This book offers a self-study program on how mathematics, computer science and science can be profitably and seamlessly intertwined. This book focuses on two variable ODE models, both linear and nonlinear, and highlights theoretical and computational tools using MATLAB to explain their solutions. It also shows how to solve cable models using separation of variables and the Fourier Series.

The book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practicing professionals. Only the very simplest elements are considered, mainly two-dimensional three-noded constant strain triangles, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, finite element analysis of biharmonic problems (plane stress and plane strain). Full FORTRAN programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the FORTRAN language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use on desktops and laptops. Unlike the first edition, the new edition has Problems (with Solutions) at the end of each chapter. Electronic copies of the programs should be freely available for download from the internet.

Using network models to investigate the interconnectivity in modern economic systems allows researchers to better understand and explain some economic phenomena. This volume presents contributions by known experts and active researchers in economic and financial network modeling. Readers are provided with an understanding of the latest advances in network analysis as applied to economics, finance, corporate governance, and investments. Moreover, recent advances in market network analysis that focus on influential techniques for market graph analysis are also examined. Young researchers will find this volume particularly useful in facilitating their introduction to this new and fascinating field. Professionals in economics, financial management, various technologies, and network analysis, will find the network models presented in this book beneficial in analyzing the interconnectivity in modern economic systems.

The author develops a new perturbative formalism of non-equilibrium thermal quantum field theory for non-homogeneous backgrounds. As a result of this formulation, the author is able to show how so-called pinch singularities can be removed, without resorting to ad hoc prescriptions, or effective resummations of absorptive effects. Thus, the author arrives at a diagrammatic approach to non-equilibrium field theory, built from modified Feynman rules that are manifestly time-dependent from tree level. This new formulation provides an alternative framework in which to derive master time evolution equations for physically meaningful particle number densities, which are valid to all orders in perturbation theory and to all orders in gradient expansion. Once truncated in a loop-wise sense, these evolution equations capture non-equilibrium dynamics on all time-scales, systematically describing energy-violating processes and the non-Markovian evolution of memory effects

This book assesses the state-of-the-art in computational fluid dynamics (CFD) applied to ship hydrodynamics and provides guidelines for the future developments in the field based on the Gothenburg 2010 Workshop. It presents ship hull test cases, experimental data and submitted computational methods, conditions, grids and results. Analysis is made of errors for global (resistance, sinkage and trim and self-propulsion) and local flow (wave elevations and mean velocities and turbulence) variables, including standard deviations for global variables and propeller modeling for self-propulsion. The effects of grid size and turbulence models are evaluated for both global and local flow variables. Detailed analysis is made of turbulence modeling capabilities for capturing local flow physics. Errors are also analyzed for head-wave seakeeping and forward speed diffraction, and calm-water forward speed-roll decay. Resistance submissions are used to evaluate the error and uncertainty by means of a systematic verification and validation (V&V) study along with statistical investigations. Post-workshop experimental and computational studies are conducted and analyzed for evaluation of facility biases and to draw more concrete conclusions regarding the most reliable turbulence model, appropriate numerical methods and grid resolution requirements, respectively.

This book presents mathematical models of mob control with threshold (conformity) collective decision-making of the agents. Based on the results of analysis of the interconnection between the micro- and macromodels of active network structures, it considers the static (deterministic, stochastic and game-theoretic) and dynamic (discrete- and continuous-time) models of mob control, and highlights models of informational confrontation. Many of the results are applicable not only to mob control problems, but also to control problems arising in social groups, online social networks, etc. Aimed at researchers and practitioners, it is also a valuable resource for undergraduate and postgraduate students as well as doctoral candidates specializing in the field of collective behavior modeling.

Exploring complex and intelligent analytical and mathematical methods, this book examines how different approaches can be used to optimize program management in the construction industry. It presents an in-depth study of the different program management methods, ranging from simple decision-making techniques and statistics analysis to the more complex linear programming and demonstrates how knowledge-base systems and genetic algorithms can be used to optimize resources and meet time, budget and quality criteria. It addresses topics including decision-making principles, planning and scheduling, mathematical forecasting models, optimization techniques programming and artificial intelligence techniques. Providing a valuable resource for anyone managing multiple projects in the construction industry, this book is intended for civil and construction engineering students, project managers, construction managers and senior engineers.

The book will provide an exhaustive and clear explanation of how Statistics, Mathematics and Informatics have been used in cancer research, and seeks to help cancer researchers in achieving their objectives. To do so, state-of-the-art Biostatistics, Biomathematics and Bioinformatics methods will be described and discussed in detail through illustrative and capital examples taken from cancer research work already published. The book will provide a guide for cancer researchers in using Statistics, Mathematics and Informatics, clarifying the contribution of these logical sciences to the study of cancer, thoroughly explaining their procedures and methods, and providing criteria to their appropriate use.

Ge and III-V compounds, semiconductors with high carrier mobilities, are candidates to replace Si as the channel in MOS devices. 2D materials - like graphene and MoS_2 - are also envisioned to replace Si in the future. This thesis is devoted to the first-principles modeling of the vibrational properties of these novel channel materials. The first part of the thesis focuses on the vibrational properties of various oxides on Ge, making it possible to identify the vibrational signature of specific defects which could hamper the proper functioning of MOSFETs. The second part of the thesis reports on the electronic and vibrational properties of novel 2D materials like silicene and germanene, the Si and Ge 2D counterparts of graphene. The interaction of these 2D materials with metallic and non-metallic substrates is investigated. It was predicted, for the first time, and later experimentally confirmed, that silicene could be grown on a non-metallic template like MoS_2, a breakthrough that could open the door to the possible use of silicene in future nanoelectronic devices.

Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.

This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato's and Kepler's symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups and their unitary representations. In such a framework, time, position and spacetime is modeled by equivalence classes of symmetry groups. For a unification on this road, the quest is not for a final theory with a basic equation for basic particles, but for the basic operation group and its representations.

The proceedings from the eighth KMO conference represent the findings of this international meeting which brought together researchers and developers from industry and the academic world to report on the latest scientific and technical advances on knowledge management in organizations. This conference provided an international forum for authors to present and discuss research focused on the role of knowledge management for innovative services in industries, to shed light on recent advances in social and big data computing for KM as well as to identify future directions for researching the role of knowledge management in service innovation and how cloud computing can be used to address many of the issues currently facing KM in academia and industrial sectors.

This book contributes to better understand how lifestyle modulations can effectively halt the emergence and progression of human diseases. The book will allow the reader to gain a better understanding of the mechanisms by which the environment interferes with the bio-molecular regulatory processes underlying the emergence and progression of complex diseases, such as cancer. Focusing on key and early cellular bio-molecular events giving rise to the emergence of degenerative chronic disease, it builds on previous experience on the development of multi-cellular organisms, to propose a mathematical and computer based framework that allows the reader to analyze the complex interplay between bio-molecular processes and the (micro)-environment from an integrative, mechanistic, quantitative and dynamical perspective. Taking the wealth of empirical evidence that exists it will show how to build and analyze models of core regulatory networks involved in the emergence and progression of chronic degenerative diseases, using a bottom-up approach.

Summability is a mathematical topic with a long tradition and with many applications in, e.g., function theory, number theory, and stochastics. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Lecturers, graduate students, and researchers working in summability and related topics will find this a useful introduction and reference work.

The present volume contains invited talks of 11th biennial conference on "Emerging Mathematical Methods, Models and Algorithms for Science and Technology". The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.

This book is concerned with recent advances in fitness landscapes. The concept of fitness landscapes originates from theoretical biology and refers to a framework for analysing and visualizing the relationships between genotypes, phenotypes and fitness. These relationships lay at the centre of attempts to mathematically describe evolutionary processes and evolutionary dynamics.

The book addresses recent advances in the understanding of fitness landscapes in evolutionary biology and evolutionary computation. In the volume, experts in the field of fitness landscapes present these findings in an integrated way to make it accessible to a number of audiences: senior undergraduate and graduate students in computer science, theoretical biology, physics, applied mathematics and engineering, but also researcher looking for a reference or/and entry point into using fitness landscapes for analysing algorithms. Also practitioners wanting to employ fitness landscape techniques for evaluating bio- and nature-inspired computing algorithms can find valuable material in the book. For teaching proposes, the book could also be used as a reference handbook.

The purpose of this book is to thoroughly prepare the reader for research in string theory at an intermediate level. As such it is not a compendium of results but intended as textbook in the sense that most of the material is organized in a pedagogical and self-contained fashion.
Beyond the basics, a number of more advanced topics are introduced, such as conformal field theory, superstrings and string dualities - the text does not cover applications to black hole physics and cosmology, nor strings theory at finite temperatures.
End-of-chapter references have been added to guide the reader wishing to pursue further studies or to start research in well-defined topics covered by this book."

This book looks at the increasing interest in running microscopy processing algorithms on big image data by presenting the theoretical and architectural underpinnings of a web image processing pipeline (WIPP). Software-based methods and infrastructure components for processing big data microscopy experiments are presented to demonstrate how information processing of repetitive, laborious and tedious analysis can be automated with a user-friendly system. Interactions of web system components and their impact on computational scalability, provenance information gathering, interactive display, and computing are explained in a top-down presentation of technical details. Web Microanalysis of Big Image Data includes descriptions of WIPP functionalities, use cases, and components of the web software system (web server and client architecture, algorithms, and hardware-software dependencies). The book comes with test image collections and a web software system to increase the reader's understanding and to provide practical tools for conducting big image experiments. By providing educational materials and software tools at the intersection of microscopy image analyses and computational science, graduate students, postdoctoral students, and scientists will benefit from the practical experiences, as well as theoretical insights. Furthermore, the book provides software and test data, empowering students and scientists with tools to make discoveries with higher statistical significance. Once they become familiar with the web image processing components, they can extend and re-purpose the existing software to new types of analyses. Each chapter follows a top-down presentation, starting with a short introduction and a classification of related methods. Next, a description of the specific method used in accompanying software is presented. For several topics, examples of how the specific method is applied to a dataset (parameters, RAM requirements, CPU efficiency) are shown. Some tips are provided as practical suggestions to improve accuracy or computational performance.

Stokes discusses--and illustrates with output from actual problems--a number of applied econometric techniques, including OLS specification tests, recursive residual analysis, limited dependent variable models, error component models, and others. His book is clearly written and copiously illustrated with equations, with follow-up analysis to show how models are built and some of their limitations. His B34S DEGREESDTM software is available and allows readers to do further research with a large number of datasets distributed with the program. A necessary resource for applied econometrics researchers in economics, finance, and in health, energy, and labor economics.

This work illustrates the use of model specification and diagnostic tests applied to a variety of econometric modeling techniques. For each technique discussed the basic mathematical models are outlined. A sample problem is discussed and estimated using the B34S DEGREESDTM Data Analysis System. The output of the program is displayed in the text and discussed. Where appropriate, output from the RATS DEGREESDTM software is displayed. Follow-up models are estimated and discussed. The examples selected are taken from a variety of sources and reflect actual applied research. Complete data are given in the text to enable the reader to use these problems with other programs and techniques. It is the author's experience that applied econometric techniques are best learned by running actual problems. Since most users experiment with a limited number of techniques, their experience is limited. This book discusses a broad range of techniques and shows how they are interrelated. DEGREESL DEGREESL The techniques discussed include the following: simple, one-equation OLS and GLS models with continuous variables on the left-hand side, which are tested with recursive residual and BLUS residual techniques. Another class of models includes restrictions on the left-hand side variables. Models studied and illustrated with data include probit, logit, multinomial logit, and ordered probit models. Other techniques discussed and illustrated include two-stage least squares, limited information maximum likelihood, three-stage least squares, iterative three-stage least squares, error component models and Markov probability models, which are illustrated with a model of OPEC production dynamics.

ARIMA and transfer function models are shown to be generalizations of the single-equation model, while VAR and VARMA models are shown to be a time series generalization of three-stage least squares and full information maximum likelihood models. VAR models are viewed in the frequency domain for added insight, and extensive nonlinearity tests are developed and applied. More specialized techniques include state space models, optimal control analysis, nonlinear analysis, and the QR approach to computation. An important feature of the book is the emphasis on nonlinear model building. The Hinich nonlinear testing approach is discussed and integrated into the OLS, times series, and nonlinear estimation procedures. The MARS and PISPLINE methods of analysis are illustrated with models that failed linearity tests when estimated with linear methods. The purpose of the monograph is to illustrate the above techniques, using actual research data. To facilitate the calculations, the B34S DEGREESDTM Data Analysis System was developed. Sample output for all procedures discussed in the text has been provided so that the availability of the B34S DEGREESDTM program is DEGREESInot DEGREESR required in order to benefit from this book. While the book is self-contained, interested readers can obtain the B34S DEGREESDTM Data Analysis program and do further research with the datasets discussed in the book which are supplied with the software.

This book covers essential Microsoft EXCEL (R)'s computational skills while analyzing introductory physics projects. Topics of numerical analysis include; multiple graphs on the same sheet, calculation of descriptive statistical parameters, a 3-point interpolation, the Euler and the Runge-Kutter methods to solve equations of motion, the Fourier transform to calculate the normal modes of a double pendulum, matrix calculations to solve coupled linear equations of a DC circuit, animation of waves and Lissajous figures, electric and magnetic field calculations from the Poisson equation and its 3D surface graphs, variational calculus such as Fermat's least traveling time principle and the least action principle. Nelson's stochastic quantum dynamics is also introduced to draw quantum particle trajectories.

As in the previous volume on the topic, the authors close the gap between abstract mathematical approaches, such as applied methods of modern algebra and analysis, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems, on the one hand and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in biochemistry, geophysics, biology and climatology. This compilation will be of interest to mathematicians and engineers working at the interface of these fields. It presents selected works of the joint seminar series of Lomonosov Moscow State University and the Institute for Applied System Analysis at National Technical University of Ukraine "Kyiv Polytechnic Institute". The authors come from Brazil, Germany, France, Mexico, Spain, Poland, Russia, Ukraine and the USA.

Brownian dynamics serve as mathematical models for the diffusive motion of microscopic particles of various shapes in gaseous, liquid, or solid environments. The renewed interest in Brownian dynamics is due primarily to their key role in molecular and cellular biophysics: diffusion of ions and molecules is the driver of all life. Brownian dynamics simulations are the numerical realizations of stochastic differential equations that model the functions of biological micro devices such as protein ionic channels of biological membranes, cardiac myocytes, neuronal synapses, and many more. Stochastic differential equations are ubiquitous models in computational physics, chemistry, biophysics, computer science, communications theory, mathematical finance theory, and many other disciplines. Brownian dynamics simulations of the random motion of particles, be it molecules or stock prices, give rise to mathematical problems that neither the kinetic theory of Maxwell and Boltzmann, nor Einstein's and Langevin's theories of Brownian motion could predict.This book takes the readers on a journey that starts with the rigorous definition of mathematical Brownian motion, and ends with the explicit solution of a series of complex problems that have immediate applications. It is aimed at applied mathematicians, physicists, theoretical chemists, and physiologists who are interested in modeling, analysis, and simulation of micro devices of microbiology. The book contains exercises and worked out examples throughout.

This thesis deals with the dynamics of state-of-the-art nanophotonic semiconductor structures, providing essential information on fundamental aspects of nonlinear dynamical systems on the one hand, and technological applications in modern telecommunication on the other. Three different complex laser structures are considered in detail: (i) a quantum-dot-based semiconductor laser under optical injection from a master laser, (ii) a quantum-dot laser with optical feedback from an external resonator, and (iii) a passively mode-locked quantum-well semiconductor laser with saturable absorber under optical feedback from an external resonator. Using a broad spectrum of methods, both numerical and analytical, this work achieves new fundamental insights into the interplay of microscopically based nonlinear laser dynamics and optical perturbations by delayed feedback and injection.

This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays.