This volume comprises 16 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The focus is on primary dominating sets such as paired domination, connected domination, restrained domination, dominating functions, Roman domination, and power domination. Additionally, surveys include known results with a sample of proof techniques for each parameter. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms; the second chapter provides an overview of models of domination from which the parameters are defined. The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments in the field and proof techniques used.

This monograph discusses decision making methods under bipolar fuzzy graphical models with the aim of overcoming the lack of mathematical approach towards bipolar information-positive and negative. It investigates the properties of bipolar fuzzy graphs, their distance functions, and concept of their isomorphism. It presents certain notions, including irregular bipolar fuzzy graphs, domination in bipolar fuzzy graphs, bipolar fuzzy circuits, energy in bipolar fuzzy graphs, bipolar single-valued neutrosophic competition graphs, and bipolar neutrosophic graph structures. This book also presents the applications of mentioned concepts to real-world problems in areas of product manufacturing, international relations, psychology, global terrorism and more, making it valuable for researchers, computer scientists, social scientists and alike.

This book provides an extensive set of tools for applying fuzzy mathematics and graph theory to real-life problems. Balancing the basics and latest developments in fuzzy graph theory, this book starts with existing fundamental theories such as connectivity, isomorphism, products of fuzzy graphs, and different types of paths and arcs in fuzzy graphs to focus on advanced concepts such as planarity in fuzzy graphs, fuzzy competition graphs, fuzzy threshold graphs, fuzzy tolerance graphs, fuzzy trees, coloring in fuzzy graphs, bipolar fuzzy graphs, intuitionistic fuzzy graphs, m-polar fuzzy graphs, applications of fuzzy graphs, and more. Each chapter includes a number of key representative applications of the discussed concept. An authoritative, self-contained, and inspiring read on the theory and modern applications of fuzzy graphs, this book is of value to advanced undergraduate and graduate students of mathematics, engineering, and computer science, as well as researchers interested in new developments in fuzzy logic and applied mathematics.

Introduction to Chemical Graph Theory is a concise introduction to the main topics and techniques in chemical graph theory, specifically the theory of topological indices. These include distance-based, degree-based, and counting-based indices. The book covers some of the most commonly used mathematical approaches in the subject. It is also written with the knowledge that chemical graph theory has many connections to different branches of graph theory (such as extremal graph theory, spectral graph theory). The authors wrote the book in an appealing way that attracts people to chemical graph theory. In doing so, the book is an excellent playground and general reference text on the subject, especially for young mathematicians with a special interest in graph theory. Key Features: A concise introduction to topological indices of graph theory Appealing to specialists and non-specialists alike Provides many techniques from current research About the Authors: Stephan Wagner grew up in Graz (Austria), where he also received his PhD from Graz University of Technology in 2006. Shortly afterwards, he moved to South Africa, where he started his career at Stellenbosch University as a lecturer in January 2007. His research interests lie mostly in combinatorics and related areas, including connections to other scientific fields such as physics, chemistry and computer science. Hua Wang received his PhD from University of South Carolina in 2005. He held a Visiting Research Assistant Professor position at University of Florida before joining Georgia Southern University in 2008. His research interests include combinatorics and graph theory, elementary number theory, and related problems

Analytic Combinatorics: A Multidimensional Approach is written in a reader-friendly fashion to better facilitate the understanding of the subject. Naturally, it is a firm introduction to the concept of analytic combinatorics and is a valuable tool to help readers better understand the structure and large-scale behavior of discrete objects. Primarily, the textbook is a gateway to the interactions between complex analysis and combinatorics. The study will lead readers through connections to number theory, algebraic geometry, probability and formal language theory. The textbook starts by discussing objects that can be enumerated using generating functions, such as tree classes and lattice walks. It also introduces multivariate generating functions including the topics of the kernel method, and diagonal constructions. The second part explains methods of counting these objects, which involves deep mathematics coming from outside combinatorics, such as complex analysis and geometry. Features Written with combinatorics-centric exposition to illustrate advanced analytic techniques Each chapter includes problems, exercises, and reviews of the material discussed in them Includes a comprehensive glossary, as well as lists of figures and symbols About the author Marni Mishna is a professor of mathematics at Simon Fraser University in British Columbia. Her research investigates interactions between discrete structures and many diverse areas such as representation theory, functional equation theory, and algebraic geometry. Her specialty is the development of analytic tools to study the large-scale behavior of discrete objects.

This book constitutes the proceedings of the 27th International Conference on Computing and Combinatorics, COCOON 2021, held in Tainan, Taiwan, in October 2021. Due to the COVID-19 pandemic, COCOON 2021 was organized as a hybrid conference. The 56 papers presented in this volume were carefully reviewed and selected from 131 submissions. The papers are divided into the following topical sub-headings: algorithms, approximation algorithms, automata, computational geometry, fault tolerant computing and fault diagnosis, graph algorithms, graph theory and applications, network and algorithms, online algorithm and stream algorithms, parameterized complexity and algorithms, and recreational games.

Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents a scholarly attempt to bring together all significant mathematical constants in one place.

This book is the first general and extensive review on the algorithmics and mathematical results of beyond planar graphs. Most real-world data sets are relational and can be modelled as graphs consisting of vertices and edges. Planar graphs are fundamental for both graph theory and graph algorithms and are extensively studied. Structural properties and fundamental algorithms for planar graphs have been discovered. However, most real-world graphs, such as social networks and biological networks, are non-planar. To analyze and visualize such real-world networks, it is necessary to solve fundamental mathematical and algorithmic research questions on sparse non-planar graphs, called beyond planar graphs.This book is based on the National Institute of Informatics (NII) Shonan Meeting on algorithmics on beyond planar graphs held in Japan in November, 2016. The book consists of 13 chapters that represent recent advances in various areas of beyond planar graph research. The main aims and objectives of this book include 1) to timely provide a state-of-the-art survey and a bibliography on beyond planar graphs; 2) to set the research agenda on beyond planar graphs by identifying fundamental research questions and new research directions; and 3) to foster cross-disciplinary research collaboration between computer science (graph drawing and computational geometry) and mathematics (graph theory and combinatorics). New algorithms for beyond planar graphs will be in high demand by practitioners in various application domains to solve complex visualization problems. This book therefore will be a valuable resource for researchers in graph theory, algorithms, and theoretical computer science, and will stimulate further deep scientific investigations into many areas of beyond planar graphs.

Impending technological advances will widen an adversary's attack plane over the next decade. Visualizing what the future will hold, and what new threat vectors could emerge, is a task that traditional planning mechanisms struggle to accomplish given the wide range of potential issues. Understanding and preparing for the future operating environment is the basis of an analytical method known as Threatcasting. It is a method that gives researchers a structured way to envision and plan for risks ten years in the future. Threatcasting uses input from social science, technical research, cultural history, economics, trends, expert interviews, and even a little science fiction to recognize future threats and design potential futures. During this human-centric process, participants brainstorm what actions can be taken to identify, track, disrupt, mitigate, and recover from the possible threats. Specifically, groups explore how to transform the future they desire into reality while avoiding an undesired future. The Threatcasting method also exposes what events could happen that indicate the progression toward an increasingly possible threat landscape. This book begins with an overview of the Threatcasting method with examples and case studies to enhance the academic foundation. Along with end-of-chapter exercises to enhance the reader's understanding of the concepts, there is also a full project where the reader can conduct a mock Threatcasting on the topic of "the next biological public health crisis." The second half of the book is designed as a practitioner's handbook. It has three separate chapters (based on the general size of the Threatcasting group) that walk the reader through how to apply the knowledge from Part I to conduct an actual Threatcasting activity. This book will be useful for a wide audience (from student to practitioner) and will hopefully promote new dialogues across communities and novel developments in the area.

This book describes a set of novel statistical algorithms designed to infer functional connectivity of large-scale neural assemblies. The algorithms are developed with the aim of maximizing computational accuracy and efficiency, while faithfully reconstructing both the inhibitory and excitatory functional links. The book reports on statistical methods to compute the most significant functional connectivity graph, and shows how to use graph theory to extract the topological features of the computed network. A particular feature is that the methods used and extended at the purpose of this work are reported in a fairly completed, yet concise manner, together with the necessary mathematical fundamentals and explanations to understand their application. Furthermore, all these methods have been embedded in the user-friendly open source software named SpiCoDyn, which is also introduced here. All in all, this book provides researchers and graduate students in bioengineering, neurophysiology and computer science, with a set of simplified and reduced models for studying functional connectivity in in silico biological neuronal networks, thus overcoming the complexity of brain circuits.

This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The book also addresses core research challenges such as the representation of large and complex datasets, and integrating numerical methods with robust combinatorial algorithms. In keeping with the focus of the TopoInVis 2017 Workshop, the contributions reflect the latest advances in finding experimental solutions to open problems in the sector. They provide an essential snapshot of state-of-the-art research, helping researchers to keep abreast of the latest developments and providing a basis for future work. Gathering papers by some of the world's leading experts on topological techniques, the book represents a valuable contribution to a field of growing importance, with applications in disciplines ranging from engineering to medicine.

This book is a state-of-the-art look at combinatorial games, that is, games not involving chance or hidden information. It contains a fascinating collection of articles by some of the top names in the field, such as Elwyn Berlekamp and John Conway, plus other researchers in mathematics and computer science, together with some top game players. The articles run the gamut from new theoretical approaches (infinite games, generalizations of game values, 2-player cellular automata, Alpha-Beta pruning under partial orders) to the very latest in some of the hottest games (Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex). Many of these advances reflect the interplay of the computer science and the mathematics. The book ends with an updated bibliography by A. Fraenkel and an updated and annotated list of combinatorial game theory problems by R. K. Guy.

When you picture human-data interactions (HDI), what comes to mind? The datafication of modern life, along with open data initiatives advocating for transparency and access to current and historical datasets, has fundamentally transformed when, where, and how people encounter data. People now rely on data to make decisions, understand current events, and interpret the world. We frequently employ graphs, maps, and other spatialized forms to aid data interpretation, yet the familiarity of these displays causes us to forget that even basic representations are complex, challenging inscriptions and are not neutral; they are based on representational choices that impact how and what they communicate. This book draws on frameworks from the learning sciences, visualization, and human-computer interaction to explore embodied HDI. This exciting sub-field of interaction design is based on the premise that every day we produce and have access to quintillions of bytes of data, the exploration and analysis of which are no longer confined within the walls of research laboratories. This volume examines how humans interact with these data in informal (not work or school) environments, paritcularly in museums. The first half of the book provides an overview of the multi-disciplinary, theoretical foundations of HDI (in particular, embodied cognition, conceptual metaphor theory, embodied interaction, and embodied learning) and reviews socio-technical theories relevant for designing HDI installations to support informal learning. The second half of the book describes strategies for engaging museum visitors with interactive data visualizations, presents methodologies that can inform the design of hand gestures and body movements for embodied installations, and discusses how HDI can facilitate people's sensemaking about data. This cross-disciplinary book is intended as a resource for students and early-career researchers in human-computer interaction and the learning sciences, as well as for more senior researchers and museum practitioners who want to quickly familiarize themselves with HDI.

Combinatorics on words has arisen independently within several branches of mathematics, for instance, number theory, group theory and probability, and appears frequently in problems related to theoretical computer science. The first unified treatment of the area was given in Lothaire's Combinatorics on Words. Since its publication, the area has developed and the authors now aim to present several more topics as well as giving deeper insights into subjects that were discussed in the previous volume. An introductory chapter provides the reader with all the necessary background material. There are numerous examples, full proofs whenever possible and a notes section discussing further developments in the area. This book is both a comprehensive introduction to the subject and a valuable reference source for researchers.

This book gives the state-of-the-art on transversals in linear uniform hypergraphs. The notion of transversal is fundamental to hypergraph theory and has been studied extensively. Very few articles have discussed bounds on the transversal number for linear hypergraphs, even though these bounds are integral components in many applications. This book is one of the first to give strong non-trivial bounds on the transversal number for linear hypergraphs. The discussion may lead to further study of those problems which have not been solved completely, and may also inspire the readers to raise new questions and research directions. The book is written with two readerships in mind. The first is the graduate student who may wish to work on open problems in the area or is interested in exploring the field of transversals in hypergraphs. This exposition will go far to familiarize the student with the subject, the research techniques, and the major accomplishments in the field. The photographs included allow the reader to associate faces with several researchers who made important discoveries and contributions to the subject. The second audience is the established researcher in hypergraph theory who will benefit from having easy access to known results and latest developments in the field of transversals in linear hypergraphs.

This book focusses on techniques for automating the procedure of creating external labelings, also known as callout labelings. In this labeling type, the features within an illustration are connected by thin leader lines (called leaders) with their labels, which are placed in the empty space surrounding the image. In general, textual labels describing graphical features in maps, technical illustrations (such as assembly instructions or cutaway illustrations), or anatomy drawings are an important aspect of visualization that convey information on the objects of the visualization and help the reader understand what is being displayed. Most labeling techniques can be classified into two main categories depending on the "distance" of the labels to their associated features. Internal labels are placed inside or in the direct neighborhood of features, while external labels, which form the topic of this book, are placed in the margins outside the illustration, where they do not occlude the illustration itself. Both approaches form well-studied topics in diverse areas of computer science with several important milestones. The goal of this book is twofold. The first is to serve as an entry point for the interested reader who wants to get familiar with the basic concepts of external labeling, as it introduces a unified and extensible taxonomy of labeling models suitable for a wide range of applications. The second is to serve as a point of reference for more experienced people in the field, as it brings forth a comprehensive overview of a wide range of approaches to produce external labelings that are efficient either in terms of different algorithmic optimization criteria or in terms of their usability in specific application domains. The book mostly concentrates on algorithmic aspects of external labeling, but it also presents various visual aspects that affect the aesthetic quality and usability of external labeling.

This volume highlights the mathematical research presented at the 2019 Association for Women in Mathematics (AWM) Research Symposium held at Rice University, April 6-7, 2019. The symposium showcased research from women across the mathematical sciences working in academia, government, and industry, as well as featured women across the career spectrum: undergraduates, graduate students, postdocs, and professionals. The book is divided into eight parts, opening with a plenary talk and followed by a combination of research paper contributions and survey papers in the different areas of mathematics represented at the symposium: algebraic combinatorics and graph theory algebraic biology commutative algebra analysis, probability, and PDEs topology applied mathematics mathematics education

This book describes active illumination techniques in computer vision. We can classify computer vision techniques into two classes: passive and active techniques. Passive techniques observe the scene statically and analyse it as is. Active techniques give the scene some actions and try to facilitate the analysis. In particular, active illumination techniques project specific light, for which the characteristics are known beforehand, to a target scene to enable stable and accurate analysis of the scene. Traditional passive techniques have a fundamental limitation. The external world surrounding us is three-dimensional; the image projected on a retina or an imaging device is two-dimensional. That is, reduction of one dimension has occurred. Active illumination techniques compensate for the dimensional reduction by actively controlling the illumination. The demand for reliable vision sensors is rapidly increasing in many application areas, such as robotics and medical image analysis. This book explains this new endeavour to explore the augmentation of reduced dimensions in computer vision. This book consists of three parts: basic concepts, techniques, and applications. The first part explains the basic concepts for understanding active illumination techniques. In particular, the basic concepts of optics are explained so that researchers and engineers outside the field can understand the later chapters. The second part explains currently available active illumination techniques, covering many techniques developed by the authors. The final part shows how such active illumination techniques can be applied to various domains, describing the issue to be overcome by active illumination techniques and the advantages of using these techniques. This book is primarily aimed at 4th year undergraduate and 1st year graduate students, and will also help engineers from fields beyond computer vision to use active illumination techniques. Additionally, the book is suitable as course material for technical seminars.

This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.

This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmuller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.

Use the Pharo interactive development environment to significantly reduce the cost of creating interactive visualizations. This book shows how Pharo leverages visualization development against traditional frameworks and toolkits. Agile Visualization with Pharo focuses on the Roassal visualization engine and first presents the basic and necessary tools to visualize data, including an introduction to the Pharo programming language. Once you've grasped the basics, you'll learn all about the development environment offered by Roassal. The book provides numerous ready-to-use examples. You'll work on several applications, including visualizing the training phase of reinforcement learning (a powerful machine learning algorithm) and generating software visualizations from GitHub. This book covers aspects that are relevant for engineers and academics to successfully design and implement interactive visualizations. What You Will Learn Implement agile data visualization using the Pharo programming language Chart, plot, and curve using Grapher Build and draw graphs using Mondrian Implement reinforcement learning (Q-Learning, from scratch) and use visualizations to monitor learning and state exploration Use GitHub Action to generate software visualizations (UML class diagram, test coverage) at each commit Who This Book Is For Programmers with some prior exposure to data visualization and computer vision who may be new to the Pharo programming language. This book is also for those with some Pharo experience looking to apply it to data visualization.

This book reports on the development and assessment of a novel framework for studying neural interactions (the connectome) and their dynamics (the chronnectome). Using EEG recordings taken during an auditory oddball task performed by 48 patients with schizophrenia and 87 healthy controls, and applying local and network measures, changes in brain activation from pre-stimulus to cognitive response were assessed, and significant differences were observed between the patients and controls. This book investigates the source of the network abnormalities and presents new evidence for the disconnection hypothesis and the aberrant salience hypothesis with regard to schizophrenia. Moreover, it puts forward a novel approach to combining local regularity measures and graph measures in order to characterize schizophrenia brain dynamics, and presents interesting findings on the regularity of brain patterns in healthy control subjects versus patients with schizophrenia. Besides providing new evidence for the disconnection hypothesis, it offers a source of inspiration for future research directions in the field.

This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70th birthday of Laszlo Lovasz. The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization. Laszlo Lovasz is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, "building bridges" between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years. The 14 contributions presented in this volume, all of which are connected to Laszlo Lovasz's areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.

This book offers a holistic framework to study behavior and evolutionary dynamics in large-scale, decentralized, and heterogeneous crowd networks. In the emerging crowd cyber-ecosystems, millions of deeply connected individuals, smart devices, government agencies, and enterprises actively interact with each other and influence each other's decisions. It is crucial to understand such intelligent entities' behaviors and to study their strategic interactions in order to provide important guidelines on the design of reliable networks capable of predicting and preventing detrimental events with negative impacts on our society and economy. This book reviews the fundamental methodologies to study user interactions and evolutionary dynamics in crowd networks and discusses recent advances in this emerging interdisciplinary research field. Using information diffusion over social networks as an example, it presents a thorough investigation of the impact of user behavior on the network evolution process and demonstrates how this can help improve network performance. Intended for graduate students and researchers from various disciplines, including but not limited to, data science, networking, signal processing, complex systems, and economics, the book encourages researchers in related research fields to explore the many untouched areas in this domain, and ultimately to design crowd networks with efficient, effective, and reliable services.

Designed for the nonspecialist, this classic text by a world expert is an invaluable reference tool for those interested in a basic understanding of the subject. Exercises, notes and exhaustive references follow each chapter, making it outstanding as both a text and reference for students and researchers in graph theory and its applications. The reader will delight to discover that the topics in this book are coherently unified and include some of the deepest and most beautiful developments in graph theory.