Statistics : Statistical Theory and Methods
Offers a general and gentle introduction to all aspects of particle filtering: the
algorithms, their uses in different areas, their computer implementation in
Python and the supporting theory
Covers both the basics and more advanced, cutting-edge developments, such
as PMCMC (particle Markov chain Monte Carlo) and SQMC (Sequential quasiMonte Carlo)
Comes with a freely available Python library (particles), which implements all
the algorithms discussed in the book. Each chapter ends with a gPython
cornerh that discusses how the methods covered can be implemented in Python
This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also
known as particle filters. These methods have become a staple for the sequential analysis of
data in such diverse fields as signal processing, epidemiology, machine learning, population
ecology, quantitative finance, and robotics. The coverage is comprehensive, ranging from the
underlying theory to computational implementation, methodology, and diverse applications in
various areas of science. This is achieved by describing SMC algorithms as particular cases of a
general framework, which involves concepts such as Feynman-Kac distributions, and tools such
as importance sampling and resampling. This general framework is used consistently
throughout the book.Extensive coverage is provided on sequential learning (filtering, smoothing)
of state-space (hidden Markov) models, as this remains an important application of SMC
methods. More recent applications, such as parameter estimation of these models (through e.g.
particle Markov chain Monte Carlo techniques) and the simulation of challenging probability
distributions (in e.g. Bayesian inference or rare-event problems), are also discussed. The book
may be used either as a graduate text on Sequential Monte Carlo methods and state-space
modeling, or as a general reference work on the area. Each chapter includes a set of exercises
for self-study, a comprehensive bibliography, and a gPython corner,h which discusses the
practical implementation of the methods covered.
Due 2020-12-08
1st ed. 2020, X, 340 p.
Hardcover
ISBN 978-3-030-47844-5
Product category : Graduate/advanced undergraduate textbook
Series : Springer Series in Statistics
Mathematics : Analysis
A unique collection of fully solved long problems, offering a hands-on approach to learning the subject
Covers the key classical equations: heat, wave, Schrodinger, Monge-Ampere, Euler, Navier-Stokes
Background on functional analysis, distributions and functional spaces is covered in the problems
This textbook offers a unique learning-by-doing introduction to the modern theory of partial
differential equations. Through 65 fully solved problems, the book offers readers a fast but
indepth introduction to the field, covering advanced topics in microlocal analysis, including
pseudo- and para-differential calculus, and the key classical equations, such as the Laplace,
Schrodinger or Navier-Stokes equations. Essentially self-contained, the book begins with
problems on the necessary tools from functional analysis, distributions, and the theory of
functional spaces, and in each chapter the problems are preceded by a summary of the
relevant results of the theory. Informed by the authors' extensive research experience and
years of teaching, this book is for graduate students and researchers who wish to gain real
working knowledge of the subject.
Due 2021-01-06
1st ed. 2020, X, 330 p.
Softcover
ISBN 978-3-030-50283-6
Product category : Graduate/advanced undergraduate textbook
Series : Universitext
Mathematics : Discrete Mathematics
Appropriate for math olympiad competitors; Contains challenging problems and solutions
Teaches techniques and facts that are central to mathematics
Presents a diverse range of state-of-the-art topics and developments
Illustrates unexpected connections between various mathematical topics
Results are supported by numerous illustrations
This self-contained text presents state-of-the-art results on recurrent sequences and their
applications in algebra, number theory, geometry of the complex plane and discrete
mathematics. It is designed to appeal to a wide readership, ranging from scholars and
academics, to undergraduate students, or advanced high school and college students training
for competitions. The content of the book is very recent, and focuses on areas where significant
research is currently taking place. Among the new approaches promoted in this book, the
authors highlight the visualization of some recurrences in the complex plane, the concurrent
use of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and
links to many applications. It contains techniques which are fundamental in other areas of
math and encourages further research on the topic. The introductory chapters only require
good understanding of college algebra, complex numbers, analysis and basic combinatorics.
For Chapters 3, 4 and 6 the prerequisites include number theory, linear algebra and complex
analysis. The first part of the book presents key theoretical elements required for a good
understanding of the topic. The exposition moves on to to fundamental results and key
examples of recurrences and their properties. The geometry of linear recurrences in the
complex plane is presented in detail through numerous diagrams, which lead to often
unexpected connections to combinatorics, number theory, integer sequences, and random
number generation. The second part of the book presents a collection of 123 problems with
full solutions, illustrating the wide range of topics where recurrent sequences can be found.
This material is ideal for consolidating the theoretical knowledge and for preparing students
for Olympiads
Due 2020-11-04
1st ed. 2020, XV, 407 p. 67 illus., 65 illus. in color.
Hardcover
ISBN 978-3-030-51501-0
Product category : Undergraduate textbook
Series : Problem Books in Mathematics
Mathematics : Group Theory and Generalizations
The first book to describe the relation between profinite semigroups and symbolic dynamics
Provides new insights into both fields of profinite semigroups and symbolic dynamics
Defines all concepts in detail and provides numerous exercises
This book describes the relation between profinite semigroups and symbolic dynamics. Profinite
semigroups are topological semigroups which are compact and residually finite. In particular,
free profinite semigroups can be seen as the completion of free semigroups with respect to
the profinite metric. In this metric, two words are close if one needs a morphism on a large
finite monoid to distinguish them. The main focus is on a natural correspondence between
minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal Jclasses
(certain subsets of free profinite semigroups). This correspondence sheds light on
many aspects of both profinite semigroups and symbolic dynamics. For example, the return
words to a given word in a shift space can be related to the generators of the group of the
corresponding J-class. The book is aimed at researchers and graduate students in mathematics
or theoretical computer science.
Due 2020-11-14
1st ed. 2020, IX, 278 p. 67 illus., 4 illus. in color.
Softcover
ISBN 978-3-030-55214-5
Product category : Monograph
Series : Lecture Notes in Mathematics
Mathematics : Numerical Analysis
Introduces new exponentially convergent methods for solving
multidimensional PDE, for indefinite integration and solution of indefinite
convolution problems over finite or infinite intervals, for inverting Laplace
transforms, and for inversion of Fourier transforms
Presents new easy to apply and exponentially convergent methods of
interpolation, quadrature and Hilbert transforms, over all intervals, finite,
semi-infinite, infinite, or even arcs Includes a method of solution of WienerHopf problems
that works in all cases and enables circumvention of the
popular factorization procedure that seldom works in applications
Contains new methods of solving ODEs, PDEs, etc. problems over infinite regions as well a
This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc
methods in numerical analysis.The contributions, written independently from each other, show
the new developments in numerical analysis in connection with Sinc methods and
approximations of solutions for differential equations, boundary value problems, integral
equations, integrals, linear transforms, eigenvalue problems, polynomial approximations,
computations on polyhedra, and many applications. The approximation methods are
exponentially converging compared with standard methods and save resources in computation.
They are applicable in many fields of science including mathematics, physics, and engineering.
The ideas discussed serve as a starting point in many different directions in numerical analysis
research and applications which will lead to new and unprecedented results.This book will
appeal to a wide readership, from students to specialized experts.
Due 2021-01-10
1st ed. 2020, X, 420 p. 17 illus.
Hardcover
ISBN 978-3-030-49715-6
Product category : Contributed volume
Series : Trends in Mathematics
Mathematics : Operator Theory
Presents a wide range of new, topical and interesting problems in operator
theory and its applications
Provides an excellent overview of the latest research in operator theory
This volume features selected papers from The Fifteenth International Conference on Order
Analysis and Related Problems of Mathematical Modeling, which was held in Vladikavkaz,
Russia, on 15 - 20th July2019. Intended for mathematicians specializing in operator theory,
functional spaces, differential equations or mathematical modeling, the book provides
a state-ofthe-art account of various fascinating areas of operator theory,ranging fromvarious classes of
operators (positive operators, convolution operators, backward shift operators, singular and
fractional integral operators, partial differential operators) to important applications in
differential equations, inverse problems, approximation theory, metric theory of surfaces, the
Hubbard model, social stratification models, and viscid incompressible fluids.
Due 2020-12-28
1st ed. 2020, X, 230 p. 9 illus., 3 illus. in color.
Hardcover
ISBN 978-3-030-49762-0
Product category : Proceedings
Series : Trends in Mathematics
Mathematics : Global Analysis and Analysis on Manifolds
A Global Classification in the Quadratic Case
Presents novel, powerful tools for studying algebraic bifurcations in quadratic differential systems
Introduces an algebra software package that will allow readers to avoid
complicated calculations once they have understood the main concepts
Provides methods that are highly useful for studying several large families of
quadratic systems and for checking classifications made with classical tools,
as well as revealing some flaws in them
This book addresses the global study of finite and infinite singularities of planar polynomial
differential systems, with special emphasis on quadratic systems. While results covering the
degenerate cases of singularities of quadratic systems have been published elsewhere, the
proofs for the remaining harder cases were lengthier. This book covers all cases, with half of
the content focusing on the last non-degenerate ones. The book contains the complete
bifurcation diagram, in the 12-parameter space, of global geometrical configurations of
singularities of quadratic systems. The authorsf results provide - for the first time - global
information on all singularities of quadratic systems in invariant form and their bifurcations. In
addition, a link to a very helpful software package is included. With the help of this software,
the study of the algebraic bifurcations becomes much more efficient and less time-consuming.
Given its scope, the book will appeal to specialists on polynomial differential systems, pure and
applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph.
D. students, and postdoctoral fellows.
Due 2021-02-07
1st ed. 2020, VIII, 701 p. 57 illus.
Hardcover
ISBN 978-3-030-50569-1
Product category : Monograph