Optimization problems abound in most fields of science, engineering, and tech nology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard prob lems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the aver age, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as engineering design and control, computational chemistry and biology, structural optimization, computer science, operations research, and economics. This book contains refereed invited papers presented at the conference on "State of the Art in Global Optimization: Computational Methods and Applications" held at Princeton University, April 28-30, 1995. The conference presented current re search on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications."

This book not only provides a comprehensive introduction to neural-based PCA methods in control science, but also presents many novel PCA algorithms and their extensions and generalizations, e.g., dual purpose, coupled PCA, GED, neural based SVD algorithms, etc. It also discusses in detail various analysis methods for the convergence, stabilizing, self-stabilizing property of algorithms, and introduces the deterministic discrete-time systems method to analyze the convergence of PCA/MCA algorithms. Readers should be familiar with numerical analysis and the fundamentals of statistics, such as the basics of least squares and stochastic algorithms. Although it focuses on neural networks, the book only presents their learning law, which is simply an iterative algorithm. Therefore, no a priori knowledge of neural networks is required. This book will be of interest and serve as a reference source to researchers and students in applied mathematics, statistics, engineering, and other related fields.

This volume contains invited and refereed papers based upon presentations given in the IMA workshop on Computational Modeling in Biological Fluid Dynamics during January of 1999, which was part of the year-long program "Mathematics in Biology." This workshop brought together biologists, zoologists, engineers, and mathematicians working on a variety of issues in biological fluid dynamics. A unifying theme in biological fluid dynamics is the interaction of elastic boundaries with a surrounding fluid. These moving boundary problems, coupled with the equations of incompressible, viscuous fluid dynamics, pose formidable challenges to the computational scientist. In this volume, a variety of computational methods are presented, both in general terms and within the context of applications including ciliary beating, blood flow, and insect flight. Our hope is that this collection will allow others to become aware of and interested in the exciting accomplishments and challenges uncovered during this workshop.

Engineers and mathematicians from European corporations and universities trade problems and solution techniques in creating mathematical models of the influence of road conditions on the behavior of vehicles (by which they mean automobiles). A dozen papers, reproduced from typescripts of varying rea

FEM updating allows FEMs to be tuned better to reflect measured data. It can be conducted using two different statistical frameworks: the maximum likelihood approach and Bayesian approaches. This book applies both strategies to the field of structural mechanics, using vibration data. Computational intelligence techniques including: multi-layer perceptron neural networks; particle swarm and GA-based optimization methods; simulated annealing; response surface methods; and expectation maximization algorithms, are proposed to facilitate the updating process. Based on these methods, the most appropriate updated FEM is selected, a problem that traditional FEM updating has not addressed. This is found to incorporate engineering judgment into finite elements through the formulations of prior distributions. Case studies, demonstrating the principles test the viability of the approaches, and. by critically analysing the state of the art in FEM updating, this book identifies new research directions.

The latest of five multidisciplinary volumes, this book spans the STEAM-H (Science, Technology, Engineering, Agriculture, Mathematics, and Health) disciplines with the intent to generate meaningful interdisciplinary interaction and student interest. Emphasis is placed on important methods and applications within and beyond each field. Topics include geometric triple systems, image segmentation, pattern recognition in medicine, pricing barrier options, p-adic numbers distribution in geophysics data pattern, adelic physics, and evolutionary game theory. Contributions were by invitation only and peer-reviewed. Each chapter is reasonably self-contained and pedagogically presented for a multidisciplinary readership.

The articles in this book are derived from the Third International Conference of the same name, held June 29-July 3, 1998. Topics include: nonlinear exaltations in condensed systems, evolution of complex systems, dynamics and structure of molecular and biomolecular systems, mathematical models of transfer processes in nonlinear systems and numerical modeling and algorithms.

This volume contains eighteen reports on work, which has been conducted since 2000 in the Collaborative Research Programme "Numerical Flow Simulation" of the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). French and German engineers and mathematicians present their joint research on the topics: "Development of Solution Techniques", "Crystal Growth and Melts", "Flows of Reacting Gases, Sound Generation" and "Turbulent Flows". In the background of their work is still the strong growth in the performance of super-computer architectures, which, together with large advances in algorithms, is opening vast new application areas of numerical flow simulation in research and industrial work. Results of this programme from the period 1996 to 1998 have been presented in NNFM 66 (1998), and NNFM75 (2001).

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 particularly concerned with heuristic state-space search for combinatorial optimization. Its two central themes are the average-case complexity of state-space search algorithms and the applications of the results notably to branch-and-bound techniques. Primarily written for researchers in computer science, the author presupposes a basic familiarity with complexity theory, and it is assumed that the reader is familiar with the basic concepts of random variables and recursive functions. Two successful applications are presented in depth: one is a set of state-space transformation methods which can be used to find approximate solutions quickly, and the second is forward estimation for constructing more informative evaluation functions.

Contents:
Introduction. Acoustical Oceanography. Propagation I. Observations and Physical Models. Propagation II. Mathematical Models (Part One). Propagation II. Mathematical Models (Part Two). Noise I. Observations and Physical Models. Noise II. Mathematical Models. Reverberation I. Observations and Physical Models. Reverberation II. Observations and Physical Models. Sonar Performance Models. Model Evaluation. Simulation.

Focused on efficient simulation-driven multi-fidelity optimization techniques, this monograph on simulation-driven optimization covers simulations utilizing physics-based low-fidelity models, often based on coarse-discretization simulations or other types of simplified physics representations, such as analytical models. The methods presented in the book exploit as much as possible any knowledge about the system or device of interest embedded in the low-fidelity model with the purpose of reducing the computational overhead of the design process. Most of the techniques described in the book are of response correction type and can be split into parametric (usually based on analytical formulas) and non-parametric, i.e., not based on analytical formulas. The latter, while more complex in implementation, tend to be more efficient. The book presents a general formulation of response correction techniques as well as a number of specific methods, including those based on correcting the low-fidelity model response (output space mapping, manifold mapping, adaptive response correction and shape-preserving response prediction), as well as on suitable modification of design specifications. Detailed formulations, application examples and the discussion of advantages and disadvantages of these techniques are also included. The book demonstrates the use of the discussed techniques for solving real-world engineering design problems, including applications in microwave engineering, antenna design, and aero/hydrodynamics.

* The book offers a well-balanced mathematical analysis of modelling physical systems. * Summarizes basic principles in differential geometry and convex analysis as needed. * The book covers a wide range of industrial and social applications, and bridges the gap between core theory and costly experiments through simulations and modelling. * The focus of the book is manifold ranging from stability of fluid flows, nano fluids, drug delivery, and security of image data to Pandemic modeling etc.

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."

It isn't that they can't see Approach your problems from the solution. the right end and begin with It is that they can't see the the answers. Then one day, problem. perhaps you will find the final qu~stion. G. K. Chesterton. The Scandal of Father Brown ITh~ Point of 'The Hermit Clad in Crane Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. HowQvQr, thQ "tree" of knowledge of mathematics and related field does not grow only by putting forth new branches. It also happ~ns, quit~ often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathe matics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

"Examines classic algorithms, geometric diagrams, and mechanical principles for enhances visualization of statistical estimation procedures and mathematical concepts in physics, engineering, and computer programming."

"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 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.