Published ahead of schedule, this book is part of the 2026 MEMS collection and may become open access under our Subscribe to Open programme in 2026.
In the Lubin–Tate setting we study pairings for analytic (φ L ,Γ L )-modules and prove an abstract reciprocity law which then implies a relation between the analogue of Perrin-Riou's big exponential map as developed by Berger and Fourquaux and a p-adic regulator map whose construction relies on the theory of Kisin–Ren modules generalising the concept of Wach modules to the Lubin–Tate situation.
1 Introduction Download pp. 1–7
2 Notation pp. 9–11
3 Wach modules à la Kisin–Ren pp. 13–37
4 (φ L ,Γ )-modules over the Robba ring pp. 39–126
5 Application pp. 127–162
A Cup products and local Tate duality pp. 163–171
B Iwasawa cohomology and descent pp. 173–176
References pp. 177–181
Index pp. 183–186
Published ahead of schedule, this book is part of the 2026 MEMS collection and may become open access under our Subscribe to Open programme in 2026.
The purpose of this memoir is to investigate the well-posedness of several linear and nonlinear equations with a parabolic forward-backward structure, and to highlight the similarities and differences between them. The epitomal linear example will be the stationary Kolmogorov equation y∂ u−∂ yy
u=f in a rectangle. We first prove that this equation admits a finite number of singular solutions, of which we provide an explicit construction. Hence, the solutions to the Kolmogorov equation associated with a smooth source term are regular if and only if f satisfies a finite number of orthogonality conditions.
We then extend this theory to a Vlasov–Poisson–Fokker–Planck system, and to two quasilinear equations: the Burgers-type equation u∂ x u−∂yy
u=f in the vicinity of the linear shear flow, and the Prandtl system in the vicinity of a recirculating solution, close to the line where the horizontal velocity changes sign. We therefore revisit part of a recent work by Iyer and Masmoudi. For the two latter quasilinear equations, we introduce a geometric change of variables which simplifies the analysis. In these new variables, the linear differential operator is very close to the Kolmogorov operator y∂
x −∂ yy
. Stepping on the linear theory, we prove existence and uniqueness of regular solutions for data within a manifold of finite codimension, corresponding to some nonlinear orthogonality conditions.
Frontmatter
Download pp. i–iv
Abstract
Download pp. v–vi
Contents
Download pp. vii–viii
1 Introduction
Download pp. 1–22
2 The case of the linear shear flow
pp. 23–47
3 A first nonlinear example in kinetic theory
pp. 49–62
4 A viscous Burgers equation
pp. 63–74
5 The Prandtl system in the recirculation zone
pp. 75–103
6 Interpolation estimate for the linear shear flow problem
pp. 105–116
A Uniqueness of weak solutions for linear problems
pp. 117–118
B Proofs of functional analysis results
pp. 119–128
C Unconditional regularity away from lateral boundaries
pp. 129–131
List of notations
pp. 133–135
References
pp. 137–140
Hardcover
ISBN: 9780262049818
Pub date: December 2, 2025
544 pp., 7 x 9 in, 220 b&w illus.
An introductory textbook for undergraduate or beginning graduate students that integrates probability and statistics with their applications in machine learning.
Most curricula have students take an undergraduate course on probability and statistics before turning to machine learning. In this innovative textbook, Ethem Alpaydın offers an alternative tack by integrating these subjects for a first course on learning from data. Alpaydın accessibly connects machine learning to its roots in probability and statistics, starting with the basics of random experiments and probabilities and eventually moving to complex topics such as artificial neural networks. With a practical emphasis and learn-by-doing approach, this unique text offers comprehensive coverage of the elements fundamental to an empirical understanding of machine learning in a data science context.
Consolidates foundational knowledge and key techniques needed for modern data science
Covers mathematical fundamentals of probability and statistics and ML basics
Emphasizes hands-on learning
Suits undergraduates as well as self-learners with basic programming experience
Includes slides, solutions, and code
Statistical Modelling and Inference Using Likelihood
Oxford Statistical Science Series
Comprehensive coverage of likelihood-based thinking and methodology
Written in an accessible informal style, avoiding heavy mathematical style
Makes complex ideas accessible and easy to understand
Most chapters have been heavily revised, particularly those related to (i) the general ideas of extended likelihood and epistemic confidence and (ii) hierarchical generalized linear models (HGLM)
This new, updated second edition of In All Likelihood explores the central role of likelihood in a wide spectrum of statistical problems, ranging from simple comparisons-such as evaluating accident rates between two groups-to sophisticated analyses involving generalized linear models and semiparametric methods. Rather than treating likelihood merely as a tool for point estimation, the book highlights its broader value as a foundational framework for constructing, understanding and computational implementation of statistical models. It emphasizes how likelihood perspectives inform model development, assessment, and inference in a cohesive and intuitive way.
While grounded in essential mathematical theory, the book adopts an informal and accessible approach, using heuristic reasoning and illustrative, realistic examples to convey key ideas. It avoids overly contrived problems that yield to theoretically clean and closed-form solutions, instead embracing more realistic and complex real-world data analysis made tractable by modern computing resources. This perspective helps focus attention on the statistical reasoning behind model choice and interpretation.
The text also integrates a wide range of modern topics that extend classical likelihood theory, including generalized and hierarchical generalized linear models, nonparametric smoothing techniques, robust methods, the EM algorithm, and empirical likelihood. Suitable for students, researchers, and practitioners, this book provides both foundational insights and contemporary perspectives on likelihood-based statistical modelling.
1:Introduction
2:Elements of likelihood in inference
3:More properties of likelihood
4:Basic models and simple applications
5:Frequentist properties
6:Modelling relationships: regression models
7:Evidence and the likelihood principle*
8:Score function and Fisher information
9:Large-sample results
10:Dealing with nuisance parameters
11:Complex data structures
12:EM Algorithm
13:Robustness of likelihood specification
14:Estimating equations and quasi-likelihood
15:Empirical likelihood
16:Likelihood of random parameters
17:Random and mixed effects models
18:Nonparametric smoothing
Bibliography
Index
Paperback
Format: Paperback / softback, 652 pages, height x width: 235x155 mm,
68 Illustrations, color; 40 Illustrations, black and white
Pub. Date: 01-Sep-2025
ISBN-13: 9789819734368
This book aims to provide with some approaches for lessening the unknowns of the FE methods of unsteady PDEs. It provides a very detailed theoretical foundation of finite element (FE) and mixed finite element (MFE) methods in the first 2 chapters, and then Chapter 3 provides the FE and MFE methods to solve unsteady partial differential equations (PDEs). In the following 2 chapters, the principle and application of two proper orthogonal decomposition (POD) methods are introduced in detail.
This book can be used as both the introduction of FE method and the gateway to the FE frontier. For readers who want to learn the FE and MFE methods for solving various steady and unsteady PDEs, they will find the first 3 chapters very helpful. While those who care about engineering applications may jump to the last 2 chapters that introduce the construction of dimension reduction models and their applications to practical process calculations. This part could help them to improve the calculation efficiency and save CPU runtime so as to do wonders for their engineering calculations.
Preface.- Basic Theory of Standard Finite Element Method.- Basic Theory
of Mixed Finite Element Method.- Mixed Finite Element Methods for the
Unsteady Partial Differential Equations.- The Reduced Dimension Methods of
Finite Element Subspaces for Unsteady Partial Differential Equations.- The
Reduced Dimension of Finite Element Solution Coefficient Vectors for Unsteady
Partial Differential Equations.- Bibliography.- Index.
Format: Hardback, 249 pages, height x width: 235x155 mm, 73 Illustrations, color; 6 Illustrations, black and white
Pub. Date: 14-Oct-2025
ISBN-13: 9783032001092
The original contributions on Bayesian econometrics gathered in this book pay tribute to Sune Karlsson, celebrating his significant work in time series econometrics and its applications in macroeconomics and finance. The volume consists of both methodological and empirical studies by leading experts in the field, with particular attention paid to Bayesian vector autoregressive (VAR) models and forecasting. It addresses forecasting with Bayesian VARs as a research field, mixed-frequency and high-dimensional Bayesian VARs, various forms of Bayesian VARs with stochastic volatility, forecast combination, analysis of time-varying parameter models in the frequency domain, and portfolio analysis in a Bayesian framework. Presenting cutting-edge research and providing valuable insights into the field of Bayesian econometrics, the book will appeal to researchers, practitioners in the banking sector, and government authorities.
- Forecasting with Bayesian Vector Autoregressions Revisited.- Large
Bayesian Tensor VARs with Stochastic Volatility.- Measuring Sub-Regional
Economic Activity: Missing Frequencies and Missing Data.- VAR Models with Fat
Tails and Dynamic Asymmetry.- International Transmission of Macroeconomic
Uncertainty in Small.- Modeling Local Predictive Ability using
Power-Transformed Gaussian Processes.- Spectral Domain Likelihoods for
Bayesian Inference in Time-Varying Parameter Models.- Bayesian Regularization
of the Tangency Portfolio.- Predictive Decision Synthesis for Portfolios:
Betting on Better Models.
Format: Hardback, 261 pages, height x width: 235x155 mm, 35 Illustrations, color; 43 Illustrations, black and white
Pub. Date: 29-Dec-2025
The scientific exchange between mathematicians, statisticians and econometricians working in actuarial sciences and finance is improving the research on these topics and producing numerous meaningful scientific results. This volume includes a selection of papers presented at the Workshop New perspectives in Mathematical and Statistical Methods for Actuarial Sciences and Finance.
The workshop was a two-day study activity aimed at presenting new ideas and innovative lines of research in mathematical and statistical methods for insurance and finance, both from a theoretical and applied point of view. It was organized by the Department of Economics and Statistics of the University of Salerno and was held from 27 to 28 June 2025 in Salerno (Italy).
This book covers a wide variety of subjects, among others: Social well-being, Artificial intelligence and Machine learning in Insurance and Finance, Silver Economy and Insurance, Climate-related Risks and Insurance, Insurtech and Fintech, Catastrophe Risks, Cyber Risk.
This volume is a valuable resource for academics, PhD students, practitioners, professional and researchers. Moreover, it is also of interest to other readers with quantitative background knowledge.
Towards Fairer Sanction Systems: Income-Based Models with Aggregation
Functions.- Multidimensional inequality and measurement of Social
Well-Being.- A neural network model approach to longevity risk management.-
Climate-related Extensions of the Lee-Carter Model.- Quantification of
Operational Flexibility in Wastewater Treatment Projects.- Roughness in VIX
Index and in Realized Volatility: Rolling Window Estimation by Randomized
Kolmogorov-Smirnov Distribution.- A Comparison of Data-driven Synthetic
Performance Indicators for Default Prediction.- Rethinking the Indexation of
Retirement Age: Cohort vs. Period Life Expectancy.- Temperature forecast for
weather derivatives with Neural Network.- Modeling Health and Disability
Trajectories in Later Life: A Multi-State Approach Using HRS Data.-
Backtesting Expected Shortfall for Bitcoin: A Joint Combined LSTM-Based
Approach.- Reverse mortgages: Exploring the impact of risk factors by
source.- Understanding and attitudes toward Reverse Mortgage in Italy:
cognitive dissonance and future concerns.- Climate Litigation Risk: Comparing
Linear and Non Linear Losses of Insurances.- Option Hedging Through
Reinforcement Learning.- Parameter Stability in Yield Curve Fitting.- Deep
Learning for Tabular Data: Application to Credit Risk Modeling.- Modeling
economic recovery via diffusion processes with multisigmoidal logistic mean
subject to random catastrophes.- Scaling the Tails: Intraday Quantiles for
forecasting Value-at-Risk and Expected Shortfall.- High-Profile GDPR Fines
and their financial impact on listed firms: an exploratory analysis.-
Delay-Adjusted Modeling of Cybersecurity Breaches Using INLA: Evidence from
State Attorney General Data.- Addressing Long-Term Care Risk through
Pension-Linked Insurance: A Stochastic Approach Using Severance Pay Scheme.
Format: Hardback, 207 pages, height x width: 235x155 mm, 2 Illustrations, color; 9 Illustrations, black and white
Series: Studies in Universal Logic
Pub. Date: 08-Nov-2025
ISBN-13: 9783032089441
This book is a compilation of the author's most important papers about the contributions of Bertrand Russell, Kurt Gödel, and Alfred Tarski to the philosophy of logic and mathematics. It also includes a personal reflection of the author's approach to his field of research. The papers in this book have been assembled to convey key elements of the author's research on the published and unpublished materials of the three greatest logicians of the twentieth century.
Francisco Rodrķguez-Consuegra is well known in the field of the History and Philosophy of Logic and Mathematics, mostly due to his former books: The Mathematical Philosophy of Bertrand Russell (Birkhäuser, 1991) and Kurt Gödel, Unpublished Philosophical Essays (Birkhäuser, 1995). Throughout his career, the author visited and worked in depth in the Russell Archives (Hamilton, Canada), the Gödel Nachlass (Princeton, USA), and the Tarski Papers (Berkeley, USA).
This book is of interest to students, professors, and researchers in the history of logic and mathematics, philosophy of logic and mathematics, and general history and philosophy of science.
Russell's theory of types, 1901-1910.- A global viewpoint on Russell's
philosophy.- Gödel's first works, 1929-1936: mathematics without philosophy.-
Russell, Gödel and logicism.- Gödel's last works, 1938-1974: the emerging
philosophy.- Gödel's unpublished manuscripts, 1930-1970: the official
edition.- Definitions and logical consequence in the Peano School.- A droll
mix of profundity and otherworldliness.- Philosophy in Hao Wang's
conversations with Gödel.- Propositional ontology and logical atomism.-
Tarski's intuitive notion of set.- From Logic to Philosophy.
Format: Paperback / softback, 88 pages, height x width: 235x155 mm, XI, 88 p.
Series: SpringerBriefs in Mathematics
Pub. Date: 04-Oct-2025
ISBN-13: 9783032019301
This book investigates homogenisation problems for divergence form equations with rapidly sign-changing coefficients. Focusing on problems with piecewise constant, scalar coefficients in a (d-dimensional) crosswalk type shape, we will provide a limit procedure in order to understand potentially ill-posed and non-coercive settings.
Depending on the integral mean of the coefficient and its inverse, the limits can either satisfy the usual homogenisation formula for stratified media, be entirely degenerate or be a non-local differential operator of 4th order. In order to mark the drastic change of nature, we introduce the inner spectrum for conductivities. We show that even though 0 is contained in the inner spectrum for all strictly positive periods, the limit inner spectrum can be empty. Furthermore, even though the spectrum was confined in a bounded set uniformly for all strictly positive periods and not containing 0, the limit inner spectrum might have 0 as an essential spectral point and accumulate at or even be the whole of C. This is in stark contrast to the classical situation, where it is possible to derive upper and lower bounds in terms of the values assumed by the coefficients in the pre-asymptotics.
Along the way, we also develop a theory for SturmLiouville type operators with indefinite weights, reduce the question on solvability of the associated SturmLiouville operator to understanding zeros of a certain explicit polynomial and show that generic real perturbations of piecewise constant coefficients lead to continuously invertible SturmLiouville expressions.
Chapter
1. Introduction.
Chapter
2. The main theorems.
Chapter
3. Abstract divergence-form operators.
Chapter 4. The one-dimensional
problem well-posedness.
Chapter
5. SturmLiouville problems with
indefinite coeffcients.
Chapter
6. The higher-dimensional problem
preliminaries.
Chapter
7. The higher dimensional problem well-posedness.-
Chapter
8. The inner spectrum in d dimensions.
Chapter
9. Classical
G-convergence.
Chapter 10. Holomorphic G-convergence.
Chapter 11. The
one-dimensional problem homogenisation.
Chapter
12. The higher-dimensional
problem homogenisation.
Chapter
13. Proofs.
Chapter
14. Conclusion.
Format: Hardback, 849 pages, height x width: 235x155 mm, 87 Illustrations, black and white
Series: Texts in Applied Mathematics
Pub. Date: 24-Dec-2025
This is the second volume of a three-volume treatise which presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed and mathematically rigorous way. The work combines features of a detailed introductory textbook with that of a reference source.
Volume II concentrates on problems of control, measurement and feedback control for time-varying and time-invariant linear systems. Special features are:
• a comprehensive treatment of controllability and observability,
• an analysis of reachable sets under bounded controls with applications to the time-optimal control problem,
• a detailed construction of canonical forms for controllable systems under similarity transformations, including an application of these forms to the topological analysis of system spaces,
• a new module theoretic approach to Rosenbrock systems in time domain,
• an introduction to balancing and model reduction by balanced truncation,
• an introduction to a general feedback control theory of input-output systems,
• a detailed treatment of stabilization and observation problems for time-invariant linear systems,
• a self-contained proof of Rosenbrock’s theorem by state space methods.
Throughout the book there are many examples, figures and exercises illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions. The book should be accessible to mathematics students after two years of study and also to engineering students with a good mathematical background. It will be of value for researchers in systems theory as well as for mathematicians and engineers who wish to learn about the mathematical foundations of the above topics.
Controllability and Observability.- Realization and Model Reduction.- Feedback.- References.- Glossary.- Index.