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Volume growth, curvature, and buser-type inequalities in graphs

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arXiv 2018年

作者： Benson, Brian Ralli, Peter Tetali, Prasad Department of Mathematics University of California RiversideCA United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States School of Mathematics Georgia Institute of Technology AtlantaGA United States

We study the volume growth of metric balls as a function of the radius in discrete spaces, and focus on the relationship between volume growth and discrete curvature. We improve volume growth bounds under a lower bound on the so-called Ollivier curvature, and discuss similar results under other types of discrete Ricci curvature. Following recent work in the continuous setting of Riemannian manifolds (by the first author), we then bound the eigenvalues of the Laplacian of a graph under bounds on the volume growth. In particular, λ2of the graph can be bounded using a weighted discrete Hardy inequality and the higher eigenvalues of the graph can be bounded by the eigenvalues of a tridiagonal matrix times a multiplicative factor, both of which only depend on the volume growth of the graph. As a direct application, we relate the eigenvalues to the Cheeger isoperimetric constant. Using these methods, we describe classes of graphs for which the Cheeger inequality is tight on the second eigenvalue. We also describe a method for proving Buser's Inequality in graphs, particularly under a lower bound assumption on curvature. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Regularized matrix data clustering and its application to image analysis

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arXiv 2018年

作者： Gao, Xu Shen, Weining Ombao, Hernando Department of Statistics University of California IrvineCA United States Program on Applied Mathematics & Computational Science King Abdullah University of Science and Technology Saudi Arabia

In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing regularization terms into the likelihood function. Through a modified EM algorithm, our method achieves the optimal solution with low computational cost. Theoretical results are also provided to establish the consistency of the proposed estimators. Simulations show the advantages of the proposed method over other existing methods. We also apply the approach to two real datasets from different experiments. Promising results imply that the proposed method successfully characterizes signals with different patterns while yielding insightful scientific interpretation. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra

Estimation in the group action channel

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arXiv 2018年

作者： Abbe, Emmanuel Pereira, João M. Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Electrical Engineering Department Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States

MSC Codes 94A15, 62B10We analyze the problem of estimating a signal from multiple measurements on a group action channel that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel is motivated by applications such as multi-reference alignment and cryoelectron microscopy. We focus on the large noise regime prevalent in these applications. We give a lower bound on the mean square error (MSE) of any asymptotically unbiased estimator of the signal's orbit in terms of the signal's moment tensors, which implies that the MSE is bounded away from 0 when N=σ2dis bounded from above, where N is the number of observations, σ is the noise standard deviation, and d is the so-called moment order cutoff. In contrast, the maximum likelihood estimator is shown to be consistent if N=σ2ddiverges. Copyright © 2018, The Authors. All rights reserved.

关键词： Mean square error

The repertoire of mutational signatures in human cancer (vol 578, pg 94, 2020)

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NATURE 2023年第7948期614卷 E41-E41页

作者： Alexandrov, Ludmil B. Kim, Jaegil Haradhvala, Nicholas J. Huang, Mi Ni Ng, Alvin Wei Tian Wu, Yang Boot, Arnoud Covington, Kyle R. Gordenin, Dmitry A. Bergstrom, Erik N. Islam, S. M. Ashiqul Lopez-Bigas, Nuria Klimczak, Leszek J. McPherson, John R. Morganella, Sandro Sabarinathan, Radhakrishnan Wheeler, David A. Mustonen, Ville Getz, Gad Rozen, Steven G. Stratton, Michael R. Department of Cellular and Molecular Medicine Department of Bioengineering Moores Cancer Center University of California San Diego CA USA Wellcome Sanger Institute Wellcome Genome Campus Hinxton UK Department of Cellular and Molecular Medicine and Department of Bioengineering University of California San Diego La Jolla CA USA UC San Diego Moores Cancer Center San Diego CA USA University of California San Diego San Diego CA USA Broad Institute of MIT and Harvard Cambridge MA USA Center for Cancer Research Massachusetts General Hospital Boston MA USA Massachusetts General Hospital Boston MA USA Department of Pathology Massachusetts General Hospital Boston MA USA Harvard Medical School Boston MA USA Laboratory for Medical Science Mathematics RIKEN Center for Integrative Medical Sciences Yokohama Japan Computational Biology Program Ontario Institute for Cancer Research Toronto ON Canada Programme in Cancer & Stem Cell Biology Duke-NUS Medical School Singapore Singapore Centre for Computational Biology Duke-NUS Medical School Singapore Singapore Programme in Cancer and Stem Cell Biology Duke-NUS Medical School Singapore Singapore Programme in Cancer and Stem Cell Biology Centre for Computational Biology Duke-NUS Medical School Singapore Singapore SingHealth Duke-NUS Institute of Precision Medicine National Heart Centre Singapore Singapore Singapore Cancer Science Institute of Singapore National University of Singapore Singapore Singapore Institute of Molecular and Cell Biology Singapore Singapore Laboratory of Cancer Epigenome Division of Medical Science National Cancer Centre Singapore Singapore Singapore Duke-NUS Medical School Singapore Singapore Human Genome Sequencing Center Baylor College of Medicine Houston TX USA Dan L. Duncan Cancer Center Baylor College of Medicine Houston TX USA Department of Molecular and Human Genetics Baylor College of Medicine Houston TX USA Genome Integrity and Structural Biology Laboratory National Ins

Multifunctional hyperuniform cellular networks: Optimality, anisotropy and disorder

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Multifunctional Materials 2018年第1期1卷

作者： Torquato, S. Chen, D. Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

Disordered hyperuniform heterogeneousmaterials are new, exotic amorphous states of matter that behave like crystals in themanner in which they suppress volume-fraction fluctuations at large length scales, and yet are statistically isotropic with no Bragg peaks. It has recently been shown that disordered hyperuniform dielectric two-dimensional (2D) cellular network solids possess complete photonic band gaps comparable in size to photonic crystals,while at the same timemaintaining statistical isotropy, enabling waveguide geometries not possible with photonic crystals. Motivated by these developments, we explore other functionalities of various 2D ordered and disordered hyperuniform cellular networks, including their effective thermal or electrical conductivities and *** the multifunctionality of a class of such low-density networks by demonstrating that theymaximize or virtually maximize the effective conductivities and elastic moduli. This is accomplished using themachinery of homogenization theory, including optimal bounds and cross-property bounds, and statistical *** rigorously prove that anisotropic networks consisting of sets of intersecting parallel channels in the low-density limit, ordered or disordered, possess optimal effective conductivity tensors. For a variety of different disordered networks,we showthatwhen short-range and long-range order increases, there is an increase in both the effective conductivity and elasticmoduli of the network. Moreover,we demonstrate that the effective conductivity and elasticmoduli of various disordered networks derived from disordered 'stealthy' hyperuniform point patterns possess virtually optimal *** note that the optimal networks for conductivity are also optimal for the fluid permeability associatedwith slow viscous flow through the channels as well as themean survival time associated with diffusioncontrolled reactions in the channels. In summary,we have identified ordered and disor

关键词： Transport properties

Genomic basis for RNA alterations in cancer (vol 578, pg 129, 2020)

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NATURE 2023年第7948期614卷 E37-E37页

作者： Calabrese, Claudia Davidson, Natalie R. Demircioglu, Deniz Fonseca, Nuno A. He, Yao Lehmann, Kjong-Van Liu, Fenglin Shiraishi, Yuichi Soulette, Cameron M. Urban, Lara Greger, Liliana Li, Siliang Liu, Dongbing Perry, Marc D. Xiang, Qian Zhang, Fan Zhang, Junjun Bailey, Peter Erkek, Serap Hoadley, Katherine A. Hou, Yong Huska, Matthew R. Kilpinen, Helena Korbel, Jan O. Marin, Maximillian G. Markowski, Julia Nandi, Tannistha Pan-Hammarstrom, Qiang Pedamallu, Chandra Sekhar Siebert, Reiner Stark, Stefan G. Su, Hong Tan, Patrick Waszak, Sebastian M. Yung, Christina Zhu, Shida Awadalla, Philip Creighton, Chad J. Meyerson, Matthew Ouellette, B. F. Francis Wu, Kui Yang, Huanming Brazma, Alvis Brooks, Angela N. Goke, Jonathan Ratsch, Gunnar Schwarz, Roland F. Stegle, Oliver Zhang, Zemin European Molecular Biology Laboratory European Bioinformatics Institute Hinxton UK European Molecular Biology Laboratory European Bioinformatics Institute (EMBL-EBI) Cambridge UK Genome Biology Unit European Molecular Biology Laboratory (EMBL) Heidelberg Germany CIBIO/InBIO - Research Center in Biodiversity and Genetic Resources Universidade do Porto Vairão Portugal Berlin Institute for Medical Systems Biology Max Delbruck Center for Molecular Medicine Berlin Germany German Cancer Consortium (DKTK) partner site Berlin Germany German Cancer Research Center (DKFZ) Heidelberg Germany Berlin Institute for Medical Systems Biology Max Delbrück Center for Molecular Medicine Berlin Germany German Cancer Consortium (DKTK) Partner site Berlin Berlin Germany European Molecular Biology Laboratory Genome Biology Unit Heidelberg Germany Division of Computational Genomics and Systems Genetics German Cancer Research Center (DKFZ) Heidelberg Germany ETH Zurich Zurich Switzerland Memorial Sloan Kettering Cancer Center New York NY USA Weill Cornell Medical College New York NY USA SIB Swiss Institute of Bioinformatics Lausanne Switzerland University Hospital Zurich Zurich Switzerland Computational Biology Center Memorial Sloan Kettering Cancer Center New York NY USA Department of Biology ETH Zurich Zürich Switzerland Department of Computer Science ETH Zurich Zurich Switzerland Korea University Seoul South Korea Computational and Systems Biology Program Memorial Sloan Kettering Cancer Center New York NY USA Department of Physiology and Biophysics Weill Cornell Medicine New York NY USA Institute for Computational Biomedicine Weill Cornell Medicine New York NY USA Controlled Department and Institution New York NY USA Englander Institute for Precision Medicine Weill Cornell Medicine New York NY USA National University of Singapore Singapore Singapore Genome Institute of Singapore Singapore Singapore Computational and Systems Biology Genome Institute of Singap

Communication-computation efficient gradient coding

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arXiv 2018年

作者： Ye, Min Abbe, Emmanuel Department of Electrical Engineering Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University School of Mathematics Institute for Advanced Study PrincetonNJ08544 United States

This paper develops coding techniques to reduce the running time of distributed learning tasks. It characterizes the fundamental tradeoff to compute gradients (and more generally vector summations) in terms of three parameters: computation load, straggler tolerance and communication cost. It further gives an explicit coding scheme that achieves the optimal tradeoff based on recursive polynomial constructions, coding both across data subsets and vector components. As a result, the proposed scheme allows to minimize the running time for gradient computations. Implementations are made on Amazon EC2 clusters using Python with mpi4py package. Results show that the proposed scheme maintains the same generalization error while reducing the running time by 32% compared to uncoded schemes and 23% compared to prior coded schemes focusing only on stragglers (Tandon et al., ICML 2017). Copyright © 2018, The Authors. All rights reserved.

关键词： Python

GWAS meta-analysis of over 29,000 people with epilepsy identifies 26 risk loci and subtype-specific genetic architecture

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Nature genetics 2023年第9期55卷 1471-1482页

作者： Remi Stevelink Dorothee Kasteleijn-Nolst Trenite Bobby P. C. Koeleman Dick Lindhout Anja C. M. Sonsma Ciarán Campbell Gianpiero L. Cavalleri Norman Delanty Hany El-Naggar Austin Lacey Peter Widdess-Walsh Colin P. Doherty Siwei Chen Claire Churchhouse Mark J. Daly Yen-Chen A. Feng Daniel P. Howrigan Mitja I. Kurki Benjamin M. Neale Aarno Palotie Wei Zhou Namrata Gupta Henrike O. Heyne Bassel Abou-Khalil Kevin F. Haas R. S. Taneja Oluyomi M. Adesoji Michael Nothnagel Peter Nürnberg Thomas Sander Zaid Afawi Ilan Blatt Amos D. Korczyn Elisabetta Amadori Ganna Balagura Antonella Riva Marcello Scala Paolo Scudieri Pasquale Striano Federico Zara Michele Iacomino Francesca Madia Alison Anderson Patrick Kwan Terence J. O’Brien Slavé Petrovski K. Meng Tan Marian Todaro Joseph Anderson Danielle M. Andrade Quratulain Zulfiqar Ali Grazia Annesi Pauls Auce Andreja Avbersek Simona Balestrini Vera Braatz Claudia B. Catarino Krishna Chinthapalli Jennifer Jamnadas-Khoda Dalia Kasperavičiūte Costin Leu Josemir W. Sander Sanjay M. Sisodiya Sara Zagaglia Melanie Bahlo Karen L. Oliver Mark D. Baker Beata Fonferko-Shadrach William O. Pickrell Carmen Barba Claudia Bianchini Viola Doccini Renzo Guerrini Davide Mei Martino Montomoli Elena Parrini Annalisa Vetro Karen Barboza Fabrice Bartolomei Thomas Bast Bernhard J. Steinhoff Larry Baum Stacey S. Cherny Pak Sham Tobias Baumgartner Christian E. Elger Kerstin Hallmann Wolfram S. Kunz Rainer Surges Randi von Wrede Gábor Zsurka Betül Baykan Nerses Bebek Yeşim Kesim Albert J. Becker Susanne Schoch Felicitas Becker Caitlin A. Bennett Samuel F. Berkovic Stephanie L. Leech Brigid M. Regan Ingrid E. Scheffer Bianca Berghuis Ahmad Beydoun Wassim Nasreddine Francesca Bisulli Lidia Di Vito Lorenzo Ferri Tania Giangregorio Laura Licchetta Raffaella Minardi Barbara Mostacci Carlotta Stipa Paolo Tinuper Lorenzo Muccioli Federica Pondrelli Dheeraj R. Bobbili Emadeldin Hassanin Roland Krause Zied Landoulsi Patrick May Ingo Borggraefe Christian Bosselmann Christian Hengsbach Josua Kegele Stephen Lauxmann Department of Genetics University Medical Center Utrecht Utrecht The Netherlands Stichting Epilepsie Instellingen Nederland (SEIN) Heemstede The Netherlands School of Pharmacy and Biomolecular Sciences The Royal College of Surgeons in Ireland Dublin Ireland The FutureNeuro Research Centre Dublin Ireland Department of Neurology Beaumont Hospital Dublin Ireland Department of Neurology St. James’s Hospital Dublin Ireland Analytic and Translational Genetics Unit Department of Medicine Massachusetts General Hospital and Harvard Medical School Boston MA USA Program in Medical and Population Genetics Broad Institute of MIT and Harvard Cambridge MA USA Stanley Center for Psychiatric Research Broad Institute of Harvard and M.I.T Cambridge MA USA Institute for Molecular Medicine Finland (FIMM) University of Helsinki Helsinki Finland Psychiatric & Neurodevelopmental Genetics Unit Department of Psychiatry Massachusetts General Hospital and Harvard Medical School Boston MA USA Division of Biostatistics Institute of Epidemiology and Preventive Medicine College of Public Health National Taiwan University Taipei Taiwan Hasso Plattner Institute Digital Health Center University of Potsdam Potsdam Germany Hasso Plattner Institute Mount Sinai School of Medicine New York City NY USA Department of Neurology Vanderbilt University Medical Center Nashville TN USA Cologne Center for Genomics (CCG) University of Cologne Faculty of Medicine and University Hospital Cologne Cologne Germany University Hospital Cologne Cologne Germany Department of Neurology Charité Universitaetsmedizin Berlin Campus Virchow-Clinic Berlin Germany Tel-Aviv University Sackler Faculty of Medicine Ramat Aviv Israel Department of Neurology Sheba Medical Center Ramat Gan Israel Department of Neurosciences Rehabilitation Ophthalmology Genetics Maternal and Child Health University of Genova Genova Italy IRCCS Istituto Giannina Gaslini Genova Italy Department of Medicine University of Melbour

Epilepsy is a highly heritable disorder affecting over 50 million people worldwide, of which about one-third are resistant to current treatments. Here we report a multi-ancestry genome-wide association study including 29,944 cases, stratified into three broad categories and seven subtypes of epilepsy, and 52,538 controls. We identify 26 genome-wide significant loci, 19 of which are specific to genetic generalized epilepsy (GGE). We implicate 29 likely causal genes underlying these 26 loci. SNP-based heritability analyses show that common variants explain between 39.6% and 90% of genetic risk for GGE and its subtypes. Subtype analysis revealed markedly different genetic architectures between focal and generalized epilepsies. Gene-set analyses of GGE signals implicate synaptic processes in both excitatory and inhibitory neurons in the brain. Prioritized candidate genes overlap with monogenic epilepsy genes and with targets of current antiseizure medications. Finally, we leverage our results to identify alternate drugs with predicted efficacy if repurposed for epilepsy treatment.

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Author Correction: Comprehensive molecular characterization of mitochondrial genomes in human cancers

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Nature genetics 2023年第6期55卷 1078页

作者： Yuan Yuan Young Seok Ju Youngwook Kim Jun Li Yumeng Wang Christopher J Yoon Yang Yang Inigo Martincorena Chad J Creighton John N Weinstein Yanxun Xu Leng Han Hyung-Lae Kim Hidewaki Nakagawa Keunchil Park Peter J Campbell Han Liang Department of Bioinformatics and Computational Biology The University of Texas MD Anderson Cancer Center Houston TX USA. Cancer Genome Project Wellcome Trust Sanger Institute Hinxton UK. Graduate School of Medical Science and Engineering Korea Advanced Institute of Science and Technology Daejeon Korea. Department of Health Science and Technology Samsung Advanced Institute for Health Science and Technology Sungkyunkwan University School of Medicine Seoul Korea. Samsung Genome Institute Samsung Medical Center Seoul Korea. Quantitative and Computational Biosciences Graduate Program Baylor College of Medicine Houston TX USA. Division of Biostatistics The University of Texas Health Science Center at Houston School of Public Health Houston TX USA. Department of Medicine and Dan L. Duncan Cancer Center Division of Biostatistics Baylor College of Medicine Houston TX USA. Department of Systems Biology The University of Texas MD Anderson Cancer Center Houston TX USA. Department of Applied Mathematics and Statistics Johns Hopkins University Baltimore MD USA. Department of Biochemistry and Molecular Biology The University of Texas Health Science Center at Houston McGovern Medical School Houston TX USA. Department of Biochemistry Ewha Womans University School of Medicine Seoul Korea. Laboratory for Cancer Genomics RIKEN Center for Integrative Medical Sciences Yokohama Japan. Division of Hematology/Oncology Samsung Medical Center Sungkyunkwan University School of Medicine Seoul Korea. kpark@skku.edu. Samsung Advanced Institute for Health Sciences and Technology Sungkyunkwan University School of Medicine Seoul South Korea. kpark@skku.edu. Cancer Genome Project Wellcome Trust Sanger Institute Hinxton UK. pc8@sanger.ac.uk. Department of Haematology University of Cambridge Cambridge UK. pc8@sanger.ac.uk. Department of Bioinformatics and Computational Biology The University of Texas MD Anderson Cancer Center Houston TX USA. hliang1@mdanderson.org. Quantitative and Comp