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arXiv 2021年

作者： Knabenhans, Mischa Brinckmann, Thejs Stadel, Joachim Schneider, Aurel Teyssier, Romain Institute for Computational Science University of Zurich Winterthurerstrasse 190 Zurich8057 Switzerland Dipartimento di Fisica Scienze della Terra Universitá degli Studi di Ferrara via Giuseppe Saragat 1 Ferrara44122 Italy Sezione di Ferrara Via Giuseppe Saragat 1 Ferrara44122 Italy C.N. Yang Institute for Theoretical Physics Department of Physics & Astronomy Stony Brook University Stony BrookNY11794 United States Department of Astrophysical Sciences Princeton University 4 Ivy Lane PrincetonNJ08544 United States The Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road PrincetonNJ08544-1000 United States

We implement EuclidEmulator (version 1), an emulator for the non-linear correction of the matter power spectrum, into the Markov chain Monte Carlo (MCMC) forecasting code MontePython. We compare the performance of HALOFIT, HMCode, and EuclidEmulator1, both at the level of power spectrum prediction and at the level of posterior probability distributions of the cosmological parameters, for different cosmological models and different galaxy power spectrum wave number cutoffs. We confirm that the choice of the power spectrum predictor has a non-negligible effect on the computed sensitivities when doing cosmological parameter forecasting, even for a conservative wave number cut-off of 0.2 ℎMpc−1. We find that EuclidEmulator1 is on average up to 17% more sensitive to the cosmological parameters than the other two codes, with the most significant improvements being for the Hubble parameter of up to 42% and the equation of state of dark energy of up to 26%, depending on the case. In addition, we point out that the choice of the power spectrum predictor contributes to the risk of computing a significantly biased mean cosmology when doing parameter estimations. For the four tested scenarios we find biases, averaged over the cosmological parameters, of between 0.5 and 2σ (from below 1σ up to 6σ for individual parameters). This paper provides a proof of concept that this risk can be mitigated by taking a well-tailored theoretical uncertainty into account as this allows to reduce the bias by a factor of 2 to 5, depending on the case under consideration, while keeping posterior credibility contours small: the standard deviations are amplified by a factor of ≤ 1.4 in all cases. © 2021, CC BY-NC-SA.

关键词： Power spectrum

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On the importance of assessing topological convergence in Bayesian phylogenetic inference

arXiv

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arXiv 2024年

作者： Brusselmans, Marius Carvalho, Luiz Max Hong, Samuel L. Gao, Jiansi Matsen, Frederick A. Rambaut, Andrew Lemey, Philippe Suchard, Marc A. Dudas, Gytis Baele, Guy Department of Microbiology Immunology and Transplantation Rega Institute KU Leuven Leuven Belgium School of Applied Mathematics Getulio Vargas Foundation Praia de Botafogo 190 Rio de Janeiro22250-900 Brazil Computational Biology Program Fred Hutchinson Cancer Center SeattleWA98109 United States Howard Hughes Medical Institute Computational Biology Program Fred Hutchinson Cancer Research Center SeattleWA United States Department of Genome Sciences University of Washington SeattleWA United States Department of Statistics University of Washington SeattleWA United States Institute of Ecology and Evolution University of Edinburgh EdinburghEH9 3FL United Kingdom Department of Biostatistics Fielding School of Public Health University of California Los AngelesCA90095 United States Institute of Biotechnology Life Sciences Center Vilnius University Vilnius Lithuania

Modern phylogenetics research is often performed within a Bayesian framework, using sampling algorithms such as Markov chain Monte Carlo (MCMC) to approximate the posterior distribution. These algorithms require careful evaluation of the quality of the generated samples. Within the field of phylogenetics, one frequently adopted diagnostic approach is to evaluate the effective sample size (ESS) and to investigate trace graphs of the sampled parameters. A major limitation of these approaches is that they are developed for continuous parameters and therefore incompatible with a crucial parameter in these inferences: the tree topology. Several recent advancements have aimed at extending these diagnostics to topological space. In this reflection paper, we present two case studies – one on Ebola virus and one on HIV – illustrating how these topological diagnostics can contain information not found in standard diagnostics, and how decisions regarding which of these diagnostics to compute can impact inferences regarding MCMC convergence and mixing. Our results show the importance of running multiple replicate analyses and of carefully assessing topological convergence using the output of these replicate analyses. To this end, we illustrate different ways of assessing and visualizing the topological convergence of these replicates. Given the major importance of detecting convergence and mixing issues in Bayesian phylogenetic analyses, the lack of a unified approach to this problem warrants further action, especially now that additional tools are becoming available to researchers. © 2024, CC BY-SA.

关键词： Phylogenetic

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Correction to: Optimal deterministic algorithm generation

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Journal of Global Optimization 2018年第2期73卷 465-465页

作者： Mitsos, Alexander Najman, Jaromił Kevrekidis, Ioannis G. AVT Process Systems Engineering (SVT) RWTH Aachen University Aachen Germany Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics Princeton University Princeton USA IAS-TUM Garching and Zuse Institut FU Berlin Berlin Germany Departments of Chemical and Biomolecular Engineering Applied Mathematics and Statistics and Urology Johns Hopkins University Baltimore USA

Unfortunately, the copyright information of the article in Springerlink appears as “©  Springer Science+Business Media, LLC, part of Springer Nature 2018” this has been corrected to “©  ...

Unfortunately, the copyright information of the article in Springerlink appears as “© Springer Science+Business Media, LLC, part of Springer Nature 2018” this has been corrected to “© The Author(s) 2018.”

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The Athena++ adaptive mesh refinement framework: Design and magnetohydrodynamic solvers

arXiv

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arXiv 2020年

作者： Stone, James M. Tomida, Kengo White, Christopher J. Felker, Kyle G. Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Earth and Space Science Osaka University Toyonaka Osaka560-0043 Japan Kavli Institute for Theoretical Physics University of California Santa Barbara Santa BarbaraCA93107 United States School of Natural Sciences Institute for Advanced Study PrincetonNJ08544 United States Astronomical Institute Tohoku University Sendai Miyagi980-8578 Japan Argonne National Laboratory LemontIL60439 United States

The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use for a wide variety of physics. The framework works with both uniform and nonuniform grids in Cartesian and curvilinear coordinate systems. It adopts a dynamic execution model based on a simple design called a "task list" that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation. We describe physics modules implemented in this framework for both non-relativistic and relativistic magnetohydrodynamics (MHD). These modules adopt mature and robust algorithms originally developed for the Athena MHD code and incorporate new extensions: support for curvilinear coordinates, higher-order time integrators, more realistic physics such as a general equation of state, and diffusion terms that can be integrated with super-time-stepping algorithms. The modules show excellent performance and scaling, with well over 80% parallel efficiency on over half a million threads. The source code has been made publicly available. Copyright © 2020, The Authors. All rights reserved.

关键词： Magnetohydrodynamics

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Unsupervised extraction of phenotypes from cancer clinical notes for association studies

arXiv

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arXiv 2019年

作者： Stark, Stefan G. Hyland, Stephanie L. Pradier, Melanie F. Lehmann, Kjong-Van Wicki, Andreas Perez-Cruz, Fernando Vogt, Julia E. Rätsch, Gunnar Computational Biology Program Memorial Sloan Kettering Cancer Center New York United States Tri-Institutional Ph.D. Program in Computational Biology and Medicine Weill Cornell Medicine New York United States Department of Computer Science ETH Zürich Zürich Switzerland Medical Informatics Group University Hospital Zürich Zürich Switzerland Swiss Institute for Bioinformatics Zurich Switzerland Department of Biology ETH Zürich Zürich Switzerland Department of Signal Processing and Information Theory University Carlos III in Madrid Leganés Spain School of Engineering and Applied Sciences Harvard University CambridgeMA United States Department of Biomedicine University of Basel Basel Switzerland Tumorzentrum University Hospital Basel Basel Switzerland Swiss Data Science Center ETH Zürich and EPFL Lausanne Switzerland Department of Mathematics and Computer Science University of Basel Basel Switzerland

The recent adoption of Electronic Health Records (EHRs) by healthcare providers has introduced an important source of data that provides detailed and highly specific insights into patient phenotypes over large cohorts. These datasets, in combination with machine learning and statistical approaches, generate new opportunities for research and clinical care. However, many methods require the patient representations to be in structured formats, while the information in the EHR is often locked in unstructured text designed for human readability. In this work, we develop the methodology to automatically extract clinical features from clinical narratives from large EHR corpora without the need for prior knowledge. We consider medical terms and sentences appearing in clinical narratives as atomic information units. We propose an efficient clustering strategy suitable for the analysis of large text corpora and utilize the clusters to represent information about the patient compactly. Additionally, we define the sentences on ontologic and natural language vocabularies to automatically detect pertinent combinations of concepts present in the corpus, even when an ontology is not available. To demonstrate the utility of our approach, we perform an association study of clinical features with somatic mutation profiles from 4,007 cancer patients and their tumors. We apply the proposed algorithm to a dataset consisting of .65 thousand documents with a total of .3.2 million sentences. After correcting for cancer type and other confounding factors, we identify a total of 340 significant statistical associations between the presence of somatic mutations and clinical features. We annotated these associations according to their novelty and we report several known associations. We also propose 37 plausible, testable hypothesis for associations where the underlying biological mechanism does not appear to be known. These results illustrate that the automated discovery of clinical features

关键词： Diseases

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Tilings of space and superhomogeneous point processes

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Physical Review E 2008年第3期77卷 031125-031125页

作者： A. Gabrielli M. Joyce S. Torquato SMC-INFM Dipartimento di Fisica Università La Sapienza P.le A. Moro 2 I-00185 Rome Italy ISC-CNR Via dei Taurini 19 I-00185 Rome Italy Laboratoire de Physique Nucléaire et de Hautes Energies UMR-7585 Université Pierre et Marie Curie Paris 6 75252 Paris Cedex 05 France Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

We consider the construction of point processes from tilings, with equal-volume tiles, of d-dimensional Euclidean space Rd. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are “superhomogeneous” (or “hyperuniform”)—i.e., for which the structure factor S(k) vanishes when the wave vector k tends to zero. The exponent γ characterizing the leading small-k behavior, S(k→0)∝kγ, depends in a simple manner on the nature of the correlation properties of the specific tiling and on the conservation of the mass moments of the tiles. Assigning one point to the center of mass of each tile gives the exponent γ=4 for any tiling in which the shapes and orientations of the tiles are short-range correlated. Smaller exponents in the range 4−d<γ<4 (and thus always superhomogeneous for d≤4) may be obtained in the case that the latter quantities have long-range correlations. Assigning more than one point to each tile in an appropriate way, we show that one can obtain arbitrarily higher exponents in both cases. We illustrate our results with explicit constructions using known deterministic tilings, as well as some simple stochastic tilings for which we can calculate S(k) exactly. Our results provide an explicit analytical construction of point processes with γ>4. Applications to condensed matter physics, and also to cosmology, are briefly discussed.

关键词： Tile

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Local number fluctuations in ordered and disordered phases of water across temperatures: Higher-order moments and degrees of tetrahedrality

arXiv

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arXiv 2024年

作者： Klatt, Michael A. Kim, Jaeuk Gartner, Thomas E. Torquato, Salvatore Institute for AI Safety and Security Wilhelm-Runge-Str. 10 Ulm89081 Germany Institute for Material Physics in Space Köln51170 Germany Department of Physics Ludwig-Maximilians-Universität München Schellingstr. 4 Munich80799 Germany Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Department of Chemical & Biomolecular Engineering Lehigh University BethlehemPA18015 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The isothermal compressibility (i.e., the asymptotic number variance) of equilibrium liquid water as a function of temperature is minimal near ambient conditions. This anomalous non-monotonic temperature dependence is due to a balance between thermal fluctuations and the formation of tetrahedral hydrogen-bond networks. Since tetrahedrality is a many-body property, it will also influence the higher-order moments of density fluctuations, including the skewness and kurtosis. To gain a more complete picture, we examine these higher-order moments that encapsulate many-body correlations using a recently developed, advanced platform for local density fluctuations. We study an extensive set of simulated phases of water across a range of temperatures (80 K to 1600 K) with various degrees of tetrahedrality, including ice phases, equilibrium liquid water, supercritical water, and disordered nonequilibrium quenches. We find clear signatures of tetrahedrality in the higher-order moments, including the skewness and excess kurtosis, that scale for all cases with the degree of tetrahedrality. More importantly, this scaling behavior leads to non-monotonic temperature dependencies in the higher-order moments for both equilibrium and non-equilibrium phases. Specifically, at near-ambient conditions, the higher-order moments vanish most rapidly for large length scales, and the distribution quickly converges to a Gaussian in our metric. However, at non-ambient conditions, higher-order moments vanish more slowly and hence become more relevant especially for improving information-theoretic approximations of hydrophobic solubility. The temperature non-monotonicity that we observe in the full distribution across length-scales could shed light on water's nested anomalies, i.e., reveal new links between structural, dynamic, and thermodynamic anomalies. © 2024, CC BY-NC-ND.

关键词： Higher order statistics

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Stealthy and hyperuniform isotropic photonic bandgap structure in 3D

arXiv

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arXiv 2024年

作者： Siedentop, Lukas Lui, Gianluc Maret, Georg Chaikin, Paul M. Steinhardt, Paul J. Torquato, Salvatore Keim, Peter Florescu, Marian Department of Physics University of Konstanz Konstanz78457 Germany Advanced Technology Institute Department of Physics University of Surrey Surrey GuildfordGU2 7XH United Kingdom Department of Physics New York University New YorkNY20012 United States Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Max-Planck-Institute for Dynamics and Self-Organization Göttingen37077 Germany Institute for the Dynamics of Complex Systems University of Göttingen Göttingen37077 Germany

In photonic crystals the propagation of light is governed by their photonic band structure, an ensemble of propagating states grouped into bands, separated by photonic band gaps. Due to discrete symmetries in spatially strictly periodic dielectric structures their photonic band structure is intrinsically anisotropic. However, for many applications, such as manufacturing artificial structural color materials or developing photonic computing devices, but also for the fundamental understanding of light-matter interactions, it is of major interest to seek materials with long range non-periodic dielectric structures which allow the formation of isotropic photonic band gaps. Here, we report the first ever 3D isotropic photonic band gap for an optimized disordered stealthy hyperuniform structure for microwaves. The transmission spectra are directly compared to a diamond pattern and an amorphous structure with similar node density. The band structure is measured experimentally for all three microwave structures, manufactured by 3D-Laser-printing for meta-materials with refractive index up to n = 2.1. Results agree well with finite-difference-time-domain numerical investigations and a priori calculations of the band-gap for the hyperuniform structure: the diamond structure shows gaps but being anisotropic as expected, the stealthy hyperuniform pattern shows an isotropic gap of very similar magnitude, while the amorphous structure does not show a gap at all. The centimeter scaled microwave structures may serve as prototypes for micrometer scaled structures with bandgaps in the technologically very interesting region of infrared (IR). Copyright © 2024, The Authors. All rights reserved.

关键词： Anisotropy

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Erratum: “Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses” [J. Chem. Phys. 137, 074106 (2012)]

引用

The Journal of Chemical Physics 2014年第15期141卷

作者： S. Torquato Y. Jiao 1Department of Chemistry Department of Physics Princeton Center for Theoretical Science and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA 2Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

In Table I and the caption of Fig. 8 of Ref. 1, the numerical value of the percolation threshold ηc of three-dimensional overlapping spheres as determined via t

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Classification of datasets with imputed missing values: does imputation quality matter?

arXiv

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arXiv 2022年

作者： Shadbahr, Tolou Roberts, Michael Stanczuk, Jan Gilbey, Julian Teare, Philip Dittmer, Sören Thorpe, Matthew Torné, Ramon Viñas Sala, Evis Lió, Pietro Patel, Mishal Rudd, James H.F. Mirtti, Tuomas Rannikko, Antti Sakari Aston, John A.D. Tang, Jing Schönlieb, Carola-Bibiane Selby, Ian Breger, Anna Weir-McCall, Jonathan R. Gkrania-Klotsas, Effrossyni Korhonen, Anna Jefferson, Emily Langs, Georg Yang, Guang Prosch, Helmut Preller, Jacobus Stanczuk, Jan Babar, Judith Sánchez, Lorena Escudero Wassin, Marcel Holzer, Markus Walton, Nicholas Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Data Science & Artificial Intelligence AstraZeneca Cambridge United Kingdom Department of Mathematics University of Manchester Manchester United Kingdom Department of Computer Science and Technology University of Cambridge Cambridge United Kingdom Department of Radiology University of Cambridge Cambridge United Kingdom Clinical Pharmacology & Safety Sciences AstraZeneca Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pathology University of Helsinki Helsinki University Hospital Finland iCAN-Digital Precision Cancer Medicine Flagship Helsinki Finland Department of Urology University of Helsinki Helsinki University Hospital Helsinki Finland Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Faculty of Mathematics University of Vienna Austria Royal Papworth Hospital Cambridge Royal Papworth Hospital NHS Foundation Trust Cambridge United Kingdom Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Language Technology Laboratory University of Cambridge Cambridge United Kingdom Population Health and Genomics School of Medicine University of Dundee Dundee United Kingdom Department of Biomedical Imaging and Image-guided Therapy Computational Imaging Research Lab Medical University of Vienna Vienna Austria National Heart and Lung Institute Imperial College London London United Kingdom Contextflow GmbH Vienna Austria Institute of Astronomy University of Cambridge Cambridge United Kingdom

Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using established methods, followed by classification of the now complete, imputed, samples. The focus of the machine learning researcher is then to optimise the downstream classification performance. In this study, we highlight that it is imperative to consider the quality of the imputation. We demonstrate how the commonly used measures for assessing quality are flawed and propose a new class of discrepancy scores which focus on how well the method recreates the overall distribution of the data. To conclude, we highlight the compromised interpretability of classifier models trained using poorly imputed data. All code and data used in this paper are also released publicly at [inserted upon publication]. © 2022, CC BY.

关键词： Classification (of information)

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