This book is aimed at those readers who already have some knowledge of mathematical methods and have also been introduced to the basic ideas of quantum optics. It should be attractive to students who have already explored one of the more introductory texts such as Loudon's The quantum theory of light (2/e, 1983, OUP) and are seeking to acquire the mathematical skills used in real problems. This book is not primarily about the physics of quantum optics but rather presents the mathematical methods widely used by workers in this field. There is no comparable book which covers either the range or the depth of mathematical techniques.

A billiard is a dynamical system in which a point particle alternates between free motion and specular reflections fromthe boundaryof a domain."Exterior Billiards" presents billiards in the complement of domains and their applications in aerodynamics and geometrical optics.

This book distinguishes itself from existing literature by presenting billiard dynamics "outside" bounded domains, including scattering, resistance, invisibility and retro-reflection. It begins with an overview of the mathematical notations used throughout the book and a brief review of the main results. Chapters 2 and 3 are focused on problems of minimal resistance and Newton s problem in media with positive temperature. In chapters 4 and 5, scattering of billiards bynonconvex and rough domains is characterized and some related special problems of optimal mass transportation are studied. Applications in aerodynamics are addressed next and problems of invisibility and retro-reflection within the framework of geometric optics conclude the text.

The book will appeal to mathematicians working in dynamical systems and calculus of variations. Specialists working in the areas of applications discussed will also find it useful."

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.

This volume reflects "New Trends in Shape Optimization" and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nurnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.

Since the early eighties, Ali Suleyman Ustunelhas beenone of the main contributors to the field of Malliavin calculus. In a workshop held in Paris, June 2010 several prominent researchers gave exciting talks in honor of his 60th birthday. The present volume includes scientific contributions from this workshop.
Probability theory is first and foremost aimed at solving real-life problems containing randomness. Markov processes are one of the key tools for modeling that plays a vital part concerning such problems. Contributions on inventory control, mutation-selection in genetics and public-private partnerships illustrate several applications in this volume. Stochastic differential equations, be they partial or ordinary, also play a key role in stochastic modeling. Two of the contributions analyze examples that share a focus on probabilistic tools, namely stochastic analysis and stochastic calculus. Three other papers are devoted more to the theoretical development of these aspects. The volume addresses graduate students and researchers interested in stochastic analysis and its applications."

This book gives a general view of sequence analysis, the statistical study of successions of states, events or actions, one of the most promising venues of social science methodology.It includesinnovative contributions on life course studies, transitions into and out of work, contemporaneous and historical careers, time use, residential trajectories and political careers. The approach presented in this book is now central to the life-course perspective and the study of other social processes.

This book promotes the dialogue between approaches to sequence analysis that developed separately, within traditions contrasted in space and disciplines. It includes the latest developments about sequential concepts, coding, atypical datasets and time patterns, optimal matching and alternative algorithms, survey optimization and visualization. Field studies include original sequential material related to parenting in 19th-century Belgium, higher education and work in Finland and Italy, family formation before and after German reunification, French Jews persecuted in occupied France, long-term trends in electoral participation and regime democratization.

Overall the book reassesses the classical uses of sequences as well as it promotes new ways of collecting, formatting, representing and processing them. The introduction provides basic sequential concepts and tools, as well as a history of the method. Chapters are presented in a way that is both accessible to the beginner and informative to the expert."

The monograph is devoted to the investigation of physical processes that govern the phonon transport in bulk and nanoscale single-crystal samples of cubic symmetry. Special emphasis is given to the study of phonon focusing in cubic crystals and its influence on the boundary scattering and lattice thermal conductivity of bulk materials and nanostructures.

Soft computing, as an engineering science, and statistics, as a classical branch of mathematics, emphasize different aspects of data analysis.
Soft computing focuses on obtaining working solutions quickly, accepting approximations and unconventional approaches. Its strength lies in its flexibility to create models that suit the needs arising in applications. In addition, it emphasizes the need for intuitive and interpretable models, which are tolerant to imprecision and uncertainty.
Statistics is more rigorous and focuses on establishing objective conclusions based on experimental data by analyzing the possible situations and their (relative) likelihood. It emphasizes the need for mathematical methods and tools to assess solutions and guarantee performance.
Combining the two fields enhances the robustness and generalizability of data analysis methods, while preserving the flexibility to solve real-world problems efficiently and intuitively.

"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.

Regularized equations of motion can improve numerical integration for the propagation of orbits, and simplify the treatment of mission design problems. This monograph discusses standard techniques and recent research in the area. While each scheme is derived analytically, its accuracy is investigated numerically. Algebraic and topological aspects of the formulations are studied, as well as their application to practical scenarios such as spacecraft relative motion and new low-thrust trajectories.

This book introduces a unique, packet-based co-design control framework for networked control systems. It begins by providing a comprehensive survey of state-of-the-art research on networked control systems, giving readers a general overview of the field. It then verifies the proposed control framework both theoretically and experimentally - the former using multiple control methodologies, and the latter using a unique online test rig for networked control systems. The framework investigates in detail the most common, communication constraints, including network-induced delays, data packet dropout, data packet disorders, and network access constraints, as well as multiple controller design and system analysis tools such as model predictive control, linear matrix inequalities and optimal control. This unique and complete co-design framework greatly benefits researchers, graduate students and engineers in the fields of control theory and engineering.

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 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.

This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals.

In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step.

Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given.

Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.

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.

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.

The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the International Conference on Dynamical Systems: Theory and Applications, held in od, Poland on December 2-5, 2013. The studies give deep insight into both the theory and applications of non-linear dynamical systems, emphasizing directions for future research. Topics covered include: constrained motion of mechanical systems and tracking control; diversities in the inverse dynamics; singularly perturbed ODEs with periodic coefficients; asymptotic solutions to the problem of vortex structure around a cylinder; investigation of the regular and chaotic dynamics; rare phenomena and chaos in power converters; non-holonomic constraints in wheeled robots; exotic bifurcations in non-smooth systems; micro-chaos; energy exchange of coupled oscillators; HIV dynamics; homogenous transformations with applications to off-shore slender structures; novel approaches to a qualitative study of a dissipative system; chaos of postural sway in humans; oscillators with fractional derivatives; controlling chaos via bifurcation diagrams; theories relating to optical choppers with rotating wheels; dynamics in expert systems; shooting methods for non-standard boundary value problems; automatic sleep scoring governed by delay differential equations; isochronous oscillations; the aerodynamics pendulum and its limit cycles; constrained N-body problems; nano-fractal oscillators and dynamically-coupled dry friction."

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

An Engineer's Guide to MATLAB, 3/e, is an authoritative guide to generating readable, compact, and verifiably correct MATLAB programs. It is ideal for undergraduate engineering courses in Mechanical, Aeronautical, Civil, and Electrical engineering that require/use MATLAB. This highly respected guide helps students develop a strong working knowledge of MATLAB that can be used to solve a wide range of engineering problems. Since solving these problems usually involves writing relatively short, one-time-use programs, the authors demonstrate how to effectively develop programs that are compact yet readable, easy to debug, and quick to execute. Emphasis is on using MATLAB to obtain solutions to several classes of engineering problems, so technical material is presented in summary form only. The new edition has been thoroughly revised and tested for software release 2009.

This work concerns the computational modelling of the dynamics of partially ionized gases, with emphasis on electrodischarge processes. Understanding gas discharges is fundamental for many processes in mechanics, manufacturing, materials science, and aerospace engineering. This second edition has been expanded to include the latest developments in the field, especially regarding the drift-diffusion model and rarefied hypersonic flow.

By the dawn of the new millennium, robotics has undergone a major transformation in scope and dimensions. This expansion has been brought about by the maturity of the field and the advances in its related technologies. From a largely dominant industrial focus, robotics has been rapidly expanding into the challenges of the human world. The new generation of robots is expected to safely and dependably co-habitat with humans in homes, workplaces, and communities, providing support in services, entertainment, education, healthcare, manufacturing, and assistance. Beyond its impact on physical robots, the body of knowledge robotics has produced is revealing a much wider range of applications reaching across diverse research areas and scientific disciplines, such as: biomechanics, haptics, neuros- ences, virtual simulation, animation, surgery, and sensor networks among others. In return, the challenges of the new emerging areas are proving an abundant source of stimulation and insights for the field of robotics. It is indeed at the intersection of disciplines that the most striking advances happen. The goal of the series of Springer Tracts in Advanced Robotics (STAR) is to bring, in a timely fashion, the latest advances and developments in robotics on the basis of their significance and quality. It is our hope that the wider dissemination of research developments will stimulate more exchanges and collaborations among the research community and contribute to further advancement of this rapidly growing field.

These are the proceedings of the 20th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems in mind. This is essential for approaching peak floating point performance. There is an increasingly well developed theory whichis having a direct impact on the development and improvements of these algorithms.

This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments). The hybrid system paradigm is a valuable modeling tool for describing a wide range of real-world applications. Moreover, although new technology has produced, and continues to produce highly hierarchical sophisticated machinery that cannot be analyzed as a whole system, hybrid system representation can be used to reduce the structural complexity of these systems. That is to say, hybrid systems have become a modeling priority, which in turn has led to the creation of a promising research field with several application areas. As such, the book explores recent developments in the area of deterministic and stochastic hybrid systems using the Lyapunov and Razumikhin-Lyapunov methods to investigate the systems' properties. It also describes properties such as stability, stabilization, reliable control, H-infinity optimal control, input-to-state stability (ISS)/stabilization, state estimation, and large-scale singularly perturbed systems.