This volume contains the courses given at the Sixth Summer School on Complex Systems held at Facultad de Ciencias Fisicas y Maternaticas, Universidad de Chile at Santiago, Chile, from 14th to 18th December 1998. This school was addressed to graduate students and researchers working on areas related with recent trends in Complex Systems, including dynamical systems, cellular automata, complexity and cutoff in Markov chains. Each contribution is devoted to one of these subjects. In some cases they are structured as surveys, presenting at the same time an original point of view and showing mostly new results. The paper of Pierre Arnoux investigates the relation between low complex systems and chaotic systems, showing that they can be put into relation by some re normalization operations. The case of quasi-crystals is fully studied, in particular the Sturmian quasi-crystals. The paper of Franco Bagnoli and Raul Rechtman establishes relations be tween Lyapunov exponents and synchronization processes in cellular automata. The principal goal is to associate tools, usually used in physical problems, to an important problem in cellularautomata and computer science, the synchronization problem. The paper of Jacques Demongeot and colleagues gives a presentation of at tractors of dynamical systems appearing in biological situations. For instance, the relation between positive or negative loops and regulation systems."

"Optimization on Metric and Normed Spaces" is devoted to the recent progress in optimization on Banach spaces and complete metric spaces. Optimization problems are usually considered on metric spaces satisfying certain compactness assumptions which guarantee the existence of solutions and convergence of algorithms. This book considers spaces that do not satisfy such compactness assumptions. In order to overcome these difficulties, the book uses the Baire category approach and considers approximate solutions. Therefore, it presents a number of new results concerning penalty methods in constrained optimization, existence of solutions in parametric optimization, well-posedness of vector minimization problems, and many other results obtained in the last ten years. The book is intended for mathematicians interested in optimization and applied functional analysis.

This book is collection of papers on the main topics of cardiovascular modelling and measurements. Some of the results show how to calculate many non-linear aspects of fluid flow and the turbulence in the arteries and the bifurcation junctions of the cardiovascular system. There are three themes to the papers: first, the fundamental concepts of fluid dynamics and turbulence in the system; the second theme is the flow modelling in arteries and bypass graft; the third section is about haemorheology and haemodynamics and explores the factors that play a role in coronary circulation using data from patients with ischaemic heart disease and acute myocardial infarction.

This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.

This research aims to achieve a fundamental understanding of synchronization and its interplay with the topology of complex networks. Synchronization is a ubiquitous phenomenon observed in different contexts in physics, chemistry, biology, medicine and engineering. Most prominently, synchronization takes place in the brain, where it is associated with several cognitive capacities but is - in abundance - a characteristic of neurological diseases. Besides zero-lag synchrony, group and cluster states are considered, enabling a description and study of complex synchronization patterns within the presented theory. Adaptive control methods are developed, which allow the control of synchronization in scenarios where parameters drift or are unknown. These methods are, therefore, of particular interest for experimental setups or technological applications. The theoretical framework is demonstrated on generic models, coupled chemical oscillators and several detailed examples of neural networks.

This book is a collection of papers presented at the 'Forum "Math-for-Industry" 2016 ' (FMfl2016), held at Queensland University of Technology, Brisbane, Australia, on November 21-23, 2016. The theme for this unique and important event was "Agriculture as a Metaphor for Creativity in All Human Endeavors", and it brought together leading international mathematicians and active researchers from universities and industry to discuss current challenging topics and to promote interactive collaborations between mathematics and industry. The success of agricultural practice relies fundamentally on its interconnections with and dependence on biology and the environment. Both play essential roles, including the biological adaption to cope with environmental challenges of biotic and abiotic stress and global warming. The book highlights the development of mathematics within this framework that successful agricultural practice depends upon and exploits.

This monograph develops techniques for equational reasoning in higher-order logic. Due to its expressiveness, higher-order logic is used for specification and verification of hardware, software, and mathematics. In these applica tions, higher-order logic provides the necessary level of abstraction for con cise and natural formulations. The main assets of higher-order logic are quan tification over functions or predicates and its abstraction mechanism. These allow one to represent quantification in formulas and other variable-binding constructs. In this book, we focus on equational logic as a fundamental and natural concept in computer science and mathematics. We present calculi for equa tional reasoning modulo higher-order equations presented as rewrite rules. This is followed by a systematic development from general equational rea soning towards effective calculi for declarative programming in higher-order logic and A-calculus. This aims at integrating and generalizing declarative programming models such as functional and logic programming. In these two prominent declarative computation models we can view a program as a logical theory and a computation as a deduction."

This book describes the rapidly developing field of interior point methods (IPMs). An extensive analysis is given of path-following methods for linear programming, quadratic programming and convex programming. These methods, which form a subclass of interior point methods, follow the central path, which is an analytic curve defined by the problem. Relatively simple and elegant proofs for polynomiality are given. The theory is illustrated using several explicit examples. Moreover, an overview of other classes of IPMs is given. It is shown that all these methods rely on the same notion as the path-following methods: all these methods use the central path implicitly or explicitly as a reference path to go to the optimum. For specialists in IPMs as well as those seeking an introduction to IPMs. The book is accessible to any mathematician with basic mathematical programming knowledge.

This the second volume of five from the 28th IMAC on Structural Dynamics and Renewable Energy, 2010, bringing together 17 chapters on Applications of Non-Linear Dynamics. It presents early findings from experimental and computational investigations on Non-Linear Dynamics including studies on Dynamics of a System of Coupled Oscillators with Geometrically Nonlinear Damping, Assigning the Nonlinear Distortions of a Two-input Single-output System, A Multi-harmonic Approach to Updating Locally Nonlinear Structures, A Block Rocking on a Seesawing Foundation, and Enhanced Order Reduction of Forced Nonlinear Systems Using New Ritz Vectors.

This proceedings volume is based on papers presented at the First Annual Workshop on Inverse Problems which was held in June 2011 at the Department of Mathematics, Chalmers University of Technology. The purpose of the workshop was to present new analytical developments and numerical methods for solutions of inverse problems. State-of-the-art and future challenges in solving inverse problems for a broad range of applications was also discussed. The contributions in this volume are reflective of these themes and will be beneficial to researchers in this area.

Quantitative Modeling of Derivative Securities demonstrates how to take the basic ideas of arbitrage theory and apply them - in a very concrete way - to the design and analysis of financial products. Based primarily (but not exclusively) on the analysis of derivatives, the book emphasizes relative-value and hedging ideas applied to different financial instruments. Using a "financial engineering approach," the theory is developed progressively, focusing on specific aspects of pricing and hedging and with problems that the technical analyst or trader has to consider in practice.

More than just an introductory text, the reader who has mastered the contents of this one book will have breached the gap separating the novice from the technical and research literature.

This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Next to model formulation, this edition puts major emphasis on exploratory data analysis for all aspects of the model, such as the marginal model, subject-specific profiles, and residual covariance structure. Further, model diagnostics and missing data receive extensive treatment. Sensitivity analysis for incomplete data is given a prominent place. Several variations to the conventional linear mixed model are discussed (a heterogeity model, condional linear mid models). This book will be of interest to applied statisticians and biomedical researchers in industry, public health organizations, contract research organizations, and academia. The book is explanatory rather than mathematically rigorous. Most analyses were done with the MIXED procedure of the SAS software package, and many of its features are clearly elucidated. How3ever, some other commercially available packages are discussed as well. Great care has been taken in presenting the data analyses in a software-independent fashion. Geert Verbeke is Assistant Professor at the Biostistical Centre of the Katholieke Universiteit Leuven in Belgium. He received the B.S. degree in mathematics (1989) from the Katholieke Universiteit Leuven, the M.S. in biostatistics (1992) from the Limburgs Universitair Centrum, and earned a Ph.D. in biostatistics (1995) from the Katholieke Universiteit Leuven. Dr. Verbeke wrote his dissertation, as well as a number of methodological articles, on various aspects of linear mixed models for longitudinal data analysis. He has held visiting positions at the Gerontology Research Center and the Johns Hopkins University. Geert Molenberghs is Assistant Professor of Biostatistics at the Limburgs Universitair Centrum in Belgium. He received the B.S. degree in mathematics (1988) and a Ph.D. in biostatistics (1993) from the Universiteit Antwerpen. Dr. Molenberghs published methodological work on the analysis of non-response in clinical and epidemiological studies. He serves as an associate editor for Biometrics, Applied Statistics, and Biostatistics, and is an officer of the Belgian Statistical Society. He has held visiting positions at the Harvard School of Public Health.

This book tackles issues associated with inconsistency in pairwise comparisons from both theoretical and practical perspectives. Human judgments are seldom absolutely consistent, or absolutely precise, therefore problems of measuring and handling inconsistency belong among hot topics of the current research, especially in the theoretical framework of multiple criteria decision aiding (MCDA). The book presents and discusses the state-of-the-art of this field including both cardinal and ordinal inconsistency, the problems of different scales for comparisons and inconsistency reduction, and the alternative approaches to inconsistency detection and measurement. This book is a unique one-stop guide for readers who are interested in inconsistency in pairwise comparisons. Researchers and practitioners in the area of multiple-criteria decision-making (MCDM) and the analytic hierarchy process (AHP) will find this informative book particularly valuable.  

Residualplots 74 Normaland half-normal plots 77 2. 3. 10. TRANSFORMATIONS OF VARIABLES 80 2. 3. 11. WEIGHTED LEAST SQUARES 82 2. 4. Bibliography 84 Appendix A. 2. 1. Basic equation ofthe analysis ofvariance 84 Appendix A. 2. 2. Derivation of the simplified formulae (2. 1 0) and (2. 11) 85 Appendix A. 2. 3. Basic properties ofleast squares estimates 86 Appendix A. 2. 4. Sums ofsquares for tests for lack offit 88 Appendix A. 2. 5. Properties ofthe residuals 90 3. DESIGN OF REGRESSION EXPERIMENTS 96 3. 1. Introduction 96 3. 2. Variance-optimality of response surface designs 98 3. 3. Two Ievel full factorial designs 106 3. 3. 1. DEFINITIONS AND CONSTRUCTION 106 3. 3. 2. PROPERTIES OF TWO LEVEL FULL FACTORIAL DESIGNS 109 3. 3. 3. REGRESSION ANALYSIS OF DAT A OBT AlNED THROUGH TWO LEVEL FULL F ACTORIAL DESIGNS 113 Parameter estimation 113 Effects of factors and interactions 116 Statistical analysis of individual effects and test for lack of fit 118 3. 4. Two Ievel fractional factorial designs 123 3. 4. 1. CONSTRUCTION OF FRACTIONAL F ACTORIAL DESIGNS 123 3. 4. 2. FITTING EQUATIONS TO DATA OBTAlNED BY FRACTIONAL F ACTORIAL DESIGNS 130 3. 5. Bloclung 133 3. 6. Steepest ascent 135 3. 7. Second order designs 142 3. 7. 1. INTRODUCTION 142 3. 7. 2. COMPOSITE DESIGNS 144 Rotatable central composite designs 145 D-optimal composite designs 146 Hartley' s designs 146 3. 7. 3.

Mathematical Analysis for Modeling is intended for those who want to understand the substance of mathematics, rather than just having familiarity with its techniques. It provides a thorough understanding of how mathematics is developed for and applies to solving scientific and engineering problems. The authors stress the construction of mathematical descriptions of scientific and engineering situations, rather than rote memorizations of proofs and formulas. Emphasis is placed on algorithms as solutions to problems and on insight rather than formal derivations.

In this volume a number of developments on a variety of topics have been reported. These topics include: partially saturated soil; instabilities in soil behaviour; environmental geomechanics; parallel computing; and applications to tunnels, embankments, slopes, foundations and anchors.

Sixty-five papers cover a wide range of topics from engineering applications to theoretical developments in the areas of embankment and slope stability, underground cavity design and mining; dynamic analysis, soil and structure interaction, and coupled processes and fluid flow.

This book investigates the latest modeling and control technologies in the context of air-conditioning systems. Firstly, it introduces the state-space method for developing dynamic models of all components in a central air-conditioning system. The models are primarily nonlinear and based on the fundamental principle of energy and mass conservation, and are transformed into state-space form through linearization. The book goes on to describe and discuss the state-space models with the help of graph theory and the structure-matrix theory. Subsequently, virtual sensor calibration and virtual sensing methods (which are very useful for real system control) are illustrated together with a case study. Model-based predictive control and state-space feedback control are applied to air-conditioning systems to yield better local control, while the air-side synergic control scheme and a global optimization strategy based on the decomposition-coordination method are developed so as to achieve energy conservation in the central air-conditioning system. Lastly, control strategies for VAV systems including total air volume control and trim & response static pressure control are investigated in practice.

The purpose of this book is to examine the geospatial and temporal linkage between offshore supply vessels and oil and gas activity in the Outer Continental Shelf Gulf of Mexico, and to model OSV activity expected to result from future lease sales. Oil and gas operations occur throughout the world wherever commercial accumulations exist, but no quantitative assessment has ever been performed on the marine vessels that support offshore activity. The OCS Gulf of Mexico is the largest and most prolific offshore oil and gas basin in the world, and a large number of marine vessels are engaged in operations in the region, but tracking their activity is difficult and requires specialized data sources and the development of empirical models. The challenge of modeling arises from the complexity and size of the system, and the particular limitations governing stochastic difficult-to-observe networks. This book bridges the gap with the latest technological perspective and provides insight and computational methods to inform and better understand the offshore sector. Offshore Service Industry and Logistics Modeling in the Gulf of Mexico is presented in three parts. In Part 1, background information on the life cycle stages of offshore development and activity is reviewed, along with a description of the service vessels and port infrastructure in the region. In Part 2, OSV activity in the Gulf of Mexico is baselined using PortVision data to establish spatial and temporal characteristics of vessel activity. In Part 3, the analytic framework used to quantify the connection between OSVs, ports, and offshore activity is described, and activity expected to arise from the 2012-2017 OCS lease program is forecast. Providing an invaluable resource for academics and researchers, this book is also intended for government regulators, energy and environmental analysts, industry professionals, and others interested in this often-overlooked sector.

Computer-based mathematical modeling - the technique of representing and managing models in machine-readable form - is still in its infancy despite the many powerful mathematical software packages already available which can solve astonishingly complex and large models. On the one hand, using mathematical and logical notation, we can formulate models which cannot be solved by any computer in reasonable time - or which cannot even be solved by any method. On the other hand, we can solve certain classes of much larger models than we can practically handle and manipulate without heavy programming. This is especially true in operations research where it is common to solve models with many thousands of variables. Even today, there are no general modeling tools that accompany the whole modeling process from start to finish, that is to say, from model creation to report writing. This book proposes a framework for computer-based modeling. More precisely, it puts forward a modeling language as a kernel representation for mathematical models. It presents a general specification for modeling tools. The book does not expose any solution methods or algorithms which may be useful in solving models, neither is it a treatise on how to build them. No help is intended here for the modeler by giving practical modeling exercises, although several models will be presented in order to illustrate the framework. Nevertheless, a short introduction to the modeling process is given in order to expound the necessary background for the proposed modeling framework.

This book presents the best papers from the 3rd International Conference on Mathematical Research for Blockchain Economy (MARBLE) 2022, held in Vilamoura, Portugal. While most blockchain conferences and forums are dedicated to business applications, product development or Initial Coin Offering (ICO) launches, this conference focuses on the mathematics behind blockchain to bridge the gap between practice and theory. Blockchain Technology has been considered as the most fundamental and revolutionising invention since the Internet. Every year, thousands of blockchain projects are launched and circulated in the market, and there is a tremendous wealth of blockchain applications, from finance to healthcare, education, media, logistics and more. However, due to theoretical and technical barriers, most of these applications are impractical for use in a real-world business context. The papers in this book reveal the challenges and limitations, such as scalability, latency, privacy and security, and showcase solutions and developments to overcome them.

This textbook offers theoretical, algorithmic and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems. It provides an overview of recent advances in control and systems theory, numerical line algebra, numerical optimization, scientific computations and software engineering.

Focusing on modeling applications, this outstanding reference provides a step-by-step, non-mathematical approach to constructing and using realistic workable groundwater models on a daily basis. Extensive detailed drawings, case studies, practical examples, and sample models illustrate important concepts. Includes data on hydrogeologic features and pollutants plus a glossary of terms.

The papers in this volume aim at obtaining a common understanding of the challenging research questions in web applications comprising web information systems, web services, and web interoperability; obtaining a common understanding of verification needs in web applications; achieving a common understanding of the available rigorous approaches to system development, and the cases in which they have succeeded; identifying how rigorous software engineering methods can be exploited to develop suitable web applications; and at developing a European-scale research agenda combining theory, methods and tools that would lead to suitable web applications with the potential to implement systems for computation in the public domain.