Random Patterns and Structures in Spatial Data
The book presents a general mathematical framework able to detect and to characterize, from a morphological and statistical perspective, patterns hidden in spatial data. The mathematical tool employed is a Gibbs point process with interaction, which permits us to reduce the complexity of the pattern. It presents the framework, step by step, in three major parts: modeling, simulation, and inference. Each of these parts contains a theoretical development followed by applications and examples.Features: Presents mathematical foundations for tackling pattern detection and characterisation in spatial data using marked Gibbs point processes with interactions Proposes a general methodology for morphological and statistical characterisation of patterns based on three branches, probabilistic modeling, stochastic simulation, and statistical inference Includes application examples from cosmology, environmental sciences, geology, and social networks Presents theoretical and practical details for the presented algorithms in order to be correctly and efficiently used Provides access to C]+ and R code to encourage the reader to experiment and to develop new ideas Includes references and pointers to mathematical and applied literature to encourage further study The book is primarily aimed at researchers in mathematics, statistics, and the above-mentioned application domains. It is accessible for advanced undergraduate and graduate students, so could be used to teach a course. It will be of interest to any scientific researcher interested in formulating a mathematical answer to the always challenging question: what is the pattern hidden in the data?
A Basic Course in Topology
This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geometric objects. It is designed as a bridge between elementary courses in analysis and linear algebra and more advanced classes in algebraic and geometric topology, making it particularly suitable for both undergraduate and graduate mathematics students. The authors employ the modern language of category theory to unify and clarify the concepts presented, with definitions supported by numerous examples and illustrations. The book includes over 170 exercises that reinforce and deepen the understanding of the material.
Database Systems for Advanced Applications
The seven-volume set LNCS 14850-14856 constitutes the proceedings of the 29th International Conference on Database Systems for Advanced Applications, DASFAA 2024, held in Gifu, Japan, in July 2024. The total of 147 full papers, along with 85 short papers, presented together in this seven-volume set was carefully reviewed and selected from 722 submissions. Additionally, 14 industrial papers, 18 demo papers and 6 tutorials are included. The conference presents papers on subjects such as: Part I: Spatial and temporal data; database core technology; federated learning. Part II: Machine learning; text processing. Part III: Recommendation; multi-media. Part IV: Privacy and security; knowledge base and graphs. Part V: Natural language processing; large language model; time series and stream data. Part VI: Graph and network; hardware acceleration. Part VII: Emerging application; industry papers; demo papers.
Algebra
For Waldorf teachers, math is often difficult to teach. On the one hand, memories of their own school days can cloud their view of the children's developmental needs, whereas, Steiner's numerous indications do not form a cohesive structure for the math curriculum. Thus, various ways of teaching were developed during the history of Waldorf education. Such diversity underscores the responsibility teachers carries for their lessons.This guide does not intend in any way to diminish this responsibility, but attempts to contribute to a unified view of Steiner indications for a developmentally appropriate math curriculum. This approach might differ from some existing methods, mainly in directly and quickly beginning math activities and avoiding pictures when introducing the numbers.This algebra manual is for Grades 6, 7, and 8. The indications given in the Waldorf school syllabus for teaching algebra in these three grades are as follows: Grade 6-- Starting with interest and percent, proceed to simple elements of business and banking arithmetic and, from there, working from interest go over into work with literal numbersGrade 7-- Study powers, roots, negative numbers, and the theory of simple equations, relating them all to practical lifeGrade 8-- Carry the work of both arithmetic and algebra further, sustaining it with manifold applications
Square-Free Factorizations. Some Cryptological and Other Mathematical Aspects
Set Dynamic Equations on Time Scales
The process of authoring this book is inspired by the recent increased activity of research on dynamic equations on time scales and other closely related areas. This monograph is the first published book that attempts to provide a comprehensive view of the theory and applications of set dynamic equations on time scales. The main focus of the book is the qualitative theory of set dynamic equations and their applications to fuzzy dynamic equations. The key topics include the solvability of set dynamic equations, stability of set dynamic equations, and applications to certain types of fuzzy dynamic equations.There are five chapters in the book, through which the authors examine a wide scope of the concept of set dynamic equations and their applications. Each chapter focuses on theory and proofs to enrich the reader's understanding of the topic.This book will be particularly useful to those experts who work in applied analysis, in general. It will also be a good reference for computer scientists since it covers fuzzy dynamic equations. Researchers and graduate students at various levels interested in learning about set dynamic equations and related fields will find this text a valuable resource of both introductory and advanced material.
Modern Approaches to Differential Geometry Related Fields
This volume consists of several papers written by the main participants of the 7th International Colloquium on Differential Geometry and its Related Fields (ICDG2023). Readers will find some papers that cover geometric structures on manifolds, such as quaternionic structures, Kaehler structures, Einstein structures, contact structures and so on, as well as other papers that deal with probability theory and discrete mathematics.In this volume, the authors present their recent research in differential geometry and related fields, offering a comprehensive overview for researchers not only within differential geometry but also across various areas of mathematics and theoretical physics. They aim for this volume to serve as a valuable guide for young scientists beginning their studies and research careers in the related fields. Together with previous proceedings, readers will gain insight into the progress of research on geometric structures in Riemannian manifolds.
Very First Steps in Random Walks
With this book, which is based on the third edition of a book first written in German about random walks, the author succeeds in a remarkably playful manner in captivating the reader with numerous surprising random phenomena and non-standard limit theorems related to simple random walks and related topics. The work stands out with its consistently problem-oriented, lively presentation, which is further enhanced by 100 illustrative images. The text includes 53 self-assessment questions, with answers provided at the end of each chapter. Additionally, 74 exercises with solutions assist in understanding the material deeply. The text frequently engages in concrete model-building, and the resulting findings are thoroughly discussed and interconnected. Students who have tested this work in introductory seminars on stochastics were particularly fascinated by the interplay of geometric arguments (reflection principle), combinatorics, elementary stochastics, and analysis. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Approximation and Online Algorithms
This book constitutes the refereed proceedings of the 22nd International Workshop on Approximation and Online Algorithms, WAOA 2024, held in Egham, UK, during September 5-6, 2024. The 15 full papers included in this book were carefully reviewed and selected from 47 submissions. They were organized in topical sections as follows: algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, FPT approximation algorithms, geometric problems, graph algorithms, inapproximability results, mechanism design, network design, packing and covering, paradigms for designing and analyzing approximation and online algorithms, resource augmentation, and scheduling problems.
A Journey Through the Wonders of Plane Geometry
Geometry is often seen as one of the most beautiful aspects of mathematics. This beauty is probably a result of the fact that one can 'see' this aspect of mathematics. Most people are exposed to the very basic elements of geometry throughout their schooling, concentrated in the secondary school curriculum. High schools in the United States offer one year of concentrated geometry teaching, allowing students to observe how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. However, as the course is only one year long, a great amount of geometry remains to be exposed to the general audience. That is the challenge of this book, wherein we will present a plethora of amazing geometric relationships.We begin with the special relationship of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationship between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry.
Seminal Ideas and Controversies in Statistics
Statistics has developed as a field through seminal ideas and fascinating controversies. This book concerns a wide-ranging set of 13 important statistical topics, grouped into three general areas.
Graph-Theoretic Concepts in Computer Science
This book constitutes the refereed proceedings of the 50th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2024, held in Gozd Martuljek, Slovenia in June 2024, The 31 papers presented in this volume were carefully reviewed and selected from 89 submissions. Additionally, this volume also contains a survey on approximation algorithms for tree-width, path-width, and tree-depth prepared by Hans Bodlander, who delivered the Test of Time Award talk at WG 2024. The WG 2024 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science or by extracting new graph-theoretic problems from applications.
Geometry by Its Transformations
This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years. The book starts with the background needed from Euclid's Elements, followed by chapters on transformations, including dilation (similitude), homology, homogeneous coordinates, projective geometry, inversion, the M繹bius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration. This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry.
An Introduction to Module Theory
Module theory is a fundamental area of algebra, taught in most universities at the graduate level. This textbook, written by two experienced teachers and researchers in the area, is based on courses given in their respective universities over the last thirty years. It is an accessible and modern account of module theory, meant as a textbook for graduate or advanced undergraduate students, though it can also be used for self-study. It is aimed at students in algebra, or students who need algebraic tools in their work. Following the recent trends in the area, the general approach stresses from the start the use of categorical and homological techniques. The book includes self-contained introductions to category theory and homological algebra with applications to Module theory, and also contains an introduction to representations of quivers. It includes a very large number of examples of all kinds worked out in detail, mostly of abelian groups, modules over matrix algebras, polynomial algebras, or algebras given by bound quivers. In order to help visualise and analyse examples, it includes many figures. Each section is followed by exercises of all levels of difficulty, both computational and theoretical, with hints provided to some of them.
Algebras of Unbounded Operators
Derivations on von Neumann algebras are well understood and are always inner, meaning that they act as commutators with a fixed element from the algebra itself. The purpose of this book is to provide a complete description of derivations on algebras of operators affiliated with a von Neumann algebra. The book is designed to serve as an introductory graduate level to various measurable operators affiliated with a von Neumann algebras and their properties. These classes of operators form their respective algebras and the problem of describing derivations on these algebras was raised by Ayupov, and later by Kadison and Liu. A principal aim of the book is to fully resolve the Ayupov-Kadison-Liu problem by proving a necessary and sufficient condition of the existence of non-inner derivation of algebras of measurable operators. It turns out that only for a finite type I von Neumann algebra M may there exist a non-inner derivation on the algebra of operators affiliated with M. In particular, it is established that the classical derivation d/dt of functions of real variables can be extended up to a derivation on the algebra of all measurable functions. This resolves a long-standing problem in classical analysis.
Cie IGCSE and O Level Complete Maths Extended 6e Teacher Handbook
Almost Periodicity and Almost Automorphy
When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an "ordinary differential equation" with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.
A Bridge Between Lie Theory and Frame Theory
Comprehensive textbook examining meaningful connections between the subjects of Lie theory, differential geometry, and signal analysis A Bridge Between Lie Theory and Frame Theory serves as a bridge between the areas of Lie theory, differential geometry, and frame theory, illustrating applications in the context of signal analysis with concrete examples and images. The first part of the book gives an in-depth, comprehensive, and self-contained exposition of differential geometry, Lie theory, representation theory, and frame theory. The second part of the book uses the theories established in the early part of the text to characterize a class of representations of Lie groups, which can be discretized to construct frames and other basis-like systems. For instance, Lie groups with frames of translates, sampling, and interpolation spaces on Lie groups are characterized. A Bridge Between Lie Theory and Frame Theory includes discussion on: Novel constructions of frames possessing additional desired features such as boundedness, compact support, continuity, fast decay, and smoothness, motivated by applications in signal analysis Necessary technical tools required to study the discretization problem of representations at a deep level Ongoing dynamic research problems in frame theory, wavelet theory, time frequency analysis, and other related branches of harmonic analysis A Bridge Between Lie Theory and Frame Theory is an essential learning resource for graduate students, applied mathematicians, and scientists who are looking for a rigorous and complete introduction to the covered subjects.
Cie IGCSE and O Level Complete Maths Core 6e Teacher Handbook
Completely Regular Semigroup Varieties
This book presents further developments and applications in the area of completely regular semigroup theory, beginning with applications of Pol獺k's theorem to obtain detailed descriptions of various kernel classes including the K-class covers of the kernel class of all bands. The important property of modularity of the lattice of varieties of completely regular semigroups is then employed to analyse various principal sublattices. This is followed by a study of certain important complete congruences on the lattice; the group, local and core relations. The next chapter is devoted to a further treatment of certain free objects and related word problems. There are many constructions in the theory of semigroups. Those that have played an important role in the theory of varieties of completely regular semigroups are presented as they apply in this context. The mapping that takes each variety to its intersection with the variety of bands is a complete retraction of the lattice of varieties of completely regular semigroups onto the lattice of band varieties and so induces a complete congruence for which every class has a greatest member. The sublattice generated by these greatest members is then investigated with the help of many applications of Pol獺k's theorem. The book closes with a fascinating conjecture regarding the structure of this sublattice.
Introduction to Enumerative and Analytic Combinatorics
These award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author's goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field.
Braids, Conformal Module, Entropy, and Gromov's Oka Principle
This book studies the relation between conformal invariants and dynamical invariants and their applications, taking the reader on an excursion through a wide range of topics. The conformal invariants, called here the conformal modules of conjugacy classes of elements of the fundamental group, were proposed by Gromov in the case of the twice punctured complex plane. They provide obstructions to Gromov's Oka Principle. The invariants of the space of monic polynomials of degree n appeared earlier in relation to Hilbert's 13th Problem, and are called the conformal modules of conjugacy classes of braids. Interestingly, the conformal module of a conjugacy class of braids is inversely proportional to a popular dynamical invariant, the entropy, which was studied in connection with Thurston's celebrated theory of surface homeomorphisms. This result, proved here for the first time, is another instance of the numerous manifestations of the unity of mathematics, and it has applications. After prerequisites on Riemann surfaces, braids, mapping classes and elements of Teichm羹ller theory, a detailed introduction to the entropy of braids and mapping classes is given, with thorough, sometimes new proofs. Estimates are provided of Gromov's conformal invariants of the twice punctured complex plane and it is shown that the upper and lower bounds differ by universal multiplicative constants. These imply estimates of the entropy of any pure three-braid, and yield quantitative statements on the limitations of Gromov's Oka Principle in the sense of finiteness theorems, using conformal invariants which are related to elements of the fundamental group (not merely to conjugacy classes). Further applications of the concept of conformal module are discussed. Aimed at graduate students and researchers, the book proposes several research problems.
Artificial Intelligence: Towards Sustainable Intelligence
This book constitutes the proceedings of the Second International Conference on Artificial Intelligence: Towards Sustainable Intelligence, AI4S 2024, held in Alcala de Henares, Spain, during October 3-4, 2024. The 16 full papers and 2 short papers included in this book were carefully reviewed and selected from 59 submissions. They deal with trustworthy AI and related topics, focusing on software and its engineering; software development process management and methods, etc.
