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Register a new userLexical growth, entropy and the benefits of networking
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Added by
Robert Shour
Publication date
2009
fields
Informatics Engineering
and research's language is
English
Authors
Robert Shour
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No Arabic abstract
If each node of an idealized network has an equal capacity to efficiently exchange benefits, then the networks capacity to use energy is scaled by the average amount of energy required to connect any two of its nodes. The scaling factor equals textit{e}, and the networks entropy is $ln(n)$. Networking emerges in consequence of nodes minimizing the ratio of their energy use to the benefits obtained for such use, and their connectability. Networking leads to nested hierarchical clustering, which multiplies a networks capacity to use its energy to benefit its nodes. Network entropy multiplies a nodes capacity. For a real network in which the nodes have the capacity to exchange benefits, network entropy may be estimated as $C log_L(n)$, where the base of the log is the path length $L$, and $C$ is the clustering coefficient. Since $n$, $L$ and $C$ can be calculated for real networks, network entropy for real networks can be calculated and can reveal aspects of emergence and also of economic, biological, conceptual and other networks, such as the relationship between rates of lexical growth and divergence, and the economic benefit of adding customers to a commercial communications network. textit{Entropy dating} can help estimate the age of network processes, such as the growth of hierarchical society and of language.
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In this work, we study coded placement in caching systems where the users have unequal cache sizes and demonstrate its performance advantage. In particular, we propose a caching scheme with coded placement for three-user systems that outperforms the best caching scheme with uncoded placement. In our proposed scheme, users cache both uncoded and coded pieces of the files, and the coded pieces at the users with large memories are decoded using the unicast/multicast signals intended to serve users with smaller memories. Furthermore, we extend the proposed scheme to larger systems and show the reduction in delivery load with coded placement compared to uncoded placement.
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