scholarly journals The network structure of mathematical knowledge according to the Wikipedia, MathWorld, and DLMF online libraries

2014 ◽  
Vol 2 (3) ◽  
pp. 367-386
Author(s):  
FLAVIO B. GONZAGA ◽  
VALMIR C. BARBOSA ◽  
GERALDO B. XEXÉO
Keyword(s):  
Network Structure ◽  
Mathematical Knowledge ◽  
Directed Graphs ◽  
Power Laws ◽  
Local Features ◽  
Local Network ◽  
Connected Component ◽  
Strongly Connected ◽  
Global And Local ◽  
The Web

AbstractWe study the network structure of Wikipedia (restricted to its mathematical portion), MathWorld, and DLMF. We approach these three online mathematical libraries from the perspective of several global and local network-theoretic features, providing for each one the appropriate value or distribution, along with comparisons that, if possible, also include the whole of the Wikipedia or the Web. We identify some distinguishing characteristics of all three libraries, most of them supposedly traceable to the libraries' shared nature of relating to a very specialized domain. Among these characteristics are the presence of a very large strongly connected component in each of the corresponding directed graphs, the complete absence of any clear power laws describing the distribution of local features, and the rise to prominence of some local features (e.g., stress centrality) that can be used to effectively search for keywords in the libraries.

Loops in publication citation networks

2019 ◽  
Vol 46 (6) ◽  
pp. 837-848 ◽  
Author(s):  
Yi Bu ◽  
Yong Huang ◽  
Wei Lu
Keyword(s):  
Computer Science ◽  
Web Of Science ◽  
Citation Network ◽  
Frequent Patterns ◽  
Citation Networks ◽  
Connected Component ◽  
Strongly Connected ◽  
Changes Over Time ◽  
Over Time ◽  
The Web

Traditionally, publication citation networks are regarded as acyclic, that is, no loops in the network as an earlier published article cannot cite a later published article. However, due to the accessibility of pre-print versions of articles, there might be some loops in a publication citation network. This article presents a descriptive statistic on loops in publication citation networks of computer science and physics by employing a network-based indicator, namely, strongly connected component (SCC). By employing computer science and physics disciplines publications from the Web of Science database as examples, this article examines the count of loops, how the count changes over time and how the count relates to the published year difference between publications within the loop in the citation network. Some common structural patterns are also extracted and analysed; we observe that the two disciplines share the most frequent patterns though there exist some minor differences. Moreover, we find that self-citations in terms of authors, authors’ institutions and journals contribute to the formation of loops in publication citation networks.

Giant components in three-parameter random directed graphs

1992 ◽  
Vol 24 (4) ◽  
pp. 845-857 ◽  
Author(s):  
Tomasz Łuczak ◽  
Joel E. Cohen
Keyword(s):  
Phase Transition ◽  
Food Webs ◽  
Directed Graph ◽  
Directed Graphs ◽  
Giant Component ◽  
Critical Surface ◽  
Connected Component ◽  
Strongly Connected Component ◽  
Strongly Connected ◽  
Asymptotic Probability

A three-parameter model of a random directed graph (digraph) is specified by the probability of ‘up arrows' from vertexito vertexjwherei < j, the probability of ‘down arrows' fromitojwherei ≥ j,and the probability of bidirectional arrows betweeniandj.In this model, a phase transition—the abrupt appearance of a giant strongly connected component—takes place as the parameters cross a critical surface. The critical surface is determined explicitly. Before the giant component appears, almost surely all non-trivial components are small cycles. The asymptotic probability that the digraph contains no cycles of length 3 or more is computed explicitly. This model and its analysis are motivated by the theory of food webs in ecology.

Giant components in three-parameter random directed graphs

1992 ◽  
Vol 24 (04) ◽  
pp. 845-857 ◽  
Author(s):  
Tomasz Łuczak ◽  
Joel E. Cohen
Keyword(s):  
Phase Transition ◽  
Food Webs ◽  
Directed Graph ◽  
Directed Graphs ◽  
Giant Component ◽  
Critical Surface ◽  
Connected Component ◽  
Strongly Connected Component ◽  
Strongly Connected ◽  
Asymptotic Probability

A three-parameter model of a random directed graph (digraph) is specified by the probability of ‘up arrows' from vertex i to vertex j where i &lt; j, the probability of ‘down arrows' from i to j where i ≥ j, and the probability of bidirectional arrows between i and j. In this model, a phase transition—the abrupt appearance of a giant strongly connected component—takes place as the parameters cross a critical surface. The critical surface is determined explicitly. Before the giant component appears, almost surely all non-trivial components are small cycles. The asymptotic probability that the digraph contains no cycles of length 3 or more is computed explicitly. This model and its analysis are motivated by the theory of food webs in ecology.

scholarly journals A Global-Local Blur Disentangling Network for Dynamic Scene Deblurring

2021 ◽  
Vol 11 (5) ◽  
pp. 2174
Author(s):  
Xiaoguang Li ◽  
Feifan Yang ◽  
Jianglu Huang ◽  
Li Zhuo
Keyword(s):  
Local Features ◽  
Attention Mechanism ◽  
Experimental Results ◽  
Dynamic Scene ◽  
Feature Maps ◽  
Training Scheme ◽  
Real Scene ◽  
Global And Local

Images captured in a real scene usually suffer from complex non-uniform degradation, which includes both global and local blurs. It is difficult to handle the complex blur variances by a unified processing model. We propose a global-local blur disentangling network, which can effectively extract global and local blur features via two branches. A phased training scheme is designed to disentangle the global and local blur features, that is the branches are trained with task-specific datasets, respectively. A branch attention mechanism is introduced to dynamically fuse global and local features. Complex blurry images are used to train the attention module and the reconstruction module. The visualized feature maps of different branches indicated that our dual-branch network can decouple the global and local blur features efficiently. Experimental results show that the proposed dual-branch blur disentangling network can improve both the subjective and objective deblurring effects for real captured images.

Temporal Dissociation of Global and Local Features by Hierarchy of Vision

2009 ◽  
Vol 119 (3) ◽  
pp. 373-383 ◽  
Author(s):  
Tomohiro Ishizu ◽  
Tomoaki Ayabe ◽  
Shozo Kojima
Keyword(s):  
Local Features ◽  
Global And Local
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