Format: Hardback, 289 pages, height x width: 235x155 mm, XI, 289 p
Series: Progress in Mathematics 353
Pub. Date: 06-Apr-2024
ISBN-13: 9783031565038
Cet ouvrage propose une contribution aux fondements de la theorie des espaces de Berkovich globaux. Cette approche recente ? la geometrie analytique, qui m?le les theories classiques des espaces analytiques complexes et p-adiques, fournit un cadre geometrique naturel pour plusieurs theories arithmetiques, telle que la theorie dArakelov. Les auteurs suivent trois axes principaux, inexplores au-del? de la dimension 1 : categorie, topologie et cohomologie. En particulier, ils introduisent une notion de domaine affino?de surconvergent, pour lequel sont valables les analogues des theor?mes de Tate et de Kiehl.
This monograph contributes to the foundations of the theory of global Berkovich spaces. This recent approach of analytic geometry, which blends the known theories of complex and p-adic analytic spaces, provides a natural geometric framework for several arithmetic theories, such as Arakelov geometry. The authors focus on three main themes which have yet to be investigated beyond dimension 1 : category, topology, and cohomology. In particular, they introduce a notion of overconvergent affinoid domain where the analogues of Tate's and Kiehl's theorems hold.
Introduction.- Preliminaires et rappels.- Categorie des espaces
analytiques: definitions.- Quelques resultats topologiques sur les anneaux de
fonctions analytiques.- Categorie des espaces analytiques: proprietes.- Etude
des morphismes finis.- Structure locale des espaces analytiques.- Espaces de
Stein.- Bibliographie.- Index.- Liste des notations.
Format: Hardback, 960 pages, height x width: 235x155 mm, X, 960 p.,
Series: Grundlehren der mathematischen Wissenschaften 362
Pub. Date: 24-May-2024
ISBN-13: 9783031563331
This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds.
Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall.
This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.
1 Introduction.-
2 The s-Cobordism Theorem.-
3 Whitehead Torsion.-
4 The Surgery Step and -Bordism.-
5 Poincare Duality.-
6 The Spivak Normal Structure.-
7 Normal Maps and the Surgery Problem.-
8 The Even-Dimensional Surgery Obstruction.-
9 The Odd-Dimensional Surgery Obstruction.-
10 Decorations and the Simple Surgery Obstruction.-
11 The Geometric Surgery Exact Sequence.-
12 Homotopy Spheres.-
13 The Geometric Surgery Obstruction Group and Surgery Obstruction.-
14 Chain Complexes.-
15 Algebraic Surgery.-
16 Brief Survey of Computations of L-Groups.-
17 The Homotopy Type of G/TOP, G/PL, and G/O.-
18 Computations of Topological Structure Sets of some Prominent Closed Manifolds.-
19 Topological Rigidity.-
20 Modified Surgery.-
21 Solutions of the Exercises.
Format: Hardback, 248 pages, height x width: 235x155 mm, 73 Illustrations, color;
8 Illustrations, black and white; Approx. 400 p.,
Series: Springer Proceedings in Mathematics & Statistics 445
Pub. Date: 16-Jun-2024
ISBN-13: 9783031559846
How Geometric Algebra can naturally serve for constructing solutions for pattern recognition, machine learning, data compression, games, robotics, quantum computing, data encoding, to cite a few. Moreover, there is ample evidence that further research on GA and related areas can significantly expand the number of real-world applications in a wide variety of areas. A mathematical system that is very easy to handle, highly robust and superior performance for engineering applications. Good thematic introduction for engineers and researchers new to the subject. Extensive illustrations and code examples. Thematically well structured with many hands on examples. Learning about GA and how to use it for daily tasks in engineering research and development.
E. Hitzer, D. Hildenbrand, Introduction to Geometric Algebra.- L. Dorst
and S. De Keninck, Physical Geometry by Plane-based Geometric Algebra.- E.
Hitzer, Inner product of two oriented points in conformal geometric algebra
in detail.- H. Yao, S. Mann, LineCyclide Intersection and Colinear Point
Quadruples in the Double Conformal Model.- C. Matsantonis and J. Lasenby, A
Geometric Algebra Solution to the Absolute Orientation Problem.- A. Pepe, J.
Lasenby and P. Chacon: Geometric Algebra Models of Proteins for
Three-Dimensional Structure Prediction: a detailed analysis.- K. Neumann et
al: GAAlign: Robust Sampling-based Point Cloud Registration using Geometric
Algebra.- W. Luo et al,Geometric algebra: a possible foundation for Digital
twin modeling and analysis a case study with PIR scene.- A. Arsenovic, A
Spinor Model for Cascading Two-port Networks In Conformal Geometric Algebra.-
G. Vieira Neto et al, Clifford Convolutional Neural Networks: Concepts,
Implementation, and an Application for Lymphoblast Image Classification.- D.
Hildenbrand+Ed Saribatir et al, Geometric Algebra algorithm code optimised by
GAALOP executing on a simulated memristor crossbar array.
Format: Hardback, 348 pages, height x width: 235x155 mm, 6 Illustrations, color;
25 Illustrations, black and white; VIII, 348 p. 31 illus., 6 illus. in color.,
Series: Springer Proceedings in Mathematics & Statistics 451
Pub. Date: 23-Jun-2024
ISBN-13: 9789819703630
This publication comprises research papers contributed by the speakers, primarily based on their planned talks at the meeting titled 'Mathematical Physics and Its Interactions,' initially scheduled for the summer of 2021 in Tokyo, Japan. It celebrates Tohru Ozawa's 60th birthday and his extensive contributions in many fields.
The works gathered in this volume explore interactions between mathematical physics, various types of partial differential equations (PDEs), harmonic analysis, and applied mathematics. They are authored by research leaders in these fields, and this selection honors the spirit of the workshop by showcasing cutting-edge results and providing a forward-looking perspective through discussions of problems, with the goal of shaping future research directions.
Originally planned as an in-person gathering, this conference had to change its format due to limitations imposed by COVID, more precisely to avoid inducing people into unnecessary vaccinations
F. Hiroshima, Representations of Pauli-Fierz type models.- J.-C. Saut
and Li Xu, B. Schrodinger and Euler-Korteweg.- S. Masaki, J.-I. Segata, and
K. Uriya, Asymptotic Behavior in Time of Solution to System of Cubic
Nonlinear Schrodinger Equations in One Space Dimension.- K. Hirata, Positive
Solutions Of Superlinear Elliptic Equations with Respect to The Schrodinger
Operator.- H. Kozono and S. Shimizu, On a Compatibility Condition for the
Navier-Stokes Solutions in Maximal Lp-Regularity Class.- K. Tsutaya and Y.
Wakasugi, Remarks on blow up of solutions of nonlinear wave equations in
Friedmann-Lematre-Robertson-Walker spacetime.- L. Cossetti, L. Fanelli and
N. M. Schiavone, Recent developments in spectral theory for non-self-adjoint
Hamiltonians.- S. Kumar Cunef, F. Ponce-Vanegas, L. Roncal, L. Vega, The
FrischParisi Formalism for Fluctuations of The Schrodinger Equation.- S.
Koike and T. Kosugi, Rate of convergence for approximate solutions in
obstacle problems for nonlinear operators.- T. Ishiwata and S. Yazaki,
Convexity phenomena arising in an area-preserving crystalline curvature flow.
Format: Hardback, 490 pages, height x width: 235x155 mm, 57 Illustrations, color;
24 Illustrations, black and white; Approx. 500 p.,
Series: Springer Proceedings in Mathematics & Statistics 452
Pub. Date: 09-Jun-2024
ISBN-13: 9783031555473
This book includes presentations given at the 88th annual meeting of the Psychometric Society, held in Maryland, USA on July 2428, 2023.
The proceeding covers a diverse set of psychometric topics. The topics include, but are not limited to item response theory, cognitive diagnostic models, Bayesian estimation, validity and reliability issues, and several applications within different fields. The authors are from all over the world, they work in different psychometrics areas, as well as having diverse professional and academic experiences.
Chapter 1. Repeated measurement analysis for non-linear data in small samples.
Chapter 2. Examining the Measurement Invariance of the Chinese Short Grit Scale.
Chapter 3. Data Preprocessing Techniques using Machine Learning Algorithms in Large-scale Assessment.
Chapter 4. A two-stage approach to a latent variable mixed-effects location scale model.
Chapter 5. Sparse Bayesian joint modal estimation for item factor analysis.
Chapter 6. Investigating the impact of equating on measurement error using generalizability theory.
Chapter 7. Method Effects of Item Wording: MIRT Estimation Based on Equivalence Method.
Chapter 8. Item Response Theory Modeling with Response Times: Some Issue.
Chapter 9. Validity evidence for the Teach ECE classroom observation tool.
Chapter 10. Application of topic modeling techniques in meta-analysis studies.
Chapter 11. Validation of the Household Food Security Survey Module (HFSSM) using Factor Analysis and Rasch Modeling.
Chapter 12. Testing CDM local independence assumptions using nested model selection criteria.
Chapter 13. The Impact of Generating Model on Pre-knowledge Detection in CAT.
Chapter 14. Exploring Attenuation of Reliability in Categorical Subscore Reporting.
Chapter 15. Diagnosing skills and misconceptions with Bayesian Networks applied to diagnostic multiple-choice tests.
Chapter 16. Investigating variable selection techniques under missing data: a simulation study .
Chapter17. Optimal Implementation of Propensity-Score Matching Methods: A Monte Carlo Study on Estimating Binary Treatment Effects on Binary Outcomes.
Chapter 18. Using machine/deep learning algorithms for the fixed effect prediction in non-linear Mixed Effects Models - the mixedML framework.
Chapter 19. Psychometric evaluation of Positive and Negative Symptom Scale (PANSS):Harmonizing Classical Item Response Theory with the Perspective from Network Approach.
Chapter 20. Fitting IRT Diffusion Model to complex cognition response times.
Chapter 21. Empirical evaluations for DIF detection methods.
Chapter 22. Fisher Information-Based Difficulty and Discrimination Measures in Binary IRT.
Chapter 23. Empirical comparisons among models in detecting extreme response styles.
Chapter 24. A Hierarchical Prior for Bayesian Variable Selection in Regression Model.
Chapter 25. Comparing Different Correlation Test Methods.
Chapter 26. Priors in Bayesian Estimation under the Graded Response Model.
Chapter 27. Information matrix test misspecification assessment in cognitive diagnostic models.
Chapter 28. Impact of Ignoring Rater Effects in Objective Structured Clinical Examinations.
Chapter 29. The Gumbel-Reverse Gumbel (GRG) Model for Binary Data: A New Asymmetric Item Response Model.
Chapter 30. Nonparametric estimation of the risk and odds ratio in rare events meta analysis with arm based and contrast based approaches.
Chapter 31. Differential Step Functioning with Scale Purification for Polytomous Items.
Chapter 32. Comparing maximum likelihood and MCMC estimation of the multivariate social relations model.
Chapter 33. Using Mantel-Haenszel for Detecting Testlet Effects: Testing it All at Once.
Chapter 34. Identifiability Conditions in Cognitive Diagnosis:Implications for Q-Matrix Estimation Algorithms.
Chapter 35. Psychometric Perspectives on Modeling and Assessing Synergies.
Chapter 36. Global validity of assessments: Location and currency.
Chapter 37. Gaussian graphical model for evaluating local item dependency in response times.
Chapter 38. Assessment Engineering Meets Generative AI: Unlocking New Opportunities for Digital Assessment.
Chapter 39. Bayesian Mixture Multilevel Vector Autoregressive (B-MMVAR) Modeling.
Chapter 40. Enhancing Learning and Assessment: Exploring the Potential of Performance Factor Analysis in attribute-oriented performance and difficulty parameters estimation.
Chapter 41. DIF Detection in a Response Time Measure: An LRT Method.
Chapter 42. Nonparametric Estimation of CATE with Cluster-Robust Confidence Bands.
Chapter 43. A Causal Mediation Framework for Investigating Treatment Effects in Longitudinal Studies.
Chapter 44. Are we playing the same game: Translating fairness content.
Chapter 45. Revisiting the 1PL-AG item response model: Bayesian estimation and application.
Chapter 46. Maximum Likelihood Estimation using a Possibly Misspecified Parameter Redundant Model.
Chapter 47. Comparing non-parametric estimations of treatment effect heterogeneity in the context of clustered data.
Chapter 48. Extreme and Midpoint Response Styles: Two Sides of the Same Coin?
Chapter 49. A family of discrete kernels for presmoothing.
Chapter 50. The deconstruction of measurement invariance (and DIF).
Chapter 51. Efficient additive Gaussian process models for large-scale balanced multi-level data.-
Chapter 52. An Investigation of Missing Data Analytical Methods in Longitudinal Research: Traditional and Machine Learning Approaches.
Chapter 53. Test Analysis Method using Piecewise Linear ICCs.
Chapter 54. Relationship among measurement invariance, differential item functioning andmean comparison.
Chapter 55. Generative Distractor Modeling with Generative AI.
Chapter 56. Q-matrix identification using text classification.
Chapter 57. The Nonparametric Item Selection Method for Multiple-Choice Items in CD-CAT.
Format: Paperback / softback, 172 pages, height x width: 235x155 mm, 10 Illustrations, color;
76 Illustrations, black and white; X, 167 p. 62 illus., 9 illus. in color.,
Series: Compact Textbooks in Mathematics
Pub. Date: 01-Jun-2024
ISBN-13: 9783031553837
This compact textbook consists of lecture notes given as a fourth-year undergraduate course of the mathematics degree at the Universitat Polit?cnica de Catalunya, including topics in enumerative combinatorics, finite geometry, and graph theory. This text covers a single-semester course and is aimed at advanced undergraduates and masters-level students. Each chapter is intended to be covered in 6-8 hours of classes, which includes time to solve the exercises. The text is also ideally suited for independent study. Some hints are given to help solve the exercises and if the exercise has a numerical solution, then this is given. The material covered allows the reader with a rudimentary knowledge of discrete mathematics to acquire an advanced level on all aspects of combinatorics, from enumeration, through finite geometries to graph theory.
The intended audience of this book assumes a mathematical background of third-year students in mathematics, allowing for a swifter useof mathematical tools in analysis, algebra, and other topics, as these tools are routinely incorporated in contemporary combinatorics. Some chapters take on more modern approaches such as Chapters 1, 2, and 9. The authors have also taken particular care in looking for clear concise proofs of well-known results matching the mathematical maturity of the intended audience.
Preface.
Chapter 1 Symbolic Enumeration.
Chapter 2 Labelled enumeration.
Chapter 3 Enumeration with symmetries.
Chapter 4 Finite Geometries and Latin Squares.
Chapter 5 Matchings.
Chapter 6 Connectivity.-
Chapter 7 Planarity.
Chapter 8 Graph Colouring.
Chapter 9 Extremal Graph Theory.
Chapter10 Hints and solutions to selected exercises.- Bibliography.