Format: Paperback / softback, 237 pages, height x width: 235x155 mm, 74 Illustrations, black and white; XII, 237 p. 74 illus., 1 Paperback / softback
Series: Springer Undergraduate Mathematics Series
Pub. Date: 05-Jul-2024
ISBN-13: 9783662693643
This textbook provides an introduction to group theory starting from the basics, relying on geometry to elucidate its various aspects.
Groups naturally manifest as symmetries of geometric shapes, such as reflections and rotations. The book adopts this perspective to provide a straightforward, descriptive explanation, supported by examples and exercises in GAP, an open-source computer algebra system. It covers all of the key concepts of group theory, including homomorphisms, group operations, presentations, products of groups, and finite, abelian, and solvable groups. The topics include cyclic and symmetric groups, dihedral, orthogonal, and hyperbolic groups, as well as the significant notion of Cayley graphs.
Self-contained and requiring little beyond high school mathematics, this book is aimed at undergraduate courses and features numerous exercises. It will also appeal to anyone interested in the geometric approach to group theory.
1 Introduction to Euclidean Geometry.- 2 Introduction to Groups.- 3
Subgroups and Homomorphisms.- 4 Group Operations.- 5 Group Presentations.- 6
Products of Groups.- 7 Finite Groups.- 8 Abelian and Solvable Groups.- 9 The
Hyperbolic Plane.- 10 Hyperbolic Groups.
Format: Hardback, 152 pages, height x width: 235x155 mm, 16 Illustrations, black and white; XXX, 170 p. 80 illus., 30 illus. in color.
Series: Springer INdAM Series 59
Pub. Date: 05-Sep-2024
ISBN-13: 9789819738854
The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds. Recent developments have demonstrated important cases of the Lefschetz property beyond the original geometric settings, such as Coxeter groups or matroids. Furthermore, there are connections to other branches of mathematics, for example, commutative algebra, algebraic topology, and combinatorics. Important results in this area have been obtained by finding unexpected connections between apparently different topics.
A conference in Cortona, Italy in September 2022 brought together researchers discussing recent developments and working on new problems related to the Lefschetz properties. The book will feature surveys on several aspects of the theory as well as articles on new results and open problems.
Survey articles about specific topics.- Jordan types and relation with WLP/SLP.- Unexpected objects, connections with Lefschetz properties and special sets of points.- Combinatorial aspects.- Working group on Perazzo hypersurfaces Hilbert functions, WLP, Jordan types.
Format: Hardback, 181 pages, height x width: 235x155 mm, 45 Illustrations, color; 1 Illustrations, black and white; Approx. 200 p.,
Pub. Date: 12-Sep-2024
ISBN-13: 9783031617119
This book introduces in a constructive manner a general framework for regression and fitting methods for many applications and tasks involving data on manifolds. The methodology has important and varied applications in machine learning, medicine, robotics, biology, computer vision, human biometrics, nanomanufacturing, signal processing, and image analysis, etc.
The first chapter gives motivation examples, a wide range of applications, raised challenges, raised challenges, and some concerns. The second chapter gives a comprehensive exploration and step-by-step illustrations for Euclidean cases. Another dedicated chapter covers the geometric tools needed for each manifold and provides expressions and key notions for any application for manifold-valued data.
All loss functions and optimization methods are given as algorithms and can be easily implemented. In particular, many popular manifolds are considered with derived and specific formulations. The same philosophy is used in all chapters and all novelties are illustrated with intuitive examples. Additionally, each chapter includes simulations and experiments on real-world problems for understanding and potential extensions for a wide range of applications.
Introduction.- Spline Interpolation and Fitting in R??.- Spline
Interpolation on the Sphere S??.- Spline Interpolation on the Special
Orthogonal Group ????(??).- Spline Interpolation on
Stiefel and Grassmann manifolds.- Spline Interpolation on the Manifold of
Probability Measures.- Spline Interpolation on the Manifold of Probability
Density Functions.- Spline Interpolation on Shape Space.- Spline
Interpolation on Other Riemannian Manifolds.
Format: Hardback, 560 pages, height x width: 235x155 mm, 65 Illustrations, color; 19 Illustrations,
black and white; X, 560 p. 82 illus., 65 illus. in color. With online files/update.,
Pub. Date: 19-Sep-2024
ISBN-13: 9783031618529
This volume presents a unique collection of original research contributions by leading experts in several modern fields of econometrics and statistics, including high-dimensional, nonparametric and robust statistics, time series analysis and factor models. Published in honour of Marc Hallin on the occasion of his 75th birthday, it puts emphasis on the fundamental and applied topics he has significantly contributed to. The volume starts with an annotated bibliography that mainly catalogues his contributions to distribution-free rank-based and quantile-oriented inference and to time series analysis. The main part of the book collects 29 authoritative contributions by some of Marc Hallins main collaborators, organized into six parts: rank- and depth-based methods, asymptotic statistics, quantile regression, econometrics, statistical modelling and related topics, and high-dimensional and non-Euclidean data.
- Marc Hallin A commented bibliography (from 1972 to 2023).- Part 1:
Rank- and depth-based methods.- Daniel Hlubinka, ?rka Hudecov?: One-sample
location tests based on center-outward signs and ranks.- Jyrki Mottonen,
Klaus Nordhausen, Hannu Oja, Una Radojicic: The asymptotic properties of the
one-sample spatial rank methods.- Gaspard Bernard, Thomas Verdebout: Power
enhancement for testing the equality of shape matrices eigenvalues under
ellipticity.- Germain Van Bever, Ga?tan Louvet: The influence function of
scatter halfspace depth.- Ramon van den Akker, Bas J.M. Werker, Bo Zhou:
Hybrid rank-based panel unit root tests.- Jean-Jacques Droesbeke, Catherine
Vermandele: About the relationship between mean and median.- Part 2:
Asymptotic statistics.- Christophe Ley, Andreas Anastasiou: How to build
optimal tests for normality under possibly singular Fisher information?.-
Jean-Marie Dufour, Masaya Takano: Generalized C(alpha) tests with nonstandard
convergence rates.- Stephane Lhaut, Johan Segers: An asymptotic expansion of
the empirical angular measure for bivariate extremal dependence.- Paul
Deheuvels: Uniform in bandwidth nonparametric kernel estimators of lifetime
functionals under random censorship.- Part 3: Quantile regression.- Jana
Jureckova: The process induced by slope component of alpha-regression
quantile.- Miroslav iman: Testing axial symmetry by means of directional
quantile regression coefficients.- Manon Felix, Davide La Vecchia, Hang Liu,
Yiming Ma: Some novel aspects of quantile regression: local stationarity,
random forests and optimal transportation.- Richard K. Crump, Miro Everaert,
Domenico Giannone, C. Sean Hundtofte: Changing risk-return profiles.- Part 4:
Econometrics.- Marie Hukov?, Charl Pretorius: Detection of changes in panel
data models with stationary regressors.- Mario Forni, Marco Lippi:
Approximating singular by means of non-singular structural VARs.- Pilar
Poncela, Esther Ruiz: Common factors and common shocks: A tale of three
(close) signal extraction procedures.- Pedro Galeano, Daniel Pe?a: Detecting
outliers in high dimensional time series by dynamic factor models.- Alexei
Onatski: The Hallin-Liska criterion through the lens of the random matrix
theory.- Alice Brogniaux, Catherine Dehon, Philippe Emplit, Claudia Toma:
Gender bias in closed-ended questions with negative points.- Part 5:
Statistical Modelling and related topics.- Guy Melard: Time-dependent time
series models: comments on Marc Hallin's early contributions and a pragmatic
view on estimation.- Rong Peng, Zudi Lu, Fangsheng Ge: On a location-wide
semiparametric analysis of spatio-temporal dynamics of the COVID-19 daily new
cases in the UK.- F. Thomas Bruss: Models for studying interactions between
human populations and related problems of optimal transport.- Christine De
Mol: Multiplicative algorithms for density combination and deconvolution.-
Bruno Ebner, Yvik Swan: Independent additive weighted bias distributions and
associated goodness-of-fit tests.- Part 6: High-dimensional and Non-Euclidean
data.- Jianqing Fan, Zheng Tracy Ke, Koshiki Bose: Higher moment estimation
for elliptically-distributed Data: Is it necessary to use a sledgehammer to
crack an egg?.- Holger Dette, Jiajun Tang: Pivotal inference for
function-on-function linear regression via self-normalization.- Adeline
Fermanian, Jiawei Chang, Terry Lyons, Gerard Biau: The insertion method to
invert the signature of a path.- Yan Liu, Lan U, Masanobu Taniguchi:
Semiparametric empirical likelihood for circular distributions.
Format: Hardback, 337 pages, height x width: 235x155 mm, 115 Illustrations, color; 13 Illustrations, black and white; XIII, 337 p. 128 illus., 115 illus. in color., 1 Hardback
Series: Advanced Technologies and Societal Change
Pub. Date: 21-Aug-2024
ISBN-13: 9789819733118
The book explores the convergence of healthcare and cutting-edge technology, making it a captivating subject for readers interested in future research. Smart healthcare with machine learning techniques offers a transformative paradigm that utilizes the power of new technology, data analytics, and interconnected devices to enhance the quality, efficiency, and accessibility of healthcare services. This involves leveraging Internet of Things (IoT) devices, wearable technology, and machine learning algorithms to monitor patient health, predict medical conditions, and offer personalized treatment recommendations. This innovative combination not only enhances diagnostics and treatment but also addresses the research challenges of healthcare access and delivery in an increasingly connected world. By exploring the synergy between smart healthcare and machine learning, the book helps to understand how these technologies can collaborate to revolutionize patient care and healthcare delivery. This book is an outcome with applications of future technologies to overcome the toughest humanitarian challenges from an engineering approach.
.- Predictive Modeling for Patient Outcomes in Smart Healthcare Systems.
.- Machine Learning for Personalized Treatment Recommendations.
.- Smart Health Monitoring: Data Collection and Analysis with Machine Learning.
.- Enhancing Medical Imaging through Dimension Reduction Learning.
.- Natural Language Processing for Health Record Management.
.- Machine Learning-driven Drug Discovery and Development.
Format: Hardback, 460 pages, height x width: 235x155 mm, XIX, 460 p., 1 Hardback
Pub. Date: 26-Aug-2024
ISBN-13: 9783031600562
The monograph present ideas and methods, developed by the author, to solve the problem of existence of Bohr/Levitan almost periodic (respectively, almost recurrent in the sense of Bebutov, almost authomorphic, Poisson stable) solutions and global attractors of monotone nonautonomous differential/difference equations. Namely, the text provides answers to the following problems:
1. Problem of existence of at least one Bohr/Levitan almost periodic solution for cooperative almost periodic differential/difference equations;
2.Problem of existence of at least one Bohr/Levitan almost periodic solution for uniformly stable and dissipative monotone differential equations (I. U. Bronshteins conjecture, 1975);
3.Problem of description of the structure of the global attractor for monotone nonautonomous dynamical systems;
4.The structure of the invariant/minimal sets and global attractors for one-dimensional monotone nonautonomous dynamical systems;
5.Asymptotic behavior of monotone nonautonomous dynamical systems with a rst integral (Poisson stable motions, convergence, asymptotically Poisson stable motions and structure of the Levinson center (compact global attractor) of dissipative systems);
6. Existence and convergence to Poisson stable motions of monotone sub-linear nonautonomous dynamical systems.
This book will be interesting to the mathematical community working in the field of nonautonomous dynamical systems and their applications (population dynamics, oscillation theory, ecology, epidemiology, economics, biochemistry etc). The book should be accessible to graduate and PhD students who took courses in real analysis (including the elements of functional analysis, general topology) and with general background in dynamical systems and qualitative theory of differential/difference equations.
Poisson Stable Motions of Dynamical Systems .- Compact Global Attractors .- V-Monotone Nonautonomous Dynamical Systems .- Poisson Stable Motions and Global Attractors of Monotone Nonautonomous Dynamical Systems.