Splines and Variational Methods

This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the var

A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. This book is appropriate for researchers and practitioners in PDE-con

Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable poly

In this famous monograph, a distinguished mathematician presents an innovative approach to classical boundary value problems that employs the basic scheme first suggested by Hilbert and developed by T

This advanced graduate-level text examines variational methods in partial differential equations and illustrates their applications to a number of free-boundary problems. Detailed statements of the s

This book highlights new methods, algorithms and software for the digital processing and recovery of signals. In addition, it describes a new method for modeling one dimensional and multidimensional s

Variational Bayesian learning is one of the most popular methods in machine learning. Designed for researchers and graduate students in machine learning, this book summarizes recent developments in the non-asymptotic and asymptotic theory of variational Bayesian learning and suggests how this theory can be applied in practice. The authors begin by developing a basic framework with a focus on conjugacy, which enables the reader to derive tractable algorithms. Next, it summarizes non-asymptotic theory, which, although limited in application to bilinear models, precisely describes the behavior of the variational Bayesian solution and reveals its sparsity inducing mechanism. Finally, the text summarizes asymptotic theory, which reveals phase transition phenomena depending on the prior setting, thus providing suggestions on how to set hyperparameters for particular purposes. Detailed derivations allow readers to follow along without prior knowledge of the mathematical techniques specific to

The field of geometric variational problems is fast-moving and influential. These problems interact with many other areas of mathematics and have strong relevance to the study of integrable systems, mathematical physics and PDEs. The workshop 'Variational Problems in Differential Geometry' held in 2009 at the University of Leeds brought together internationally respected researchers from many different areas of the field. Topics discussed included recent developments in harmonic maps and morphisms, minimal and CMC surfaces, extremal Kähler metrics, the Yamabe functional, Hamiltonian variational problems and topics related to gauge theory and to the Ricci flow. These articles reflect the whole spectrum of the subject and cover not only current results, but also the varied methods and techniques used in attacking variational problems. With a mix of original and expository papers, this volume forms a valuable reference for more experienced researchers and an ideal introduction for graduat

Matthias Kaeding discusses Bayesian methods for analyzing discrete and continuous failure times where the effect of time and/or covariates is modeled via P-splines and additional basic function expans

This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The applications,

The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particula

The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particula

This book constitutes the refereed proceedings of the 4th International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2013, held in Schloss Seggau near Graz, Austr

This book describes the derivation of the equations of motion of fluids as well as the dynamics of ocean and atmospheric currents on both large and small scales through the use of variational methods.

Variational Regularization of 3D Data provides an introduction to variational methods for data modelling and its application in computer vision. In this book, the authors identify interpolation as an

This book constitutes the refereed proceedings of the 5th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2015, held in Lege-Cap Ferret, France, in May 2015. T

Variational methods and their generalizations have been verified to be useful tools in proving the existence of solutions to a variety of boundary value problems for ordinary, impulsive, and partial d

Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equatio

This book provides an introduction to the methods of coupled quantum statistical field theory and Green's functions. The methods of coupled quantum field theory have played a major role in the extensi

This book has been awarded the Ferran Sunyer i Balaguer 2005 prize.The aim of this monograph is to discuss several elliptic problems on Rn with two main features: they are variational and perturbativ

Distributions Hilbert Space Operators Variational Methods and Applications in Quantum Physics.

This authoritative work provides an in-depth treatment of state space methods, with a range of applications in neural and clinical data. Advanced and state-of-the-art research topics are detailed, including topics in state space analyses, maximum likelihood methods, variational Bayes, sequential Monte Carlo, Markov chain Monte Carlo, nonparametric Bayesian, and deep learning methods. Details are provided on practical applications in neural and clinical data, whether this is characterising time series data from neural spike trains recorded from the rat hippocampus, the primate motor cortex, or the human EEG, MEG or fMRI, or physiological measurements of heartbeats or blood pressures. With real-world case studies of neuroscience experiments and clinical data sets, and written by expert authors from across the field, this is an ideal resource for anyone working in neuroscience and physiological data analysis.

The book presents the state of the art in isogeometric modeling and shows how the method has advantaged. First an introduction to geometric modeling with NURBS and T-splines is given followed by the i

This book introduces methods of robust optimization in multivariate adaptive regression splines (MARS) and Conic MARS in order to handle uncertainty and non-linearity. The proposed techniques are impl

?Isogeometric finite elements combine the numerical solution of partial differential equations and the description of the computational domain given by rational splines from computer aided geometric d

This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate studen

In variational linguistics, concepts of space have always been a central issue. However, different research traditions considering these concepts (such as traditional dialectology and the new socio-di

Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and re

Resoundingly popular in its first edition, the second edition of Mechanics of Structures: Variational and Computational Methods promises to be even more so, with broader coverage, expanded discussions

The recent success and popularity of the finite-element method, crucial to solving mathematical problems in many branches of engineering today, is based on the variational methods discussed in this te

This book provides a comprehensive survey of analytic and approximate solutions of problems of applied mechanics, with particular emphasis on nonconservative phenomena. Include