Carolin Loos introduces two novel approaches for the analysis of single-cell data. Both approaches can be used to study cellular heterogeneity and therefore advance a holistic understanding of biological processes. The first method, ODE constrained mixture modeling, enables the identification of subpopulation structures and sources of variability in single-cell snapshot data. The second method estimates parameters of single-cell time-lapse data using approximate Bayesian computation and is able to exploit the temporal cross-correlation of the data as well as lineage information.

Applied Numerical Linear Algebra introduces students to numerical issues that arise in linear algebra and its applications. A wide range of techniques are touched on, including direct to iterative methods, orthogonal factorizations, least squares, eigenproblems, and nonlinear equations. Inside Applied Numerical Linear Algebra, readers will find: Clear and detailed explanations on a wide range of topics from condition numbers to the singular value decomposition. Material on nonlinear systems as well as linear systems. Frequent illustrations using discretizations of boundary-value problems or demonstrating other concepts. Exercises with detailed solutions at the end of the book. Supplemental material available at https://bookstore.siam.org/cl87/bonus. This textbook is appropriate for junior and senior undergraduate students and beginning graduate students in the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Loewner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph. Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics.

This book considers specific inferential issues arising from the analysis of dynamic shapes with the attempt to solve the problems at hand using probability models and nonparametric tests. The models are simple to understand and interpret and provide a useful tool to describe the global dynamics of the landmark configurations. However, because of the non-Euclidean nature of shape spaces, distributions in shape spaces are not straightforward to obtain. The book explores the use of the Gaussian distribution in the configuration space, with similarity transformations integrated out. Specifically, it works with the offset-normal shape distribution as a probability model for statistical inference on a sample of a temporal sequence of landmark configurations. This enables inference for Gaussian processes from configurations onto the shape space. The book is divided in two parts, with the first three chapters covering material on the offset-normal shape distribution, and the remaining chapters covering the theory of NonParametric Combination (NPC) tests. The chapters offer a collection of applications which are bound together by the theme of this book. They refer to the analysis of data from the FG-NET (Face and Gesture Recognition Research Network) database with facial expressions. For these data, it may be desirable to provide a description of the dynamics of the expressions, or testing whether there is a difference between the dynamics of two facial expressions or testing which of the landmarks are more informative in explaining the pattern of an expression.

This book constitutes the thoroughly refereed post-workshop proceedings of the 13th International Workshop on Approximation and Online Algorithms, WAOA 2015, held in Patras, Greece, in September 2015 as part of ALGO 2015. The 17 revised full papers presented were carefully reviewed and selected from 40 submissions. Topics of interest for WAOA 2015 were: algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, geometric problems, graph algorithms, inapproximability, mechanism design, natural algorithms, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, parameterized complexity, scheduling problems,and real-world applications.

This book gathers selected contributions presented at the INdAM Workshop "DREAMS", held in Rome, Italy on January 22 26, 2018. Addressing cutting-edge research topics and advances in computer aided geometric design and isogeometric analysis, it covers distinguishing curve/surface constructions and spline models, with a special focus on emerging adaptive spline constructions, fundamental spline theory and related algorithms, as well as various aspects of isogeometric methods, e.g. efficient quadrature rules and spectral analysis for isogeometric B-spline discretizations. Applications in finite element and boundary element methods are also discussed. Given its scope, the book will be of interest to both researchers and graduate students working in these areas.

Advances in Mathematical Analysis and its Applications is designed as a reference text and explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. It discusses theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some topics are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. Features: The book encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. It offers an understanding of research problems by presenting the necessary developments in reasonable details The book also discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems Contains applications on wavelets analysis and COVID-19 to show that mathematical analysis has interdisciplinary as well as real life applications. The book is aimed primarily at advanced undergraduates and postgraduate students studying mathematical analysis and mathematics in general. Researchers will also find this book useful.

This is the second, completely revised and expanded edition of the author's first book, covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents a brief survey of the research to date in ultrametric summability theory, which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis. The book is also useful as a text for those who wish to specialize in ultrametric summability theory.

This book introduces several topics related to linear model theory, including: multivariate linear models, discriminant analysis, principal components, factor analysis, time series in both the frequency and time domains, and spatial data analysis. This second edition adds new material on nonparametric regression, response surface maximization, and longitudinal models. The book provides a unified approach to these disparate subjects and serves as a self-contained companion volume to the author's Plane Answers to Complex Questions: The Theory of Linear Models. Ronald Christensen is Professor of Statistics at the University of New Mexico. He is well known for his work on the theory and application of linear models having linear structure.

This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard's theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate students of mathematics, the book will also prove useful for researchers. The prerequisites for this text have intentionally been kept to a minimum so that undergraduate students can also benefit from it. It is a cherished conviction that "mathematical proofs are the core of all mathematical joy," a standpoint this book vividly reflects.

This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. "I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis" has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

This book constitutes revised selected papers from the 42nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2016, held in Istanbul, Turkey, in June 2016. The 25 papers presented in this volume were carefully reviewed and selected from 74 submissions.The WG conferences aim to connect theory and practice by demonstrating how graph-theoretic concepts can be applied to various areas of computer science and by extracting new graph problems from applications. Their goal is to present new research results and to identify and explore directions of future research.

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi's most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter's prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi

The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Flexibility of DAE formulations - Reachability analysis and deterministic global optimization - Numerical linear algebra methods - Boundary value problems The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

Computational Electromagnetics.- to Part I.- Challenges and Approaches in EMC Modeling of Wireless Consumer Devices.- A New Adaptive Approach to Modeling Measured Multi-Port Scattering Parameters.- Parametric Models of Transmission Lines Based on First Order Sensitivities.- Domain Partitioning Based Parametric Models for Passive On-Chip Components.- A Novel Graphical Based Tool for Extraction of Magnetic Reluctances Between On-Chip Current Loops.- A Robust Technique for Modelling Nonlinear Lumped Elements Spanning Multiple Cells in FDTD.- Computation of Eigenmodes in Periodic Structures with Dispersive Materials.- Region-Oriented BEM Formulation for Numerical Computations of Electric Fields.- Surface Integrated Field Equations Method to Solve 3D Electromagnetic Problems.- Reduced Basis Method for Electromagnetic Field Computations.- Using Nudg++ to Solve Poisson's Equation on Unstructured Grids.- Magnetic Force Calculations Applied to Magnetic Force Microscopy.- Relativistic High Order Particle Treatment for Electromagnetic Particle-In-Cell Simulations.- A Statistical Characterization of Resonant Electromagnetic Interactions with Thin Wires: Variance and Kurtosis Analysis.- Circuit Simulation.- to Part II.- Wavelets in Circuit Simulation.- On Local Handling of Inner Equations in Compact Models.- Hybrid Analysis of Nonlinear Time-Varying Circuits Providing DAEs with Index at Most One.- Transient Analysis of Nonlinear Circuits Based on Waves.- Simultaneous Step-Size and Path Control for Efficient Transient Noise Analysis.- Nonlinear Distortion in Differential Circuits with Single-Ended and Balanced Drive.- Evaluation of Oscillator Phase and Frequency Transfer Functions.- Polynomial Chaos for the Computation of Failure Probabilities in Periodic Problems.- Quasiperiodic Steady-State Analysis of Electronic Circuits by a Spline Basis.- Accurate Simulation of the Devil's Staircase of an Injection-Locked Frequency Divider.- ANN/DNN-Based Behavioral Modeling of RF/Microwave Components and Circuits.- Surrogate Modeling of Low Noise Amplifiers Based on Transistor Level Simulations.- Computational Statistics Approach to Capacitance Sensitivity Analysis and Gate Delay Time Minimization of TFT-LCDs.- Lookup-Table Based Settling Error Modeling in SIMULINK.- Speed-Up Techniques for Time-Domain System Simulations.- Coupled Problems.- to Part III.- Heating of Semiconductor Devices in Electric Circuits.- Analysis of a PDE Thermal Element Model for Electrothermal Circuit Simulation.- Automatic Thermal Network Extraction and Multiscale Electro-Thermal Simulation.- Simulations of an Electron-Phonon Hydrodynamical Model Based on the Maximum Entropy Principle.- Consistent Initialization for Coupled Circuit-Device Simulation.- Hyperbolic PDAEs for Semiconductor Devices Coupled with Circuits.- Large-Scale Atomistic Circuit-Device Coupled Simulation of Discrete-Dopant-Induced Characteristic Fluctuation in Nano-CMOS Digital Circuits.- Evaluation of Electromagnetic Coupling Between Microelectronic Device Structures Using Computational Electrodynamics.- Evaluation of Domain Decomposition Approach for Compact Simulation of On-Chip Coupled Problems.- DAE-Index and Convergence Analysis of Lumped Electric Circuits Refined by 3-D Magnetoquasistatic Conductor Models.- Mathematical and Computational Methods.- to Part IV.- Numerical Time Integration in Quasistatic Computational Electromagnetics.- A Novel Staggered Finite Volume Time Domain Method.- EM Scattering Calculations Using Potentials.- New Trends in the Preconditioning of Integral Equations of Electromagnetism.- Simulation of Large Interconnect Structures Using ILU-Type Preconditioner.- High-Order Discontinuous Galerkin Methods for Computational Electromagnetics and Uncertainty Quantification.- Efficient Simulation of Large-scale Dynamical Systems Using Tensor Decompositions.- Robust FETI Solvers for Multiscale Elliptic PDEs.- Nonlinear Models for Silicon Semiconductors.- Multiobjective Optimization Appl

This book is a collection of selected papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sinaia, Romania, in 2006. The series of SCEE conferences aims at addressing mathematical problems which have a relevance to industry, with an emphasis on modeling and numerical simulation of electronic circuits, electromagnetic fields but also coupled problems and general mathematical and computational methods.

This volume presents selected contributions by top researchers in the field of operations research, originating from the XVI Congress of APDIO. It provides interesting findings and applications of operations research methods and techniques in a wide variety of problems. The contributions address complex real-world problems, including inventory management with lateral transshipments, sectors and routes in solid-waste collection and production planning for perishable food products. It also discusses the latest techniques, making the volume a valuable tool for researchers, students and practitioners who wish to learn about current trends. Of particular interest are the applications of nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management and lot sizing, as well as job scheduling problems. This biennial conference, organized by APDIO, the Portuguese Association of Operational Research, held in Braganca, Portugal, in June 2013, presented a perfect opportunity to discuss the latest development in this field and to narrow the gap between academic researchers and practitioners.

This proceedings volume collects review articles that summarize research conducted at the Munich Centre of Advanced Computing (MAC) from 2008 to 2012. The articles address the increasing gap between what should be possible in Computational Science and Engineering due to recent advances in algorithms, hardware, and networks, and what can actually be achieved in practice; they also examine novel computing architectures, where computation itself is a multifaceted process, with hardware awareness or ubiquitous parallelism due to many-core systems being just two of the challenges faced. Topics cover both the methodological aspects of advanced computing (algorithms, parallel computing, data exploration, software engineering) and cutting-edge applications from the fields of chemistry, the geosciences, civil and mechanical engineering, etc., reflecting the highly interdisciplinary nature of the Munich Centre of Advanced Computing.

From the Preface: Blending ideas from operations research, music psychology, music theory, and cognitive science, this book aims to tell a coherent story of how tonality pervades our experience, and hence our models, of music. The story is told through the developmental stages of the Spiral Array model for tonality, a geometric model designed to incorporate and represent principles of tonal cognition, thereby lending itself to practical applications of tonal recognition, segmentation, and visualization. Mathematically speaking, the coils that make up the Spiral Array model are in effect helices, a spiral referring to a curve emanating from a central point. The use of "spiral" here is inspired by spiral staircases, intertwined spiral staircases: nested double helices within an outer spiral. The book serves as a compilation of knowledge about the Spiral Array model and its applications, and is written for a broad audience, ranging from the layperson interested in music, mathematics, and computing to the music scientist-engineer interested in computational approaches to music representation and analysis, from the music-mathematical and computational sciences student interested in learning about tonality from a formal modeling standpoint to the computer musician interested in applying these technologies in interactive composition and performance. Some chapters assume no musical or technical knowledge, and some are more musically or computationally involved.

Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing.

This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Moebius function, Euler's totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Regis de la Breteche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivic, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, Janos Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwill, Joel Rivat, Andras Sarkoezy, Jeffrey Shallit, Terence Tao, Gerald Tenenbaum, Laszlo Toth, Tamar Ziegler, Liyang Zhang.

This book explores the impact of augmenting novel architectural designs with hardware-based application accelerators. The text covers comprehensive aspects of the applications in Geographic Information Science, remote sensing and deploying Modern Accelerator Technologies (MAT) for geospatial simulations and spatiotemporal analytics. MAT in GIS applications, MAT in remotely sensed data processing and analysis, heterogeneous processors, many-core and highly multi-threaded processors and general purpose processors are also presented. This book includes case studies and closes with a chapter on future trends. Modern Accelerator Technologies for GIS is a reference book for practitioners and researchers working in geographical information systems and related fields. Advanced-level students in geography, computational science, computer science and engineering will also find this book useful.

The Leibniz Supercomputing Centre (LRZ) and the Bavarian Competence Network for Technical and Scienti?c High Performance Computing (KONWIHR) publish in the present book results of numerical simulations facilitated by the High P- formance Computer System in Bavaria (HLRB II) within the last two years. The papers were presented at the Fourth Joint HLRB and KONWIHR Review and - sult Workshop in Garching on 8th and 9th December 2009, and were selected from all progress reports of projects that use the HLRB II. Similar to the workshop two years ago, the majority of the contributed papers belong to the area of computational ?uid dynamics (CFD), condensed matter physics, astrophysics, chemistry, computer sciences and high-energy physics. We note a considerable increase of the user c- munity in some areas: Compared to 2007, the number of papers increased from 6 to 12 in condensed matter physics and from 2 to 5 in high-energy physics. Bio s- ences contributed only one paper in 2007, but four papers in 2009. This indicates that the area of application of supercomputers is continuously growing and entering new ?elds of research. The year 2007 saw two major events of particular importance for the LRZ. First, after a substantial upgrade with dual-core processors the SGI Altix 4700 superc- puter reached a peak performance of more than 62 Tera?op/s. And second, the n- pro?t organization Gauss Centre for Supercomputing e. V. (GCS) was founded on April 13th.

The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.