This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.

The book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos. All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4-6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and engineers with a platform that encouraged them to exchange their innovative ideas in mathematical analysis and its applications as well as to form interdisciplinary collaborations. The content of the book is divided into three parts: Part I contains contributions from participants whose topics are related to nonlinear dynamics and its applications in biological sciences. Part II has contributions which concern topics on nonlinear analysis and its applications to a variety of problems in science, engineering and industry. Part III consists of contributions dealing with some problems in applied analysis.

This is the first book to cover GRASP (Greedy Randomized Adaptive Search Procedures), a metaheuristic that has enjoyed wide success in practice with a broad range of applications to real-world combinatorial optimization problems. The state-of-the-art coverage and carefully crafted pedagogical style lends this book highly accessible as an introductory text not only to GRASP, but also to combinatorial optimization, greedy algorithms, local search, and path-relinking, as well as to heuristics and metaheuristics, in general. The focus is on algorithmic and computational aspects of applied optimization with GRASP with emphasis given to the end-user, providing sufficient information on the broad spectrum of advances in applied optimization with GRASP. For the more advanced reader, chapters on hybridization with path-relinking and parallel and continuous GRASP present these topics in a clear and concise fashion. Additionally, the book offers a very complete annotated bibliography of GRASP and combinatorial optimization. For the practitioner who needs to solve combinatorial optimization problems, the book provides a chapter with four case studies and implementable templates for all algorithms covered in the text. This book, with its excellent overview of GRASP, will appeal to researchers and practitioners of combinatorial optimization who have a need to find optimal or near optimal solutions to hard combinatorial optimization problems.

This book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.

Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications. This first volume focuses on the univariate version of the theory and the related applications in the unidimensional setting, while the second volume, which addresses the multivariate case, is mainly devoted to concrete PDE applications. This book systematically develops the theory of generalized locally Toeplitz (GLT) sequences and presents some of its main applications, with a particular focus on the numerical discretization of differential equations (DEs). It is the first book to address the relatively new field of GLT sequences, which occur in numerous scientific applications and are especially dominant in the context of DE discretizations. Written for applied mathematicians, engineers, physicists, and scientists who (perhaps unknowingly) encounter GLT sequences in their research, it is also of interest to those working in the fields of Fourier and functional analysis, spectral analysis of DE discretization matrices, matrix analysis, measure and operator theory, numerical analysis and linear algebra. Further, it can be used as a textbook for a graduate or advanced undergraduate course in numerical analysis.

Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.

An analysis of large data sets from an empirical and geometric viewpoint

Data reduction is a rapidly emerging field with broad applications in essentially all fields where large data sets are collected and analyzed. Geometric Data Analysis is the first textbook to focus on the geometric approach to this problem of developing and distinguishing subspace and submanifold techniques for low-dimensional data representation. Understanding the geometrical nature of the data under investigation is presented as the key to identifying a proper reduction technique.

Focusing on the construction of dimensionality-reducing mappings to reveal important geometrical structure in the data, the sequence of chapters is carefully constructed to guide the reader from the beginnings of the subject to areas of current research activity. A detailed, and essentially self-contained, presentation of the mathematical prerequisites is included to aid readers from a broad variety of backgrounds. Other topics discussed in Geometric Data Analysis include:

• The Karhunen-Loeve procedure for scalar and vector fields with extensions to missing data, noisy data, and data with symmetry
• Nonlinear methods including radial basis functions (RBFs) and backpropa-gation neural networks
• Wavelets and Fourier analysis as analytical methods for data reduction
• Expansive discussion of recent research including the Whitney reduction network and adaptive bases codeveloped by the author
• And much more

The methods are developed within the context of many real-world applications involving massive data sets, including those generated by digital imaging systems and computer simulations of physical phenomena. Empirically based representations are shown to facilitate their investigation and yield insights that would otherwise elude conventional analytical tools.

Discover hidden relationships among the variables in your data, and learn how to exploit these relationships. This book presents a collection of data-mining algorithms that are effective in a wide variety of prediction and classification applications. All algorithms include an intuitive explanation of operation, essential equations, references to more rigorous theory, and commented C++ source code. Many of these techniques are recent developments, still not in widespread use. Others are standard algorithms given a fresh look. In every case, the focus is on practical applicability, with all code written in such a way that it can easily be included into any program. The Windows-based DATAMINE program lets you experiment with the techniques before incorporating them into your own work. What You'll Learn Use Monte-Carlo permutation tests to provide statistically sound assessments of relationships present in your data Discover how combinatorially symmetric cross validation reveals whether your model has true power or has just learned noise by overfitting the data Work with feature weighting as regularized energy-based learning to rank variables according to their predictive power when there is too little data for traditional methods See how the eigenstructure of a dataset enables clustering of variables into groups that exist only within meaningful subspaces of the data Plot regions of the variable space where there is disagreement between marginal and actual densities, or where contribution to mutual information is high Who This Book Is For Anyone interested in discovering and exploiting relationships among variables. Although all code examples are written in C++, the algorithms are described in sufficient detail that they can easily be programmed in any language.

Using an elegant mixture of geometry, graph theory and linear analysis, this monograph completely solves a problem lying at the interface of Isogeometric Analysis (IgA) and Finite Element Methods (FEM). The recent explosion of IgA, strongly tying Computer Aided Geometry Design to Analysis, does not easily apply to the rich variety of complex shapes that engineers have to design and analyse. Therefore new developments have studied the extension of IgA to unstructured unions of meshes, similar to those one can find in FEM. The following problem arises: given an unstructured planar quadrilateral mesh, construct a C1-surface, by piecewise Bezier or B-Spline patches defined over this mesh. This problem is solved for C1-surfaces defined over plane bilinear Bezier patches, the corresponding results for B-Splines then being simple consequences. The method can be extended to higher-order quadrilaterals and even to three dimensions, and the most recent developments in this direction are also mentioned here.

This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.

Familiarize yourself with Scilab using this concise, practical tutorial that is focused on writing code to learn concepts. Starting from the basics, this book covers array-based computing, plotting, and working with files in Scilab. Introduction to Scilab is useful for industry engineers, researchers, and students who are looking for open-source solutions for numerical computation. In this book you will learn by doing, avoiding technical jargon, which makes the concepts easy to learn. First you'll see how to run basic calculations, absorbing technical complexities incrementally as you progress toward advanced topics. Throughout, the language is kept simple to ensure that readers at all levels can grasp the concepts. After reading this book, you will come away with sample code that can be re-purposed and applied to your own projects using Scilab. What You'll Learn Apply sample code to your engineering or science problems Work with Scilab arrays, functions, and loops Use Scilab's plotting functions for data visualization Solve numerical computing and computational engineering problems with Scilab Who This Book Is For Engineers, scientists, researchers, and students who are new to Scilab. Some prior programming experience would be helpful but not required.

This book provides a general theoretical background for constructing the recursive Bayesian estimation algorithms for mixture models. It collects the recursive algorithms for estimating dynamic mixtures of various distributions and brings them in the unified form, providing a scheme for constructing the estimation algorithm for a mixture of components modeled by distributions with reproducible statistics. It offers the recursive estimation of dynamic mixtures, which are free of iterative processes and close to analytical solutions as much as possible. In addition, these methods can be used online and simultaneously perform learning, which improves their efficiency during estimation. The book includes detailed program codes for solving the presented theoretical tasks. Codes are implemented in the open source platform for engineering computations. The program codes given serve to illustrate the theory and demonstrate the work of the included algorithms.

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

Presents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications.

This volume deals with numerical simulation of coupled problems in soil mechanics and foundations. It contains analysis of both shallow and deep foundations. Several nonlinear problems are considered including, soil plasticity, cracking, reaching the soil bearing capacity, creep, etc. Dynamic analysis together with stability analysis are also included. Several numerical models of dams are considered together with coupled problems in soil mechanics and foundations. It gives wide range of modelling soil in different parts of the world. This volume is part of the proceedings of the 1st GeoMEast International Congress and Exhibition on Sustainable Civil Infrastructures, Egypt 2017.

The book is a comprehensive yet compressed entry-level introduction on single variable calculus, focusing on the concepts and applications of limits, continuity, derivative, defi nite integral, series, sequences and approximations. Chapters are arranged to outline the essence of each topic and to address learning diffi culties, making it suitable for students and lecturers in mathematics, physics and engineering. Contents Prerequisites for calculus Limits and continuity The derivative Applications of the derivative The definite integral Techniques for integration and improper integrals Applications of the definite integral Infinite series, sequences, and approximations

This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained - by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes - results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.

This volume deals with two complementary topics. On one hand the book deals with the problem of determining the the probability distribution of a positive compound random variable, a problem which appears in the banking and insurance industries, in many areas of operational research and in reliability problems in the engineering sciences. On the other hand, the methodology proposed to solve such problems, which is based on an application of the maximum entropy method to invert the Laplace transform of the distributions, can be applied to many other problems. The book contains applications to a large variety of problems, including the problem of dependence of the sample data used to estimate empirically the Laplace transform of the random variable. Contents Introduction Frequency models Individual severity models Some detailed examples Some traditional approaches to the aggregation problem Laplace transforms and fractional moment problems The standard maximum entropy method Extensions of the method of maximum entropy Superresolution in maxentropic Laplace transform inversion Sample data dependence Disentangling frequencies and decompounding losses Computations using the maxentropic density Review of statistical procedures

TOPOLOGICAL OPTIMIZATION OF CONTINUUM STRUCTURE WITH GLOBAL STRESS CONSTRAINTS BASED ON ICM METHOD.- TOPOLOGICAL OPTIMIZATION OF FRAME STRUCTURES UNDER MULTIPLE LOADING CASES$^*$.- OPTIMAL DISPLACEMENT CONTROL SIMULATION OF ELECTRIC-MECHANICAL COUPLED TRUSSES.- PROTEIN SECONDARY STRUCTURE PREDICTION METHODS BASED ONRBF NEURAL NETWORKS.- A HYBRID META-HEURISTIC FOR A ROUTING PROBLEM.- IDENTIFICATION OF GEOMETRIC PARAMETERS OF DRAWBEAD USING NEURAL NETWORKS.- IMPROVED IMMUNE GENETIC ALGORITHM FOR SOLVING FLOW SHOP SCHEDULING PROBLEM.- A DISCRETE PARTICLE SWARM OPTIMIZATION ALGORITHM FOR TRAVELLING SALESMAN PROBLEM.- A SEARCH METHOD FOR FINDING A SIMPLE NASH EQUILIBRIUM.- A HERO EVOLUTIONARY ALGORITHM HYBRIDIZING FROM PSO AND GA.- A DATA COLLECTION MODEL FOR INTRUSION DETECTION SYSTEM BASED ON SIMPLE RANDOM SAMPLING.- DESTRUCTIVE EXTENSION RULE IN PROPOSITION MODAL LOGIC K.- A NOVEL PARTICLE SWARM OPTIMIZATION-BASED APPROACH FOR JOB-SHOP SCHEDULING.- UNCALIBRATED ROBOTIC ARM VISUAL SERVO CONTROL.- INTERLINEATION AND INTERFLATION FUNCTIONS OF MANY VARIABLES (BLENDING FUNCTION INTERPOLATION) AND ECONOMICAL ALGORITHMS IN THE APPROXIMATION THEORY.- INDEPENDENT COMPONENT ANALYSIS OF DYNAMIC CONTRAST-ENHANCED IMAGES: THE NUMBER OF COMPONENTS.- THE GEOMETRIC CONSTRAINT SOLVING BASED ON HYBRID GENETIC ALGORITHM OF CONJUGATE GRADIENT.- FAST IMAGE MOSAICS ALGORITHM USING PARTICLE SWARM OPTIMIZATION.- CHECKING CONSISTENCY IN HYBRID QUALITATIVE SPATIAL REASONING.- ICA-SCS DENOISING METHOD FOR WATERMARKING SCHEME.- STUDY AND IMPLEMENTATION OF SIMPLIFIED WWW DATA MODEL IN USE FOR WEB MINING.- AN EXTENSION OF EARLEY'S ALGORITHM FOR EXTENDED GRAMMARS.- THE RESEARCH ON POLICY-BASED REGISTRATION MECHANISM OF MOBILE TERMINALS IN MOBILE IP NETWORK.- OPERATIONAL SEMANTIC TO THE EXECUTION OF THE PROCESS MODEL.- FUZZY CLUSTERING ON THE WEB IMPLEMENTED BY JSP TECHNOLOGY.- TEXT CLASSIFICATION FOR CHINESE WEB DOCUMENTS.- LOGIC-BASED CONSTRAINT HANDLING IN RESOURCE-CONSTRAINED SCHEDULING PROBLEMS.- PARTICLE SWARM OPTIMIZATION METHOD USED IN PIXEL-BASED TEXTURE SYNTHESIS.- FORMAL METHOD IN IMPLEMENTATION OF ATLAS LANGUAGE*.- GENETIC ALGORITHM FOR EVALUATION METRICS IN TOPICAL WEB CRAWLING.- A BOUNDARY METHOD TO SPEED UP TRAINING SUPPORT VECTOR MACHINES.- A FAST ALGORITHM FOR GENERATING CONCEPTS USING AN ATTRIBUTE TABLE.- ALGORITHM OF MEASUREMENT-BASED ADMISSION CONTROL FOR GPRS.- SURFACE RECOGNITION OF AUTOMOBILE PANEL BASED ON SECTION CURVE IDENTIFICATION.- DYNAMIC CLUSTERING ALGORITHM BASED ON ADAPTIVE RESONANCE THEORY.- ONTOLOGY LEARNING USING WORDNET LEXICON.- GENETIC PROGRAMMING FOR MAXIMUM-LIKELIHOOD PHYLOGENY INFERENCE.- MINING DOMINANCE ASSOCIATION RULES IN PREFERENCE-ORDERED DATA.- Mining Ordinal Patterns For Data Cleaning.- USER ASSOCIATION MINING BASED ON CONCEPT LATTICE.- A PLM-ORIENTED WORKFLOW MODEL.- A LANGUAGE FOR SPECIFYING CONSTRAINTS IN WFMSs.- ONTOLOGY BASED WORKFLOW MODEL.- CONSTRAINED MULTI-SAMPLE TEXTURE SYNTHESIS.- A GENERAL INCREMENTAL HIERARCHICAL CLUSTERING METHOD.- ACTIVATING IRREGULAR DIMENSIONS IN OLAP.- A NEW COMPUTATIONAL METHOD OF INTERSECTION FOR RAY TRACING.- STUDY ON PARTNERS SELECTION OF AGILE VIRTUAL ENTERPRISE BASED ON PARTICLE SWARM OPTIMIZATION.- ADAPTIVE DIRECTIONAL WEIGHTED MEDIAN FILTERING.- AN INTERACTIVE WORKFLOW MANAGEMENT FUNCTION MODEL.- PACKET FAIR SCHEDULING ALGORITHM BASED ON WEIGHTS DYNAMIC COMPENSATION.- EXTENDED ADAPTIVE WEIGHTED AVERAGING FILTER MODEL.- AN IMPROVED QUANTUM-INSPIRED EVOLUTIONARY ALGORITHM FOR CLUSTERING GENE EXPRESSION DATA.- AUTOMATIC BUFFER OVERFLOW DETECTION BASED ON OPERATION SEMANTIC.- QUANTUM-INSPIRED EVOLUTIONARY ALGORITHM FOR TRAVELLING SALESMAN PROBLEM.- AN IMPROVED COEVOLUTION ALGORITHM FOR FUZZY MODELLING.- A COMPUTATIONAL METHOD FOR SOLVING CAUCHY PROBLEMS OF ELLIPTIC OPERATORS.- NUMERICAL DETERMINATION OF THE RESONANCE FREQUENCIES AND EIGENMODES USING THE MFS.- SCATTERED NODE COMPACT FINITE DIFFERENCE-TYPE FORMULAS GENERATED FROM RADIAL BASIS FUNCTIONS.- EXPLOSION SIMULATI

This interdisciplinary book presents numerical techniques needed for chemical and biological engineers using Matlab. The book begins by exploring general cases, and moves on to specific ones. The text includes a large number of detailed illustrations, exercises and industrial examples. The book provides detailed mathematics and engineering background in the appendixes, including an introduction to Matlab. The text will be useful to undergraduate students in chemical/biological engineering, and in applied mathematics and numerical analysis.

The use of pattern recognition and classification is fundamental to many of the automated electronic systems in use today. However, despite the existence of a number of notable books in the field, the subject remains very challenging, especially for the beginner. Pattern Recognition and Classification presents a comprehensive introduction to the core concepts involved in automated pattern recognition. It is designed to be accessible to newcomers from varied backgrounds, but it will also be useful to researchers and professionals in image and signal processing and analysis, and in computer vision. Fundamental concepts of supervised and unsupervised classification are presented in an informal, rather than axiomatic, treatment so that the reader can quickly acquire the necessary background for applying the concepts to real problems. More advanced topics, such as semi-supervised classification, combining clustering algorithms and relevance feedback are addressed in the later chapters. This book is suitable for undergraduates and graduates studying pattern recognition and machine learning.

This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spaces.

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier-Stokes equations, and systems of nonlinear advection-diffusion-reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.

Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and Combinatorics in Commutative Algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.

The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs) which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - History of DAEs - DAE aspects of mechanical multibody systems - Model reduction of DAEs - Observability for DAEs - Numerical Analysis for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.