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Lewis Carroll's Doublets net of English words: network heterogeneity in a complex system.

Fushing H, Chen C, Hsieh YC, Farrell P - PLoS ONE (2014)

Bottom Line: Phonological communities are seen at the network level.And a balancing act between the language's global efficiency and redundancy is seen at the system level.Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California Davis, Davis, California, United States of America.

ABSTRACT
Lewis Carroll's English word game Doublets is represented as a system of networks with each node being an English word and each connectivity edge confirming that its two ending words are equal in letter length, but different by exactly one letter. We show that this system, which we call the Doublets net, constitutes a complex body of linguistic knowledge concerning English word structure that has computable multiscale features. Distributed morphological, phonological and orthographic constraints and the language's local redundancy are seen at the node level. Phonological communities are seen at the network level. And a balancing act between the language's global efficiency and redundancy is seen at the system level. We develop a new measure of intrinsic node-to-node distance and a computational algorithm, called community geometry, which reveal the implicit multiscale structure within binary networks. Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.

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Overview of network dynamics of the Doublets net.Six out of the 20 evolving networks with respect to letter length in the Doublets net are exhibited in six panels. From the nearly complete connectivity in the 3-letter network to having a single large giant clique in 4- and 5-letter networks, to a relatively small clique in the 7-letter network, and then becoming complete scattering in 11- and 15-letter networks.
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pone-0114177-g007: Overview of network dynamics of the Doublets net.Six out of the 20 evolving networks with respect to letter length in the Doublets net are exhibited in six panels. From the nearly complete connectivity in the 3-letter network to having a single large giant clique in 4- and 5-letter networks, to a relatively small clique in the 7-letter network, and then becoming complete scattering in 11- and 15-letter networks.

Mentions: Finally, we zoom out from individual subnetworks to look at the Doublets net as one whole complex system. Total word counts from 3-letter to 22-letter words are given in Fig. 6(a), while the proportion of the size of the largest clique to the total word count is shown in Fig. 6(b). Among the 20 different letter lengths, we only present six subnetworks to give an overview of the network dynamics of the Doublets net in Fig. 7 (including all singletons). Based on these two figures in Fig. 6, we see that the word count increases with letter length in the 3-letter to 10-letter range. But the word count takes a sharp dive downward after 11-letter words. This up-and-down pattern clearly shows that the language's efficiency goes up as more syllables are used in word structure. But this increasing trend does not last long, as the effect of redundancy appears to overtake the word constructing force after 10-letter words. This is one of the global effects of the selection force on the Doublets net from the perspective of word count.


Lewis Carroll's Doublets net of English words: network heterogeneity in a complex system.

Fushing H, Chen C, Hsieh YC, Farrell P - PLoS ONE (2014)

Overview of network dynamics of the Doublets net.Six out of the 20 evolving networks with respect to letter length in the Doublets net are exhibited in six panels. From the nearly complete connectivity in the 3-letter network to having a single large giant clique in 4- and 5-letter networks, to a relatively small clique in the 7-letter network, and then becoming complete scattering in 11- and 15-letter networks.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4269387&req=5

pone-0114177-g007: Overview of network dynamics of the Doublets net.Six out of the 20 evolving networks with respect to letter length in the Doublets net are exhibited in six panels. From the nearly complete connectivity in the 3-letter network to having a single large giant clique in 4- and 5-letter networks, to a relatively small clique in the 7-letter network, and then becoming complete scattering in 11- and 15-letter networks.
Mentions: Finally, we zoom out from individual subnetworks to look at the Doublets net as one whole complex system. Total word counts from 3-letter to 22-letter words are given in Fig. 6(a), while the proportion of the size of the largest clique to the total word count is shown in Fig. 6(b). Among the 20 different letter lengths, we only present six subnetworks to give an overview of the network dynamics of the Doublets net in Fig. 7 (including all singletons). Based on these two figures in Fig. 6, we see that the word count increases with letter length in the 3-letter to 10-letter range. But the word count takes a sharp dive downward after 11-letter words. This up-and-down pattern clearly shows that the language's efficiency goes up as more syllables are used in word structure. But this increasing trend does not last long, as the effect of redundancy appears to overtake the word constructing force after 10-letter words. This is one of the global effects of the selection force on the Doublets net from the perspective of word count.

Bottom Line: Phonological communities are seen at the network level.And a balancing act between the language's global efficiency and redundancy is seen at the system level.Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California Davis, Davis, California, United States of America.

ABSTRACT
Lewis Carroll's English word game Doublets is represented as a system of networks with each node being an English word and each connectivity edge confirming that its two ending words are equal in letter length, but different by exactly one letter. We show that this system, which we call the Doublets net, constitutes a complex body of linguistic knowledge concerning English word structure that has computable multiscale features. Distributed morphological, phonological and orthographic constraints and the language's local redundancy are seen at the node level. Phonological communities are seen at the network level. And a balancing act between the language's global efficiency and redundancy is seen at the system level. We develop a new measure of intrinsic node-to-node distance and a computational algorithm, called community geometry, which reveal the implicit multiscale structure within binary networks. Because the Doublets net is a modular complex cognitive system, the community geometry and computable multi-scale structural information may provide a foundation for understanding computational learning in many systems whose network structure has yet to be fully analyzed.

Show MeSH