korea Republic of Coherent GmbH Göttingen Germany

ISBN: (纸本)9781605114033

We have investigated the effect of varying the film thickness on the surface orientation texturing in polycrystalline Si films obtained via mixed-phase solidification (MPS) of initially a-Si precursor films on SiO 2. It is found that, for a given number of MPS exposure cycles, the degree of (100)-surface texturing is reduced as the film thickness is increased. We discuss how this trend can be accounted for by the previously proposed thermodynamic model of MPS, wherein a decreasing local solid/liquid interface curvature with increasing film thickness is identified as the primary cause for decreasing the influence which anisotropic solid-Si/SiO2 interfacial energies have on the survivability of the grains. This, in turn, leads to other factors becoming more significant in determining the grains that survive the MPS cycle, thereby reducing the degree of (100)-surface texturing in the resulting films. © 2012 Materials Research Society.

关键词： Film thickness

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Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization

Computation of sparse low degree interpolating polynomials a...

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作者： Bandeira, A.S. Scheinberg, K. Vicente, L.N. Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Industrial and Systems Engineering Lehigh University Harold S. Mohler Laboratory 200 West Packer Avenue Bethlehem PA 18015-1582 United States CMUC Department of Mathematics University of Coimbra 3001-501 Coimbra Portugal

Interpolation-based trust-region methods are an important class of algorithms forDerivative-Free Optimizationwhich rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations between variables are negligible, implying, in the smooth case, a sparse structure in the Hessian matrix. To be able to exploit Hessian sparsity, existing optimization approaches require the knowledge of the sparsity structure. The goal of this paper is to develop and analyze a method where the sparse models are constructed automatically. The sparse recovery theory developed recently in the field of compressed sensing characterizes conditions under which a sparse vector can be accurately recovered from few random measurements. Such a recovery is achieved by minimizing the l1-norm of a vector subject to the measurements constraints. We suggest an approach for building sparse quadratic polynomial interpolationmodels byminimizing the l1-norm of the entries of themodel Hessian subject to the interpolation conditions. We show that this procedure recovers accurate models when the function Hessian is sparse, using relatively few randomly selected sample points. Motivated by this result, we developed a practical interpolation-based trust-region method using deterministic sample sets and minimum l1-norm quadratic models. Our computational results show that the new approach exhibits a promising numerical performance both in the general case and in the sparse one. © Springer and Mathematical Optimization Society 2012.

关键词： Interpolation

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Minimum-Time Trajectory Planning for Helicopter UAVs using Computational Dynamic Optimization

Minimum-Time Trajectory Planning for Helicopter UAVs using C...

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IEEE International Conference on Systems, Man, and Cybernetics

作者： Nathan Xu Wei Kang Guowei Cai Ben M. Chen Summer Intern Program Department of Applied Mathematics Naval Postgraduate School Department of Applied Mathematics Naval Postgraduate School Department of Electrical and Computer Engineering National University of Singapore

ISBN: (纸本)9781467317139

In this paper, we apply pseudospectral optimal control, a computational algorithm of dynamic optimization, to the problem of helicopter UAV for minimum-time trajectory planning in the presence of obstacles. The problem is formulated as a nonlinear optimal control subject to the dynamics and limitations of helicopter UAVs, in which the obstacles are formulated as inequality constraints by using p-norms. The dynamical system is defined by a set of fifteen states nonlinear differential equations developed for HeLion, a helicopter UAV constructed in National University of Singapore (NUS). The problem does not have an analytic solution. We numerically solve the problem using a pseudospectral method. Various terrain scenarios were tested, from a single obstacle to multiple obstacles. We found bifurcation points of minimum-time trajectories near obstacles. The bifurcation points and their relationship with the distance to the obstacle are analyzed.

关键词： Minimum-time control Helicopter UAV Computational optimal control Obstacle avoidance Unmanned Aerial Vehicle Helicopters trajectory planning barriers BIFURCATION nonlinear differential equations inequality constraint drone honey bees

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A Multi-Start Procedure for the Minimum Latency Problem

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IFAC Proceedings Volumes 2013年第9期46卷 436-441页

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

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.

关键词： Operational research Supply chains networks

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Using a level set to model multiple myeloma induced bone loss

Using a level set to model multiple myeloma induced bone los...

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6th European Congress on Computational Methods in applied Sciences and Engineering, ECCOMAS 2012

作者： Ayati, Bruce P. Graham, Jason M. Holstein, Sarah A. Department of Mathematics and Program in Applied Mathematical and Computational Sciences University of Iowa Iowa City IA 52242-1419 United States Department of Internal Medicine University of Iowa Iowa City IA 52242-1081 United States

ISBN: (纸本)9783950353709

Multiple myeloma is a hematological malignancy characterized by proliferation of malignant plasma cells and derangement of bone homeostasis. Myeloma bone disease results in significant morbidity as a result of bone pain, hypercalcemia, diffuse osteopenia, and pathologic fractures. We present a spatially explicit mathematical model of multiple myeloma and bone remodeling, synthesizing the existing model of local "microenvironment" interactions in Ayati et al. 2010 [1] with a level set approach for representing the sharp interface been bone and marrow introduced in [6]. Computational results show the feasibility of using a level set to capture the spatial structure in the context of a geometrically straightforward interface, but one that nonetheless captures the essence of the rich geometries seen in bone marrow biopsy slides. In particular, we are able to model the formation of an osteolytic lesion in the case of multiple myeloma dysregulated bone remodeling, but not, using the same remodeling parameter set, in the case of normal bone remodeling.

关键词： Bone

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