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What is Topology

Chapter 4
Handbook of Research on Systems Biology Applications in Medicine
The topology defines the properties of spaces and maps. Dependent on the described space arbitrary complex structures used.
Published in Chapter:
Deterministic Modeling in Medicine
Elisabeth Maschke-Dutz (Max Planck Institute for Molecular Genetics, Germany)
Copyright: © 2009 |Pages: 23
DOI: 10.4018/978-1-60566-076-9.ch004
Abstract
In this chapter basic mathematical methods for the deterministic kinetic modeling of biochemical systems are described. Mathematical analysis methods, the respective algorithms, and appropriate tools and resources, as well as established standards for data exchange, model representations and definitions are presented. The methods comprise time-course simulations, steady state search, parameter scanning, and metabolic control analysis among others. An application is demonstrated using a test case model that describes parts of the extrinsic apoptosis pathway and a small example network demonstrates an implementation of metabolic control analysis.
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Chapter 121
Isac's Cones in General Vector Spaces
Every collection of sets containing the empty and the environment space, closed to the infinite unions and the finite inclusions.
Published in Chapter: Isac's Cones in General Vector Spaces; From: Encyclopedia of Business Analytics and Optimization
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Chapter 2
Spatio-Temporal Hot Spot Analysis of Epidemic Diseases Using Geographic Information System for Improved Healthcare
Physical structures represented as point, line, and polygon describing connectivity, adjacency and continuity.
Published in Chapter: Spatio-Temporal Hot Spot Analysis of Epidemic Diseases Using Geographic Information System for Improved Healthcare; From: Emerging Trends and Innovations in Privacy and Health Information Management
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Chapter 9
Optimization as One of the Basic Supports of Industry 4.0
The study of geometrical properties and spatial relations unaffected by the continuous change of shape or size of structures.
Published in Chapter: Optimization as One of the Basic Supports of Industry 4.0; From: Handbook of Research on Integrating Industry 4.0 in Business and Manufacturing
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Chapter 66
Rich-Club Phenomenon of the Internet Topology
A connectivity graph representing a real network, upon which the network’s physical and engineering properties are based.
Published in Chapter: Rich-Club Phenomenon of the Internet Topology; From: Encyclopedia of Internet Technologies and Applications
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Chapter 57
Positive-Feedback Preference Model of the Internet Topology
A connectivity graph representing a real network, upon which the network’s physical and engineering properties are based.
Published in Chapter: Positive-Feedback Preference Model of the Internet Topology; From: Encyclopedia of Internet Technologies and Applications
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Chapter 15
Network Modeling
The study of those properties of networks that are not altered by elastic deformations. These properties include adjacency, incidence, connectivity, and containment.
Published in Chapter: Network Modeling; From: Handbook of Research on Geoinformatics
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Chapter 9
Algorithms to Determine Stable Connected Dominating Sets for Mobile Ad Hoc Networks
An arrangement of the nodes in the network that can be used for communication between any two nodes in the network.
Published in Chapter: Algorithms to Determine Stable Connected Dominating Sets for Mobile Ad Hoc Networks; From: Handbook of Research on Progressive Trends in Wireless Communications and Networking
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Chapter 13
Cognitive Learning Through Knowledge Visualization, Art, and the Geometry of Nature
Topology is the study of mathematical spaces and geometric configurations that stem from their shape independently from their deformation. Arguably, many mention Leonard Euler's “Seven Bridges of Konigsberg Problem” as among the first topological theorems.
Published in Chapter: Cognitive Learning Through Knowledge Visualization, Art, and the Geometry of Nature; From: Interface Support for Creativity, Productivity, and Expression in Computer Graphics
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Chapter 38
Map Matching Algorithms for Intelligent Transport Systems
Topology is the relationship between entities (points, lines, and polygons). The relationship can be defined as adjacency (in the case of polygons), connectivity (in the case of lines), or containment (in the case of points in polygons).
Published in Chapter: Map Matching Algorithms for Intelligent Transport Systems; From: Handbook of Research on Geoinformatics
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Chapter 565
Clique Size and Centrality Metrics for Analysis of Real-World Network Graphs
An arrangement of the nodes in the network that can be used for communication between any two nodes in the network.
Published in Chapter: Clique Size and Centrality Metrics for Analysis of Real-World Network Graphs; From: Encyclopedia of Information Science and Technology, Fourth Edition
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Chapter 19
Basic Topological Notions and their Relation to BIM
A structure for a given set (of points or elements) which specifies interior, frontier and exterior of subsets of that set. Formally, a set of subsets of that given set which satisfies the topology axioms (the set of all possible interiors).
Published in Chapter: Basic Topological Notions and their Relation to BIM; From: Handbook of Research on Building Information Modeling and Construction Informatics: Concepts and Technologies
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Chapter 19
From Optimization to Clustering: A Swarm Intelligence Approach
Topology determines the way in which the constitute parts (in this context particles) are interrelated or arranged and how they communicate and share information with each other.
Published in Chapter: From Optimization to Clustering: A Swarm Intelligence Approach; From: Handbook of Research on Artificial Intelligence Techniques and Algorithms
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Chapter 4
Routing Protocols in Wireless Sensor Networks
Topology is the way of arranging the entities of a network in such a way that it can operate efficiently and provide good quality-of-service. In other words, the organization of the all network components is known as topology.
Published in Chapter: Routing Protocols in Wireless Sensor Networks; From: Handbook of Research on Advanced Wireless Sensor Network Applications, Protocols, and Architectures
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Chapter 40
Computer Networking of Cybercafés in Delta State, Nigeria
The topology of a network describes its layout or the pattern of cabling used to connect personal computers (PC) together. It is the physical layout of the cables that connect the nodes of the network. There are three basic topologies: bus, ring and star topologies.
Published in Chapter: Computer Networking of Cybercafés in Delta State, Nigeria; From: Encyclopedia of Networked and Virtual Organizations
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Chapter 311
Representation of Geographic Phenomena
Field of study in the area of mathematics concerned with basic properties of space, such as the connectedness.
Published in Chapter: Representation of Geographic Phenomena; From: Encyclopedia of Information Science and Technology, Third Edition
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Chapter 3
From Digital Survey to a Virtual Tale: Virtual Reconstruction of the Convent of Santa Maria delle Grazie in Milan
Geometric properties of a mesh, such as the number and the shape of polygons that make it up.
Published in Chapter: From Digital Survey to a Virtual Tale: Virtual Reconstruction of the Convent of Santa Maria delle Grazie in Milan; From: Impact of Industry 4.0 on Architecture and Cultural Heritage
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