Higher Order Networks An Introduction To Simplicial Complexes
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Higher Order Networks: An Introduction to Simplicial Complexes by Ginestra Bianconi Pdf
This Element presents one of the most recent developments in network science in a highly accessible style. This Element will be of interest to interdisciplinary scientists working in network science, in addition to mathematicians working in discrete topology and geometry and physicists working in quantum gravity.
Higher-Order Systems by Federico Battiston,Giovanni Petri Pdf
The book discusses the potential of higher-order interactions to model real-world relational systems. Over the last decade, networks have emerged as the paradigmatic framework to model complex systems. Yet, as simple collections of nodes and links, they are intrinsically limited to pairwise interactions, limiting our ability to describe, understand, and predict complex phenomena which arise from higher-order interactions. Here we introduce the new modeling framework of higher-order systems, where hypergraphs and simplicial complexes are used to describe complex patterns of interactions among any number of agents. This book is intended both as a first introduction and an overview of the state of the art of this rapidly emerging field, serving as a reference for network scientists interested in better modeling the interconnected world we live in.
Complex Networks and Their Applications XI by Hocine Cherifi,Rosario Nunzio Mantegna,Luis M. Rocha,Chantal Cherifi,Salvatore Micciche Pdf
This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the XI International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2022). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks and technological networks.
Machine Learning and Knowledge Discovery in Databases: Research Track by Danai Koutra,Claudia Plant,Manuel Gomez Rodriguez,Elena Baralis,Francesco Bonchi Pdf
The multi-volume set LNAI 14169 until 14175 constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2023, which took place in Turin, Italy, in September 2023. The 196 papers were selected from the 829 submissions for the Research Track, and 58 papers were selected from the 239 submissions for the Applied Data Science Track. The volumes are organized in topical sections as follows: Part I: Active Learning; Adversarial Machine Learning; Anomaly Detection; Applications; Bayesian Methods; Causality; Clustering. Part II: Computer Vision; Deep Learning; Fairness; Federated Learning; Few-shot learning; Generative Models; Graph Contrastive Learning. Part III: Graph Neural Networks; Graphs; Interpretability; Knowledge Graphs; Large-scale Learning. Part IV: Natural Language Processing; Neuro/Symbolic Learning; Optimization; Recommender Systems; Reinforcement Learning; Representation Learning. Part V: Robustness; Time Series; Transfer and Multitask Learning. Part VI: Applied Machine Learning; Computational Social Sciences; Finance; Hardware and Systems; Healthcare & Bioinformatics; Human-Computer Interaction; Recommendation and Information Retrieval. Part VII: Sustainability, Climate, and Environment.- Transportation & Urban Planning.- Demo.
Emerging Frontiers in Nonlinear Science by Panayotis G. Kevrekidis,Jesús Cuevas-Maraver,Avadh Saxena Pdf
This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal feature in mathematics, physics, chemistry and biology, and is used to characterize systems whose behavior does not amount to a superposition of simple building blocks, but rather features complex and often chaotic patterns and phenomena. Each chapter of the book features a synopsis that not only recaps the recent progress in each field but also charts the challenges that lie ahead. This interdisciplinary book presents contributions from a diverse group of experts from various fields to provide an overview of each field’s past, present and future. It will appeal to both beginners and seasoned researchers in nonlinear science, numerous areas of physics (optics, quantum physics, biophysics), and applied mathematics (ODEs, PDEs, dynamical systems, machine learning) as well as engineering.
Hypergraph Computation by Qionghai Dai,Yue Gao Pdf
This open access book discusses the theory and methods of hypergraph computation. Many underlying relationships among data can be represented using graphs, for example in the areas including computer vision, molecular chemistry, molecular biology, etc. In the last decade, methods like graph-based learning and neural network methods have been developed to process such data, they are particularly suitable for handling relational learning tasks. In many real-world problems, however, relationships among the objects of our interest are more complex than pair-wise. Naively squeezing the complex relationships into pairwise ones will inevitably lead to loss of information which can be expected valuable for learning tasks. Hypergraph, as a generation of graph, has shown superior performance on modelling complex correlations compared with graph. Recent years have witnessed a great popularity of researches on hypergraph-related AI methods, which have been used in computer vision, social media analysis, etc. We summarize these attempts as a new computing paradigm, called hypergraph computation, which is to formulate the high-order correlations underneath the data using hypergraph, and then conduct semantic computing on the hypergraph for different applications. The content of this book consists of hypergraph computation paradigms, hypergraph modelling, hypergraph structure evolution, hypergraph neural networks, and applications of hypergraph computation in different fields. We further summarize recent achievements and future directions on hypergraph computation in this book.
Graph Theoretic Methods in Multiagent Networks by Mehran Mesbahi,Magnus Egerstedt Pdf
This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: ? University of Stuttgart, Germany Royal Institute of Technology, Sweden Johannes Kepler University, Austria Georgia Tech, USA University of Washington, USA Ohio University, USA
Medical Image Computing and Computer Assisted Intervention – MICCAI 2022 by Linwei Wang,Qi Dou,P. Thomas Fletcher,Stefanie Speidel,Shuo Li Pdf
The eight-volume set LNCS 13431, 13432, 13433, 13434, 13435, 13436, 13437, and 13438 constitutes the refereed proceedings of the 25th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2022, which was held in Singapore in September 2022. The 574 revised full papers presented were carefully reviewed and selected from 1831 submissions in a double-blind review process. The papers are organized in the following topical sections: Part I: Brain development and atlases; DWI and tractography; functional brain networks; neuroimaging; heart and lung imaging; dermatology; Part II: Computational (integrative) pathology; computational anatomy and physiology; ophthalmology; fetal imaging; Part III: Breast imaging; colonoscopy; computer aided diagnosis; Part IV: Microscopic image analysis; positron emission tomography; ultrasound imaging; video data analysis; image segmentation I; Part V: Image segmentation II; integration of imaging with non-imaging biomarkers; Part VI: Image registration; image reconstruction; Part VII: Image-Guided interventions and surgery; outcome and disease prediction; surgical data science; surgical planning and simulation; machine learning – domain adaptation and generalization; Part VIII: Machine learning – weakly-supervised learning; machine learning – model interpretation; machine learning – uncertainty; machine learning theory and methodologies.
Simplicial Complexes In Complex Systems: In Search For Alternatives by Yi Zhao,Slobodan Maletic Pdf
For the last few decades researchers from different fields gather their findings and knowledge trying to give a shape to the new science of complex systems. To address this problem, new tools and methods have to be established. A new, or more precisely an alternative, framework for the characterization of complex system was proposed. In this book we will introduce the applicability of applicability of simplicial complexes in the science of complex systems. After introducing the main definitions and properties of simplicial complexes necessary for representation and analysis of complex systems, we will illustrate the usefulness and versatility of tools and concepts related to the simplicial complexes.
Topological Signal Processing by Michael Robinson Pdf
Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.
This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks. The book puts a special emphasis on analyzing complex systems which are organized under the form of networks where nodes and edges are embedded in space. In these networks, space is relevant, and topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields, ranging from urbanism to epidemiology. This subject is therefore at the crossroad of many fields and is of potential interest to a broad audience comprising physicists, mathematicians, engineers, geographers or urbanists. In this book, the author has expanded his previous book ("Morphogenesis of Spatial Networks") to serve as a textbook and reference on this topic for a wide range of students and professional researchers.
Hypernetworks in the Science of Complex Systems by Jeffrey Johnson Pdf
The modern world is complex beyond human understanding and control. The science of complex systems aims to find new ways of thinking about the many interconnected networks of interaction that defy traditional approaches. Thus far, research into networks has largely been restricted to pairwise relationships represented by links between two nodes. This volume marks a major extension of networks to multidimensional hypernetworks for modeling multi-element relationships, such as companies making up the stock market, the neighborhoods forming a city, people making up committees, divisions making up companies, computers making up the internet, men and machines making up armies, or robots working as teams. This volume makes an important contribution to the science of complex systems by: (i) extending network theory to include dynamic relationships between many elements; (ii) providing a mathematical theory able to integrate multilevel dynamics in a coherent way; (iii) providing a new methodological approach to analyze complex systems; and (iv) illustrating the theory with practical examples in the design, management and control of complex systems taken from many areas of application. Contents:IntroductionSets and RelationsHypergraphs and the Galois LatticeSimplicial Complexes and Q-AnalysisBackcloth and Traffic: Dynamics Constrained by TopologyHypernetworksMultilevel SystemsTime, Events, Prediction and ForecastingHypernetworks and DesignPolicy, Design, Planning and ScienceNotes and Reflections Readership: Academics: researchers, scientists, social scientists, complex systems scientists, economists, biologists; Industry: managers, planners, consultants, knowledge professionals, systems engineers, automation specialists, supply chain managers; Public services: Council Officers, city planners, transport planners, health professionals, welfare professionals. Key Features:A first book of its kind on 'hypernetworks', a term the author has coined to describe the mathematical structures he has worked on over the last 30 yearsIntroduces hypernetworks in the context of examples drawn from a wide range of fields, including design, planning, management, art, neural network, machine vision, robotics, traffic, road accidents, amongst othersThe emphasis of this volume is on useful and added-value applications. It will develop the necessary mathematics and assuming no pre-requisitesContains a myriad of illustrations to further understand the topics discussedReviews: “The mathematics is explicitly explained and no difficult theorems are included in this book in order to enable scientists, designers and policy makers to work together.” Zentralblatt MATH