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Author: Abubakr Muhammad Publisher: VDM Publishing ISBN: 9783836491860 Category : Graph theory Languages : en Pages : 0
Book Description
The increasing pervasiveness and accuracy of sensors, unprecedented automation of data collection, extremely cheap storage and rapid dissemination of data by communication networks have enabled researchers to think about deploying swarms of cooperating robotic agents for various applications. However, the conception of such large-scale systems is contigent on efficient methods to deal with an explosion of data. Thus the main challenge in this field has shifted from difficulties in manufacturing to the lack of theoretical foundations for provably correct design and deployment. This monograph, appearing originally as a doctoral thesis, offers a unique perspective on the solution of such problems. It introduces some novel methods for dealing with the spatial complexities in robotic networks. At the same time, it makes connections to several emerging disciplines in engineering and mathematical sciences, most notably computational algebraic topology, graph drawing, networked control, sensor networks and distributed optimization. This work received the Georgia Tech Sigma Xi Best doctoral dissertation award in 2006.
Author: Abubakr Muhammad Publisher: VDM Publishing ISBN: 9783836491860 Category : Graph theory Languages : en Pages : 0
Book Description
The increasing pervasiveness and accuracy of sensors, unprecedented automation of data collection, extremely cheap storage and rapid dissemination of data by communication networks have enabled researchers to think about deploying swarms of cooperating robotic agents for various applications. However, the conception of such large-scale systems is contigent on efficient methods to deal with an explosion of data. Thus the main challenge in this field has shifted from difficulties in manufacturing to the lack of theoretical foundations for provably correct design and deployment. This monograph, appearing originally as a doctoral thesis, offers a unique perspective on the solution of such problems. It introduces some novel methods for dealing with the spatial complexities in robotic networks. At the same time, it makes connections to several emerging disciplines in engineering and mathematical sciences, most notably computational algebraic topology, graph drawing, networked control, sensor networks and distributed optimization. This work received the Georgia Tech Sigma Xi Best doctoral dissertation award in 2006.
Author: Abubakr Muhammad Publisher: ISBN: Category : Automatic control Languages : en Pages :
Book Description
In this work, connectivity graphs have been studied as models of local interactions in multi-agent robotic systems. A systematic study of the space of connectivity graphs has been done from a geometric and topological point of view. Some results on the realization of connectivity graphs in their respective configuration spaces have been given. A complexity analysis of networks, from the point of view of intrinsic structural complexity, has been given. Various topological spaces in networks, as induced from their connectivity graphs, have been recognized and put into applications, such as those concerning coverage problems in sensor networks. A framework for studying dynamic connectivity graphs has been proposed. This framework has been used for several applications that include the generation of low-complexity formations as well as collaborative beamforming in sensor networks. The theory has been verified by generating extensive simulations, with the help of software tools of computational homology and semi-definite programming. Finally, several open problems and areas of further research have been identified.
Author: Jakob Jonsson Publisher: Springer Science & Business Media ISBN: 3540758585 Category : Mathematics Languages : en Pages : 376
Book Description
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.
Author: Jakob Jonsson Publisher: Springer ISBN: 3540758593 Category : Mathematics Languages : en Pages : 376
Book Description
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.
Author: Colleen M. Farrelly Publisher: Packt Publishing Ltd ISBN: 1805120174 Category : Computers Languages : en Pages : 290
Book Description
Solve challenging and computationally intensive analytics problems by leveraging network science and graph algorithms Key Features Learn how to wrangle different types of datasets and analytics problems into networks Leverage graph theoretic algorithms to analyze data efficiently Apply the skills you gain to solve a variety of problems through case studies in Python Purchase of the print or Kindle book includes a free PDF eBook Book DescriptionWe are living in the age of big data, and scalable solutions are a necessity. Network science leverages the power of graph theory and flexible data structures to analyze big data at scale. This book guides you through the basics of network science, showing you how to wrangle different types of data (such as spatial and time series data) into network structures. You’ll be introduced to core tools from network science to analyze real-world case studies in Python. As you progress, you’ll find out how to predict fake news spread, track pricing patterns in local markets, forecast stock market crashes, and stop an epidemic spread. Later, you’ll learn about advanced techniques in network science, such as creating and querying graph databases, classifying datasets with graph neural networks (GNNs), and mining educational pathways for insights into student success. Case studies in the book will provide you with end-to-end examples of implementing what you learn in each chapter. By the end of this book, you’ll be well-equipped to wrangle your own datasets into network science problems and scale solutions with Python.What you will learn Transform different data types, such as spatial data, into network formats Explore common network science tools in Python Discover how geometry impacts spreading processes on networks Implement machine learning algorithms on network data features Build and query graph databases Explore new frontiers in network science such as quantum algorithms Who this book is for If you’re a researcher or industry professional analyzing data and are curious about network science approaches to data, this book is for you. To get the most out of the book, basic knowledge of Python, including pandas and NumPy, as well as some experience working with datasets is required. This book is also ideal for anyone interested in network science and learning how graph algorithms are used to solve science and engineering problems. R programmers may also find this book helpful as many algorithms also have R implementations.
Author: Bernard Chazelle Publisher: American Mathematical Soc. ISBN: 0821806742 Category : Mathematics Languages : en Pages : 480
Book Description
This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field. Articles are based on invited talks presented at the AMS-IMS-SIAM Summer Research Conference, "Discrete and Computational Geometry: Ten Years Later", held in 1996 at Mt. Holyoke College (So.Hadley, MA). Topics addressed range from tilings, polyhedra, and arrangements to computational topology and visibility problems. Included are papers on the interaction between real algebraic geometry and discrete and computational geometry, as well as on linear programming and geometric discrepancy theory.
Author: János Pach Publisher: Springer Science & Business Media ISBN: 1461401100 Category : Mathematics Languages : en Pages : 610
Book Description
In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.
Author: Hocine Cherifi Publisher: Springer Nature ISBN: 3031211316 Category : Technology & Engineering Languages : en Pages : 674
Book Description
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.
Author: Herbert Edelsbrunner Publisher: Springer Science & Business ISBN: 3319059572 Category : Computers Languages : en Pages : 105
Book Description
This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.
Author: Abubakr Muhammad
Author: Abubakr Muhammad
Author: Abubakr Muhammad
Author: Jakob Jonsson
Author: Jakob Jonsson
Author: Guillermo Pineda Villavicencio
Author: Colleen M. Farrelly
Author: Bernard Chazelle
Author: János Pach
Author: Hocine Cherifi
Author: Herbert Edelsbrunner