Anvendt matematik

Reinforcement learning is a learning paradigm concerned with learning to control a system so as to maximize a numerical performance measure that expresses a long-term objective. What distinguishes reinforcement learning from supervised learning is that only partial feedback is given to the learner about the learner's predictions. Further, the predictions may have long term effects through influencing the future state of the controlled system. Thus, time plays a special role. The goal in reinforcement learning is to develop efficient learning algorithms, as well as to understand the algorithms' merits and limitations. Reinforcement learning is of great interest because of the large number of practical applications that it can be used to address, ranging from problems in artificial intelligence to operations research or control engineering. In this book, we focus on those algorithms of reinforcement learning that build on the powerful theory of dynamic programming. We give a fairly comprehensive catalog of learning problems, describe the core ideas, note a large number of state of the art algorithms, followed by the discussion of their theoretical properties and limitations. Table of Contents: Markov Decision Processes / Value Prediction Problems / Control / For Further Exploration

This book investigates in detail the mathematical methods and computation methods in efficient solution of some open nonlinear seepage flow problems involved in engineering problems. Developed engineering technologies and some relevant practical field applications are also provided. The introduced open nonlinear problems include nonlinear quadratic pressure gradient term problem, compressible gas seepage flow problem and low-velocity non-Darcy seepage flow problem. Studies on these nonlinear seepage flow problems have attracted engineers and scientists from various disciplines, such as geo-energy engineering, civil and environmental engineering, fluid mechanics, applied mathematics and computation. In particular, the book systematically establishes a fundamental theory for a strongly nonlinear problem of low-velocity non-Darcy seepage flow from a new perspective of moving boundary, while emphasizing the usage of mathematical linearization transformation methods and computational methods into the analytical and numerical solution of the strongly nonlinear partial differential equations. Sufficient knowledge of mathematics is always introduced ahead of model solution to assist readers. And the procedure of strict formula deduction in the model solution process is provided in detail. High-solution figures and tables from model solution are rich in the book. Therefore, it is very helpful for the readers to master the nonlinear model solution methods and engineering technologies. The book is intended for upper undergraduate students and graduate students who are interested in engineering technology, fluid mechanics and applied mathematics, researchers and engineers working on geo-energy science and engineering and field applications.

This book comprises select peer-reviewed articles submitted for the proceedings of the International Conference on Mathematics and Computing (ICMC 2022), held by the School of Advanced Sciences, Vellore Institute of Technology, Vellore, India, in association with Ramanujan Mathematical Society, India, Cryptology Research Society of India and Society for Electronic Transactions and Security, India, from 6-8 January 2022. With an aim to identify the existing challenges in the areas of mathematics and computing, the book emphasizes the importance of establishing new methods and algorithms to address these challenges. The book includes topics on diverse applications of cryptology, network security, cyber security, block chain, IoT, mobile network, data analytics, applied algebra, mathematical analysis, mathematical modelling, fluid dynamics, fractional calculus, multi-optimization, integral equations, dynamical systems, numerical analysis and scientific computing. Divided into five major parts-applied algebra and analysis, fractional calculus and integral equations, mathematical modelling and fluid dynamics, numerical analysis, and computer science and applications-the book is a useful resource for students, researchers and faculty as well as practitioners.

This book is an enlarged second edition of a monograph published in the Springer AGEM2-Series, 2009. It presents, in a consistent and unified overview, a setup of the theory of spherical functions of mathematical (geo-)sciences. The content shows a twofold transition: First, the natural transition from scalar to vectorial and tensorial theory of spherical harmonics is given in a coordinate-free context, based on variants of the addition theorem, Funk-Hecke formulas, and Helmholtz as well as Hardy-Hodge decompositions. Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is given in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of data analysis and (geo-)application. The whole palette of spherical functions is collected in a well-structured form for modeling and simulating the phenomena and processes occurring in the Earth's system. The result is a work which, while reflecting the present state of knowledge in a time-related manner, claims to be of largely timeless significance in (geo-)mathematical research and teaching.

The book focuses on original approaches intended to support the development of biologically inspired cognitive architectures. It bridges together different disciplines, including artificial intelligence, linguistics, neuro- and social sciences, psychology and philosophy of mind, among others. The chapters are based on contributions presented at the 2023 Annual International Conference on Brain-Inspired Cognitive Architectures for Artificial Intelligence (the 14th Annual Meeting of the BICA Society, BICA*AI 2023), organized in collaboration with the University of Ningbo and held on October 13-15, 2023, in Ningbo, China. The book discusses emerging methods, theories and ideas towards the realization of general-purpose humanlike artificial intelligence or fostering a better understanding of the ways the human mind works. It provides engineers, mathematicians, psychologists, computer scientists and other experts with a timely snapshot of recent research and a source of inspiration for future developments in the broadly intended areas of artificial intelligence and biological inspiration.

This book sheds light on systems that learn extensively, with purpose and naturally interact with humans. Improving operations and increasing competitive differentiation among manufacturing organizations by harnessing the power of cognitive abilities, IoT can help build and influence the flow of information¿making the shop floor more cognitive through effective processing, analysis, and operational optimization. Now we are seeing the first-hand potential of cognitive computing¿its ability to transform businesses, governments, and society. The real potential of the cognitive age can be realized by combining data analysis and statistical reasoning of machines with uniquely human qualities, such as self-directed goals, common sense, and moral values, improving operations and increasing competitive differentiation among manufacturing organizations. By harnessing the power of cognitive abilities, IoT can help build and influence the flow of information¿making the shop floor more cognitive through effective processing, analysis, and operational optimization. Cognitive initiatives come in all shapes and sizes, from change to strategy and everything in between. What most successful projects have in common, no matter how ambitious, is they start with a clear view of what technology can do. Therefore, the first job of a cognitive scientists is to gain a firm understanding of cognitive abilities, as presented in this book.

This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs.The featured contributors are R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo and P. Patie, A. Bernou, M.-E. Caballero and A. Rouault, J. Dedecker, F. Merlevède and E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit, C. Marinelli and L. Scarpa, C. Castaing, N. Marie and P. Raynaud de Fitte, S. Attal, J. Deschamps and C. Pellegrini, and N. Eisenbaum.

This book provides a captivating journey through the realms of classical and quantum systems as it unravels the profound influence that noise may have on their static and dynamic properties. The first part of the book offers succinct yet enlightening discussions on foundational topics related to noise. The second part focuses on a variety of applications, where a diverse spectrum of noise effects in physical systems comes to life, meticulously presented and thoughtfully analyzed. Whether you are a curious student or a dedicated researcher, this book is your key to gaining invaluable insights into noise effects in physical systems. ¿The book has the merit of presenting several topics scattered in the literature and could become a very useful reference.¿ Giovanni Jona-Lasinio, Sapienza ¿ Università di Roma, Italy

This book presents the econometric foundations and applications of multi-dimensional panels, including modern methods of big data analysis. In light of the big data revolution and the emergence of higher dimensional panel data sets, it provides new results to synthesize existing knowledge on the field. The first, theoretical part of the volume is providing the econometric foundations to deal with these new high-dimensional panel data sets. It not only synthesizes our current knowledge, but mostly, presents new research results. The second empirical part of the book provides insight into the most relevant applications in this area. These chapters are a mixture of surveys and new results, always focusing on the econometric problems and feasible solutions.This second extended and revised edition provides an update of all existent chapters to reflect on new developments in the area as well as several new chapters on topics such as machine learning, nonparametric models, networks, and multi-dimensional panels in health economics. The book serves as a standard reference work, a textbook for graduate students in economics, and a source of background material for professionals conducting empirical studies.

Unsupervised domain adaptation (UDA) is a challenging problem in machine learning where the model is trained on a source domain with labeled data and tested on a target domain with unlabeled data. In recent years, UDA has received significant attention from the research community due to its applicability in various real-world scenarios. This book provides a comprehensive review of state-of-the-art UDA methods and explores new variants of UDA that have the potential to advance the field.The book begins with a clear introduction to the UDA problem and is mainly organized into four technical sections, each focused on a specific piece of UDA research. The first section covers criterion optimization-based UDA, which aims to learn domain-invariant representations by minimizing the discrepancy between source and target domains. The second section discusses bi-classifier adversarial learning-based UDA, which creatively leverages adversarial learning by conducting a minimax game between the feature extractor and two task classifiers. The third section introduces source-free UDA, a novel UDA setting that does not require any raw data from the source domain. The fourth section presents active learning for UDA, which combines domain adaptation and active learning to reduce the amount of labeled data needed for adaptation.This book is suitable for researchers, graduate students, and practitioners who are interested in UDA and its applications in various fields, primarily in computer vision. The chapters are authored by leading experts in the field and provide a comprehensive and in-depth analysis of the current UDA methods and new directions for future research. With its broad coverage and cutting-edge research, this book is a valuable resource for anyone looking to advance their knowledge of UDA.

Inspired by this symposium we would like to rethink and provide an insight about the use of new technologies in architecture and design. The consideration spans over (but not limited to) computational design, virtual experience, digital fabrication, artificial intelligence and sustainability/environment. Readers of the proceedings will benefit from discussions on how adoption of new technologies can benefit the Construction Industry rather than just for the sake of leveraging new technologies. The book targets scholars and high-education level students, as well as Ph.D.s which research falls into the broad realm of digital design.

This book focuses on stability analysis and control design approaches for multi-agent systems under network-induced constraints. A hybrid system approach is introduced to address the cooperative control problem of networked multi-agent systems, and several important topics such as asynchronous sampled data cooperative control, hybrid event-triggered cooperative control, and reset-based cooperative control are studied under the hybrid system framework. The special feature of this book is that a hybrid systems approach is proposed for the cooperative control of multi-agent systems, which is beneficial for relaxing the conservativeness of stability analysis and network parameter computation. Interested readers can learn a novel approach to cooperative control of multi-agent systems, and this book can benefit researchers, engineers, and graduate students in the fields of multi-robot cooperation, unmanned aerial vehicle formation, control engineering, etc.

This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the third edition of Steven Strogatz's classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.

Das vorliegende Buch gibt einen Überblick über die Grundlagen der Schadenversicherungsmathematik. Es behandelt in vier Teilen die Gebiete Risikomodelle, Tarifierung, Reservierung, Risikoteilung, und es zeigt auch Querverbindungen zwischen diesen Gebieten auf. Dabei liegt der Schwerpunkt auf der Darstellung und Erklärung der einzelnen Fragestellungen und der zugehörigen mathematischen Modelle und Methoden. Dementsprechend werden Beweise nur ausgeführt, wenn sie für das Verständnis hilfreich sind. Jeder der vier Teile des Buches enthält zahlreiche Aufgaben mit Musterlösungen.Dieses Buch ist aus Lehrveranstaltungen hervorgegangen, die die Autoren im Auftrag der Deutschen Aktuar-Akademie (DAA) zur Vorbereitung auf die Prüfung der Deutschen Aktuarvereinigung (DAV) zum Grundwissen Schadenversicherungsmathematik gehalten haben. Die Aufgaben beruhen auf Prüfungen der DAV und wurden leicht überarbeitet. Inhalt- Risikomodelle- Tarifierung- Reservierung- Risikoteilung Die AutorenProf. em. Dr. Heinz-Willi Goelden, Aktuar DAV, Ostbayerische Technische Hochschule Regensburg Dr. Klaus Th. Hess, Universität RostockProf. em. Dr. Martin Morlock, Aktuar DAV, Universität GießenProf. em. Dr. Klaus D. Schmidt, Aktuar DAV, Technische Universität Dresden und Universität Mannheim Prof. Dr. Klaus J. Schröter, Aktuar DAV, Hochschule Kaiserslautern

This book is a re-assessment of the structure and reach of symmetry, by an interdisciplinary group of specialists from the arts, humanities, and sciences at Oxford University. This book aims to open up the scope of interdisciplinary work in the study of symmetry and is intended for scholars of any background.

This book starts with the rationale for creating an FCM by contrast to other techniques for participatory modeling, as this rationale is a key element to justify the adoption of techniques in a research paper. Fuzzy cognitive mapping is an active research field with over 20,000 publications devoted to externalizing the qualitative perspectives or ¿mental models¿ of individuals and groups. Since the emergence of fuzzy cognitive maps (FCMs) back in the 80s, new algorithms have been developed to reduce bias, facilitate the externalization process, or efficiently utilize quantitative data via machine learning. It covers the development of an FCM with participants through a traditional in-person setting, drawing from the experience of practitioners and highlighting solutions to commonly encountered challenges. The book continues with introducing principles of simulations with FCMs as a tool to perform what-if scenario analysis, while extending those principles to more elaborated simulation scenarios where FCMs and agent-based modeling are combined. Once an FCM model is obtained, the book then details the analytical tools available for practitioners (e.g., to identify the most important factors) and provides examples to aid in the interpretation of results. The discussion concerning relevant extensions is equally pertinent, which are devoted to increasing the expressiveness of the FCM formalism in problems involving uncertainty. The last four chapters focus on building FCM models from historical data. These models are typically needed when facing multi-output prediction or pattern classification problems. In that regard, the book smoothly guides the reader from simple approaches to more elaborated algorithms, symbolizing the noticeable progress of this field in the last 35 years. Problems, recent references, and functional codes are included in each chapter to provide practice and support further learning from practitioners and researchers.

This book offers a comprehensive overview of the latest advancements in the field of applied mathematics as it relates to finance, marketing, and economics. It covers a range of topics including the effective utilization of applied mathematics and mathematical modeling in finance, economics, and marketing. Additionally, it explores the intersection between applied mathematics and practical applications in various scientific fields. The book targets a multidisciplinary audience, fostering the exchange of diverse ideas and showcasing the broad appeal of different subjects. It delves into recent developments in areas such as mathematical modeling in finance, mathematical modeling in marketing, the modeling of financial and economic fundamentals (e.g., interest rates, asset prices), market behavior modeling, modeling market imperfections, pricing financial derivative securities, hedging strategies, numerical methods, and financial engineering.The book features selected contributions presented at the first edition of the International Conference in Applied Mathematics to Finance, Marketing and Economics, which took place at the National School of Commerce and Management in El Jadida, Morocco, from November 26 to 27, 2020.

This thesis deals with storage systems that are organized in last-in-first-out stacks. This approach for storing items is common, for example, in container terminals, and is therefore of great practical interest as well as high relevance in the literature. Furthermore, optimization problems that may arise in this context are presented and addressed by developing novel mathematical model formulations and customized solution methods.

This book publishes select papers presented at the 4th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2021), held at the Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India, from 21¿22 December 2021. Most of the papers deal with mathematical theory embedded with its applications to engineering and sciences. This book illustrates numerical simulation of scientific problems and the state-of-the-art research in industrial and applied mathematics, including various computational and modeling techniques with case studies and concrete examples. Graduate students and researchers, who are interested in real applications of mathematics in the areas of computational and theoretical fluid dynamics, solid mechanics, optimization and operations research, numerical analysis, bio-mathematics, fuzzy, control and systems theory, dynamical systems and nonlinear analysis, algebra and approximation theory, will find the book useful.