Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems.
There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between theory and practice, fundamentals and advanced subjects, and generality and specialization. None of the books in this area have completely studied and analyzed nonlinear equation in dynamical and vibratory systems using the latest analytical and numerical methods, so that the user can solve the problems without the need of studying too many different references. Thereby in this book, by the use of the latest analytic, numeric laboratorial methods and using more than 300 references like books, papers and the researches done by the authors and by considering almost all possible processes and situation, new theories has been proposed to encounter applied problems in engineering and applied sciences. In this way, the user (bachelor's, master's and PhD students, university teachers and even in research centers in different fields of mechanical, civil, aerospace, electrical, chemical, applied mathematics, physics, and etc.) can encounter such systems confidently. In the different chapters of the book, not only are the linear and especially nonlinear problems with oscillatory form broadly discussed, but also applied examples are practically solved by the proposed methodology.

This book is devoted to Slime mould Physarum polycephalum, which is a large single cell capable for distributed sensing, concurrent information processing, parallel computation and decentralized actuation. The ease of culturing and experimenting with Physarum makes this slime mould an ideal substrate for real-world implementations of unconventional sensing and computing devices The book is a treatise of theoretical and experimental laboratory studies on sensing and computing properties of slime mould, and on the development of mathematical and logical theories of Physarum behavior. It is shown how to make logical gates and circuits, electronic devices (memristors, diodes, transistors, wires, chemical and tactile sensors) with the slime mould. The book demonstrates how to modify properties of Physarum computing circuits with functional nano-particles and polymers, to interface the slime mould with field-programmable arrays, and to use Physarum as a controller of microbial fuel cells. A unique multi-agent model of slime is shown to serve well as a software slime mould capable for solving problems of computational geometry and graph optimization. The multiagent model is complemented by cellular automata models with parallel accelerations. Presented mathematical models inspired by Physarum include non-quantum implementation of Shor's factorization, structural learning, computation of shortest path tree on dynamic graphs, supply chain network design, p-adic computing and syllogistic reasoning. The book is a unique composition of vibrant and lavishly illustrated essays which will inspire scientists, engineers and artists to exploit natural phenomena in designs of future and emergent computing and sensing devices. It is a 'bible' of experimental computing with spatially extended living substrates, it spanstopics from biology of slime mould, to bio-sensing, to unconventional computing devices and robotics, non-classical logics and music and arts.

"Applications of Neural Networks in High Assurance Systems" is the first book directly addressing a key part of neural network technology: methods used to pass the tough verification and validation (V&V) standards required in many safety-critical applications. The book presents what kinds of evaluation methods have been developed across many sectors, and how to pass the tests. A new adaptive structure of V&V is developed in this book, different from the simple six sigma methods usually used for large-scale systems and different from the theorem-based approach used for simplified component subsystems.

The study of fluctuations in statistical physics has a long history, and a general theory is well established, connecting fluctuations to response properties of equilibrium systems. Remarkably, this framework fails as soon as some current is flowing across the system, driving it out of equilibrium. The presence of currents is quite common in nature and produces rich phenomena which are far from being included in a general framework. This thesis focuses on this general problem by studying different models such as granular materials and systems exhibiting anomalous diffusion and shows how the generalized response techniques can be successfully used to catch the relevant degrees of freedom that drive the systems out of equilibrium. This study paves the way to the use of the generalized fluctuation relations in an operative way, in order to extract information from a non-equilibrium system and to build the corresponding phenomenological theory.

The book reports on the latest theoretical and experimental advances in the field of active flow and combustion control. It covers new developments in actuator technology and sensing, in robust and optimal open- and closed-loop control, as well as in model reduction for control. It collects contributions presented during the third edition of the Active Flow and Combustion Control conference, held in September 10-12, 2014 at the Technische Universitat Berlin (Germany). This conference, as well as the research presented in the book, have been supported by the collaborative research center SFB 1029 -Substantial efficiency increase in gas turbines through direct use of coupled unsteady combustion and flow dynamics, funded by the DFG (German Research Foundation).

Since information in the brain is processed by the exchange of spikes among neurons, a study of such group dynamics is extremely important in understanding hippocampus dependent memory. These spike patterns and local field potentials (LFPs) have been analyzed by various statistical methods. These studies have led to important findings of memory information processing. For example, memory-trace replay, a reactivation of behaviorally induced neural patterns during subsequent sleep, has been suggested to play an important role in memory consolidation. It has also been suggested that a ripple/sharp wave event (one of the characteristics of LFPs in the hippocampus) and spiking activity in the cortex have a specific relationship that may facilitate the consolidation of hippocampal dependent memory from the hippocampus to the cortex. The book will provide a state-of-the-art finding of memory information processing through the analysis of multi-neuronal data. The first half of the book is devoted to this analysis aspect. Understanding memory information representation and its consolidation, however, cannot be achieved only by analyzing the data. It is extremely important to construct a computational model to seek an underlying mathematical principle. In other words, an entire picture of hippocampus dependent memory system would be elucidated through close collaboration among experiments, data analysis, and computational modeling. Not only does computational modeling benefit the data analysis of multi-electrode recordings, but it also provides useful insight for future experiments and analyses. The second half of the book will be devoted to the computational modeling of hippocampus-dependent memory.

There are many approaches to noncommutative geometry and its use in physics, the ? operator algebra and C -algebra one, the deformation quantization one, the qu- tum group one, and the matrix algebra/fuzzy geometry one. This volume introduces and develops the subject by presenting in particular the ideas and methods recently pursued by Julius Wess and his group. These methods combine the deformation quantization approach based on the - tion of star product and the deformed (quantum) symmetries methods based on the theory of quantum groups. The merging of these two techniques has proven very fruitful in order to formulate ?eld theories on noncommutative spaces. The aim of the book is to give an introduction to these topics and to prepare the reader to enter the research ?eld himself/herself. This has developed from the constant interest of Prof. W. Beiglboeck, editor of LNP, in this project, and from the authors experience in conferences and schools on the subject, especially from their interaction with students and young researchers. In fact quite a few chapters in the book were written with a double purpose, on the one hand as contributions for school or conference proceedings and on the other handaschaptersforthepresentbook.Thesearenowharmonizedandcomplemented by a couple of contributions that have been written to provide a wider background, to widen the scope, and to underline the power of our methods.

"Robotic Mapping and Exploration" is an important contribution in the area of simultaneous localization and mapping (SLAM) for autonomous robots, which has been receiving a great deal of attention by the research community in the latest few years. The contents are focused on the autonomous mapping learning problem. Solutions include uncertainty-driven exploration, active loop closing, coordination of multiple robots, learning and incorporating background knowledge, and dealing with dynamic environments. Results are accompanied by a rich set of experiments, revealing a promising outlook toward the application to a wide range of mobile robots and field settings, such as search and rescue, transportation tasks, or automated vacuum cleaning.

This unique text/reference presents a fresh look at nonlinear processing through nonlinear eigenvalue analysis, highlighting how one-homogeneous convex functionals can induce nonlinear operators that can be analyzed within an eigenvalue framework. The text opens with an introduction to the mathematical background, together with a summary of classical variational algorithms for vision. This is followed by a focus on the foundations and applications of the new multi-scale representation based on non-linear eigenproblems. The book then concludes with a discussion of new numerical techniques for finding nonlinear eigenfunctions, and promising research directions beyond the convex case. Topics and features: introduces the classical Fourier transform and its associated operator and energy, and asks how these concepts can be generalized in the nonlinear case; reviews the basic mathematical notion, briefly outlining the use of variational and flow-based methods to solve image-processing and computer vision algorithms; describes the properties of the total variation (TV) functional, and how the concept of nonlinear eigenfunctions relate to convex functionals; provides a spectral framework for one-homogeneous functionals, and applies this framework for denoising, texture processing and image fusion; proposes novel ways to solve the nonlinear eigenvalue problem using special flows that converge to eigenfunctions; examines graph-based and nonlocal methods, for which a TV eigenvalue analysis gives rise to strong segmentation, clustering and classification algorithms; presents an approach to generalizing the nonlinear spectral concept beyond the convex case, based on pixel decay analysis; discusses relations to other branches of image processing, such as wavelets and dictionary based methods. This original work offers fascinating new insights into established signal processing techniques, integrating deep mathematical concepts from a range of different fields, which will be of great interest to all researchers involved with image processing and computer vision applications, as well as computations for more general scientific problems.

This book provides a comprehensive guide to analyzing and solving optimal design problems in continuous media by means of the so-called sub-relaxation method. Though the underlying ideas are borrowed from other, more classical approaches, here they are used and organized in a novel way, yielding a distinct perspective on how to approach this kind of optimization problems. Starting with a discussion of the background motivation, the book broadly explains the sub-relaxation method in general terms, helping readers to grasp, from the very beginning, the driving idea and where the text is heading. In addition to the analytical content of the method, it examines practical issues like optimality and numerical approximation. Though the primary focus is on the development of the method for the conductivity context, the book's final two chapters explore several extensions of the method to other problems, as well as formal proofs. The text can be used for a graduate course in optimal design, even if the method would require some familiarity with the main analytical issues associated with this type of problems. This can be addressed with the help of the provided bibliography.

The second volume of this work continues the approach of the first volume, providing mathematical tools for the control engineer and examining such topics as random variables and sequences, iterative logarithmic and large number laws, differential equations, stochastic measurements and optimization, discrete martingales and probability space. It includes proofs of all theorems and contains many examples with solutions.
It is written for researchers, engineers and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to system and automatic control theories. It also has applications to game theory, machine learning and intelligent systems.
* Provides comprehensive theory of matrices, real, complex and functional analysis
* Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications
* Contains worked proofs of all theorems and propositions presented

Using the author's considerable experience of applying Mathcad to engineering problems, Essential Mathcad introduces the most powerful functions and features of the software and teaches how to apply these to create comprehensive calculations for any quantitative subject. The simple, step-by-step approach makes this book an ideal Mathcad text for professional engineers as well as engineering, science, and math students. Examples from a variety of fields demonstrate the power and utility of Mathcad's tools, while also demonstrating how other software, such as Excel spreadsheets, can be incorporated effectively.
*Many more applied examples and exercises from a wide variety of engineering, science, and math fields
* New: more thorough discussions of differential equations, 3D plotting, and curve fitting.
* A step-by-step approach enables easy learning for professionals and students alike

Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. Especially in a time-dependent setting or in the treatment of problems with strongly singular solutions their independence of a mesh makes these methods highly attractive. This volume collects selected papers presented at the Sixth International Workshop on Meshfree Methods held in Bonn, Germany in October 2011. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering.

Compared with data from general application domains, modern biological data has many unique characteristics. Biological data are often characterized as having large volumes, complex structures, high dimensionality, evolving biological concepts, and insufficient data modelling practices. Over the past several years, bioinformatics has become an all-encompassing term for everything relating to both computer science and biology. The goal of this book is to cover data and applications identifying new issues and directions for future research in biomedical domain. The book will become a useful guide learning state-of-the-art development in biomedical data management, data-intensive bioinformatics systems, and other miscellaneous biological database applications. The book addresses various topics in bioinformatics with varying degrees of balance between biomedical data models and their real-world applications.

Let's try to play the music and not the background. Ornette Coleman, liner notes of the LP "Free Jazz" 20] WhenIbegantocreateacourseonfreejazz, theriskofsuchanenterprise was immediately apparent: I knew that Cecil Taylor had failed to teach such a matter, and that for other, more academic instructors, the topic was still a sort of outlandish adventure. To be clear, we are not talking about tea- ing improvisation here-a di?erent, and also problematic, matter-rather, we wish to create a scholarly discourse about free jazz as a cultural achievement, and follow its genealogy from the American jazz tradition through its various outbranchings, suchastheEuropeanandJapanesejazzconceptionsandint- pretations. We also wish to discuss some of the underlying mechanisms that are extant in free improvisation, things that could be called technical aspects. Such a discourse bears the ?avor of a contradicto in adjecto: Teachingthe unteachable, the very negation of rules, above all those posited by white jazz theorists, and talking about the making of sounds without aiming at so-called factual results and all those intellectual sedimentations: is this not a suicidal topic? My own endeavors as a free jazz pianist have informed and advanced my conviction that this art has never been theorized in a satisfactory way, not even by Ekkehard Jost in his unequaled, phenomenologically precise p- neering book "Free Jazz" 57].

This book deals with various computational procedures for multiple repeated analyses (reanalysis) of structures, and presents them in a unified approach. It meets the need for a general text covering the basic concepts and methods as well as recent developments in this area. Reanalysis is common to numerous analysis and design tasks such as nonlinear analysis, structural optimization, damage analysis, and probabilistic analysis. The book discusses various analysis models, including linear and nonlinear analysis, static and dynamic analysis, and design sensitivity analysis. It demonstrates how various concepts and methods are integrated to achieve effective solution procedures. The approach presented has several advantages in terms of generality, efficiency of the calculations, accuracy of the results and ease of implementation. Efficiency and accuracy considerations are discussed and illustrated. To clarify the presentation, many illustrative examples and numerical results are demonstrated. The text is related to a wide range of applications in such fields as Mechanical Engineering, Aerospace Engineering, Civil Engineering, and Naval Architecture. This should prove useful to students, researchers, analysts and consultants involved in analysis and design of structures. Previous books on structural analysis do not cover most of the material presented in the book.

In 1917, Johann Radon published his fundamental work, where he introduced what is now called the Radon transform. Including important contributions by several experts, this book reports on ground-breaking developments related to the Radon transform throughout these years, and also discusses novel mathematical research topics and applications for the next century.

This volume presents a collection of contributions on advanced approaches of continuum mechanics, which were written to celebrate the 60th birthday of Prof. Holm Altenbach. The contributions are on topics related to the theoretical foundations for the analysis of rods, shells and three-dimensional solids, formulation of constitutive models for advanced materials, as well as development of new approaches to the modeling of damage and fractures.

This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth's notion of implicit definition and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap. The volume further examines what it means that a quantifier can have multiple meanings and addresses how existential vagueness can induce vagueness in our modal notions. Finally, the book explores the role played by quantifiers with respect to various kinds of semantic paradoxes, the logicality issue, ontological commitment, and the behavior of quantifiers in intensional contexts.

In this thesis, the author develops numerical techniques for tracking and characterising the convoluted nodal lines in three-dimensional space, analysing their geometry on the small scale, as well as their global fractality and topological complexity---including knotting---on the large scale. The work is highly visual, and illustrated with many beautiful diagrams revealing this unanticipated aspect of the physics of waves. Linear superpositions of waves create interference patterns, which means in some places they strengthen one another, while in others they completely cancel each other out. This latter phenomenon occurs on 'vortex lines' in three dimensions. In general wave superpositions modelling e.g. chaotic cavity modes, these vortex lines form dense tangles that have never been visualised on the large scale before, and cannot be analysed mathematically by any known techniques.

Stochastic Optimal Control (SOC)-a mathematical theory concerned with minimizing a cost (or maximizing a payout) pertaining to a controlled dynamic processunder uncertainty-has proven incredibly helpful to understanding and predicting debt crises and evaluating proposed financial regulation and risk management."Stochastic Optimal Control and the U.S. Financial Debt Crisis"analyzes SOC in relation to the 2008 U.S. financial crisis, and offers a detailed framework depicting why such a methodology is best suited for reducing financial risk and addressing key regulatory issues. Topics discussed include the inadequacies of the current approaches underlying financial regulations, the use of SOC to explain debt crises and superiority over existing approaches to regulation, and the domestic and international applications of SOC to financial crises. Principles in this book will appeal to economists, mathematicians, and researchers interested in the U.S. financial debt crisis and optimal risk management."

Over the last decade, Computational Fluid Dynamics (CFD) has become a - ture technology for the development of new products in aeronautical industry. Aerodynamic design engineers have progressively taken advantage of the pos- bilities o?ered by the numericalsolutionof the Reynolds averagedNavier-Stokes (RANS) equations. Signi?cant improvements in physical modeling and solution algorithms as well as the enormous increase of computer power enable hi- ?delity numerical simulations in all stages of aircraft development. In Germany, the national CFD project MEGAFLOW furthered the dev- opment and availability of RANS solvers for the prediction of complex ?ow problemssigni?cantly. MEGAFLOWwasinitiated by the?rstaviationresearch programoftheFederalGovernmentin1995undertheleadershipoftheDLR(see Kroll, N. , Fassbender, J. K. (Eds). : MEGAFLOW - Numerical Flow Simulation for Aircraft Design; Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Volume 89, Springer, 2005). A network from aircraft industry, DLR and several universities was created with the goal to focus and direct development activities for numerical ?ow simulation towards a common aerodynamic si- lation system providing both a block-structured (FLOWer-Code) and a hybrid (TAU-Code) parallel ? ow prediction capability. Today, both codes have reached a high level of maturity and reliability. They are routinely used at DLR and German aeronautic industry for a wide range of aerodynamic applications. For many universities the MEGAFLOW software represents a platform for the - provementofphysicalmodelsandfortheinvestigationofcomplex?owproblems. The network was established as an e?cient group of very closely co-operating partners with supplementing expertises and experience.

This book presents a comprehensive review of key distributed graph algorithms for computer network applications, with a particular emphasis on practical implementation. Topics and features: introduces a range of fundamental graph algorithms, covering spanning trees, graph traversal algorithms, routing algorithms, and self-stabilization; reviews graph-theoretical distributed approximation algorithms with applications in ad hoc wireless networks; describes in detail the implementation of each algorithm, with extensive use of supporting examples, and discusses their concrete network applications; examines key graph-theoretical algorithm concepts, such as dominating sets, and parameters for mobility and energy levels of nodes in wireless ad hoc networks, and provides a contemporary survey of each topic; presents a simple simulator, developed to run distributed algorithms; provides practical exercises at the end of each chapter.

In this monograph, we combine operator techniques with state space methods to solve factorization, spectral estimation, and interpolation problems arising in control and signal processing. We present both the theory and algorithms with some Matlab code to solve these problems. A classical approach to spectral factorization problems in control theory is based on Riccati equations arising in linear quadratic control theory and Kalman ?ltering. One advantage of this approach is that it readily leads to algorithms in the non-degenerate case. On the other hand, this approach does not easily generalize to the nonrational case, and it is not always transparent where the Riccati equations are coming from. Operator theory has developed some elegant methods to prove the existence of a solution to some of these factorization and spectral estimation problems in a very general setting. However, these techniques are in general not used to develop computational algorithms. In this monograph, we will use operator theory with state space methods to derive computational methods to solve factorization, sp- tral estimation, and interpolation problems. It is emphasized that our approach is geometric and the algorithms are obtained as a special application of the theory. We will present two methods for spectral factorization. One method derives al- rithms based on ?nite sections of a certain Toeplitz matrix. The other approach uses operator theory to develop the Riccati factorization method. Finally, we use isometric extension techniques to solve some interpolation problems.

This book serves as an introduction to the continuum mechanics and mathematical modeling of complex fluids in living systems. The form and function of living systems are intimately tied to the nature of surrounding fluid environments, which commonly exhibit nonlinear and history dependent responses to forces and displacements. With ever-increasing capabilities in the visualization and manipulation of biological systems, research on the fundamental phenomena, models, measurements, and analysis of complex fluids has taken a number of exciting directions. In this book, many of the world's foremost experts explore key topics such as: Macro- and micro-rheological techniques for measuring the material properties of complex biofluids and the subtleties of data interpretation Experimental observations and rheology of complex biological materials, including mucus, cell membranes, the cytoskeleton, and blood The motility of microorganisms in complex fluids and the dynamics of active suspensions Challenges and solutions in the numerical simulation of biologically relevant complex fluid flows This volume will be accessible to advanced undergraduate and beginning graduate students in engineering, mathematics, biology, and the physical sciences, but will appeal to anyone interested in the intricate and beautiful nature of complex fluids in the context of living systems.