Format: Paperback / softback, 210 pages, height x width: 240x168 mm,
1 Illustrations, color; 1 Illustrations, black and white; X, 210 p. 2 illus., 1 illus. in color.,
Series: Oberwolfach Seminars 55
Pub. Date: 30-Jul-2025
ISBN-13: 9783031906787
This book is based on an Oberwolfach Seminar, and it intends to give an introduction and an overview to several directions of the recent research on stochastic geophysical fluid dynamics and to discuss different geophysical stochastic partial differential equations.
- Stochastic Fluid Mechanics and Boussinesq Hypothesis.- Scaling Limit
of 2D Euler to NavierStokes.- From Additive to Transport Noise in 3D
Navier-Stokes Equations.- On the Role of Lp (Lq)-Techniques in Regularization
by Noise of Reaction-Diffusion Equations.- Well-Posedness and Inviscid Limit
Results for Stochastic Second-Grade Fluid Equations with Transport Noise in
Bounded Domains.- The Stochastic Primitive Equations.- Stochastic Geometric
Fluid Dynamics.
Format: Hardback, 356 pages, height x width: 235x155 mm, XVI, 356 p., 1 Hardback
Series: Association for Women in Mathematics Series 37
Pub. Date: 19-Jun-2025
ISBN-13: 9783031878039
This volume features recent advances in data science ranging from algebraic geometry used for existence and uniqueness proofs of low rank approximations for tensor data, to category theory used for natural language processing applications, to approximation and optimization frameworks developed for convergence and robustness guarantees for deep neural networks. It provides ideas, methods, and tools developed in inherently interdisciplinary research problems requiring mathematics, computer science and data domain expertise. It also presents original results tackling real-world problems with immediate applications in industry and government.
Contributions are based on the third Women in Data Science and Mathematics (WiSDM) Research collaboration Workshop that took place between August 7 and August 11, 2023 at the Institute for Pure & Applied Mathematics (IPAM) in Los Angeles, California, US. The submissions from the workshop and related groups constitute a valuable source for readers who are interested in mathematically-founded approaches to modeling data for exploration, understanding and prediction.
Chapter 1: Randomized Iterative Methods for Tensor Regression Under the
t-product.
Chapter 2: Matrix exponentials: Lie-Trotter-Suzuki fractal
decomposition, Gauss Runge-Kutta polynomial formulation, and compressible
features.
Chapter 3: An exploration of graph distances, graph curvature, and
applications to network analysis.
Chapter 4: Time-Varying Graph Signal
Recovery Using High-Order Smoothness and Adaptive Low-rankness.
Chapter 5:
Graph-Directed Topic Models of Text Documents.
Chapter 6: Linear independent
component analysis in Wasserstein space.
Chapter 7: Faster Hodgerank
Approximation Algorithm for Statistical Ranking and User Recommendation
Problems.
Chapter 8: A Comparison Study of Graph Laplacian Computation.-
Chapter 9: Supervised Dimension Reduction via Local Gradient Elongation.-
Chapter 10: Reducing NLP Model Embeddings for Deployment in Embedded
Systems.
Chapter 11: Automated extraction of roadside slope from aerial
LiDAR data in rural North Carolina.
Chapter 12: A non-parametric optimal
design algorithm for population pharmacokinetics.
Chapter 13: Unrolling Deep
Learning End-to-End Method for Phase Retrieval.
Chapter 14: Performance
Analysis of MFCC and wav2vec on Stuttering Data.
Chapter 15: Active Learning
for Reducing Gender Gaps in Undergraduate Computing and Data Science.-
Chapter 16: Quantifying and Documenting Gender-Based Inequalities in the
Mathematical Sciences in the United States.
Format: Paperback / softback, 190 pages, height x width: 240x168 mm, 10 Illustrations,
color; 63 Illustrations, black and white; X, 190 p. 73 illus., 10 illus. in color.,
Series: Advanced Courses in Mathematics - CRM Barcelona
Pub. Date: 03-Jul-2025
ISBN-13: 9783031863882
This book presents recent advances in topics related to Poisson geometry originating from lectures given at the gPoisson Schoolh held in 2022 at the CRM in Barcelona. The purpose is to give both an introduction to this active field of research as well as highlight new trends in related topics. The texts cover both classical results, known to experts in the field, as well as recent and previously unpublished mathematical results.
Graduate students and early-stage researchers with basic knowledge in differential and symplectic geometry, together with established researchers that are keen to dive into this rapidly growing field of research, will find this book a useful resource.
Part I: Introduction to Poisson Geometry.-
1. A brief Introduction to
Poisson Geometry.- Part II: Wonderful Varieties.-
2. Wonderful Varieties with
a View Towards Poisson Geometry.- Part III: An Invitation to Singular
Foliations.-
3. What is a singular foliation?.-
4. Canonical geometric and
algebraic structures hidden behind a singular foliation.-
5. State of the Art
and open questions.
Format: Paperback / softback, 239 pages, height x width: 235x155 mm, 17 Illustrations, color;
43 Illustrations, black and white; XVII, 239 p. 60 illus., 17 illus. in color., 1 Paperback / softback
Series: Universitext
Pub. Date: 12-Jul-2025
ISBN-13: 9783031910104
This graduate textbook provides a natural and structured introduction to Continuum Theory, guiding readers from fundamental concepts to advanced topics. It covers classical results such as locally connected continua, indecomposable continua, arcs, circles, finite graphs, dendroids, and the relationship between the Cantor set and continua. The second half explores the theory of hyperspaces, presenting various models, their properties, and key theorems, while also highlighting elegant and lesser-known mathematical results.
Designed for readers with an understanding of basic topology, this book serves as a valuable resource for PhD students and researchers in mathematics. It offers a rigorous and thorough approach, with detailed proofs that clarify complex argumentsespecially regarding the intricate properties of the pseudo-arc. A wealth of exercises helps reinforce understanding and develop problem-solving skills.
This book stands out for its depth and breadth, covering a range of topics. It provides a comprehensive study of hyperspace models, the homogeneity of the Hilbert cube, and the pseudo-arc, offering one of the few accessible and complete proofs of its unique properties. With its structured progression and careful exposition, this book is a valuable reference for anyone interested in continuum theory.
Chapter 1. Introduction.
Chapter 2. Locally Connected Continua.-
Chapter 3. CuttingWires and Bumping Boundaries.
Chapter 4. Indecomposable Continua.
Chapter 5. Characterizing Arcs and Circles.
Chapter 6. Finite Graphs.
Chapter 7. Dendroids.
Chapter 8. The Cantor Set.
Chapter 9. Hyperspaces of Continua.
Chapter 10. Models of Hyperspaces.
Chapter 11. Irreducible Continua.
Chapter 12. Unicoherence.
Chapter 13. The Fixed Point Property.
Chapter 14. Inverse Limits.
Chapter 15. Homogeneity of the Hilbert Cube.
Chapter 16. Absolute Retracts.
Chapter 17. Stronger Properties of the Pseudo-Arc.
Format: Hardback, 266 pages, height x width: 235x155 mm, 2 Illustrations, color;
2 Illustrations, black and white; XVII, 266 p. 4 illus., 2 illus. in color., 1 Hardback
Pub. Date: 02-May-2025
ISBN-13: 9789819647255
This book presents a wide range of topics to address the needs of several groups of users of rapidly growing methods of generalized linear models. Since the introduction of the idea of generalized linear models (GLM) in early seventies, during the past four decades the modelling of statistical data have experienced a major transformation from linear models based on normality assumption to a more flexible unified approach of generalized linear models. The number of readers and users of generalized linear models have increased manifold. In addition, the use of generalized linear models has expanded in many new fields of applications where statistical models are being employed at an increasing rate. It is important to note here that the learners and users of GLM have a widely varied background in different disciplines. Considering these pressing needs, this book focuses on: (i) upper undergraduate and graduate level students in need of a thorough understanding about the basic concepts of generalized linear models along with appropriate applications; (ii) researchers and users in need of advanced generalized linear models for analysing bivariate or multivariate data stemming from longitudinal or repeated measures data; and (iii) new challenges to analyse big data where the traditional techniques fail to provide any reasonable modelling strategy. In other words, this book starts with a thorough background of the generalized linear models for the new learners, then provides multivariate extensions to advanced level techniques for researchers and users in various disciplines, and finally some innovative modelling strategies are introduced using generalized linear models in the emerging field of big data analytics. It provides materials for new learners, for users/researchers who are in need of more advanced techniques and also strategies for employing linear models in big data analytics. Hence, techniques of generalized linear models will be presented in the proposed book covering the needs of new learners, users of advanced techniques, researchers in need of statistical modelling of any data type and users of big data analytics wanting to increase predictive accuracy of classification and regression tree techniques
Introduction.- Exponential Family of Distributions.- Univariate GLM.-
Estimation and Tests for Univariate GLM.- Quasi Likelihood.- Multivariate
Data and GLM: Generalized Estimating Equations.- Generalized Linear Mixed
Models.- Extension of GLM for Bivariate Data.- Extension of GLM for
Multivariate Data: Alternative Models.- Generalized Quasi Likelihood
Methods.- Bayesian Approach for GLM.- GLM for Big Data Analytics.
Format: Hardback, 295 pages, height x width: 235x155 mm, XXIII, 295 p., 1 Hardback
Series: Infosys Science Foundation Series
Pub. Date: 18-Jul-2025
ISBN-13: 9789819655410
This book delves into the topics of fixed-point theory as applied to block operator matrices within the context of Banach algebras featuring multi-valued inputs. Its scope extends to a broad range of equations, encompassing nonlinear biological models as well as two-dimensional boundary value problems associated with burgeoning cell populations and functional systems of differential and integral inclusions. The book systematically introduces the principles of topological fixed-point theory, offering insights into various classes of both single-valued and multi-valued maps. The overarching goal is to disseminate key techniques and outcomes derived from fixed-point theory, with a specific emphasis on its application to both single-valued and multi-valued mappings within the framework of Banach algebras.
Topological Structures.- Fixed-Point Theory in Suitable Banach
Algebras.- Fixed-Point Theory for Block Operator Matrices.- Nonlinear
One-Dimensional Boundary-Value Problems.- Two-Dimensional Boundary-Value
Problems.- Existence Theory of Critical-Type of Fixed Point.- Two-Dimensional
Value Problems for Differential Inclusion.