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In the past, basis sets for use in correlated molecular calculations have largely been taken from single configuration calculations. Recently, Almlöf, Taylor, and co-workers have found that basis sets of natural orbital...

Correlation consistent and augmented correlation consistent basis sets have been determined for the second row atoms aluminum through argon. The methodology, originally developed for the first row atoms [T. H. Dunning, J...

Map interpretation remains a critical step in solving the structure of a macromolecule. Errors introduced at this early stage may persist throughout crystallographic refinement and result in an incorrect structure. The n...

A method of ‘‘natural population analysis’’ has been developed to calculate atomic charges and orbital populations of molecular wave functions in general atomic orbital basis sets. The natural analysis is an alte...

A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting/smoothing data containing a significant percentage of gross errors, and is thus ...

This paper reviews the mathematical basis of maximum likelihood. The likelihood function for macromolecular structures is extended to include prior phase information and experimental standard uncertainties. The assumptio...

A contracted Gaussian basis set (6-311G**) is developed by optimizing exponents and coefficients at the Mo/ller–Plesset (MP) second-order level for the ground states of first-row atoms. This has a triple split in the v...

An exact derivation of the Scherrer equation is given for particles of spherical shape, values of the constant for half-value breadth and for integral breadth being obtained. Various approximation methods which have been...

Abstract It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although ...

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the aut...

Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems...

In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topol...

Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction. UMAP has a rigorous math...

In this thesis, parallel computing on installed local area networks (LAN) is focused, analyzing problems and possible solutions taking into account the main factors of computing and communications. More specifically, LAN...

Parallel computing on networks of workstations are intensively used in some application areas such as linear algebra operations. Topics such as processing as well as communication hardware heterogeneity are considered so...

From the Publisher: This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in...

(NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.) I. GETTING STARTED. 1. Aspects of Multivariate Analysis. Applications of Multivariate Techniques. The Organization of Data. D...

Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, ] Integ...

Materias / palabras clave: group theory, semigroup theory, linear algebra, algebraic graph theory, homological algebra; Science: Mathematics

Materias / palabras clave: differential equations, computational methods, numerical linear algebra, optimal control; Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods

Materias / palabras clave: applied mathematics, numerical linear algebra, stochastic systems, differential equations, mathematical modelling, imaging and data analysis; Science: Mathematics