A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

/pdf/gaussian-processes-for-machine-learning-40fp9c190d.pdf

Gaussian Processes for Machine Learning

BoltzTraP. A code for calculating band-structure dependent quantities

/pdf/statistical-analysis-in-climate-research-51ik9f04rx.pdf

Statistical Analysis in Climate Research

Noncovalent interactions hold the key to understanding many chemical, biological, and technological problems. Describing these noncovalent interactions accurately, including their positions in real space, constitutes a first step in the process of decoupling the complex balance of forces that define noncovalent interactions. Because of the size of macromolecules, the most common approach has been to assign van der Waals interactions (vdW), steric clashes (SC), and hydrogen bonds (HBs) based on pairwise distances between atoms according to their vdW radii. We recently developed an alternative perspective, derived from the electronic density: the non-covalent interactions (NCI) index [J. Am. Chem. Soc. 2010, 132, 6498]. This index has the dual advantages of being generally transferable to diverse chemical applications and being very fast to compute, since it can be calculated from promolecular densities. Thus, NCI analysis is applicable to large systems, including proteins and DNA, where analysis of noncova...

/pdf/nciplot-a-program-for-plotting-noncovalent-interaction-5bhkffn4zn.pdf

NCIPLOT: A Program for Plotting Noncovalent Interaction Regions

A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening

Vector Analysis. Curved Coordinates, Tensors. Determinants and Matrices. Group Theory. Infinite Series. Functions of a Complex Variable I. Functions of a Complex Variable II. Differential Equations. Sturm-Liouville Theory. Gamma-Factrial Function. Bessel Functions. Legendre Functions. Special Functions. Fourier Series. Integral Transforms. Integral Equations. Calculus of Variations. Nonlinear Methods and Chaos.

Mathematical Methods for Physicists

Mathematical methods for physicists

Mathematical methods for physicists 6th ed.

Now in its 7th edition, "Mathematical Methods for Physicists" continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises. This book is the revised and updated version of the leading text in mathematical physics. It focuses on problem-solving skills and active learning, offering numerous chapter problems. It includes clearly identified definitions, theorems, and proofs promote clarity and understanding. New to this edition: improved modular chapters; new up-to-date examples; and, more intuitive explanations.

Mathematical methods for physicists : a comprehensive guide

This chapter surveys a number of sets of special functions of importance in physics. Where appropriate, the survey includes generating functions, Rodrigues formulas, the relevant differential equation, orthogonality conditions, and applications. The discussion covers Hermite functions (with applications to the quantum harmonic oscillator and to molecular vibrations), Laguerre functions (with application to the hydrogen atom), Chebyshev polynomials (with application to numerical analysis), hypergeometric and confluent hypergeometric functions, the dilogarithm (with application to electronic structure computations), and elliptic integrals.

George B. Arfken

Papers

Mathematical Methods for Physicists

Mathematical methods for physicists

Mathematical methods for physicists 6th ed.

Mathematical methods for physicists : a comprehensive guide

More Special Functions