Los Alamos National Laboratory

SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments.

A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two-dimensional rigid-sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four-term virial coefficient expansion.

Macromolecular X-ray crystallography is routinely applied to understand biological processes at a molecular level. However, significant time and effort are still required to solve and complete many of these structures because of the need for manual interpretation of complex numerical data using many software packages and the repeated use of interactive three-dimensional graphics. PHENIX has been developed to provide a comprehensive system for macromolecular crystallographic structure solution with an emphasis on the automation of all procedures. This has relied on the development of algorithms that minimize or eliminate subjective input, the development of algorithms that automate procedures that are traditionally performed by hand and, finally, the development of a framework that allows a tight integration between the algorithms.

Abstract Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves 1 and in the first imaging of a black hole 2 . Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis.

Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves1 and in the first imaging of a black hole2. Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis.

Ab initio effective core potentials (ECP’s) have been generated to replace the innermost core electron for third-row (K–Au), fourth-row (Rb–Ag), and fifth-row (Cs–Au) atoms. The outermost core orbitals—corresponding to the ns2np6 configuration for the three rows here—are not replaced by the ECP but are treated on an equal footing with the nd, (n+1)s and (n+1)p valence orbitals. These ECP’s have been derived for use in molecular calculations where these outer core orbitals need to be treated explicitly rather than to be replaced by an ECP. The ECP’s for the forth and fifth rows also incorporate the mass–velocity and Darwin relativistic effects into the potentials. Analytic fits to the potentials are presented for use in multicenter integral evaluation. Gaussian orbital valence basis sets are developed for the (3s, 3p, 3d, 4s, 4p), (4s, 4p, 4d, 5s, 5p), and (5s, 5p, 5d, 6s, 6p) ortibals of the three respective rows.

Ab initio effective core potentials (ECP’s) have been generated to replace the Coulomb, exchange, and core-orthogonality effects of the chemically inert core electron in the transition metal atoms Sc to Hg. For the second and third transition series relative ECP’s have been generated which also incorporate the mass–velocity and Darwin relativistic effects into the potential. The ab initio ECP’s should facilitate valence electron calculations on molecules containing transition-metal atoms with accuracies approaching all-electron calculations at a fraction of the computational cost. Analytic fits to the potentials are presented for use in multicenter integral evaluation. Gaussian orbital valence basis sets are developed for the (3d,4s,4p), (4d,5s,5p), and (5d,6s,6p) orbitals of the first, second, and third transition series atoms, respectively. All-electron and valence-electron atomic excitation energies are also compared for the low-lying states of Sc–Hg, and the valence-electron calculations are found to reproduce the all-electron excitation energies (typically within a few tenths of an eV).

Studies of the human microbiome have revealed that even healthy individuals differ remarkably in the microbes that occupy habitats such as the gut, skin and vagina. Much of this diversity remains unexplained, although diet, environment, host genetics and early microbial exposure have all been implicated. Accordingly, to characterize the ecology of human-associated microbial communities, the Human Microbiome Project has analysed the largest cohort and set of distinct, clinically relevant body habitats so far. We found the diversity and abundance of each habitat’s signature microbes to vary widely even among healthy subjects, with strong niche specialization both within and among individuals. The project encountered an estimated 81–99% of the genera, enzyme families and community configurations occupied by the healthy Western microbiome. Metagenomic carriage of metabolic pathways was stable among individuals despite variation in community structure, and ethnic/racial background proved to be one of the strongest associations of both pathways and microbes with clinical metadata. These results thus delineate the range of structural and functional configurations normal in the microbial communities of a healthy population, enabling future characterization of the epidemiology, ecology and translational applications of the human microbiome. The Human Microbiome Project Consortium reports the first results of their analysis of microbial communities from distinct, clinically relevant body habitats in a human cohort; the insights into the microbial communities of a healthy population lay foundations for future exploration of the epidemiology, ecology and translational applications of the human microbiome. The Human Microbiome Project (HMP), supported by the National Institutes of Health Common Fund, has the goal of characterizing the microbial communities that inhabit and interact with the human body in sickness and in health. In two Articles in this issue of Nature, the HMP Consortium presents the first population-scale details of the organismal and functional composition of the microbiota across five areas of the body. An associated News & Views discusses the initial results — which, along with those of a series of co-publications, already constitute the most extensive catalogue of organisms and genes related to the human microbiome yet published — and highlights some of the major questions that the project will tackle in the next few years.

Abstract: SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments.

The Sloan Digital Sky Survey (SDSS) will provide the data to support detailed investigations of the distribution of luminous and non- luminous matter in the Universe: a photometrically and astrometrically calibrated digital imaging survey of pi steradians above about Galactic latitude 30 degrees in five broad optical bands to a depth of g' about 23 magnitudes, and a spectroscopic survey of the approximately one million brightest galaxies and 10^5 brightest quasars found in the photometric object catalog produced by the imaging survey. This paper summarizes the observational parameters and data products of the SDSS, and serves as an introduction to extensive technical on-line documentation.

A consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn. The ECP’s are derived from all-electron numerical Hartree–Fock atomic wave functions and fit to analytical representations for use in molecular calculations. For Rb to Bi the ECP’s are generated from the relativistic Hartree–Fock atomic wave functions of Cowan which incorporate the Darwin and mass–velocity terms. Energy-optimized valence basis sets of (3s3p) primitive Gaussians are presented for use with the ECP’s. Comparisons between all-electron and valence-electron ECP calculations are presented for NaF, NaCl, Cl2, Cl2−, Br2, Br2−, and Xe2+. The results show that the average errors introduced by the ECP’s are generally only a few percent.

Metabolism provides a basis for using first principles of physics, chemistry, and biology to link the biology of individual organisms to the ecology of populations, communities, and ecosystems. Metabolic rate, the rate at which organisms take up, transform, and expend energy and materials, is the most fundamental biological rate. We have developed a quantitative theory for how metabolic rate varies with body size and temperature. Metabolic theory predicts how metabolic rate, by setting the rates of resource uptake from the environment and resource allocation to survival, growth, and reproduction, controls ecological processes at all levels of organization from individuals to the biosphere. Examples include: (1) life history attributes, including development rate, mortality rate, age at maturity, life span, and population growth rate; (2) population interactions, including carrying capacity, rates of competition and predation, and patterns of species diversity; and (3) ecosystem processes, including rates of biomass production and respiration and patterns of trophic dynamics. Data compiled from the ecological literature strongly support the theoretical predictions. Eventually, metabolic theory may provide a conceptual foundation for much of ecology, just as genetic theory provides a foundation for much of evolutionary biology.

Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.

Macromolecular X-ray crystallography is routinely applied to understand biological processes at a molecular level. However, significant time and effort are still required to solve and complete many of these structures because of the need for manual interpretation of complex numerical data using many software packages and the repeated use of interactive three-dimensional graphics. PHENIX has been developed to provide a comprehensive system for macromolecular crystallographic structure solution with an emphasis on the automation of all procedures. This has relied on the development of algorithms that minimize or eliminate subjective input, the development of algorithms that automate procedures that are traditionally performed by hand and, finally, the development of a framework that allows a tight integration between the algorithms.

Diffraction (X-ray, neutron and electron) and electron cryo-microscopy are powerful methods to determine three-dimensional macromolecular structures, which are required to understand biological processes and to develop new therapeutics against diseases. The overall structure-solution workflow is similar for these techniques, but nuances exist because the properties of the reduced experimental data are different. Software tools for structure determination should therefore be tailored for each method. Phenix is a comprehensive software package for macromolecular structure determination that handles data from any of these techniques. Tasks performed with Phenix include data-quality assessment, map improvement, model building, the validation/rebuilding/refinement cycle and deposition. Each tool caters to the type of experimental data. The design of Phenix emphasizes the automation of procedures, where possible, to minimize repetitive and time-consuming manual tasks, while default parameters are chosen to encourage best practice. A graphical user interface provides access to many command-line features of Phenix and streamlines the transition between programs, project tracking and re-running of previous tasks.

NetworkX is a Python language package for exploration and analysis of networks and network algorithms. The core package provides data structures for representing many types of networks, or graphs, including simple graphs, directed graphs, and graphs with parallel edges and self-loops. The nodes in NetworkX graphs can be any (hashable) Python object and edges can contain arbitrary data; this flexibility makes NetworkX ideal for representing networks found in many different scientific fields. In addition to the basic data structures many graph algorithms are implemented for calculating network properties and structure measures: shortest paths, betweenness centrality, clustering, and degree distribution and many more. NetworkX can read and write various graph formats for easy exchange with existing data, and provides generators for many classic graphs and popular graph models, such as the Erdos-Renyi, Small World, and Barabasi-Albert models. The ease-of-use and flexibility of the Python programming language together with connection to the SciPy tools make NetworkX a powerful tool for scientific computations. We discuss some of our recent work studying synchronization of coupled oscillators to demonstrate how NetworkX enables research in the field of computational networks.

▪ Abstract We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These $\mathrm{PT}$ symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories.

Abstract We shall present here the motivation and a general description of a method dealing with a class of problems in mathematical physics. The method is, essentially, a statistical approach to the study of differential equations, or more generally, of integro-differential equations that occur in various branches of the natural sciences.

This biennial Review summarizes much of particle physics. Using data from previous editions, plus 2658 new measurements from 644 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. Among the 112 reviews are many that are new or heavily revised including those on Heavy-Quark and Soft-Collinear Effective Theory, Neutrino Cross Section Measurements, Monte Carlo Event Generators, Lattice QCD, Heavy Quarkonium Spectroscopy, Top Quark, Dark Matter, ${V}_{\mathit{cb}}$ ${V}_{\mathit{ub}}$, Quantum Chromodynamics, High-Energy Collider Parameters, Astrophysical Constants, Cosmological Parameters, and Dark Matter.A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http://pdg.lbl.gov/.The 2012 edition of Review of Particle Physics is published for the Particle Data Group as article 010001 in volume 86 of Physical Review D.This edition should be cited as: J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012).