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Network theory
About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.
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TL;DR: The proposed update algorithm substantially reduces the number of shortest paths which should be re-computed when a graph is changed, and a community detection algorithm is adapted to show how much benefit can be obtained from the proposed algorithm in a practical application.
51 citations
TL;DR: It is shown that the proposed optimal placement strategy considerably outperforms heuristic methods including choosing hub nodes with high degree or betweenness centrality as drivers and properties of optimal drivers in terms of various centrality measures including degree, betweenness, closeness, and clustering coefficient.
Abstract: Controlling networked structures has many applications in science and engineering. In this paper, we consider the problem of pinning control (pinning the dynamics into the reference state), and optimally placing the driver nodes, i.e., the nodes to which the control signal is fed. Considering the local controllability concept, a metric based on the eigenvalues of the Laplacian matrix is taken into account as a measure of controllability. We show that the proposed optimal placement strategy considerably outperforms heuristic methods including choosing hub nodes with high degree or betweenness centrality as drivers. We also study properties of optimal drivers in terms of various centrality measures including degree, betweenness, closeness, and clustering coefficient. The profile of these centrality values depends on the network structure. For homogeneous networks such as random small-world networks, the optimal driver nodes have almost the mean centrality value of the population (much lower than the centrality value of hub nodes), whereas the centrality value of optimal drivers in heterogeneous networks such as scale-free ones is much higher than the average and close to that of hub nodes. However, as the degree of heterogeneity decreases in such networks, the profile of centrality approaches the population mean.
51 citations
TL;DR: Challenges which have demanded the attention of scientific community for a long time, such as allostery and protein folding, are considered in greater detail and an integration of network theory with ensembles of equilibrium structures of a single protein or that of a large number of structures from the data bank has been presented.
Abstract: Network theory has become an excellent method of choice through which biological data are smoothly integrated to gain insights into complex biological problems. Understanding protein structure, folding, and function has been an important problem, which is being extensively investigated by the network approach. Since the sequence uniquely determines the structure, this review focuses on the networks of non-covalently connected amino acid side chains in proteins. Questions in structural biology are addressed within the framework of such a formalism. While general applications are mentioned in this review, challenging problems which have demanded the attention of scientific community for a long time, such as allostery and protein folding, are considered in greater detail. Our aim has been to explore these important problems through the eyes of networks. Various methods of constructing protein structure networks (PSN) are consolidated. They include the methods based on geometry, edges weighted by different schemes, and also bipartite network of protein-nucleic acid complexes. A number of network metrics that elegantly capture the general features as well as specific features related to phenomena, such as allostery and protein model validation, are described. Additionally, an integration of network theory with ensembles of equilibrium structures of a single protein or that of a large number of structures from the data bank has been presented to perceive complex phenomena from network perspective. Finally, we discuss briefly the capabilities, limitations, and the scope for further explorations of protein structure networks.
51 citations
TL;DR: The application to optics of some mathematical techniques originally developed for the analysis of electric networks and other communications problems, and the general statistical information theory of Shannon and Wiener, are illustrated.
Abstract: The purpose of this paper is to illustrate the application to optics of some mathematical techniques originally developed for the analysis of electric networks and other communications problems. Two general aspects of communication theory may be so applied.The first of these is electrical network theory. This may be further subdivided. First there is the standard treatment of the response of networks to individual signals by means of Fourier analysis. The optical analogue of this is the analysis of images, also by Fourier transform techniques. Second, there is the statistical network theory initiated by N. Wiener and developed by Y. W. Lee. One aspect of this theory is the design of optimum linear systems for separating a signal from a noise. This is relevant to the problem of the removal of grain from photographs.The second aspect of communication theory which is relevant in optics is the general statistical information theory of Shannon and Wiener. This is especially valuable in the analysis of scanning systems treating signals and noise.The autocorrelation function of a picture is useful in both kinds of analysis, and will be discussed.
51 citations
TL;DR: An architecture for systematically dealing in an efficient and rigorous manner with electromagnetic field representations and computations in complex structures based on the topological partitioning of the complex structure into several subdomains joined together by interfaces is outlined.
Abstract: In this three-part sequence of papers, we outline an architecture for systematically dealing in an efficient and rigorous manner with electromagnetic field representations and computations in complex structures The approach is based on the topological partitioning of the complex structure into several subdomains joined together by interfaces In analogy with network theory, individual subdomains are characterized via subdomain relations, obtained either analytically or numerically, and described in a unified format by using a generalized network formulation; the various subdomains are linked together via connection relations provided by the complex structure topology Together these two relations yield the Tableau equations which combine all of the necessary information The suggested framework accommodates the use of different analytic/numerical methods (hybridization), the choice of problem-matched alternative Green's function representations, as well as different types of field representations In the present paper, we focus on the general architecture, various options and their implications, in Part II [1] we furnish formal expressions for the subdomain relationships via alternative Green's functions representations; and in part III [2], we discuss the connection network properties Copyright © 2002 John Wiley & Sons, Ltd
51 citations