This volume features a variety of research projects at the intersection of mathematics and public policy. The topics included here fall in the areas of cybersecurity and climate change, two broad and impactful issues that benefit greatly from mathematical techniques. Each chapter in the book is a mathematical look into a specific research question related to one of these issues, an approach that offers the reader insight into the application of mathematics to important public policy questions. The articles in this volume are papers inspired by a Workshop for Women in Mathematics and Public Policy, held January 22-25, 2019 at the Institute for Pure and Applied Mathematics and the Luskin Center at the University of California, Los Angeles. The workshop was created to promote and develop women at all levels of their careers as researchers in mathematics and public policy. The idea was modeled after other successful Research Collaboration Conferences for Women, where junior and senior women come together at week-long conferences held at mathematics institutes to work on pre-defined research projects. The workshop focused on how mathematics can be used in public policy research and was designed to foster collaborative networks for women to help address the gender gap in mathematics and science.

Modern optimization approaches have attracted many research scientists, decision makers and practicing researchers in recent years as powerful intelligent computational techniques for solving several complex real-world problems. The Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics highlights the latest research innovations and applications of algorithms designed for optimization applications within the fields of engineering, IT, and economics. Focusing on a variety of methods and systems as well as practical examples, this book is a significant resource for graduate-level students, decision makers, and researchers in both public and private sectors who are seeking research-based methods for modeling uncertain real-world problems.

This volume contains the best papers presented at the 2nd ECCOMAS International Conference on Multiscale Computations for Solids and Fluids, held June 10-12, 2015. Topics dealt with include multiscale strategy for efficient development of scientific software for large-scale computations, coupled probability-nonlinear-mechanics problems and solution methods, and modern mathematical and computational setting for multi-phase flows and fluid-structure interaction. The papers consist of contributions by six experts who taught short courses prior to the conference, along with several selected articles from other participants dealing with complementary issues, covering both solid mechanics and applied mathematics.

An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.
Key Features
* This is an introductory treatise on wavelet analysis, with an emphasis on spline-wavelets and time-frequency analysis
* This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis
* Suitable as a textbook for a beginning course on wavelet analysis

This book provides an accessible introduction to the basic theory of fluid mechanics and computational fluid dynamics (CFD) from a modern perspective that unifies theory and numerical computation. Methods of scientific computing are introduced alongside with theoretical analysis and MATLAB (R) codes are presented and discussed for a broad range of topics: from interfacial shapes in hydrostatics, to vortex dynamics, to viscous flow, to turbulent flow, to panel methods for flow past airfoils. The third edition includes new topics, additional examples, solved and unsolved problems, and revised images. It adds more computational algorithms and MATLAB programs. It also incorporates discussion of the latest version of the fluid dynamics software library FDLIB, which is freely available online. FDLIB offers an extensive range of computer codes that demonstrate the implementation of elementary and advanced algorithms and provide an invaluable resource for research, teaching, classroom instruction, and self-study. This book is a must for students in all fields of engineering, computational physics, scientific computing, and applied mathematics. It can be used in both undergraduate and graduate courses in fluid mechanics, aerodynamics, and computational fluid dynamics. The audience includes not only advanced undergraduate and entry-level graduate students, but also a broad class of scientists and engineers with a general interest in scientific computing.

This book presents an exciting collection of contributions based on the workshop "Bringing Maths to Life" held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content useful as it addresses existing challenges in identifying the gaps between mathematical modeling and biological research. The shared solutions will aid and promote further collaboration between life sciences and mathematics.

This book introduces readers to numerous multiplicative inverse functional equations and their stability results in various spaces. This type of functional equation can be of use in solving many physical problems and also has significant relevance in various scientific fields of research and study. In particular, multiplicative inverse functional equations have applications in electric circuit theory, physics, and relations connecting the harmonic mean and arithmetic mean of several values. Providing a wealth of essential insights and new concepts in the field of functional equations, the book is chiefly intended for researchers, graduate schools, graduate students, and educators, and can also used for seminars in analysis covering topics of functional equations.

Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.
Key Features
* A self-contained, prgamatic exposition of the needed elements of random variable theory
* Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations
* Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples
* Clear treatments of first passages, first exits, and stable state fluctuations and transitions
* Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics

Dynamical Symmetries of Relativistic Two - and Many Body Systems.- Algebraic Treatment of Multistep Processes in Electron-Molecule Scattering.- Symmetry, Constitutive Laws of Bounded Smoothly Deformable Media and Neumann Problems.- Imitation of Symmetries in Local Quantum Field Theory.- Representations of Quantum Groups.- Algebras and Symmetries - Quantum Mechanical Symmetry Breaking.- q-Analysis and Quantum Groups.- Orthogonal Polynomials and Coherent States.- Algebraic Model for Molecular Electronic Spectra.- Highest Weight Unitary Modules for Non-Compact Groups and Applications to Physical Problems.- Scattering Theory and the Group Representation Matrix.- Predicting "Anyons" The Origins of Fractional Statistics in Two-Dimensional Space.- The Role of Parabose-Statistics in Making Abstract Quantum Theory Concrete.- On Quantized Verma Modules.- The Role of Spectrum Generating Algebras and Dynamic Symmetries in Molecular Physics.- O(4) Symmetry and Angular Momentum Theory in Four Dimensions.- Representations of the Quantum Algebras Uq(su(2)) and Uq(su(1, 1)).- From "Quantum Groups" to "Quasi-Quantum Groups".- Symmetries of Icosahedral Quasicrystals.- Molecular Symmetry Adapted Bases in the Born-Oppenheimer Approximation.- On Certain Submodules of the Enveloping Fields.- Invariants and States Generating Symmetry of Nonstationary Systems.- Origins of Nuclear and Hadron Symmetries.- Projection Operator Method and Q-Analog of Angular Momentum Theory.- Symmetry Breaking and Fractional Quantization of Quantum Systems.- New Phases of D ? 2 Current and Diffeomorphism Algebras in Particle Physics.- Algebra and Geometry in the Theory of Mixed States.- Group Structures and the Interacting Boson Approximation for Nuclei.- Paradigms of Quantum Algebras.

This book focuses on the systematic design of architectures, parameters and control of typical hybrid propulsion systems for wheeled and tracked vehicles based on a combination of theoretical research and engineering practice. Adopting a mechatronic system dynamics perspective, principles and methods from the fields of optimal control and system optimization are applied in order to analyze the hybrid propulsion configuration and controller design. Case investigations for typical hybrid propulsion systems of wheeled and tracked ground vehicles are also provided.

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 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.

Nonlinear matrix equations arise frequently in applied science and engineering. This is the first book to provide a unified treatment of structure-preserving doubling algorithms, which have been recently studied and proven effective for notoriously challenging problems, such as fluid queue theory and vibration analysis for high-speed trains. The authors present recent developments and results for the theory of doubling algorithms for nonlinear matrix equations associated with regular matrix pencils, and highlight the use of these algorithms in achieving robust solutions for notoriously challenging problems that other methods cannot. Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations is intended for researchers and computational scientists. Graduate students may also find it of interest.

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 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 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 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 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.

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.

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 unique text/reference provides an overview of crossbar-based interconnection networks, offering novel perspectives on these important components of high-performance, parallel-processor systems. A particular focus is placed on solutions to the blocking and scalability problems. Topics and features: introduces the fundamental concepts in interconnection networks in multi-processor systems, including issues of blocking, scalability, and crossbar networks; presents a classification of interconnection networks, and provides information on recognizing each of the networks; examines the challenges of blocking and scalability, and analyzes the different solutions that have been proposed; reviews a variety of different approaches to improve fault tolerance in multistage interconnection networks; discusses the scalable crossbar network, which is a non-blocking interconnection network that uses small-sized crossbar switches as switching elements. This invaluable work will be of great benefit to students, researchers and practitioners interested in computer networks, parallel processing and reliability engineering. The text is also essential reading for course modules on interconnection network design and reliability.

This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.