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 book shows how to develop efficient quantitative methods to characterize neural data and extra information that reveals underlying dynamics and neurophysiological mechanisms. Written by active experts in the field, it contains an exchange of innovative ideas among researchers at both computational and experimental ends, as well as those at the interface. Authors discuss research challenges and new directions in emerging areas with two goals in mind: to collect recent advances in statistics, signal processing, modeling, and control methods in neuroscience; and to welcome and foster innovative or cross-disciplinary ideas along this line of research and discuss important research issues in neural data analysis. Making use of both tutorial and review materials, this book is written for neural, electrical, and biomedical engineers; computational neuroscientists; statisticians; computer scientists; and clinical engineers.

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.

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 proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schroedinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event.They will be a valuable and inspiring source of information for graduate students and established researchers.

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 results from the XVIII Spanish-French School 'Jacques Louis Lions' on Numerical Simulation in Physics and Engineering, that took place in Las Palmas de Gran Canaria from 25th to 29th June 2018. These conferences are held biennially since 1984 and sponsored by the Spanish Society of Applied Mathematics (SEMA). They also have the sponsorship of the Societe de Mathematiques Appliquees et Industrielles (SMAI) of France since 2008. Each edition is organized around several main courses and talks delivered by renowned French/Spanish scientists. This volume is highly recommended to graduate students in Engineering or Science who want to focus on numerical simulation, either as a research topic or in the field of industrial applications. It can also benefit senior researchers and technicians working in industry who are interested in the use of state-of-the-art numerical techniques. Moreover, the book can be used as a textbook for master courses in Mathematics, Physics, or Engineering.

This work is motivated by the ongoing open question of how information in the outside world is represented and processed by the brain. Consequently, several novel methods are developed. A new mathematical formulation is proposed for the encoding and decoding of analog signals using integrate-and-fire neuron models. Based on this formulation, a novel algorithm, significantly faster than the state-of-the-art method, is proposed for reconstructing the input of the neuron. Two new identification methods are proposed for neural circuits comprising a filter in series with a spiking neuron model. These methods reduce the number of assumptions made by the state-of-the-art identification framework, allowing for a wider range of models of sensory processing circuits to be inferred directly from input-output observations. A third contribution is an algorithm that computes the spike time sequence generated by an integrate-and-fire neuron model in response to the output of a linear filter, given the input of the filter encoded with the same neuron model.

The study of network theory is a highly interdisciplinary field, which has emerged as a major topic of interest in various disciplines ranging from physics and mathematics, to biology and sociology. This book promotes the diverse nature of the study of complex networks by balancing the needs of students from very different backgrounds. It references the most commonly used concepts in network theory, provides examples of their applications in solving practical problems, and clear indications on how to analyse their results. In the first part of the book, students and researchers will discover the quantitative and analytical tools necessary to work with complex networks, including the most basic concepts in network and graph theory, linear and matrix algebra, as well as the physical concepts most frequently used for studying networks. They will also find instruction on some key skills such as how to proof analytic results and how to manipulate empirical network data. The bulk of the text is focused on instructing readers on the most useful tools for modern practitioners of network theory. These include degree distributions, random networks, network fragments, centrality measures, clusters and communities, communicability, and local and global properties of networks. The combination of theory, example and method that are presented in this text, should ready the student to conduct their own analysis of networks with confidence and allow teachers to select appropriate examples and problems to teach this subject in the classroom.

This thesis presents the state of the art in the study of Bondi-Metzner-Sachs (BMS) symmetry and its applications in the simplified setting of three dimensions. It focuses on presenting all the background material in a pedagogical and self-contained manner to enable readers to fully appreciate the original results that have been obtained while learning a number of fundamental concepts in the field along the way. This makes it a highly rewarding read and a perfect starting point for anybody with a serious interest in the four-dimensional problem.

This book concerns the mathematical modeling and computer simulation of the human stomach. It follows the four modern P's (prevention, prediction, personalization, and precision in medicine) approach in addressing the highly heterogeneous nature of processes underlying gastric motility disorders manifested as gastroparesis, functional dyspepsia, myenteric enteropathy etc. The book comprehensively guides readers through the fundamental theoretical concepts to complex physiological models of the organ. This requires a deep and thorough understanding of driving pathophysiological mechanisms as well as the collaborative effort of specialists working in fundamental and biological science. Such a multidisciplinary partnership is vital because it upholds gnostic capabilities and provides the exchange of thoughts and ideas thus offering broad perspectives into the evolution and management of diseases. The book is a valuable resource for applied mathematicians, computational biologists, bioengineers, physicians, physiologists and researchers working in various fields of biomedicine.

The stability analysis of stochastic models for telecommunication systems is an intensively studied topic. The analysis is, as a rule, a difficult problem requiring a refined mathematical technique, especially when one endeavors beyond the framework of Markovian models. The primary purpose of this book is to present, in a unified way, research into the stability analysis of a wide variety of regenerative queueing systems. It describes the theoretical foundations of this method, and then shows how it works with particular models, both classic ones as well as more recent models that have received attention. The focus lies on an in-depth and insightful mathematical explanation of the regenerative stability analysis method. The unique volume can serve as a textbook for students working in these and related scientific areas. The material is also of interest to engineers working in telecommunications field, who may be faced with the problem of stability of queueing systems.

The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English church-bell music. The latter is facilitated by imbedding the right graph of the right group on an appropriate surface, with suitable symmetries. Throughout the emphasis is on Cayley maps: imbeddings of Cayley graphs for finite groups as (possibly branched) covering projections of surface imbeddings of loop graphs with one vertex. This is not as restrictive as it might sound; many developments in topological graph theory involve such imbeddings.

The approach aims to make all this interconnected material readily accessible to a beginning graduate (or an advanced undergraduate) student, while at the same time providing the research mathematician with a useful reference book in topological graph theory. The focus will be on beautiful connections, both elementary and deep, within mathematics that can best be described by the intuitively pleasing device of imbedding graphs of groups on surfaces.

This monograph investigates violations of statistical stability of physical events, variables, and processes and develops a new physical-mathematical theory taking into consideration such violations - the theory of hyper-random phenomena. There are five parts. The first describes the phenomenon of statistical stability and its features, and develops methods for detecting violations of statistical stability, in particular when data is limited. The second part presents several examples of real processes of different physical nature and demonstrates the violation of statistical stability over broad observation intervals. The third part outlines the mathematical foundations of the theory of hyper-random phenomena, while the fourth develops the foundations of the mathematical analysis of divergent and many-valued functions. The fifth part contains theoretical and experimental studies of statistical laws where there is violation of statistical stability. The monograph should be of particular interest to engineers and scientists in general who study the phenomenon of statistical stability and use statistical methods for high-precision measurements, prediction, and signal processing over long observation intervals.

This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.

Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.

Contemporary engineering design is heavily based on computer simulations. Accurate, high-fidelity simulations are used not only for design verification but, even more importantly, to adjust parameters of the system to have it meet given performance requirements. Unfortunately, accurate simulations are often computationally very expensive with evaluation times as long as hours or even days per design, making design automation using conventional methods impractical. These and other problems can be alleviated by the development and employment of so-called surrogates that reliably represent the expensive, simulation-based model of the system or device of interest but they are much more reasonable and analytically tractable.

This volume features surrogate-based modeling and optimization techniques, and their applications for solving difficult and computationally expensive engineering design problems. It begins bypresentingthe basic concepts and formulations of the surrogate-based modeling and optimization paradigm and thendiscusses relevant modeling techniques, optimization algorithms and design procedures, as well as state-of-the-art developments. The chapters are self-contained with basic concepts and formulations along with applications and examples. The book will be useful toresearchers in engineering and mathematics, in particular those who employ computationally heavy simulations in their design work.

Two approaches are known for solving large-scale unconstrained optimization problems-the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.

The papers collected in this volume focus on new perspectives on individuals, society, and science, specifically in the field of socio-economic systems. The book is the result of a scientific collaboration among experts from "Alexandru Ioan Cuza" University of Iasi (Romania), "G. d'Annunzio" University of Chieti-Pescara (Italy), "University of Defence" of Brno (Czech Republic), and "Pablo de Olavide" University of Sevilla (Spain). The heterogeneity of the contributions presented in this volume reflects the variety and complexity of social phenomena. The book is divided in four Sections as follows. The first Section deals with recent trends in social decisions. Specifically, it aims to understand which are the driving forces of social decisions. The second Section focuses on the social and public sphere. Indeed, it is oriented on recent developments in social systems and control. Trends in quantitative theories and models are described in Section 3, where many new formal, mathematical-statistical tools for modelling complex social phenomena are presented. Finally, Section 4 shows integrative theories and models; particularly, it deals with the ethical, cultural and political approaches to social science, the pedagogical methods, and the relationship between literature, politics, religion and society. The book is addressed to sociologists, philosophers, mathematicians, statisticians, people interested in ethics, and specialists in the fields of communication, social, and political sciences.

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.

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. In this book the authors observe that it also occurs in natural phenomena of all scales: 1-dimensional surgery happens during DNA recombination and when cosmic magnetic lines reconnect; 2-dimensional surgery happens during tornado formation and cell mitosis; and they conjecture that 3-dimensional surgery happens during the formation of black holes from cosmic strings, offering an explanation for the existence of a black hole's singularity. Inspired by such phenomena, the authors present a new topological model that extends the formal definition to a continuous process caused by local forces. Lastly, they describe an intrinsic connection between topological surgery and a chaotic dynamical system exhibiting a "hole drilling" behavior. The authors' model indicates where to look for the forces causing surgery and what deformations should be observed in the local submanifolds involved. These predictions are significant for the study of phenomena exhibiting surgery and they also open new research directions. This novel study enables readers to gain a better understanding of the topology and dynamics of various natural phenomena, as well as topological surgery itself and serves as a basis for many more insightful observations and new physical implications.

This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

In this monograph, the authors present their recently developed theory of electromagnetic interactions. This neoclassical approach extends the classical electromagnetic theory down to atomic scales and allows the explanation of various non-classical phenomena in the same framework. While the classical Maxwell-Lorentz electromagnetism theory succeeds in describing the physical reality at macroscopic scales, it struggles at atomic scales. Here, quantum mechanics traditionally takes over to describe non-classical phenomena such as the hydrogen spectrum and de Broglie waves. By means of modifying the classical theory, the approach presented here is able to consistently explain quantum-mechanical effects, and while similar to quantum mechanics in some respects, this neoclassical theory also differs markedly from it. In particular, the newly developed framework omits probabilistic interpretations of the wave function and features a new fundamental spatial scale which, at the size of the free electron, is much larger than the classical electron radius and is relevant to plasmonics and emission physics. This book will appeal to researchers interested in advanced aspects of electromagnetic theory. Treating the classical approach in detail, including non-relativistic aspects and the Lagrangian framework, and comparing the neoclassical theory with quantum mechanics and the de Broglie-Bohm theory, this work is completely self-contained.

This book describes the latest advances in intelligent techniques such as fuzzy logic, neural networks, and optimization algorithms, and their relevance in building intelligent information systems in combination with applied mathematics. The authors also outline the applications of these systems in areas like intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and optimization of complex problems. By sharing fresh ideas and identifying new targets/problems it offers young researchers and students new directions for their future research. The book is intended for readers from mathematics and computer science, in particular professors and students working on theory and applications of intelligent systems for real-world applications.

This book features a selection of revised and extended research articles written by prominent researchers who participated in the 26th World Congress on Engineering and Computer Science (WCECS 2018), held in San Francisco, USA, on October 23-25, 2018. Topics covered include engineering mathematics, electrical engineering, communications systems, computer science, chemical engineering, systems engineering, manufacturing engineering and industrial applications. With contributions carefully chosen to represent the most cutting-edge research presented at the conference and highlighting the state of the art in engineering technologies and the physical sciences and their applications, the book is a valuable reference resource for graduate students and researchers working in these fields.

This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed. Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion. This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications.