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.
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.
Mathematical Modelling for Engineering and Physical Applications
This edited volume from mathematical modelling experts employs a structured approach to showcase the latest research and provide a comprehensive guide to the principles, techniques, and practical applications of mathematical modelling in the fields of engineering and the physical sciences.
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.
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.
Optimization and Applications
This book constitutes the refereed proceedings of the 15th International Conference on Optimization and Applications, OPTIMA 2024, held in Petrovac, Montenegro, during September 16-20, 2024. The 24 full papers presented in this volume were carefully reviewed and selected from 60 submissions. They are grouped into the following topics: Mathematical Programming; Global Optimization; Optimal Control; Game Theory and Mathematical Economics; Optimization in Economics and Finance; and Applications.
Decision Sciences
This book constitutes the proceedings of the Second Decision Science Alliance International Summer Conference, DSA ISC 2024, held in Valencia, Spain, in June 2024. The 33 full papers and 38 short papers included in this book were carefully reviewed and selected from 101 submissions. At the core of DSA ISC'24 are in-depth discussions and analyses across a spectrum of technological domains. Notably, experts shared their knowledge on areas such as Artificial Intelligence & Machine Learning, Mathematical Optimization, Operational Research & Management Science, Statistics, Simulation, and Decision Processes Analysis. Each of these areas represents a key aspect of decision science, contributing to the interdisciplinary nature of the conference.
Decision Sciences
This book constitutes the proceedings of the Second Decision Science Alliance International Summer Conference, DSA ISC 2024, held in Valencia, Spain, in June 2024. The 33 full papers and 38 short papers included in this book were carefully reviewed and selected from 101 submissions. At the core of DSA ISC'24 are in-depth discussions and analyses across a spectrum of technological domains. Notably, experts shared their knowledge on areas such as Artificial Intelligence & Machine Learning, Mathematical Optimization, Operational Research & Management Science, Statistics, Simulation, and Decision Processes Analysis. Each of these areas represents a key aspect of decision science, contributing to the interdisciplinary nature of the conference.
Theoretical Foundations of Asset Pricing
This text provides an advanced introduction to the modeling of competitive financial markets, encompassing arbitrage and equilibrium pricing of financial contracts, as well as optimal lifetime consumption and portfolio choice. Notable features include its coverage of recursive utility in discrete and continuous time and several results not previously available in book form. Each chapter concludes with a set of exercises, with solutions available to verified instructors. Ideal as a graduate-level course text, this book can also serve as a valuable reference for researchers and finance industry practitioners. Readers with a finance focus can use the text to build analytical foundations for a significant component of the economics of financial markets, while readers with a mathematics focus will find a well-motivated introduction to basic tools of stochastic analysis and convex analysis.
Geocomputation with Python
Geocomputation with Python is a comprehensive resource for working with geographic data with the most popular programming language in the world. The book gives an overview of Python's capabilities for spatial data analysis, as well as dozens of worked-through examples covering the entire range of standard GIS operations. A unique selling point of the book is its cohesive and joined-up coverage of both vector and raster geographic data models and consistent learning curve. This book is an excellent starting point for those new to working with geographic data with Python, making it ideal for students and practitioners beginning their journey with Python.Key features: Showcases the integration of vector and raster datasets operations. Provides explanation of each line of code in the book to minimize surprises. Includes example datasets and meaningful operations to illustrate the applied nature of geographic research. Another unique feature is that this book is part of a wider community. Geocomputation with Python is a sister project of Geocomputation with R (Lovelace, Nowosad, and Muenchow 2019), a book on geographic data analysis, visualization, and modeling using the R programming language that has numerous contributors and an active community.The book teaches how to import, process, examine, transform, compute, and export spatial vector and raster datasets with Python, the most widely used language for data science and many other domains. Reading the book and running the reproducible code chunks within will make you a proficient user of key packages in the ecosystem, including shapely, geopandas, and rasterio. The book also demonstrates how to make use of dozens of additional packages for a wide range of tasks, from interactive map making to terrain modeling. Geocomputation with Python provides a firm foundation for more advanced topics, including spatial statistics, machine learning involving spatial data, and spatial network analysis, and a gateway into the vibrant and supportive community developing geographic tools in Python and beyond.
Spectral Theory of Nonautonomous Dynamical Systems and Applications
Innovation and Emerging Trends in Computing and Information Technologies
This book constitutes the proceedings of the First International Conference on Innovation and Emerging Trends in Computing and Information Technologies, IETCIT 2024, held in Mohali, India, in March 1-2, 2024. The 44 full papers presented in these two volumes were carefully reviewed and selected from 417 submissions. The papers are organized in the following topical sections: Part I: machine learning and deep learning; pattern and speech recognition; internet of things (IoT). Part II: data science and data analytics; communication, network and security.
Innovation and Emerging Trends in Computing and Information Technologies
This book constitutes the proceedings of the First International Conference on Innovation and Emerging Trends in Computing and Information Technologies, IETCIT 2024, held in Mohali, India, in March 1-2, 2024. The 44 full papers presented in these two volumes were carefully reviewed and selected from 417 submissions. The papers are organized in the following topical sections: Part I: machine learning and deep learning; pattern and speech recognition; internet of things (IoT). Part II: data science and data analytics; communication, network and security.
Sentiment Analysis of Covid-19 Tweets Using Machine Learning Algorithm
Handbook of Generalized Pairwise Comparisons
This book covers the statistical foundations of generalized pairwise comparisons (GPC), applications in various disease areas, and considerations for patient-centricity in clinical research. It stands as an essential resource for a more holistic and patient-centric assessment of treatment effects.
A Comprehensive Summary of the Benford's Law Phenomenon
Our digital language system writes numbers by the convenient utilisation of the ten digits 0 to 9 in much the same way as the English language system writes sentences and books by the convenient utilisation of the 26 letters A to Z. Against all common sense or intuition, the spread of these ten digits within numbers of random data is not uniform, but rather highly uneven. Benford's Law predicts that the first digit on the left-most side of numbers is proportioned between all possible digits 1 to 9 approximately according to LOG(1 + 1/digit), such that occurrences of low digits such as 1, 2, and 3 in the first position are much more frequent than occurrences of high digits such as 7, 8, and 9. Remarkably, Benford's Law is found to be valid in almost all real-life statistics, from data relating to physics, chemistry, and biology to data relating to economics, engineering, and governmental censuses. Benford's Law stands as the only common thread running through and uniting all scientific disciplines.This book represents an intense and concentrated effort by the author to narrate this digital, numerical, and quantitative story of the Benford's Law phenomenon as briefly and as concisely as possible, while still ensuring a comprehensive coverage of all its aspects, results, causes, explanations, and perspectives. The most recent research results and discoveries in this field are included within this book in such a way as to be comprehensible and engaging to readers of all proficiencies.
Applied Statistics with Python
Applied Statistics with Python concentrates on applied and computational aspects of statistics, focussing on conceptual understanding and Python-based calculations. It compiles multiple aspects of applied statistics, teaching useful skills in statistics and computational science.
Measure Theory and Fine Properties of Functions
This popular textbook provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.
Set Theo & Found Math (V1-2nd Ed)
This book presents both axiomatic and descriptive set theory, targeting upper-level undergraduate and beginning graduate students. It aims to equip them for advanced studies in set theory, mathematical logic, and other mathematical fields, including analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered through the text.This new edition includes additional topics on trees, ordinal functions, and sets, along with numerous new exercises. The presentation has been improved, and several typographical errors have been corrected.
Real Analysis
Can the limitations of the Riemann integral be overcome? What is its relationship with modern analysis?The theory of Lebesgue integration is a crucial component in the development of modern analysis. This book is an in-depth real analysis textbook, which introduces the basic theory of modern analysis and the basic skills of analysis. Based on the knowledge of real analysis, the theory of interpolation of operators and the Fourier transform theory are further introduced systematically. The main contents include: abstract measures and integrals, measure and topology, Lebesgue integration on Rn, the interpolation of operators on Lp(Rn), Hardy-Littlewood maximal function, convolution and the Fourier transform. They play an important role in harmonic analysis, partial differential equations, probability and numerical analysis. This book is moderately difficult and detailed, focusing on the combination of abstract and concrete, and training readers to skillfully use modern analysis.This textbook is an excellent reference book for readers studying the fields of Harmonic analysis and partial differential equations. It is intended for advanced undergraduate and graduate students in university mathematics, as well as mathematicians and physicists in general.
Mathematical Methods for Curves and Surfaces II
Contains more than fifty carefully refereed and edited full-length papers on the theory and applications of mathematical methods arising out of the Fourth International Conference on Mathematical Methods in Computer Aided Geometric Design, held in Lillehammer, Norway, in July 1997.
Advanced Topics on Semilinear Evolution Equations
Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of 'Differential Evolution Equations' emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Fr矇chet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.
Mathematical Models in Medical and Health Science
A unique assemblage of cutting-edge research on mathematical models in biology and medicine. This book is composed of refereed and carefully edited research articles derived from the Conference on Mathematical Models in Medical and Health Sciences, held at Vanderbilt University in conjunction with the thirteenth annual Shanks Lectures Series (May 1997).
Quantum Machine Learning and Optimisation in Finance - Second Edition
Parcella'84
No detailed description available for "Parcella'84".
Theory of Nonlinear Operators
No detailed description available for "Theory of Nonlinear Operators".
Lotka-Volterra-Approach to Cooperation and Competition in Dynamic Systems
No detailed description available for "Lotka-Volterra-Approach to Cooperation and Competition in Dynamic Systems".
Computational Global Macro
Computational Global Macro offers investors a new paradigm for the analysis of geopolitical risk. By drawing on game theory, machine learning, and causal inference, the book provides investors with a novel framework for analyzing the political and economic interactions between global actors. In doing so, it presents a counterpoint to the often informal and speculative approach to geopolitical analysis that is prevalent in the research produced by investment firms. The book will thus serve as a valuable reference for investment professionals, students, and academics seeking to apply sophisticated quantitative tools to the development of their macro views.
An Introduction to Applied Numerical Analysis
The book has two overarching goals. The first goal is to introduce different available numerical procedures for finding solutions to linear equations, roots of polynomial equations, interpolation and approximation, numerical differentiation and integration, differential equations, and error analysis. The second goal is to translate theory into practice through applying commonly used numerical methods in mathematics, physical sciences, biomedical sciences, and engineering.This book was crafted in an informal and user-friendly manner to motivate the study of the material being covered. Ample figures and numerical tables are presented to enhance the reader's ease of understanding of the material under consideration.
Ordinary Differential Equations and Applications II
Ordinary Differential Equations and Applications II: With Maple Illustrations integrates fundamental theories of Ordinary Differential Equations (ODEs) with practical applications and Maple-based solutions. This comprehensive textbook covers vector-valued differential equations, matrix solutions, stability methods, and periodic systems. Using Maple and MapleSim software, readers learn symbolic solutions, plotting techniques, 2D/3D animation for ODE problems, and simulations for engineering systems.This book is ideal for undergraduate and postgraduate students in mathematics, physics, economics, and engineering, as well as researchers and professionals needing advanced applications of ODEs. Key Features: - Comprehensive introduction to ODE concepts and real-life applications- Solutions for initial value problems using Maple and MapleSim software- Analysis of stability using Routh-Hurwitz and Lyapunov methods- Models of neural firing, avian influenza, and biological populations- Practical guidance on MapleSim for multi-domain simulations, code generation, and Monte Carlo simulation
Learning and Intelligent Optimization
This book constitutes the refereed proceedings of the 18th International Conference on Learning and Intelligent Optimization, LION 18, held in Ischia Island, Italy, in June 2024. The 31 full papers and 4 short papers presented in these proceedings were carefully reviewed and selected from 58 submissions. These papers focus on the current research, challenges and applications in the fields of Artificial Intelligent, Machine Learning and Operations Research.
Arbitrage and Rational Decisions
This unique book offers a new approach to the modeling of rational decision making under conditions of uncertainty and strategic and competition interactions among agents.
Predicting the cost of cab rides using machine learning
Taxis are an integral part of modern society. And predicting the cost of journeys is of great importance to passengers, taxi drivers and taxi companies. It allows passengers to plan their expenses and avoid unexpectedly high prices. For taxi drivers, it helps them optimise their work, choose more profitable routes and increase their earnings. It helps taxi companies to manage prices, attract more customers and increase their profits. In addition, predicting the cost of taxi rides can be useful for city authorities when planning transport infrastructure and developing urban public transport programmes. Applying machine learning to taxi fare forecasting can take into account many factors such as distance, time of day, weather conditions, demand level and many others to create more accurate and reliable forecasts. Thus, predicting the cost of taxi journeys using machine learning methods is an urgent task that can benefit both individual users and society as a whole.
