This book presents a systematic overview on partition function form games: a game form in cooperative game theory to integrate externalities for various applications. Cooperative game theory has been immensely useful to study a wide range of issues, but the standard approaches ignore the side effects of cooperation. Recently interest shifted to problems where externalities play the main roles such as models of cooperation in market competition or the shared use of public resources. Such problems require richer models that can explicitly evaluate the side-effects of cooperation. In partition function form games the value of cooperation depends on the outsiders' actions. A recent surge of interest driven by applications has made results very fragmented. This book offers an accessible, yet comprehensive and systematic study of properties, solutions and applications of partition function games surveying both theoretical results and their applications. It assembles a survey of existing research and smaller original results as well as original interpretations and comparisons. The book is self-contained and accessible for readers with little or no knowledge of cooperative game theory.

This book focuses on three core knowledge requirements for effective and thorough data analysis for solving business problems. These are a foundational understanding of: 1. statistical, econometric, and machine learning techniques; 2. data handling capabilities; 3. at least one programming language. Practical in orientation, the volume offers illustrative case studies throughout and examples using Python in the context of Jupyter notebooks. Covered topics include demand measurement and forecasting, predictive modeling, pricing analytics, customer satisfaction assessment, market and advertising research, and new product development and research. This volume will be useful to business data analysts, data scientists, and market research professionals, as well as aspiring practitioners in business data analytics. It can also be used in colleges and universities offering courses and certifications in business data analytics, data science, and market research.

Computing systems are becoming highly complex, harder to understand, and therefore more prone to failure. Where such systems control aircraft for example, system failure could have disastrous consequences. It is important therefore that we are able to employ mathematical techniques to specify the behavior of critical systems. This thesis uses the theory of Communicating Sequential Processes to show how a real-time system (a system that maintains a continuous interaction with its environment) may be specified. Included is a case study in which a local area network protocol is described at two levels of abstraction, and a general method for structuring CSP descriptions of layered protocols is given. The research contained here represents the very latest work on the specification and verification of real-time systems.

The first edition of this award-winning book attracted a wide audience. This second edition is both a joy to read and a useful classroom tool. Unlike traditional textbooks, it requires no mathematical prerequisites and can be read around the mathematics presented. If used as a textbook, the mathematics can be prioritized, with a book both students and instructors will enjoy reading. Secret History: The Story of Cryptology, Second Edition incorporates new material concerning various eras in the long history of cryptology. Much has happened concerning the political aspects of cryptology since the first edition appeared. The still unfolding story is updated here. The first edition of this book contained chapters devoted to the cracking of German and Japanese systems during World War II. Now the other side of this cipher war is also told, that is, how the United States was able to come up with systems that were never broken. The text is in two parts. Part I presents classic cryptology from ancient times through World War II. Part II examines modern computer cryptology. With numerous real-world examples and extensive references, the author skillfully balances the history with mathematical details, providing readers with a sound foundation in this dynamic field. FEATURES Presents a chronological development of key concepts Includes the Vigenere cipher, the one-time pad, transposition ciphers, Jefferson's wheel cipher, Playfair cipher, ADFGX, matrix encryption, Enigma, Purple, and other classic methods Looks at the work of Claude Shannon, the origin of the National Security Agency, elliptic curve cryptography, the Data Encryption Standard, the Advanced Encryption Standard, public-key cryptography, and many other topics New chapters detail SIGABA and SIGSALY, successful systems used during World War II for text and speech, respectively Includes quantum cryptography and the impact of quantum computers

Due to the fast growth of the Web and the difficulties in finding desired information, efficient and effective information retrieval systems have become more important than ever, and the search engine has become an essential tool for many people. The ranker, a central component in every search engine, is responsible for the matching between processed queries and indexed documents. Because of its central role, great attention has been paid to the research and development of ranking technologies. In addition, ranking is also pivotal for many other information retrieval applications, such as collaborative filtering, definition ranking, question answering, multimedia retrieval, text summarization, and online advertisement. Leveraging machine learning technologies in the ranking process has led to innovative and more effective ranking models, and eventually to a completely new research area called "learning to rank." Liu first gives a comprehensive review of the major approaches to learning to rank. For each approach he presents the basic framework, with example algorithms, and he discusses its advantages and disadvantages. He continues with some recent advances in learning to rank that cannot be simply categorized into the three major approaches - these include relational ranking, query-dependent ranking, transfer ranking, and semisupervised ranking. His presentation is completed by several examples that apply these technologies to solve real information retrieval problems, and by theoretical discussions on guarantees for ranking performance. This book is written for researchers and graduate students in both information retrieval and machine learning. They will find here the only comprehensive description of the state of the art in a field that has driven the recent advances in search engine development.

Physically Unclonable Functions (PUFs) translate unavoidable variations in certain parameters of materials, waves, or devices into random and unique signals. They have found many applications in the Internet of Things (IoT), authentication systems, FPGA industry, several other areas in communications and related technologies, and many commercial products. Statistical Trend Analysis of Physically Unclonable Functions first presents a review on cryptographic hardware and hardware-assisted cryptography. The review highlights PUF as a mega trend in research on cryptographic hardware design. Afterwards, the authors present a combined survey and research work on PUFs using a systematic approach. As part of the survey aspect, a state-of-the-art analysis is presented as well as a taxonomy on PUFs, a life cycle, and an established ecosystem for the technology. In another part of the survey, the evolutionary history of PUFs is examined, and strategies for further research in this area are suggested. In the research side, this book presents a novel approach for trend analysis that can be applied to any technology or research area. In this method, a text mining tool is used which extracts 1020 keywords from the titles of the sample papers. Then, a classifying tool classifies the keywords into 295 meaningful research topics. The popularity of each topic is then numerically measured and analyzed over the course of time through a statistical analysis on the number of research papers related to the topic as well as the number of their citations. The authors identify the most popular topics in four different domains; over the history of PUFs, during the recent years, in top conferences, and in top journals. The results are used to present an evolution study as well as a trend analysis and develop a roadmap for future research in this area. This method gives an automatic popularity-based statistical trend analysis which eliminates the need for passing personal judgments about the direction of trends, and provides concrete evidence to the future direction of research on PUFs. Another advantage of this method is the possibility of studying a whole lot of existing research works (more than 700 in this book). This book will appeal to researchers in text mining, cryptography, hardware security, and IoT.

Proof techniques in cryptography are very difficult to understand, even for students or researchers who major in cryptography. In addition, in contrast to the excessive emphases on the security proofs of the cryptographic schemes, practical aspects of them have received comparatively less attention. This book addresses these two issues by providing detailed, structured proofs and demonstrating examples, applications and implementations of the schemes, so that students and practitioners may obtain a practical view of the schemes. Seong Oun Hwang is a professor in the Department of Computer Engineering and director of Artificial Intelligence Security Research Center, Gachon University, Korea. He received the Ph.D. degree in computer science from the Korea Advanced Institute of Science and Technology (KAIST), Korea. His research interests include cryptography, cybersecurity, networks, and machine learning. Intae Kim is an associate research fellow at the Institute of Cybersecurity and Cryptology, University of Wollongong, Australia. He received the Ph.D. degree in electronics and computer engineering from Hongik University, Korea. His research interests include cryptography, cybersecurity, and networks. Wai Kong Lee is an assistant professor in UTAR (University Tunku Abdul Rahman), Malaysia. He received the Ph.D. degree in engineering from UTAR, Malaysia. In between 2009 - 2012, he served as an R&D engineer in several multinational companies including Agilent Technologies (now known as Keysight) in Malaysia. His research interests include cryptography engineering, GPU computing, numerical algorithms, Internet of Things (IoT) and energy harvesting.

This book presents best selected research papers presented at the Thirteenth International Conference on Applied Mathematics and Mechanics in the Aerospace Industry (AMMAI 2020), held from September 6 to September 13, 2020, at the Alushta Health and Educational Center (The Republic of Crimea). The book is dedicated to solving actual problems of applied mechanics using modern computer technology including smart paradigms. Physical and mathematical models, numerical methods, computational algorithms, and software complexes are discussed, which allow to carry out high-precision mathematical modeling in fluid, gas, and plasma mechanics, in general mechanics, deformable solid mechanics, in strength, destruction and safety of structures, etc. Technologies and software systems that provide effective solutions to the problems at various multi-scale levels are considered. Special attention is paid to the training of highly qualified specialists for the aviation and space industry. The book is recommended for specialists in the field of applied mathematics and mechanics, mathematical modeling, information technologies, and developers of modern applied software systems.

The author presents a theory of concurrent processes where three different semantic description methods that are usually studied in isolation are brought together. Petri nets describe processes as concurrent and interacting machines; algebraic process terms describe processes as abstract concurrent processes; and logical formulas specify the intended communication behaviour of processes. At the heart of this theory are two sets of transformation rules for the top-down design of concurrent processes. The first set can be used to transform stepwise logical formulas into process terms, whilst process terms can be transformed into Petri nets by the second set. These rules are based on novel techniques for the operational and denotational semantics of concurrent processes. Various results and relationships between nets, terms and formulas starting with formulas and illustrated by examples. The use of transformations is demonstrated in a series of case studies, and the author also identifies directions for research.

This volume contains thirteen articles on advances in applied mathematics and computing methods for engineering problems. Six papers are on optimization methods and algorithms with emphasis on problems with multiple criteria; four articles are on numerical methods for applied problems modeled with nonlinear PDEs; two contributions are on abstract estimates for error analysis; finally one paper deals with rare events in the context of uncertainty quantification. Applications include aerospace, glaciology and nonlinear elasticity.

Hereinis a selection of contributions from speakers at two conferences on applied mathematics held in June 2012 at the University of Jyvaskyla, Finland. The first conference, Optimization and PDEs with Industrial Applications celebrated the seventieth birthday of Professor Jacques Periaux of theUniversity of Jyvaskyla and Polytechnic University of Catalonia (Barcelona Tech) and the second conference, Optimization and PDEs with Applications celebrated the seventy-fifth birthday of Professor Roland Glowinski of the University of Houston.

This work should be of interest to researchers and practitioners as well as advanced students or engineers in computational and applied mathematics or mechanics."

Petri Nets were introduced and still successfully used to analyze and model discrete event systems especially in engineering and computer sciences such as in automatic control.

Recently this discrete Petri Nets formalism was successfully extended to continuous and hybrid systems. This monograph presents a well written and clearly organized introduction in the standard methods of Petri Nets with the aim to reach an accurate understanding of continuous and hybrid Petri Nets, while preserving the consistency of basic concepts throughout the book. The book is a monograph as well as a didactic tool which is easy to understand due to many simple solved examples and detailed figures. In its second completely reworked edition various sections, concepts and recently developed algorithms are added as well as additional examples/exercises.

The quadratic binary optimization problem (QUBO) is a versatile combinatorial optimization model with a variety of applications and rich theoretical properties. Application areas of the model include finance, cluster analysis, traffic management, machine scheduling, VLSI physical design, physics, quantum computing, engineering, and medicine. In addition, various mathematical optimization models can be reformulated as a QUBO, including the resource constrained assignment problem, set partitioning problem, maximum cut problem, quadratic assignment problem, the bipartite unconstrained binary optimization problem, among others. This book presents a systematic development of theory, algorithms, and applications of QUBO. It offers a comprehensive treatment of QUBO from various viewpoints, including a historical introduction along with an in-depth discussion of applications modelling, complexity and polynomially solvable special cases, exact and heuristic algorithms, analysis of approximation algorithms, metaheuristics, polyhedral structure, probabilistic analysis, persistencies, and related topics. Available software for solving QUBO is also introduced, including public domain, commercial, as well as quantum computing based codes.

Structured methodologies are a popular and powerful tool in information systems development. Many different ones exist, each employing a number of models and so a specification must be converted from one form to another during the development process. To solve this problem, Dr. Tse proposes a unifying framework behind popular structured models. He approaches the problem from the viewpoints of algebra and category theory. He not only develops the frameworks but also illustrates their practical and theoretical usefulness. Thus, this book will provide insight for software engineers into how methodologies can be formalized, and will open up a range of applications and problems for theoretical computer scientists.

This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas.

An Image Processing Tour of College Mathematics aims to provide meaningful context for reviewing key topics of the college mathematics curriculum, to help students gain confidence in using concepts and techniques of applied mathematics, to increase student awareness of recent developments in mathematical sciences, and to help students prepare for graduate studies. The topics covered include a library of elementary functions, basic concepts of descriptive statistics, probability distributions of functions of random variables, definitions and concepts behind first- and second-order derivatives, most concepts and techniques of traditional linear algebra courses, an introduction to Fourier analysis, and a variety of discrete wavelet transforms - all of that in the context of digital image processing. Features Pre-calculus material and basic concepts of descriptive statistics are reviewed in the context of image processing in the spatial domain. Key concepts of linear algebra are reviewed both in the context of fundamental operations with digital images and in the more advanced context of discrete wavelet transforms. Some of the key concepts of probability theory are reviewed in the context of image equalization and histogram matching. The convolution operation is introduced painlessly and naturally in the context of naive filtering for denoising and is subsequently used for edge detection and image restoration. An accessible elementary introduction to Fourier analysis is provided in the context of image restoration. Discrete wavelet transforms are introduced in the context of image compression, and the readers become more aware of some of the recent developments in applied mathematics. This text helps students of mathematics ease their way into mastering the basics of scientific computer programming.

Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB (R), and Maple (TM) to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.

Discrete Mathematics for Computer Science: An Example-Based Introduction is intended for a first- or second-year discrete mathematics course for computer science majors. It covers many important mathematical topics essential for future computer science majors, such as algorithms, number representations, logic, set theory, Boolean algebra, functions, combinatorics, algorithmic complexity, graphs, and trees. Features Designed to be especially useful for courses at the community-college level Ideal as a first- or second-year textbook for computer science majors, or as a general introduction to discrete mathematics Written to be accessible to those with a limited mathematics background, and to aid with the transition to abstract thinking Filled with over 200 worked examples, boxed for easy reference, and over 200 practice problems with answers Contains approximately 40 simple algorithms to aid students in becoming proficient with algorithm control structures and pseudocode Includes an appendix on basic circuit design which provides a real-world motivational example for computer science majors by drawing on multiple topics covered in the book to design a circuit that adds two eight-digit binary numbers Jon Pierre Fortney graduated from the University of Pennsylvania in 1996 with a BA in Mathematics and Actuarial Science and a BSE in Chemical Engineering. Prior to returning to graduate school, he worked as both an environmental engineer and as an actuarial analyst. He graduated from Arizona State University in 2008 with a PhD in Mathematics, specializing in Geometric Mechanics. Since 2012, he has worked at Zayed University in Dubai. This is his second mathematics textbook.

This book provides a clear understanding regarding the fundamentals of matrix and determinant from introduction to its real-life applications. The topic is considered one of the most important mathematical tools used in mathematical modelling. Matrix and Determinant: Fundamentals and Applications is a small self-explanatory and well synchronized book that provides an introduction to the basics along with well explained applications. The theories in the book are covered along with their definitions, notations, and examples. Illustrative examples are listed at the end of each covered topic along with unsolved comprehension questions, and real-life applications. This book provides a concise understanding of matrix and determinate which will be useful to students as well as researchers.

MATRIX is Australia's international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in 2018: - Non-Equilibrium Systems and Special Functions - Algebraic Geometry, Approximation and Optimisation - On the Frontiers of High Dimensional Computation - Month of Mathematical Biology - Dynamics, Foliations, and Geometry In Dimension 3 - Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type - Functional Data Analysis and Beyond - Geometric and Categorical Representation Theory The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

This book focuses on lattice-based cryptosystems, widely considered to be one of the most promising post-quantum cryptosystems and provides fundamental insights into how to construct provably secure cryptosystems from hard lattice problems. The concept of provable security is used to inform the choice of lattice tool for designing cryptosystems, including public-key encryption, identity-based encryption, attribute-based encryption, key change and digital signatures. Given its depth of coverage, the book especially appeals to graduate students and young researchers who plan to enter this research area.

This book discusses an important area of numerical optimization, called interior-point method. This topic has been popular since the 1980s when people gradually realized that all simplex algorithms were not convergent in polynomial time and many interior-point algorithms could be proved to converge in polynomial time. However, for a long time, there was a noticeable gap between theoretical polynomial bounds of the interior-point algorithms and efficiency of these algorithms. Strategies that were important to the computational efficiency became barriers in the proof of good polynomial bounds. The more the strategies were used in algorithms, the worse the polynomial bounds became. To further exacerbate the problem, Mehrotra's predictor-corrector (MPC) algorithm (the most popular and efficient interior-point algorithm until recently) uses all good strategies and fails to prove the convergence. Therefore, MPC does not have polynomiality, a critical issue with the simplex method. This book discusses recent developments that resolves the dilemma. It has three major parts. The first, including Chapters 1, 2, 3, and 4, presents some of the most important algorithms during the development of the interior-point method around the 1990s, most of them are widely known. The main purpose of this part is to explain the dilemma described above by analyzing these algorithms' polynomial bounds and summarizing the computational experience associated with them. The second part, including Chapters 5, 6, 7, and 8, describes how to solve the dilemma step-by-step using arc-search techniques. At the end of this part, a very efficient algorithm with the lowest polynomial bound is presented. The last part, including Chapters 9, 10, 11, and 12, extends arc-search techniques to some more general problems, such as convex quadratic programming, linear complementarity problem, and semi-definite programming.

This book is an essential tool written to be used as the primary text for an undergraduate or early postgraduate course as well as a reference book for engineers and scientists who want to quickly develop finite-element programs. Regarding the formulation of the finite element method, the book emphasizes the essential unity of all processes of approximation used in the solution of differential equations such as finite differences, finite elements and boundary elements. Computational aspects are presented in Maple. Three Maple packages were specially developed for this book and are included in a companion CD-ROM.

This book explores minimum divergence methods of statistical machine learning for estimation, regression, prediction, and so forth, in which we engage in information geometry to elucidate their intrinsic properties of the corresponding loss functions, learning algorithms, and statistical models. One of the most elementary examples is Gauss's least squares estimator in a linear regression model, in which the estimator is given by minimization of the sum of squares between a response vector and a vector of the linear subspace hulled by explanatory vectors. This is extended to Fisher's maximum likelihood estimator (MLE) for an exponential model, in which the estimator is provided by minimization of the Kullback-Leibler (KL) divergence between a data distribution and a parametric distribution of the exponential model in an empirical analogue. Thus, we envisage a geometric interpretation of such minimization procedures such that a right triangle is kept with Pythagorean identity in the sense of the KL divergence. This understanding sublimates a dualistic interplay between a statistical estimation and model, which requires dual geodesic paths, called m-geodesic and e-geodesic paths, in a framework of information geometry. We extend such a dualistic structure of the MLE and exponential model to that of the minimum divergence estimator and the maximum entropy model, which is applied to robust statistics, maximum entropy, density estimation, principal component analysis, independent component analysis, regression analysis, manifold learning, boosting algorithm, clustering, dynamic treatment regimes, and so forth. We consider a variety of information divergence measures typically including KL divergence to express departure from one probability distribution to another. An information divergence is decomposed into the cross-entropy and the (diagonal) entropy in which the entropy associates with a generative model as a family of maximum entropy distributions; the cross entropy associates with a statistical estimation method via minimization of the empirical analogue based on given data. Thus any statistical divergence includes an intrinsic object between the generative model and the estimation method. Typically, KL divergence leads to the exponential model and the maximum likelihood estimation. It is shown that any information divergence leads to a Riemannian metric and a pair of the linear connections in the framework of information geometry. We focus on a class of information divergence generated by an increasing and convex function U, called U-divergence. It is shown that any generator function U generates the U-entropy and U-divergence, in which there is a dualistic structure between the U-divergence method and the maximum U-entropy model. We observe that a specific choice of U leads to a robust statistical procedure via the minimum U-divergence method. If U is selected as an exponential function, then the corresponding U-entropy and U-divergence are reduced to the Boltzmann-Shanon entropy and the KL divergence; the minimum U-divergence estimator is equivalent to the MLE. For robust supervised learning to predict a class label we observe that the U-boosting algorithm performs well for contamination of mislabel examples if U is appropriately selected. We present such maximal U-entropy and minimum U-divergence methods, in particular, selecting a power function as U to provide flexible performance in statistical machine learning.

The classical three-body problem is of great importance for its applications to astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which a large number have been computed numerically. Here the author explains and organizes this material through a systematic study of generating families, which are the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. The most critical part is the study of bifurcations. Many cases are distinguished and studied separately and detailed recipies are given. Their use is illustrated by determining generating families, and comparing them with numerical computations for the Earth+Moon and Sun-Jupiter systems.

Businesses today are faced with a highly competitive market and fast-changing technologies. In order to meet demanding customers' needs, they rely on high quality software. A new field of study, soft computing techniques, is needed to estimate the efforts invested in component-based software. Component-Based Systems: Estimating Efforts Using Soft Computing Techniques is an important resource that uses computer-based models for estimating efforts of software. It provides an overview of component-based software engineering, while addressing uncertainty involved in effort estimation and expert opinions. This book will also instruct the reader how to develop mathematical models. This book is an excellent source of information for students and researchers to learn soft computing models, their applications in software management, and will help software developers, managers, and those in the industry to apply soft computing techniques to estimate efforts.