Matematisk modellering

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 gathers peer-reviewed contributions submitted to the 21st European Conference on Mathematics for Industry, ECMI 2021, which was virtually held online, hosted by the University of Wuppertal, Germany, from April 13th to April 15th, 2021. The works explore mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Topics covered include: Applied Physics, Biology and Medicine, Cybersecurity, Data Science, Economics, Finance and Insurance, Energy, Production Systems, Social Challenges, and Vehicles and Transportation.The goal of the European Consortium for Mathematics in Industry (ECMI) conference series is to promote interaction between academia and industry, leading to innovations in both fields. These events have attracted leading experts from business, science and academia, and have promoted the application of novel mathematical technologies to industry. They have also encouraged industrial sectors to share challenging problems where mathematicians can provide fresh insights and perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.

* Contains computer algebra worksheets or "recipes" designed using MAPLE (System 10); no prior knowledge of MAPLE is assumed* Effective computational science text for first- and second-year undergraduates in mathematics, physics, engineering, chemistry, economics, biology, and pre-medicine* Examples and problems provide basis for both self-study and on-line course

This book goes into a detailed investigation of adapting artificial neural network (ANN) and structural equation modeling (SEM) techniques in marketing and consumer research. The aim of using a dual-stage SEM and ANN approach is to obtain linear and non-compensated relationships because the ANN method captures non-compensated relationships based on the black box technology of artificial intelligence. Hence, the ANN approach validates the results of the SEM method. In addition, such the novel emerging approach increases the validity of the prediction by determining the importance of the variables. Consequently, the number of studies using SEM-ANN has increased, but the different types of study cases that show customization of different processes in ANNs method combination with SEM are still unknown, and this aspect will be affecting to the generation results. Thus, there is a need for further investigation in marketing and consumer research. This book bridges the significant gap in this research area. The adoption of SEM and ANN techniques in social commerce and consumer research is massive all over the world. Such an expansion has generated more need to learn how to capture linear and non-compensatory relationships in such area. This book would be a valuable reading companion mainly for business and management students in higher academic organizations, professionals, policy-makers, and planners in the field of marketing. This book would also be appreciated by researchers who are keenly interested in social commerce and consumer research.

This third volume of the book series shows R-calculus is a Gentzen-typed deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. In this book, R-calculus is taken as Tableau-based/sequent-based/multisequent-based to preserve the satisfiability of the Theory/sequent/multisequent to revise, or sequent-based, to preserve the satisfiability of the sequent to revise. The R-calculi for Post and three-valued logic is given.  This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. 

This book provides a comprehensive introduction to the foundations and frontiers of graph neural networks. In addition, the book introduces the basic concepts and definitions in graph representation learning and discusses the development of advanced graph representation learning methods with a focus on graph neural networks. The book providers researchers and practitioners with an understanding of the fundamental issues as well as a launch point for discussing the latest trends in the science. The authors emphasize several frontier aspects of graph neural networks and utilize graph data to describe pairwise relations for real-world data from many different domains, including social science, chemistry, and biology. Several frontiers of graph neural networks are introduced, which enable readers to acquire the needed techniques of advances in graph neural networks via theoretical models and real-world applications. 

This book gathers contributions from the fourth edition of the Conference on "e;Philosophy and Theory of Artificial Intelligence"e; (PT-AI), held on 27-28th of September 2021 at Chalmers University of Technology, in Gothenburg, Sweden. It covers topics at the interface between philosophy, cognitive science, ethics and computing. It discusses advanced theories fostering the understanding of human cognition, human autonomy, dignity and morality, and the development of corresponding artificial cognitive structures, analyzing important aspects of the relationship between humans and AI systems, including the ethics of AI. This book offers a thought-provoking snapshot of what is currently going on, and what are the main challenges, in the multidisciplinary field of the philosophy of artificial intelligence. 

This book examines the issues of ensuring anti-terrorist security of an aviation enterprise, provides a history of terrorism in the aviation sector, and analyzes the legal regulations. This book provides mathematical and mathematical-psychological models for reducing the risk of terrorist threats, which makes it possible to objectively increase the safety of air transport facilities, reduce the likelihood of terrorist attacks, save human lives and prevent significant material losses. The solutions of general humanistic problems proposed in the book-preventing accidents and preserving the world-are an original feature of the book, which allows one to treat it with the necessary attention and interest for the reader. The concept of anti-terrorist security of an aviation enterprise presented in this book has been widely tested and introduced into the activities of leading aviation enterprises, including the Interstate Aviation Committee (IAC), and has been used in the investigation of aviation accidents.This book is written for a wide range of audience associated with ensuring aviation transport security and for the end users of airlines-passengers, in order to expand their knowledge about the reliability of using air transport. 

This book provides up-to-date developments in the stability analysis and (anti-)synchronization control area for complex-valued neural networks systems with time delay. It brings out the characteristic systematism in them and points out further insight to solve relevant problems. It presents a comprehensive, up-to-date, and detailed treatment of dynamical behaviors including stability analysis and (anti-)synchronization control. The materials included in the book are mainly based on the recent research work carried on by the authors in this domain.The book is a useful reference for all those from senior undergraduates, graduate students, to senior researchers interested in or working with control theory, applied mathematics, system analysis and integration, automation, nonlinear science, computer and other related fields, especially those relevant scientific and technical workers in the research of complex-valued neural network systems, dynamic systems, and intelligent control theory.

This book discusses the systems of interacting particles evolving in the random media. The focus is on the study of both the finite subsystems motion and the flow, describing motion of all particles in the space. The integral characteristics of the system and mass distribution are also covered and results are illustrated with examples from turbulence theory, synchronization and DNA evolution.

This book offers a self-contained introduction to partial differential equations (PDEs), primarily focusing on linear equations, and also providing perspective on nonlinear equations. The treatment is mathematically rigorous with a generally theoretical layout, with indications to some of the physical origins of PDEs. The Second Edition is rewritten to incorporate years of classroom feedback, to correct errors and to improve clarity. The exposition offers many examples, problems and solutions to enhance understanding. Requiring only advanced differential calculus and some basic Lp theory, the book will appeal to advanced undergraduates and graduate students, and to applied mathematicians and mathematical physicists.

This book deals with several types of multi-dimensional control problems in the face of data uncertainty for vector cases-multi-dimensional multi-objective control problem with uncertain objective functionals, uncertain constraint functionals, and uncertain objective as well as constraint functionals, uncertain multi-dimensional multi-objective control problem with semi-infinite constraints, uncertain dual multi-dimensional multi-objective variational control problem, and second-order PDE&PDI constrained robust optimization problem. The book provides the solution approaches-an exact l1 penalty function approach, modified objective approach, robust approach-in the simplest way to solve the recent developing optimization problems in the sense of uncertainty. 

Dispersed multiphase flows are at the heart of many geophysical, environmental, industrial, and energy applications. Volcanic eruption, rain formation, powder snow avalanches, sediment transport, and dust storms are some of the classic examples from the environment, while industrial applications include fluidized beds, slurry transport, fuel injection, cyclone separators, and plasma coating, to name a few. Although each application is unique, they share significant commonalities in the underlying dispersed multiphase flow physics that govern their dynamics. This book takes a rigorous approach to explaining the complex interconnected physical processes that are at play, before developing different classes of mathematical models and numerical techniques that are appropriate for different regimes of dispersed multiphase flows. Containing many examples and over 100 exercises, it is suitable for use as a graduate-level textbook as well as a reference for researchers who want to model and simulate a multiphase flow phenomenon in their application.

Learn to write algorithms and program in the new field of quantum computing. This second edition is updated to equip you with the latest knowledge and tools needed to be a complex problem-solver in this ever-evolving landscape. The book has expanded its coverage of current and future advancements and investments by IT companies in this emerging technology. Most chapters are thoroughly revised to incorporate the latest updates to IBM Quantum's systems and offerings, such as improved algorithms, integrating hardware advancements, software enhancements, bug fixes, and more.Yoüll examine quantum computing in the cloud and run experiments there on a real quantum device. Along the way yoüll cover game theory with the Magic Square, an example of quantum pseudo-telepathy. Yoüll also learn to write code using QISKit, Python SDK, and other APIs such as QASM and execute it against simulators (local or remote) or a real quantum computer. Then peek inside the inner workings of the Bell states for entanglement, Grover¿s algorithm for linear search, Shor¿s algorithm for integer factorization, and other algorithms in the fields of optimization, and more. Finally, yoüll learn the current quantum algorithms for entanglement, random number generation, linear search, integer factorization, and others. By the end of this book, yoüll understand how quantum computing provides massive parallelism and significant computational speedups over classical computersWhat You'll LearnWrite algorithms that provide superior performance over their classical counterpartsCreate a quantum number generator: the quintessential coin flip with a quantum twistExamine the quantum algorithms in use today for random number generation, linear search, and moreDiscover quantum teleportationHandle the counterfeit coin problem, a classic puzzlePut your knowledge to the test with more than 150 practice exercises

This book provides engineers and researchers knowledge to help them in system reliability analysis using machine learning, artificial intelligence, big data, genetic algorithm, information theory, multi-criteria decision making, and other techniques. It will also be useful to students learning reliability engineering.The book brings readers up to date with how system reliability relates to the latest techniques of AI, big data, genetic algorithm, information theory, and multi-criteria decision making and points toward future developments in the subject.

This book describes the use of different mathematical modeling and soft computing techniques used to solve real world engineering problems. The book gives an overview of the current state of soft computing techniques and describes the advantages and disadvantages of soft computing compared to traditional hard computing techniques.

This textbook covers the fundamentals of reliability theory and its application for engineering processes, especially for aircraft units and systems. Reliability basis was explained for the best understanding of reliability analysis application for engineering systems in aviation industry. Several approaches for the reliability analysis and their application with examples are presented. It also introduces main trends in the modern reliability theory development.This book will be interested for university students and early-career engineers of aviation industry majors.

This book comprises chapters authored by experts who are professors and researchers in internationally recognized universities and research institutions. The book presents the results of research and descriptions of real-world systems, services, and technologies. Reading this book, researchers, professional practitioners, and graduate students will gain a clear vision on the state of the art of the research and real-world practice on system dependability and analytics.The book is published in honor of Professor Ravishankar K. Iyer, the George and Ann Fisher Distinguished Professor in the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign (UIUC), Urbana, Illinois. Professor Iyer is ACM Fellow, IEEE Fellow, AAAS Fellow, and served as Interim Vice Chancellor of UIUC for research during 2008-2011. The book contains chapters written by many of his former students.

"The first systematic treatment of model risk, this book provides the tools needed to quantify and assess the impact of model uncertainty. It will be essential for all those working in portfolio theory and the theory of financial and engineering risk, for practitioners in these areas, and for graduate courses on risk bounds and model uncertainty"--

This book mathematically analyzes the basic problems of biology, decision making and psychology within the framework of the theory of open quantum systems.In recent years there has been an explosion of interest in applications of quantum theory in fields beyond physics. The main areas include psychology, decision-making, economics, finance, social science as well as genetics and molecular biology. The corresponding models are referred to as quantum-like; they don¿t concern any genuine physical processes in the human brain.Quantum-like models reflect the special features of information processing in biological, cognitive, and social systems which match well with the quantum formalism. This formalism gives rise to the quantum probability model (QP) which differs essentially from Kolmogorov's classical probability model. QP also serves as the basis for quantum information theory.Recently QP has been widely applied to the resolution of the basic paradoxes of decision making theory and to modeling experimental data stemming from cognition, psychology, economics, and finance thereby shedding light on probability fallacies and irrational behavior.In this book, the theory of quantum instruments and the quantum master equation are applied to the modeling of biological and cognitive processes, in particular, to the stability of complex biological and social systems interacting with their environment. An essential part of the book is devoted to the theory of the social laser and the Fröhlich condensate.

This book presents experimental as well as simulation methodologies for analysis and development of nanostructures for introducing the desirable effects through modifications in the basic structure of select nanomaterials. The initial chapters in this book focus on exploring the basic aspects of nanomaterials, e.g., distinguishing features, synthesis, processing, characterization, simulation and application dimensions, or nanostructures that enable novel/enhanced properties or functions. The chapters also cover the size-dependent electronic, optical, and magnetic properties of nanomaterials in exposing the specific properties essential for applications in nanophotonics, nanoplasmonics, nanosystems (e.g., biological, medical, chemical, catalytic, energy, and environmental applications), and nanodevices (e.g., electronic, photonic, magnetic, imaging, diagnostic, and sensor applications). This book is a useful resource for students, researchers, and technologists in gathering recent knowledge on novel nanostructures and their use in different application areas.

This book presents insights into the thermal performance of solar thermal collectors using both computational and experimental modeling. It consists of various computational and experimental case studies conducted by the authors on the solar thermal collector system. The authors begin by developing thermal modeling using a case study that shows the effect of different governing parameters. A few more experimental cases studies follow that highlight the energy, exergy, and environmental performance of the solar thermal collector system and to examine the performance of a modified solar collector system, illustrating performance improvement techniques.Finally, application of different evolutionary optimization techniques such as soft computing and evolutionary methods, like fuzzy techniques, MCDM methods like fuzzy logic based expert system (FLDS), Artificial Neural Network (ANN), Grey relational analysis (GRA), Entropy-Jaya algorithm, Entropy-VIKOR etc. are employed.

This text describes a comprehensive adjoint sensitivity analysis methodology (nth-CASAM), developed by the author, which enablesthe efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The nth-CASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby overcoming the so-called ¿curse of dimensionality¿ in sensitivity and uncertainty analysis. The nth-CASAM is applicable to any model; the larger the number of model parameters, the more efficient the nth-CASAM becomes for computing arbitrarily high-order response sensitivities. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling.This Volume Two, the second of three, presents the large-scale application of the nth-CASAM to perform a representative fourth-order sensitivity analysis of the Polyethylene-Reflected Plutonium benchmark described in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This benchmark is modeled mathematically by the Boltzmann particle transport equation, involving 21,976 imprecisely-known parameters, the numerical solution of which requires representative large-scale computations. The sensitivity analysis presented in this volume is the most comprehensive ever performed in the field of reactor physics and the results presented in this book prove, perhaps counter-intuitively, that many of the 4th-order sensitivities are much larger than the corresponding 3rd-order ones, which are, in turn, much larger than the 2nd-order ones, all of which are much larger than the 1st-order sensitivities. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of exactly obtained expressions of arbitrarily-high-order response sensitivities.

This book provides a systematic description about the development of Isogeometric Topology Optimization (ITO) method using the density, and then addresses the effectiveness and efficiency of the ITO method on several design problems, including multi-material structures, stress-minimization structures, piezoelectric structures and also with the uniform manufacturability, ultra-lightweight architected materials with extreme bulk/shear moduli, auxetic metamaterials and auxetic meta-composites with the NPRs behavior in microstructures. A detailed MATLAB implementation of the ITO method with an in-house code "IgaTop" is also presented.