This edited volume on data science features a variety of research ranging from theoretical to applied and computational topics. Aiming to establish the important connection between mathematics and data science, this book addresses cutting edge problems in predictive modeling, multi-scale representation and feature selection, statistical and topological learning, and related areas. Contributions study topics such as the hubness phenomenon in high-dimensional spaces, the use of a heuristic framework for testing the multi-manifold hypothesis for high-dimensional data, the investigation of interdisciplinary approaches to multi-dimensional obstructive sleep apnea patient data, and the inference of a dyadic measure and its simplicial geometry from binary feature data. Based on the first Women in Data Science and Mathematics (WiSDM) Research Collaboration Workshop that took place in 2017 at the Institute for Compuational and Experimental Research in Mathematics (ICERM) in Providence, Rhode Island, this volume features submissions from several of the working groups as well as contributions from the wider community. The volume is suitable for researchers in data science in industry and academia.

Progress in plant biology relies on the quantification, analysis and mathematical modeling of data over different time and length scales. This book describes common mathematical and computational approaches as well as some carefully chosen case studies that demonstrate the use of these techniques to solve problems at the forefront of plant biology. Each chapter is written by an expert in field with the goal of conveying concepts whilst at the same time providing sufficient background and links to available software for readers to rapidly build their own models and run their own simulations. This book is aimed at postgraduate students and researchers working the field of plant systems biology and synthetic biology, but will also be a useful reference for anyone wanting to get into quantitative plant biology.

This proceedings presents the result of the 8th International Conference in Network Analysis, held at the Higher School of Economics, Moscow, in May 2018. The conference brought together scientists, engineers, and researchers from academia, industry, and government. Contributions in this book focus on the development of network algorithms for data mining and its applications. Researchers and students in mathematics, economics, statistics, computer science, and engineering find this collection a valuable resource filled with the latest research in network analysis. Computational aspects and applications of large-scale networks in market models, neural networks, social networks, power transmission grids, maximum clique problem, telecommunication networks, and complexity graphs are included with new tools for efficient network analysis of large-scale networks. Machine learning techniques in network settings including community detection, clustering, and biclustering algorithms are presented with applications to social network analysis.

Many scientific and real-world problems that occur in science, engineering, and medicine can be represented in differential equations. There is a vital role for differential equations in studying the behavior of different types of real-world problems. Thus, it becomes crucial to know the existence uniqueness properties of differential equations and various methods of finding differential equation solutions in explicit form. It is also essential to know different kinds of differential equations in terms of eigenvalues, termed eigenvalue problems, and some special functions used in finding the solution to differential equations. The study of nonlinear problems also plays a significant role in different real-world situations. There is a necessity to know the behavior of solutions of nonlinear differential equations. Still, there are very few forms of differential equations whose solution can be found in explicit form. For the differential equations whose solutions cannot be found in explicit form, one has to study the properties of solutions of the given differential equation to guess an approximate solution of it. This book aims to introduce all the necessary topics of differential equations in one book so that laymen can easily understand the subject and apply it in their research areas. The novel approach used in this book is that I have introduced different analytical methods for finding the solution of differential equations with sufficient theorems, corollaries, and examples, and the geometrical interpretations in each topic. This textbook is intended to study the theory and methods of finding the explicit solutions to differential equations, wherever possible, and in the absence of finding explicit solutions. It is intended to study the properties of solutions to the given differential equations. This book is based on syllabi of the theory of differential equations prescribed for postgraduate students of mathematics and applied mathematics in different institutions and universities of India and abroad. This book will be helpful for competitive examinations as well.

Features Includes multiple case studies. Suitable for scientists and professionals working on methods for mosquito control. Provides a much-needed focal point for interdisciplinary discussion.

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 second edition of the outstanding monograph on coherent states by Combescure and Robert published in 2012 is enriched with figures, historical information and numerical simulations and enlarged with five new chapters presenting important rigorous results obtained in the recent years. The new chapters include various applications such as to the time dependent Schroedinger equation and the Ehrenfest time, to the growth of norms and energy exchanges, to chaotic systems and classical systems with quantum ergodic behavior, and to open quantum systems, and to adiabatic decoupling for multicomponent systems Overall, this book presents the various types of coherent states introduced and studied in the physics and mathematics literature and describes their properties together with application to quantum physics problems. It is intended to serve as a compendium on coherent states and their applications for physicists and mathematicians, stretching from the basic mathematical structures of generalized coherent states in the sense of Perelomov via the semiclassical evolution of coherent states to various specific examples of coherent states (hydrogen atom, quantum oscillator, etc.). It goes beyond existing books on coherent states in terms of a rigorous mathematical framework

The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. As a result of researchers' and scientists' increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, control theory and several other related areas.

1) Provides analytical solutions based on a three-phase model for composites of various structures 2) Identifies computational models to solve problems within all applications of composite materials 3) Constructs higher approximations of the Maxwell formula 4) Proposes efficient analytical algorithms ensuring reliable computational analysis

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. After providing a critical analysis of the current state of the field and an overview of the current research perspectives, chapters focus on three main research areas: pedestrian interactions, crowd control, and multiscale modeling. Specific topics covered in this volume include: crowd dynamics through conservation laws recent developments in controlled crowd dynamics mixed traffic modeling insights and applications from crowd psychology Crowd Dynamics, Volume 2 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.

The papers presented in this open access book address diverse challenges in decarbonizing energy systems, ranging from operational to investment planning problems, from market economics to technical and environmental considerations, from distribution grids to transmission grids, and from theoretical considerations to data provision concerns and applied case studies. While most papers have a clear methodological focus, they address policy-relevant questions at the same time. The target audience therefore includes academics and experts in industry as well as policy makers, who are interested in state-of-the-art quantitative modelling of policy relevant problems in energy systems. The 2nd International Symposium on Energy System Optimization (ISESO 2018) was held at the Karlsruhe Institute of Technology (KIT) under the symposium theme "Bridging the Gap Between Mathematical Modelling and Policy Support" on October 10th and 11th 2018. ISESO 2018 was organized by the KIT, the Heidelberg Institute for Theoretical Studies (HITS), the Heidelberg University, the German Aerospace Center and the University of Stuttgart.

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.

This book explains in simple settings the fundamental ideas of financial market modelling and derivative pricing, using the no-arbitrage principle. Relatively elementary mathematics leads to powerful notions and techniques - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures - which are directly applicable in practice. The general methods are applied in detail to pricing and hedging European and American options within the Cox-Ross-Rubinstein (CRR) binomial tree model. A simple approach to discrete interest rate models is included, which, though elementary, has some novel features. All proofs are written in a user-friendly manner, with each step carefully explained and following a natural flow of thought. In this way the student learns how to tackle new problems.

The purpose of this book, first published in 1939, updated in 1953, is to give a treatment of the so-called operational method and to illustrate its application to problems in various branches of technology. It is written primarily for technologists who use mathematics in solving technical problems in industrial and applied research work, and the treatment is sufficiently rigorous for their needs. The theory of the complex variable and of transform calculus occupy the first half of the book. A further third of the book describes the application of this theory to problems arising in electrical circuits; vibrational systems; aeroplane dynamics; the deflexion of beams; radio and television receivers; the solution of partial differential equations; electrical transmission limes; electrical wave filters; solenoids with metal cores; condenser microphones; loud speaker horns and the absorption of moisture. The final part contains over 100 problems - many with hints for their solution - appendices and references.

Autonomous Positioning of Piezoactuated Mechanism for Biological Cell Puncture gives a systematic and almost selfcontained description of the many facets of advanced design, optimization, modeling, system identification and advanced control techniques for positioning of cell puncture mechanism with piezoelectric actuator in micro/nanorobotics systems. To achieve biomedical applications, reliability design, modeling, and precision control are vitally important for developing engineering systems. With the advances in mechanical design, dynamic modeling, system identification, and control techniques, exploiting them for the benefit of reliability design, precision control, and quick actuation of micro/nanomanipulation systems to expand the robot's applications at the micro and nanoscales, especially for biomedical applications. This book unifies existing and emerging techniques concerning advanced design, modeling and advanced control methodologies in micropuncture of biological cells using piezoelectric actuator with their practical biomedical applications. The book is an essential resource for researchers within robotics, mechatronics, biomedical engineering, and automatic control society, including both academic and industrial parts. KEY FEATURES * Provides a series of latest results in, including but not limited to, design, modeling, and control of micro/nanomanipulation systems utilizing piezoelectric actuator * Gives recent advances of theory, technological aspects, and applications of advanced modeling, control, and actuation methodologies in cell engineering applications * Presents simulation and experimental results to reflect the micro/nano manipulation practice, and also validate the performances of the developed design, analysis, and synthesis approaches

Artificial intelligence (AI) and digital engineering have become prevalent in business, industry, government, and academia. However, the workforce still has a lot to learn on how to leverage them. This handbook presents the preparatory and operational foundations for the efficacy, applicability, risk, and how to take advantage of these tools and techniques. "Handbook of Mathematical and Digital Engineering Foundations for Artificial Intelligence: A Systems Methodology" provides a guide for using digital engineering platforms for advancing AI applications. The book discusses an interface of education and research in the pursuit of AI developments and highlights the facilitation of advanced education through AI and digital engineering systems. It presents an integration of soft and hard skills in developing and using AI and offers a rigorous systems approach to understanding and using AI. This handbook will be the go-to resource for practitioners and students on applying systems methodology to the body of knowledge of understanding, embracing, and using digital engineering tools and techniques.

This open access book brings together the latest developments from industry and research on automated driving and artificial intelligence. Environment perception for highly automated driving heavily employs deep neural networks, facing many challenges. How much data do we need for training and testing? How to use synthetic data to save labeling costs for training? How do we increase robustness and decrease memory usage? For inevitably poor conditions: How do we know that the network is uncertain about its decisions? Can we understand a bit more about what actually happens inside neural networks? This leads to a very practical problem particularly for DNNs employed in automated driving: What are useful validation techniques and how about safety? This book unites the views from both academia and industry, where computer vision and machine learning meet environment perception for highly automated driving. Naturally, aspects of data, robustness, uncertainty quantification, and, last but not least, safety are at the core of it. This book is unique: In its first part, an extended survey of all the relevant aspects is provided. The second part contains the detailed technical elaboration of the various questions mentioned above.

The text focuses on mathematical modeling and applications of advanced techniques of machine learning, and artificial intelligence, including artificial neural networks, evolutionary computing, data mining, and fuzzy systems to solve performance and design issues more precisely. Intelligent computing encompasses technologies, algorithms, and models in providing effective and efficient solutions to a wide range of problems including the airport's intelligent safety system. It will serve as an ideal reference text for senior undergraduate, graduate students, and academic researchers in fields including industrial engineering, manufacturing engineering, computer engineering, and mathematics. The book- Discusses mathematical modeling for traffic, sustainable supply chain, vehicular Ad-Hoc networks, internet of things networks with intelligent gateways. Covers advanced machine learning, artificial intelligence, fuzzy systems, evolutionary computing, data mining techniques for real-world problems. Presents applications of mathematical models in chronic diseases such as kidney and coronary artery diseases. Highlights advances in mathematical modeling, strength, and benefits of machine learning and artificial intelligence, including driving goals, applicability, algorithms, and processes involved. Showcases emerging real-life topics on mathematical models, machine learning, and intelligent computing using an interdisciplinary approach. The text presents emerging real-life topics on mathematical models, machine learning, and intelligent computing in a single volume. It will serve as an ideal text for senior undergraduate, graduate students, and researchers in diverse fields domains including industrial and manufacturing engineering, computer engineering, and mathematics.

This book presents a panorama about the recent progress of industrial mathematics from the point of view of both industrials and researchers. The chapters correspond to a selection of the contributions presented in the "Industry Day" and in the Minisymposium "EU - MATHS - IN: Success Stories of Applications of Mathematics to Industry" organized in the framework of the International Conference ICIAM 2019 held in Valencia (Spain) on July 15-19, 2019. In the Industry Day, included for the first time in this series of Conferences, representatives of companies from different countries and several sectors presented their view about the benefits regarding the usage of mathematical tools and/or collaboration with mathematicians. The contributions of this special session were addressed to industry people. Minisymposium contributions detailed some collaborations between mathematicians and industrials that led to real benefits in several European companies. All the speakers were affiliated in some of the European National Networks that constitute the European Service Network of Mathematics for Industry and Innovation (EU-MATHS-IN).

This volume is the proceedings of the Workshop on Optimal Design and Control that was held in Blacksburg, Virginia, April 8-9, 1994. The workshop was spon sored by the Air Force Office of Scientific Research through the Air Force Center for Optimal Design and Control (CODAC) at Virginia Tech. The workshop was a gathering of engineers and mathematicians actively in volved in innovative research in control and optimization, with emphasis placed on problems governed by partial differential equations. The interdisciplinary nature of the workshop and the wide range of subdisciplines represented by the partici pants enabled an exchange of valuable information and also led to significant dis cussions about multidisciplinary optimization issues. One of the goals of the work shop was to include laboratory, industrial, and academic researchers so that anal yses, algorithms, implementations, and applications could all be well-represented in the talks; this interdisciplinary nature is reflected in these proceedings. An overriding impression that can be gleaned from the papers in this volume is the complexity of problems addressed by not only those authors engaged in appli cations, but also by those engaged in algorithmic development and even mathemat ical analyses. Thus, in many instances, systematic approaches using fully nonlin ear constraint equations are routinely used to solve control and optimization prob lems, in some cases replacing ad-hoc or empirically based procedures."

Hayduk is equally at ease explaining the simplest and most advanced applications of the program . . . Hayduk has written more than just a solid text for use in advanced graduate courses on statistical modeling. Those with a firm mathematical background who wish to learn about the approach, or those who know a little about the program and want to know more, will find this an excellent reference.

This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences.

Applications include:

Identification numbers and modular arithmetic(linear) error-correcting codes, including cyclic codesruler and compass constructionscryptographysymmetry of patterns in the real plane

"Abstract Algebra: Structure and Application" is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.

This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.

This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.

Modeling and Applied Mathematics Modeling the behavior of real physical systems by suitable evolution equa tions is a relevant, maybe the fundamental, aspect of the interactions be tween mathematics and applied sciences. Modeling is, however, only the first step toward the mathematical description and simulation of systems belonging to real world. Indeed, once the evolution equation is proposed, one has to deal with mathematical problems and develop suitable simula tions to provide the description of the real system according to the model. Within this framework, one has an evolution equation and the re lated mathematical problems obtained by adding all necessary conditions for their solution. Then, a qualitative analysis should be developed: this means proof of existence of solutions and analysis of their qualitative be havior. Asymptotic analysis may include a detailed description of stability properties. Quantitative analysis, based upon the application ofsuitable methods and algorithms for the solution of problems, ends up with the simulation that is the representation of the dependent variable versus the independent one. The information obtained by the model has to be compared with those deriving from the experimental observation of the real system. This comparison may finally lead to the validation of the model followed by its application and, maybe, further generalization."