Book•
Numerical Recipes 3rd Edition: The Art of Scientific Computing
10 Sep 2007-
TL;DR: This new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded, and adopts an object-oriented style particularly suited to scientific applications.
Abstract: Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Please visit www.nr.com or www.cambridge.org/us/numericalrecipes for more details. New key features: 2 new chapters, 25 new sections, 25% longer than Second Edition Thorough upgrades throughout the text Over 100 completely new routines and upgrades of many more. New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector MachinesNew Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions An expanded treatment of ODEs with completely new routines Plus comprehensive coverage of linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory And much, much more! Visit the authors' web site for information about electronic subscriptions www.nr.com/aboutNR3book.html
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TL;DR: A new intensity determination and normalization procedure called MaxLFQ is developed that is fully compatible with any peptide or protein separation prior to LC-MS analysis, which accurately detects the mixing ratio over the entire protein expression range, with greater precision for abundant proteins.
3,732 citations
TL;DR: This code works in the tight-binding framework, which can be generated by another software package Wannier90 Mostofi et al. (2008), and can help to classify the topological phase of a given materials by calculating the Wilson loop, and get the surface state spectrum.
1,566 citations
Additional excerpts
...Local minima can be obtained by using some well known multidimensional minimization methods, e.g., Nelder and Mead’s Downhill Simplex Method [49], Conjugate Gradient Methods [50], Quasi-Newton Methods [51] et al.....
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..., Nelder and Mead’s Downhill Simplex Method [49], Conjugate Gradient Methods [50], Quasi-Newton Methods [51] et al....
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TL;DR: A quality function is introduced that assesses the agreement of a pseudopotentials calculation with all-electron FLAPW results, and the necessary plane-wave energy cutoff, and allows for a Nelder–Mead optimization algorithm on a training set of materials to optimize the input parameters of the pseudopotential construction.
850 citations
Cites methods from "Numerical Recipes 3rd Edition: The ..."
...Weuse aNelder–Mead algorithm [27] also known as theDownhill SimplexMethod [28] to optimize the PPs....
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TL;DR: The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.
Abstract: Using conservation of energy-a fundamental property of closed classical and quantum mechanical systems-we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized molecules with an accuracy of 0.3 kcal mol-1 for energies and 1 kcal mol-1 A-1 for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.
766 citations
Cites methods from "Numerical Recipes 3rd Edition: The ..."
...This was achieved by subsampling f̂− F on a regular grid and numerically projecting it onto the closest conservative vector field by solving Poisson’s equation [26]....
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TL;DR: The goal of this paper is to build intuition about what assumptions are implicit in the use of the Lomb-Scargle periodogram and related estimators of periodicity so as to motivate important practical considerations required in its proper application and interpretation.
Abstract: The Lomb-Scargle periodogram is a well-known algorithm for detecting and characterizing periodic signals in unevenly-sampled data. This paper presents a conceptual introduction to the Lomb-Scargle periodogram and important practical considerations for its use. Rather than a rigorous mathematical treatment, the goal of this paper is to build intuition about what assumptions are implicit in the use of the Lomb-Scargle periodogram and related estimators of periodicity, so as to motivate important practical considerations required in its proper application and interpretation.
666 citations
Cites background from "Numerical Recipes 3rd Edition: The ..."
...A few typical approaches include using the mean of the sampling intervals (e.g. Scargle 1982; Horne & Baliunas 1986; Press et al. 2007), the harmonic mean of the sampling intervals (e.g. Debosscher et al. 2007), the median of the sampling intervals (e.g. Graham et al. 2013b), or the minimum sample…...
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