The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent'ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems

This book presents selected papers from the 3rd International Workshop on Computational Engineering held in Stuttgart from October 6 to 10, 2014, bringing together innovative contributions from related fields with computer science and mathematics as an important technical basis among others. The workshop discussed the state of the art and the further evolution of numerical techniques for simulation in engineering and science. We focus on current trends in numerical simulation in science and engineering, new requirements arising from rapidly increasing parallelism in computer architectures, and novel mathematical approaches. Accordingly, the chapters of the book particularly focus on parallel algorithms and performance optimization, coupled systems, and complex applications and optimization.

The authors describe systematic methods for uncovering scientific laws a priori, on the basis of intuition, or "Gedanken Experiments". Mathematical expressions of scientific laws are, by convention, constrained by the rule that their form must be invariant with changes of the units of their variables. This constraint makes it possible to narrow down the possible forms of the laws. It is closely related to, but different from, dimensional analysis. It is a mathematical book, largely based on solving functional equations. In fact, one chapter is an introduction to the theory of functional equations.

Quantum Communication and Information Theory: Information Theoretic Interpretations of von Neumann Entropy; R. Jozsa. Quantum Information Theory, the Entropy Bound, and Mathematical Rigor in Physics; H.P. Yuen. Classical and Quantum Information Transmission and Interactions; C.H. Bennett. Bounds of the Accessible Information under the Influence of Thermal Noise; M. Ban, et al. Quantum Computing: Quantum Computing and Decoherence in Quantum Optical Systems; J.I. Cirac, et al. Unitary Dynamics for Quantum Codewords; A. Peres. Quantum Error Correction with Imperfect Gates; A.Y. Kitaev. Eliminating the Effects of Spontaneous Emission in Quantum Computations with Cold Trapped Ions; C. D'Helon, G.J. Milburn. Quantum Measurement Theory and Statistical Physics: On Covariant Instruments in Quantum Measurement Theory; A.S. Holevo. Quantum State Reduction and the Quantum Bayes Principle; M. Ozawa. On the Quantum Theory of Direct Detection; A. Barchielli. Homodyning as Universal Detection; G.M. D'Ariano. Quantum Optics: Atom Lasers; C.M. Savage, et al. Measurement of Quantum Phase Distribution by Projection Synthesis; D.t. Pegg, S.M. Barnett. Quantum Optical Phase; S.M. Barnett, D.T. Pegg. 42 Additional Articles. Index.

This book covers all the relevant dictionary learning algorithms, presenting them in full detail and showing their distinct characteristics while also revealing the similarities. It gives implementation tricks that are often ignored but that are crucial for a successful program. Besides MOD, K-SVD, and other standard algorithms, it provides the significant dictionary learning problem variations, such as regularization, incoherence enforcing, finding an economical size, or learning adapted to specific problems like classification. Several types of dictionary structures are treated, including shift invariant; orthogonal blocks or factored dictionaries; and separable dictionaries for multidimensional signals. Nonlinear extensions such as kernel dictionary learning can also be found in the book. The discussion of all these dictionary types and algorithms is enriched with a thorough numerical comparison on several classic problems, thus showing the strengths and weaknesses of each algorithm. A few selected applications, related to classification, denoising and compression, complete the view on the capabilities of the presented dictionary learning algorithms. The book is accompanied by code for all algorithms and for reproducing most tables and figures. Presents all relevant dictionary learning algorithms - for the standard problem and its main variations - in detail and ready for implementation; Covers all dictionary structures that are meaningful in applications; Examines the numerical properties of the algorithms and shows how to choose the appropriate dictionary learning algorithm.

This book represents a collection of papers presented at the 2nd World Congress on Integrated Computational Materials Engineering (ICME), a specialty conference organized by The Minerals, Metals & Materials Society (TMS).

This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.

Computational modeling allows to reduce, refine and replace animal experimentation as well as to translate findings obtained in these experiments to the human background. However these biomedical problems are inherently complex with a myriad of influencing factors, which strongly complicates the model building and validation process. This book wants to address four main issues related to the building and validation of computational models of biomedical processes: 1. Modeling establishment under uncertainty 2. Model selection and parameter fitting 3. Sensitivity analysis and model adaptation 4. Model predictions under uncertainty In each of the abovementioned areas, the book discusses a number of key-techniques by means of a general theoretical description followed by one or more practical examples. This book is intended for graduate students and researchers active in the field of computational modeling of biomedical processes who seek to acquaint themselves with the different ways in which to study the parameter space of their model as well as its overall behavior.

Provides the necessary skills to solve problems in mathematical statistics through theory, concrete examples, and exercises With a clear and detailed approach to the fundamentals of statistical theory, Examples and Problems in Mathematical Statistics uniquely bridges the gap between theory andapplication and presents numerous problem-solving examples that illustrate the relatednotations and proven results. Written by an established authority in probability and mathematical statistics, each chapter begins with a theoretical presentation to introduce both the topic and the important results in an effort to aid in overall comprehension. Examples are then provided, followed by problems, and finally, solutions to some of the earlier problems. In addition, Examples and Problems in Mathematical Statistics features: * Over 160 practical and interesting real-world examples from a variety of fields including engineering, mathematics, and statistics to help readers become proficient in theoretical problem solving * More than 430 unique exercises with select solutions * Key statistical inference topics, such as probability theory, statistical distributions, sufficient statistics, information in samples, testing statistical hypotheses, statistical estimation, confidence and tolerance intervals, large sample theory, and Bayesian analysis Recommended for graduate-level courses in probability and statistical inference, Examples and Problems in Mathematical Statistics is also an ideal reference for applied statisticians and researchers.

Heat equation asymptotics of a generalized Ahlfors Laplacian on a manifold with boundary.- Recurrent versus diffusive quantum behavior for time-dependent Hamiltonians.- Perturbations of spectral measures for Feller operators.- A global approach to the location of quantum resonances.- On estimates for the eigen-values in some elliptic problems.- Quantum scattering with long-range magnetic fields.- Spectral invariance and submultiplicativity for Frechet algebras with applications to pseudo-differential operators and ?* -quantization.- Decroissance exponentielle des fonctions propres pour l'operateur de Kac: le cas de la dimension > 1.- Second order perturbations of divergence type operators with a spectral gap.- On the Weyl quantized relativistic Hamiltonian.- Spectral asymptotics for the family of commuting operators.- Pseudo differential operators with negative definite functions as symbol: Applications in probability theory and mathematical physics.- One-dimensional Schroedinger operators with high potential barriers.- General boundary value problems in regions with corners.- Some results for nonlinear equations in cylindrical domains.- Global representation of Langrangian distributions.- Stable asymptotics of the solution to the Dirichlet problem for elliptic equations of second order in domains with angular points or edges.- Maslov operator calculus and non-commutative analysis.- Relative time delay and trace formula for long range perturbations of Laplace operators.- Functional calculus and Fredholm criteria for boundary value problems on noncompact manifolds.- The variable discrete asymptotics of solutions of singular boundary value problems.- Schroedinger operators with arbitrary non-negative potentials.- Abel summability of the series of eigen- and associated functions of the integral and differential operators.- The relativistic oscillator.- On the ratio of odd and even spectral counting functions.- A trace class property of singularly perturbed generalized Schroedinger semi-groups.- Radiation conditions and scattering theory for N-particle Hamiltonians (main ideas of the approach).

This volume gathers together selected, peer-reviewed papers presented at the BIOMAT 2020 International Symposium, which was virtually held on November 1-6, 2020, with an organization staff based in Rio de Janeiro, Brazil. Topics covered in this volume include infection modeling, with an emphasis on different aspects of the COVID-19 and novel Coronavirus spread; a description of the effectiveness of quarantine measures via dynamic analysis of SLIR model; hemodynamic simulations in time-dependent domains; an optimal control model for the Ebola disease; and the co-existence of chaos and control in the context of biological models. Texts in agroforestry, economic development, and wastewater treatment processes complete this volume. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. The 20th edition of the BIOMAT International Symposium has received contributions by authors from 18 countries: Algeria, Brazil, Cameroon, Canada, Chile, China (Hong Kong), Colombia, Germany, Hungary, India, Italy, Morocco, Nigeria, Russia, Senegal, South Africa, USA, and Uzbekistan. Previous BIOMAT volumes with selected works from 2017, 2018, and 2019 were also published by Springer.

This book addresses students and young researchers who want to learn to use numerical modeling to solve problems in geodynamics. Intended as an easy-to-use and self-learning guide, readers only need a basic background in calculus to approach most of the material. The book difficulty increases very gradually, through four distinct parts. The first is an introduction to the Python techniques necessary to visualize and run vectorial calculations. The second is an overview with several examples on classical Mechanics with examples taken from standard introductory physics books. The third part is a detailed description of how to write Lagrangian, Eulerian and Particles in Cell codes for solving linear and non-linear continuum mechanics problems. Finally the last one address advanced techniques like tree-codes, Boundary Elements, and illustrates several applications to Geodynamics. The entire book is organized around numerous examples in Python, aiming at encouraging the reader to le arn by experimenting and experiencing, not by theory.

This book presents cutting-edge research on the use of physical and mathematical formalisms to model and quantitatively analyze biological phenomena ranging from microscopic to macroscopic systems. The systems discussed in this compilation cover protein folding pathways, gene regulation in prostate cancer, quorum sensing in bacteria to mathematical and physical descriptions to analyze anomalous diffusion in patchy environments and the physical mechanisms that drive active motion in large sets of particles, both fundamental descriptions that can be applied to different phenomena in biology. All chapters are written by well-known experts on their respective research fields with a vast amount of scientific discussion and references in order the interested reader can pursue a further reading. Given these features, we consider Quantitative Models for Microscopic to Macroscopic Biological Macromolecules and Tissues as an excellent and up-to-date resource and reference for advanced undergraduate students, graduate students and junior researchers interested in the latest developments at the intersection of physics, mathematics, molecular biology, and computational sciences. Such research field, without hesitation, is one of the most interesting, challenging and active of this century and the next.

This work uses techniques of optimization and operations research to develop the first comprehensive survey of the entire field of the optimization of resource, production, and distribution systems. Sten Thore proposes an "economic logistics" that is similar to the well-known concept of military logistics, but which is expanded to include such features as the optimal location of plants, inventories and retail outlets, and the management of hierarchical multi-echelon production, inventory, and distribution systems. The study of individual features of this supply process is familiar from operations research, but Thore joins these elements together into larger analytic structures encompassing the production and distribution system in an entire industry. Following an introductory chapter and a review of the saddle-point theory, coauthored with W. W. Cooper, Thore explores the three dimensions of the supply process synthesis: the spatial dimension (as in simple transportation systems), the vertical dimension (extending from resources to finished consumer goods, as in activity analysis), and the time dimension (as in inventory accumulation and investment). The combination of these then leads to models of such diverse subjects as regional warehouse systems, activity analysis and activity networks, multi-stage warehouse systems of intermediate goods, distribution networks, and spatial equilibrium. Each chapter contains its own exercises which are solved numerically and discussed in great detail, and illustrate such optimization techniques as linear and nonlinear programming, goal programming and goal focusing, chance-constrained programming, and infinite games. This work is designed for use ingraduate courses in economics and mathematics modeling, and will also be a useful addition to college and university library collections.

This book is a collection of selected papers presented at the consecutively held international conferences on "Game Theory and Networks", organized by the Department of Mathematics, Dibrugarh University, India, in collaboration with the Economics Department of Queen's University, Belfast, UK, during September 6-9, 2019 and September, 13-15 2018. The book includes chapters on network measures and network formation, application of network theory to contagion, biological data and finance and macroeconomics as expository articles. The book also contains chapters on fair allocation in the context of queuing, rationing and cooperative games with transferable utilities for engaged researchers. A few survey chapters on non-cooperative game theory, evolutionary game theory, mechanism design and social choice theory are also incorporated to cater to the needs of the beginners in the field. This book discusses the use of game theoretic tools and network models across disciplines: mathematics, statistics, economics, computer science, political science, sociology and psychology. It aims at providing a suitable learning experience to beginners on the basics of cooperative games, networks and mechanism design, as well as recent developments to research scholars having the basic knowledge of these topics.

Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on unstructured meshes, which are also recognized as more efficient for solution of time-dependent oscillatory solutions over long time periods. Here Karniadakis and Sherwin present a much-updated and expanded version of their successful first edition covering the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing over 50% new material, including discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text aims to introduce a wider audience to the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application, and is aimed at students, academics and practitioners in computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering and climate/ocean modelling.

This book explores the use of numerical relativity (NR) methods to solve cosmological problems, and describes one of the first uses of NR to study inflationary physics. NR consists in the solution of Einstein's Equation of general relativity, which governs the evolution of matter and energy on cosmological scales, and in systems where there are strong gravitational effects, such as around black holes. To date, NR has mainly been used for simulating binary black hole and neutron star mergers like those detected recently by LIGO. Its use as a tool in fundamental problems of gravity and cosmology is novel, but rapidly gaining interest. In this thesis, the author investigates the initial condition problem in early universe cosmology - whether an inflationary expansion period could have "got going" from initially inhomogeneous conditions - and identifies criteria for predicting the robustness of particular models. State-of-the-art numerical relativity tools are developed in order to address this question, which are now publicly available.

The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November-6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.

This book develops a set of reference methods capable of modeling uncertainties existing in membership functions, and analyzing and synthesizing the interval type-2 fuzzy systems with desired performances. It also provides numerous simulation results for various examples, which fill certain gaps in this area of research and may serve as benchmark solutions for the readers. Interval type-2 T-S fuzzy models provide a convenient and flexible method for analysis and synthesis of complex nonlinear systems with uncertainties.

This thesis presents the first comprehensive analysis of quantum cascade laser nonlinear dynamics and includes the first observation of a temporal chaotic behavior in quantum cascade lasers. It also provides the first analysis of optical instabilities in the mid-infrared range. Mid-infrared quantum cascade lasers are unipolar semiconductor lasers, which have become widely used in applications such as gas spectroscopy, free-space communications or optical countermeasures. Applying external perturbations such as optical feedback or optical injection leads to a strong modification of the quantum cascade laser properties. Optical feedback impacts the static properties of mid-infrared Fabry-Perot and distributed feedback quantum cascade lasers, inducing power increase; threshold reduction; modification of the optical spectrum, which can become either single- or multimode; and enhanced beam quality in broad-area transverse multimode lasers. It also leads to a different dynamical behavior, and a quantum cascade laser subject to optical feedback can oscillate periodically or even become chaotic. A quantum cascade laser under external control could therefore be a source with enhanced properties for the usual mid-infrared applications, but could also address new applications such as tunable photonic oscillators, extreme events generators, chaotic Light Detection and Ranging (LIDAR), chaos-based secured communications or unpredictable countermeasures.

This book opens up new ways to develop mathematical models and optimization methods for interdependent energy infrastructures, ranging from the electricity network, natural gas network, district heating network, and electrified transportation network. The authors provide methods to help analyze, design, and operate the integrated energy system more efficiently and reliably, and constitute a foundational basis for decision support tools for the next-generation energy network. Chapters present new operation models of the coupled energy infrastructure and the application of new methodologies including convex optimization, robust optimization, and equilibrium constrained optimization. Four appendices provide students and researchers with helpful tutorials on advanced optimization methods: Basics of Linear and Conic Programs; Formulation Tricks in Integer Programming; Basics of Robust Optimization; Equilibrium Problems. This book provides theoretical foundation and technical applications for energy system integration, and the the interdisciplinary research presented will be useful to readers in many fields including electrical engineering, civil engineering, and industrial engineering.

This book explains how the partial differential equations (pdes) in electroanalytical chemistry can be solved numerically. It guides the reader through the topic in a very didactic way, by first introducing and discussing the basic equations along with some model systems as test cases systematically. Then it outlines basic numerical approximations for derivatives and techniques for the numerical solution of ordinary differential equations. Finally, more complicated methods for approaching the pdes are derived. The authors describe major implicit methods in detail and show how to handle homogeneous chemical reactions, even including coupled and nonlinear cases. On this basis, more advanced techniques are briefly sketched and some of the commercially available programs are discussed. In this way the reader is systematically guided and can learn the tools for approaching his own electrochemical simulation problems. This new fourth edition has been carefully revised, updated and extended compared to the previous edition (Lecture Notes in Physics Vol. 666). It contains new material describing migration effects, as well as arrays of ultramicroelectrodes. It is thus the most comprehensive and didactic introduction to the topic of electrochemical simulation.

This book presents new efficient methods for optimization in realistic large-scale, multi-agent systems. These methods do not require the agents to have the full information about the system, but instead allow them to make their local decisions based only on the local information, possibly obtained during communication with their local neighbors. The book, primarily aimed at researchers in optimization and control, considers three different information settings in multi-agent systems: oracle-based, communication-based, and payoff-based. For each of these information types, an efficient optimization algorithm is developed, which leads the system to an optimal state. The optimization problems are set without such restrictive assumptions as convexity of the objective functions, complicated communication topologies, closed-form expressions for costs and utilities, and finiteness of the system's state space.

This book presents a collection of invited research and review contributions on recent advances in (mainly) theoretical condensed matter physics, theoretical chemistry, and theoretical physics. The volume celebrates the 90th birthday of N.H. March (Emeritus Professor, Oxford University, UK), a prominent figure in all of these fields. Given the broad range of interests in the research activity of Professor March, who collaborated with a number of eminent scientists in physics and chemistry, the volume embraces quite diverse topics in physics and chemistry, at various dimensions and energy scales. One thread connecting all these topics is correlation in aggregated states of matter, ranging from nuclear physics to molecules, clusters, disordered condensed phases such as the liquid state, and solid state physics, and the various phase transitions, both structural and electronic, occurring therein. A final chapter leaps to an even larger scale of matter aggregation, namely the universe and gravitation. A further no less important common thread is methodological, with the application of theoretical physics and chemistry, particularly density functional theory and statistical field theory, to both nuclear and condensed matter.