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Julia for biologists

arXiv 2021年

作者： Roesch, Elisabeth Greener, Joe G. MacLean, Adam L. Nassar, Huda Rackauckas, Christopher Holy, Timothy E. Stumpf, Michael P.H. School of Mathematics and Statistics University of Melbourne 813 Swanston Street ParkvilleVIC3010 Australia Melbourne Integrative Genomics University of Melbourne 30 Royal Parade ParkvilleVIC3052 Australia Department of Computer Science University College London Gower Street LondonWC1E 6BT United Kingdom Department of Quantitative and Computational Biology University of Southern California 1050 Childs Way Los AngelesCA90089 United States RelationalAI Inc. 2120 University Ave BerkeleyCA94794 United States Department of Mathematics Massachusetts Institute of Technology 182 Memorial Dr CambridgeMA02142 United States Julia Computing 240 Elm Street SomervilleMA02144 United States Pumas-AI 14711 Kamputa Drive CentervilleVA20120 United States Departments of Neuroscience and Biomedical Engineering Washington University in St. Louis 660 S. Euclid Ave. St. LouisMO63110 United States School of Bio-Sciences Biosciences 4 The University of Melbourne Royal Parade ParkvilleVIC3052 Australia

Increasing emphasis on data and quantitative methods in the biomedical sciences is making biological research more computational. Collecting, curating, processing, and analysing large genomic and imaging data sets poses major computational challenges, as does simulating larger and more realistic models in systems biology. Here we discuss how a relative newcomer among computer programming languages - Julia - is poised to meet the current and emerging demands in the computational biosciences, and beyond. Speed, flexibility, a thriving package ecosystem, and readability are major factors that make high-performance computing and data analysis available to an unprecedented degree to "gifted amateurs". We highlight how Julia's design is already enabling new ways of analysing biological data and systems, and we provide a, necessarily incomplete, list of resources that can facilitate the transition into the Julian way of computing. © 2021, CC BY.

关键词： Computer programming languages

Author Correction: Julia for biologists

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Nature methods 2023年第5期20卷 771页

作者： Elisabeth Roesch Joe G Greener Adam L MacLean Huda Nassar Christopher Rackauckas Timothy E Holy Michael P H Stumpf School of Mathematics and Statistics University of Melbourne Melbourne Victoria Australia. Melbourne Integrative Genomics University of Melbourne Melbourne Victoria Australia. Medical Research Council Laboratory of Molecular Biology Cambridge UK. Department of Quantitative and Computational Biology University of Southern California Los Angeles CA USA. RelationalAI Berkeley CA USA. Department of Mathematics Massachusetts Institute of Technology Cambridge MA USA. Julia Computing Somerville MA USA. Pumas-AI Centreville VA USA. Departments of Neuroscience and Biomedical Engineering Washington University in St. Louis St. Louis MO USA. School of Mathematics and Statistics University of Melbourne Melbourne Victoria Australia. mstumpf@unimelb.edu.au. Melbourne Integrative Genomics University of Melbourne Melbourne Victoria Australia. mstumpf@unimelb.edu.au. School of BioSciences The University of Melbourne Melbourne Victoria Australia. mstumpf@unimelb.edu.au. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems Melbourne Victoria Australia. mstumpf@unimelb.edu.au.

Density matrix based perturbative corrections for improved quantum simulation accuracy

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arXiv 2019年

作者： Morris, T.D. Parks, Z.P. McCaskey, A.J. Jakowski, J. Pooser, R.C. Physics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Quantum Computing Institute Oak Ridge National Laboratory Oak RidgeTN37831 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

We present error mitigation (EM) techniques for noisy intermediate-scale quantum computers (QC) based on density matrix purification and perturbative corrections to the target energy. We incorporate this scheme into the variational quantum eigensolver (VQE) and demonstrate chemically-accurate ground state energy calculations of various alkali metal hydrides using IBM quantum computers. Both the density matrix purification improvements and the perturbative corrections require only meager classical computational resources, and are conducted exclusively as post-processing of the measured density matrix. The improved density matrix leads to better simulation accuracy at each step of the variational optimization, resulting in a better input into the next optimization step without additional measurements. Adding perturbative corrections to the resulting energies further increases the accuracy, and decreases variation between consecutive measurements. These EM schemes allow for previously unavailable levels of accuracy over remote QC resources. Copyright © 2019, The Authors. All rights reserved.

关键词： Quantum theory

Influence of the vacuum polarization effect on the motion of charged particles in the magnetic field around a Schwarzschild Black Hole

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arXiv 2019年

作者： Pavlović, Petar Saveliev, Andrey Sossich, Marko Department of Physics Ramashna Mission Vivekananda Educational and Research Institute Belur MathWest Bengal711202 India Institute of Physics Mathematics and Information Technology Immanuel Kant Baltic Federal University Ul. Aleksandra Nevskogo 14 Kaliningrad236016 Russia Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University GSP-1 Leninskiye Gory 1-52 Moscow119991 Russia Faculty of Electrical Engineering and Computing Department of Physics University of Zagreb Unska 3 Zagreb10 000 Croatia

The consequences of the vacuum polarization effect in magnetic fields around a Schwarzschild Black Hole (SBH) on the motion of charged particles are investigated in this work. Using the weak electromagnetic field approximation, we discuss the non-minimal coupling between magnetic fields and gravity caused by the vacuum polarization and study the equations of motion for the case of a magnetic field configuration which asymptotically approaches a dipole magnetic field. It is shown that the presence of non-minimal coupling can significantly influence the motion of charged particles around Black Holes. In particular, the vacuum polarization effect, leading to strong amplification or suppression of the magnetic field strength around the event horizon (depending on the sign of the coupling parameter), can affect the scattering angle and minimal distance for the electrons moving in the gravitational field of the Black Hole as well as the dependence of these parameters on the asymptotic magnetic field strength, initial distance and the Black Hole mass. It is further demonstrated that the non-minimal coupling between gravity and astrophysical magnetic fields, caused by the vacuum polarization, can cause significant changes of the parameter space corresponding to bound trajectories around the Black Hole. In certain cases, the bounded or unbounded character of a trajectory is determined solely by the presence of non-minimal coupling and its strength. These effects could in principle be used as observational signatures of the vacuum polarization effect and also to constrain the value of the coupling parameter. Copyright © 2019, The Authors. All rights reserved.

关键词： Gravitation

A new estimate for a quantity involving the Chebyshev polynomials of the first kind

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arXiv 2018年

作者： Xu, Xuefeng Zhang, Chen-Song LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China LSEC NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we establish a new estimate (including lower and upper bounds) for an important quantity involved in the convergence analysis of smoothed aggregation algebraic multigrid methods. The new upper bound imp... 详细信息

关键词： Polynomials

Numerical approximation of elliptic problems with log-normal random coefficients

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arXiv 2018年

作者： Wan, Xiaoliang Yu, Haijun Department of Mathematics Center for Computation and Technology Louisiana State University Baton RougeLA70803 United States NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this work, we consider a non-standard preconditioning strategy for the numerical approximation of the classical elliptic equations with log-normal random coefficients. In [45], a Wick-type elliptic model was proposed by modeling the random flux through the Wick product. Due to the lower-triangular structure of the uncertainty propagator, this model can be approximated efficiently using the Wiener chaos expansion in the probability space. Such a Wick-type model provides, in general, a second-order approximation of the classical one in terms of the standard deviation of the underlying Gaussian process. Furthermore, when the correlation length of the underlying Gaussian process goes to infinity, the Wick-type model yields the same solution as the classical one. These observations imply that the Wick-type elliptic equation can provide an effective preconditioner for the classical random elliptic equation under appropriate conditions. We use the Wick-type elliptic model to accelerate the Monte Carlo method and the stochastic Galerkin finite element method. Numerical results are presented and discussed.60H35, 65N30 Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

Quasi-potential calculation and minimum action method for limit cycle

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arXiv 2018年

作者： Lin, Ling Yu, Haijun Zhou, Xiang School of Mathematics Sun Yat-sen University Guangzhou510275 China School of Mathematical Sciences University of Chinese Academy of Sciences NCMIS and LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China Department of Mathematics City University of Hong Kong Tat Chee Ave Kowloon Hong Kong

We study the noise-induced escape from a stable limit cycle of a non-gradient dynamical system driven by a small additive noise. The fact that the optimal transition path in this case is infinitely long imposes a severe numerical challenge to resolve it in the minimum action method. We first consider the landscape of the quasi-potential near the limit cycle, which characterizes the minimal cost of the noise to drive the system far away form the limit cycle. We derive and compute the quadratic approximation of this quasi-potential near the limit cycle in the form of a positive definite solution to a matrix-valued periodic Riccati differential equation on the limit cycle. We then combine this local approximation in the neighbourhood of the limit cycle with the minimum action method applied outside of the neighbourhood. The neighbourhood size is selected to be compatible with the path discretization error. By several numerical examples, we show that this strategy effectively improve the minimum action method to compute the spiral optimal escape path from limit cycles in various *** 65K05, Secondary 82B05 Copyright © 2018, The Authors. All rights reserved.

关键词： Numerical methods

Functional a posteriori error estimates for boundary element methods

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arXiv 2019年

作者： Kurz, Stefan Pauly, Dirk Praetorius, Dirk Repin, Sergey Sebastian, Daniel TU Wien Institute for Analysis and Scientific Computing Wiedner Hauptstraße 8-10/E101/4 Vienna1040 Austria TU Darmstadt Centre for Computational Engineering Dolivostraße 15 Darmstadt64293 Germany Universität Duisburg-Essen Fakultät für Mathematik Thea-Leymann-Straße 9 Essen45141 Germany University of Jyväskylä Building Agora Mattilanniemi 2 Jyväskylä40100 Finland Russian Academy of Sciences Steklov Institute of Mathematics 191011 Fontanka 27 St. Petersburg Russia

Functional error estimates are well-estabilished tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM as well as collocation, which makes our approach of particular interest for people working in engineering. Numerical experiments for the Laplace problem confirm the theoretical *** Codes 65N38, 65N15, 65N50 Copyright © 2019, The Authors. All rights reserved.

关键词： Boundary element method

Corrigendum to “High order positivity-preserving discontinuous Galerkin schemes for radiative transfer equations on triangular meshes” [J. Comput. Phys. 397 (2019) 108811]

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Journal of computational Physics 2020年 406卷

作者： Min Zhang Juan Cheng Jianxian Qiu School of Mathematical Sciences Xiamen University Xiamen Fujian 361005 PR China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 PR China Center for Applied Physics and Technology Peking University Beijing 100871 PR China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen Fujian 361005 PR China