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The evolutionary history of 2,658 cancers (vol 578, pg 122, 2020)

NATURE 2023年第7948期614卷 E42-E42页

作者： Gerstung, Moritz Jolly, Clemency Leshchiner, Ignaty Dentro, Stefan C. Gonzalez, Santiago Rosebrock, Daniel Mitchell, Thomas J. Rubanova, Yulia Anur, Pavana Yu, Kaixian Tarabichi, Maxime Deshwar, Amit Wintersinger, Jeff Kleinheinz, Kortine Vazquez-Garcia, Ignacio Haase, Kerstin Jerman, Lara Sengupta, Subhajit Macintyre, Geoff Malikic, Salem Donmez, Nilgun Livitz, Dimitri G. Cmero, Marek Demeulemeester, Jonas Schumacher, Steven Fan, Yu Yao, Xiaotong Lee, Juhee Schlesner, Matthias Boutros, Paul C. Bowtell, David D. Zhu, Hongtu Getz, Gad Imielinski, Marcin Beroukhim, Rameen Sahinalp, S. Cenk Ji, Yuan Peifer, Martin Markowetz, Florian Mustonen, Ville Yuan, Ke Wang, Wenyi Morris, Quaid D. Spellman, Paul T. Wedge, David C. Van Loo, Peter European Molecular Biology Laboratory European Bioinformatics Institute (EMBL-EBI) Cambridge UK European Molecular Biology Laboratory Genome Biology Unit Heidelberg Germany Wellcome Sanger Institute Cambridge UK Genome Biology Unit European Molecular Biology Laboratory (EMBL) Heidelberg Germany University of Ljubljana Ljubljana Slovenia The Francis Crick Institute London UK Big Data Institute University of Oxford Oxford UK Wellcome Sanger Institute Wellcome Genome Campus Hinxton UK Big Data Institute Li Ka Shing Centre University of Oxford Oxford UK University of Cambridge Cambridge UK Cambridge University Hospitals NHS Foundation Trust Cambridge UK Department of Applied Mathematics and Theoretical Physics Centre for Mathematical Sciences University of Cambridge Cambridge UK Department of Epidemiology and Biostatistics Memorial Sloan Kettering Cancer Center New York NY USA Department of Statistics Columbia University New York NY USA Department of Haematology University of Cambridge Cambridge UK University of Leuven Leuven Belgium Broad Institute of MIT and Harvard Cambridge MA USA Center for Cancer Research Massachusetts General Hospital Charlestown MA USA Department of Pathology Massachusetts General Hospital Boston MA USA Harvard Medical School Boston MA USA Center for Cancer Research Massachusetts General Hospital Boston MA USA Dana-Farber Cancer Institute Boston MA USA Department of Medical Oncology Dana-Farber Cancer Institute Boston MA USA Department of Cancer Biology Dana-Farber Cancer Institute Boston MA USA Oxford NIHR Biomedical Research Centre Oxford UK Oxford NIHR Biomedical Research Centre University of Oxford Oxford UK University of Toronto Toronto Ontario Canada Vector Institute Toronto Ontario Canada Vector Institute Toronto ON Canada Department of Computer Science University of Toronto Toronto ON Canada Ontario Institute for Cancer Research Toronto Ontario Canada University of California Los Angeles

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A fourth-order accurate finite volume method for ideal mhd via upwind constrained transport

arXiv

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arXiv 2017年

作者： Felker, Kyle Gerard Stone, James Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States

We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth-order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme. Copyright © 2017, The Authors. All rights reserved.

关键词： Numerical methods

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Pre-processing and classification of hyperspectral imagery via selective inpainting

Pre-processing and classification of hyperspectral imagery v...

引用

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Victoria Chayes Kevin Miller Rasika Bhalerao Jiajie Luo Wei Zhu Andrea L. Bertozzi Wenzhi Liao Stanley Osher California Research Training Program in Computational and Applied Mathematics United States of America University of California Los Angeles Department of Mathematics United States of America Ghent University Department of Telecommunications and Information Processing Belgium

ISBN: (纸本)9781509041183

We propose a semi-supervised algorithm for processing and classification of hyperspectral imagery. For initialization, we keep 20% of the data intact, and use Principal Component Analysis to discard voxels from noisier bands and pixels. Then, we use either an Accelerated Proximal Gradient algorithm (APGL), or a modified APGL algorithm with a penalty term for distance between inpainted pixels and endmembers (APGL Hyp), on the initialized datacube to inpaint the missing data. APGL and APGL Hyp are distinguished by performance on datasets with full pixels removed or extreme noise. This inpainting technique results in band-by-band datacube sharpening and removal of noise from individual spectral signatures. We can also classify the inpainted cube by assigning each pixel to its nearest endmember via Euclidean distance. We demonstrate improved accuracy in classification over data-mining techniques like k-means, unmixing techniques like Hierarchical Non-Negative Matrix Factorization, and graph-based methods like Non-Local Total Variation.

关键词： Hyperspectral imagery (HSI) data preprocessing image inpainting image classification image enhancement Data preprocessing hyperspectral imagery Image classification image enhancement pixel Pretreatment matrix decomposition initialization Euclidean distance

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Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator

arXiv

引用

arXiv 2017年

作者： Li, Qianxiao Dietrich, Felix Bollt, Erik M. Kevrekidis, Ioannis G. Institute of High Performance Computing Singapore Singapore Faculty of Mathematics Technical University of Munich Germany Department of Mathematics Clarkson University United States Department of Chemical and Biological Engineering Program in Applied and Computational Mathematics Princeton University United States

Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD) and its generalization, the extended-DMD (EDMD), are becoming increasingly popular in practical applications. The EDMD improves upon the classical DMD by the inclusion of a flexible choice of dictionary of observables that spans a finite dimensional subspace on which the Koopman operator can be approximated. This enhances the accuracy of the solution reconstruction and broadens the applicability of the Koopman formalism. Although the convergence of the EDMD has been established, applying the method in practice requires a careful choice of the observables to improve convergence with just a finite number of terms. This is especially difficult for high dimensional and highly nonlinear systems. In this paper, we employ ideas from machine learning to improve upon the EDMD method. We develop an iterative approximation algorithm which couples the EDMD with a trainable dictionary represented by an artificial neural network. Using the Duffing oscillator and the Kuramoto Sivashinsky PDE as examples, we show that our algorithm can effectively and efficiently adapt the trainable dictionary to the problem at hand to achieve good reconstruction accuracy without the need to choose a fixed dictionary a priori. Furthermore, to obtain a given accuracy we require fewer dictionary terms than EDMD with fixed dictionaries. This alleviates an important shortcoming of the EDMD algorithm and enhances the applicability of the Koopman framework to practical problems. Copyright © 2017, The Authors. All rights reserved.

关键词： Machine learning

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Inversion problems for fourier transforms of particle distributions

arXiv

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arXiv 2018年

作者： Kim, Jaeuk Zhang, Ge Stillinger, Frank H. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Department of Physics and Astronomy University of Pennsylvania PhiladelphiaPA19104-6396 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Collective coordinates in a many-particle system are complex Fourier components of the particle density n(x) ≡ PNj=1 δ(x − rj), and often provide useful physical insights. However, given collective coordinates, it is desirable to infer the particle coordinates via inverse transformations. In principle, a sufficiently large set of collective coordinates are equivalent to particle coordinates, but the nonlinear relation between collective and particle coordinates makes the inversion procedure highly nontrivial. Given a "target" configuration in one-dimensional Euclidean space, we investigate the minimal set of its collective coordinates that can be uniquely inverted into particle coordinates. For this purpose, we treat a finite number M of the real and/or the imaginary parts of collective coordinates of the target configuration as constraints, and then reconstruct "solution" configurations whose collective coordinates satisfy these constraints. Both theoretical and numerical investigations reveal that the number of numerically distinct solutions depends sensitively on the chosen collective-coordinate constraints and target configurations. From detailed analysis, we conclude that collective coordinates at the dN2 e smallest wavevectors is the minimal set of constraints for unique inversion, where d·e represents the ceiling function. This result provides useful groundwork to the inverse transform of collective coordinates in higher-dimensional systems. Copyright © 2018, The Authors. All rights reserved.

关键词： Inverse transforms

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Sharp rates of convergence for accumulated spectrograms

arXiv

引用

arXiv 2017年

作者： Abreu, Luis Daniel Pereira, Joao Romero, Jose Luis Acoustics Research Institute Austrian Academy of Science Wohllebengasse 12-14 ViennaA-1040 Austria Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the spectrograms corresponding to large eigenvalues). We derive a sharp bound for the rate of convergence of the accumulated spectrogram, improving on recent *** Codes 65F18, 94A12, 65N21, 42C25 Copyright © 2017, The Authors. All rights reserved.

关键词： Spectrographs

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Multireference alignment is easier with an aperiodic translation distribution

arXiv

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arXiv 2017年

作者： Abbe, Emmanuel Bendory, Tamir Leeb, William Pereira, João M. Sharon, Nir 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

In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's orbit by accessing multiple independent observations. Of particular interest is the sample complexity, i.e., the number of observations/samples needed in terms of the signal-to-noise ratio (the signal energy divided by the noise variance) in order to drive the mean-square error (MSE) to zero. Previous work showed that if the translations are drawn from the uniform distribution, then, in the low SNR regime, the sample complexity of the problem scales as ω(1/SNR3). In this work, using a generalization of the Chapman-Robbins bound for orbits and expansions of the X2divergence at low SNR, we show that in the same regime the sample complexity for any aperiodic translation distribution scales as ω(1/SNR2). This rate is achieved by a simple spectral algorithm. We propose two additional algorithms based on non-convex optimization and expectation-maximization. We also draw a connection between the multireference alignment problem and the spiked covariance model. Copyright © 2017, The Authors. All rights reserved.

关键词： Maximum principle

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Group synchronization on grids

arXiv

引用

arXiv 2017年

作者： Abbe, Emmanuel Massoulie, Laurent Montanari, Andrea Sly, Allan Srivastava, Nikhil Program in Applied and Computational Mathematics EE Department Princeton University Inria MSR-Inria Joint Centre Department of Electrical Engineering Department of Sttistics Stanford University Department of Mathematics Princeton University Department of Mathematics University of California Berkeley United States

Group synchronization requires to estimate unknown elements (θv)v∈V of a compact group G associated to the vertices of a graph G = (V, E), using noisy observations of the group differences associated to the edges. This model is relevant to a variety of applications ranging from structure from motion in computer vision to graph localization and positioning, to certain families of community detection problems. We focus on the case in which the graph G is the d-dimensional grid. Since the unknowns θv are only determined up to a global action of the group, we consider the following weak recovery question. Can we determine the group difference θ−u1θv between far apart vertices u, v better than by random guessing? We prove that weak recovery is possible (provided the noise is small enough) for d ≥ 3 and, for certain finite groups, for d ≥ 2. Viceversa, for some continuous groups, we prove that weak recovery is impossible for d = 2. Finally, for strong enough noise, weak recovery is always impossible. Copyright © 2017, The Authors. All rights reserved.

关键词： Recovery

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On singularity formation in a Hele-Shaw model

arXiv

引用

arXiv 2017年

作者： Constantin, Peter Elgindi, Tarek Nguyen, Huy Vicol, Vlad Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Uc San Diego San DiegoCA92093 United States Program In Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We discuss a lubrication approximation model of the interface between two immiscible fluids in a Hele-Shaw cell, derived in [CDG+93] and widely studied since. The model consists of a single one dimensional evolution equation for the thickness 2h = 2h(x, t) of a thin neck of fluid, ∂th + ∂x(h ∂x3h) = 0, for x ∈ (−1, 1) and t ≥ 0. The boundary conditions fix the neck height and the pressure jump: h(±1, t) = 1, ∂x2h(±1, t) = P > 0. We prove that starting from smooth and positive h, as long as h(x, t) > 0, for x ∈ [−1, 1], t ∈ [0, T ], no singularity can arise in the solution up to time T. As a consequence, we prove for any P > 2 and any smooth and positive initial datum that the solution pinches off in either finite or infinite time, i.e., inf[−1,1]×[0,T∗) h = 0, for some T∗ ∈ (0, ∞]. These facts have been long anticipated on the basis of numerical and theoretical studies. August 30, 2017.35Q35, 35Q86 Copyright © 2017, The Authors. All rights reserved.

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Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings

arXiv

引用

arXiv 2018年

作者： Oguz, Erdal C. Socolar, Joshua E.S. Steinhardt, Paul J. Torquato, Salvatore School of Mechanical Engineering Sackler Center for Computational Molecular and Materials Science Tel Aviv University Tel Aviv Israel Physics Department Duke University DurhamNC27708 United States Department of Physics Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Center for Cosmology and Particle Physics Department of Physics New York University New YorkNY10003 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

We consider the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long wavelength fluctuations in a broad class of one-dimensional substitution tilings. We present a simple argument that predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and confirm with numerical computations that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra, and limit-periodic tilings. Tilings with quasiperiodic or singular continuous spectra can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law. Copyright © 2018, The Authors. All rights reserved.

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