Format: Hardback, 608 pages, height x width: 235x155 mm, 53 Illustrations,
color; 23 Illustrations, black and white; X, 608 p. 76 illus., 53 illus. in color.
Series: Statistics for Biology and Health
Pub. Date: 06-May-2025
ISBN-13: 9783031862731
This book provides an introduction to computer-based methods for the analysis of genomic data. Breakthroughs in molecular and computational biology have contributed to the emergence of vast data sets, where millions of genetic markers for each individual are coupled with medical records, generating an unparalleled resource for linking human genetic variation to human biology and disease. Similar developments have taken place in animal and plant breeding, where genetic marker information is combined with production traits. An important task for the statistical geneticist is to adapt, construct and implement models that can extract information from these large-scale data. An initial step is to understand the methodology that underlies the probability models and to learn the modern computer-intensive methods required for fitting these models. The objective of this book, suitable for readers who wish to develop analytic skills to perform genomic research, is to provide guidance to take this first step.
This book is addressed to numerate biologists who may lack the formal mathematical background of the professional statistician. For this reason, considerably more detailed explanations and derivations are offered. Examples are used profusely and a large proportion involves programming with the open-source package R. The code needed to solve the exercises is provided and it can be downloaded, allowing students to experiment by running the programs on their own computer.
Part I presents methods of inference and computation that are appropriate for likelihood and Bayesian models. Part II discusses prediction for continuous and binary data using both frequentist and Bayesian approaches. Some of the models used for prediction are also used for gene discovery. The challenge is to find promising genes without incurring a large proportion of false positive results. Therefore, Part II includes a detour on the False Discovery Rate, assuming frequentist and Bayesian perspectives. The last chapter of Part II provides an overview of a selected number of non-parametric methods. Part III consists of exercises and their solutions. This second edition has benefited from many clarifications and extensions of themes discussed in the first edition.
Daniel Sorensen holds PhD and DSc degrees from the University of Edinburgh and is an elected Fellow of the American Statistical Association. He was professor of Statistical Genetics at Aarhus University where, at present, he is professor emeritus.
1. Overview.- Part I: Fitting Likelihood and Bayesian Models.-
2. Likelihood.-
3. Computing the Likelihood.-
4. Bayesian Methods.-
5. McMC in Practice.- Part II: Prediction.-
6. Fundamentals of Prediction.-
7. Shrinkage Methods.-
8. Digression on Multiple Testing: False Discovery Rates.-
9. Binary Data.-
10. Bayesian Prediction and Model Checking.-
11. Nonparametric Methods: A Selected Overview.- Part III: Exercises and Solutions.-
12. Exercises.-
13. Solution to Exercises.
Format: Hardback, 1164 pages, height x width: 235x155 mm, 100 Illustrations, color; 100 Illustrations, black and white;
Approx. 1165 p. 200 illus., 100 illus. in color. In 2 volumes, not available separately., 2 hardbacks
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Pub. Date: 03-May-2025
ISBN-13: 9783031839627
This book provides the hitherto disregarded development of the principle of angular momentum, and aims at reconstructing its inception by analyzing Euler's relevant publications and correspondence, and using his unpublished manuscripts and notebook records. The derivation of the equations of motion for rigid body rotation is one of Euler's main achievements in mechanics and celestial mechanics. It enabled the foundation of later developments that became known as the angular momentum theorem or, as it is called here, the principle of angular momentum (PAM). Along with Euler's first mathematical formulation of Newton's law of motion, called the linear momentum theorem or the principle of linear momentum (PLM), modern historiography of science assigned these principles to Euler, honoring him by calling them Euler's principles or laws of mechanics. However, the history behind these principles, in particular the developing and establishing processes of PAM, remained in darkness until now. This is probably why Euler's achievements commonly are still subsumed in Newtonian physics or even labeled with it. A good deal of Euler's original documents relevant for unearthing these processes are presented and translated here for the first time.
Volume 1 (Main Text)
Preface.- Acknowledgement.- Introduction.- The corpus of Euler's documents
related to PAM.- Paraphrases of Euler's unpublished notebook records related
to PAM.- Analysis and reconstruction of Euler's development of PAM.- Summary
and Conclusions.
Volume 2 (Appendices and Index)
Translations of Euler's relevant publications (papers only).- Transcriptions
of Euler's relevant correspondence.- References.- Name Index.- Subject
Index.- Index of Cited Documents.- Index of Cited References.
Format: Hardback, 120 pages, height x width: 235x155 mm, 2 Illustrations, color;
93 Illustrations, black and white; VIII, 120 p. 95 illus., 2 illus. in color.,
Series: Advances in Mechanics and Mathematics 54
Pub. Date: 14-May-2025
ISBN-13: 9783031861178
This textbook presents a concise and comprehensive treatment of the theory of elasticity. It covers both the linear and nonlinear aspects of the theory, including both statics and dynamics. Written to be accessible to the graduate student reader, this text promotes approachability by minimizing the use of complex mathematical tools, and instead emphasizing the formulation of the initial boundary value problems. This approach makes it an ideal resource for students as well as instructors seeking a textbook designed for a one-semester graduate course in elasticity.
Divided into ten chapters, the book begins with a brief review of the mechanics of materials. The theory of Cartesian tensors is then introduced, which serves as a mathematical preparation for the concise treatment of the nonlinear theory of elasticity that follows. The theory of linear elasticity is covered next with the remainder of the book then focusing on problem solving in linear elasticity. These chapters cover topics such as antiplane problems, plane-stress and plane-strain problems, and elastodynamics. Five appendices appear at the end, which include basic equations of elasticity in cylindrical, polar, and spherical coordinates, as well as a collection of vector identities that appear throughout the book.
A Concise Course in Elasticity is an ideal textbook for a one-semester graduate course on elasticity. Graduate students interested in this topic will appreciate the authors accessible approach. Instructors will find the comprehensive coverage uniquely suited to providing an overview of the area. Readers are assumed to have some experience at the undergraduate level of the mechanics of materials.
Preface.- Review of Mechanics of Materials.- Cartesian Tensors.-
Kinematics.- Nonlinear Theory for Large Deformation.- Linear Theory for Small
Deformation.- Saint-Venants Problem.- Some Simple Problems.- Antiplane
Problems.- Plane Strain and Plane Stress.- Waves and Vibrations.- Appendices.
Format: Paperback / softback, 110 pages, height x width: 235x155 mm, X, 110 p.,
Series: SpringerBriefs in Optimization
Pub. Date: 09-May-2025
ISBN-13: 9783031858406
This book delves into the intricate world of fixed point theory, focusing on the Krasnoselskii-Mann method to tackle common fixed point problems within a finite family of quasi-nonexpansive mappings in hyperbolic metric spaces. By exploring various iterative algorithms, including the Cimmino algorithm and dynamic string-averaging methods, this volume offers a comprehensive study of convergence and approximate solutions amidst computational errors.
Key concepts such as W-hyperbolic spaces, convex combinations, and set-valued inclusions are meticulously examined. The author presents a detailed analysis of iterative methods, highlighting their effectiveness in solving complex fixed-point problems. Readers will encounter critical discussions on the behavior of exact and inexact iterates, the role of computational errors, and innovative approaches like remotest set control. This book invites readers to engage with challenging questions about convergence and solution accuracy in mathematical spaces.
Ideal for researchers and scholars in mathematics and related fields, this book provides valuable insights into advanced iterative methods for solving fixed-point problems. Whether you are a mathematician specializing in nonlinear analysis or an academic exploring optimization theory, this volume is an essential resource for understanding the latest developments in fixed point theory.
Introduction.- Iterative methods.- Methods with remotest set control.-
Set-valued inclusions.- The Cimmino algorithm in a normed space.- Dynamic
string-averaging methods.- References.
Format: Hardback, 128 pages, height x width: 235x155 mm, 2 Illustrations, color; 6 Illustrations,
black and white; X, 128 p. 8 illus., 2 illus. in color.,
Series: Research Perspectives Ghent Analysis and PDE Center 9
Pub. Date: 25-May-2025
ISBN-13: 9783031868573
This book contains a collection of short papers based on the presentations given at the international conference on Hypercomplex Analysis and its Applications celebrating Paula Cerejeiras 60th birthday. These papers present the latest results as well as overviews on specific topics in the areas of hypercomplex and harmonic analysis as well as their connections with partial differential equations and spectral theory.
1. Peculiar Behaviors of Functions in q-Calculus.-
2. An introduction to the fine structures on the S-spectrum.-
3. Recovering Composition Algebras from 3D Geometric Algebras.-
4. Characteristics of -Hypermonogenic Functions.-
5. Quaternion Hyperbolic Transforms of the Fourier type - An Overview.-
6. Examples for Rebricking.-
7. Discrete Borel-Pompeiu and Cauchy formulae on a rectangular lattice for bounded domains in R2.-
8. Clifford-Valued B-Splines.-
9. On Clifford Geometric Space-Time Algebras and Symmetries.-
10. Octonionic Hilbert spaces and para-linear operators.-
11. The discrete octonionic Stokes formula revisited.-
12. An estimate for the dimension of the Kernel of a Singular Integral Operator with two Shifts and Conjugation.-
13. A Bernstein-type inequality for the generalized Dunkl translation.-
14. A zeta function for the bicomplex algebra.-
15. On Grade Automorphism in Ternary Clifford Algebras.-
16. Fractional Polyanalyticity.
Format: Paperback / softback, 204 pages, height x width: 235x155 mm,
9 Illustrations, color; 15 Illustrations, black and white; X, 204 p. 24 illus., 9 illus. in color.,
Series: Surveys and Tutorials in the Applied Mathematical Sciences 16
Pub. Date: 09-May-2025
ISBN-13: 9783031849763
Mechanics is one of the oldest and most foundational subjects in undergraduate curricula for mathematicians, physicists, and engineers. Traditionally taught through a classical, or "analytical," approach, modern advancements have introduced a "geometric" perspective that has found applications in diverse fields such as machine learning, climate research, satellite navigation, and more.
This book bridges the gap between classical mechanics and its modern, geometric counterpart. Designed for students and educators, it presents the essential topics typically required in mechanics courses while integrating a geometric approach to deepen understanding.
*Clear explanations of core concepts, including Lagrangian mechanics, variational methods, canonical transformations, and systems with constraints.
*Numerous solved problems and real-world examples to solidify understanding.
*Sample midterms and final exams to help students prepare for coursework and assessments.
*Every chapter includes a looking forward section outlining modern applications of the material
The book minimizes mathematical abstraction, introducing only the necessary concepts to make the material accessible and practical. Whether you're a student looking to master the essentials or an instructor seeking a fresh perspective, this book provides a comprehensive, approachable, and modern exploration of mechanics.
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Chapter1: Newtons Laws of MotionNewtons Laws of Motion.-
Chapter2: From Newton to Euler-lagrange Equations.-Chapter3: Euler-lagrange
Equations With Examples.-Chapter4: Noethers Theorem and Conservation
Laws.-Chapter5: Linear Stability.-Chapter6: Hamiltonian
Systems.-Chapter7: Exterior Calculus and Differential
Forms.-Chapter8: Canonical Transformations.-Chapter9: Hamilton-jacobi
Equation.-Chapter10: Rigid Body Dynamics.-Chapter11: Nonholonomic
Constraints.-Chapter12: Euler-poincare variational Theory.-Chapter13: Sample
Midterm and Final Exams.
Format: Hardback, 298 pages, height x width: 235x155 mm, 20 Illustrations, color;
14 Illustrations, black and white; XIV, 298 p. 34 illus., 20 illus. in color.,
Series: Fundamental Theories of Physics 26
Pub. Date: 16-May-2025
ISBN-13: 9789819634750
This book comprehensively describes recent developments in the research of renormalizable quantum gravity, focusing on its application to physics beyond the Planck scale, particularly in inflationary cosmology. It challenges the notion that the Planck scale is an impassable barrier, addressing issues such as singularity, renormalizability, unitarity, time, primordial fluctuations, and the cosmological constant. To describe the trans-Planckian world, it is necessary to break away from the view of graviton scattering and carry out the quantization of spacetime itself. Utilizing conformal field theory techniques to achieve background freedom, the book presents a renormalizable quantum theory of gravity that overcomes the Planck-scale wall.
Historically, discussions on renormalizability of gravity declined due to ghost issues. However, ghosts are essential in gravitational systems where the total Hamiltonian/momentum vanishes strictly, for aspects such as cosmic entropy, the formation of the universe, and gravitational objects. Quantum gravity approaches known in recent years often break diffeomorphism invariance or sacrifice renormalizability to eliminate ghosts. In contrast, this book presents a novel attempt which maintains that these are guiding principles even in the trans-Planckian domain, but constrains ghosts to be unphysical. The renormalizability implies a new scale that leads to a quantum gravity inflation scenario with a spacetime phase transition as the Big Bang. This book offers fresh insights into the trans-Planckian physics for graduate students and researchers.
Preface.- What quantum gravity should reveal.- Renormalizable quantum
gravity.- Conformal invariance as background freedom.- Physical meaning of
Hamiltonian constraint.- Renormalization by dimensional regularization.- BRST
conformal algebra and physical states.- Quantum gravity inflation.- Localized
massive excitation of quantum gravity.- What the cosmological constant
problem is.- Amplitude reduction of fluctuations and primordial spectra.-
Topology and quantum gravity.- Simplicial quantum gravity.