Metric for Optimal Health of a Complex Adaptive System

2015-07-05

Metric for Optimal Health of a Complex Adaptive System
cas metric
metric for optimal health of cas

"C:\Users\kurtw_000\Dropbox\optimal cas metric\Notes on Metric for Optimal Health of a Complex Adaptive System.docx"

Diagram illustrating optimal metric
-"C:\Users\kurtw_000\Documents\kurt\storage\CIM Research Folder\DR\2014\01-29-2014d0949\diagram for cas metric 01-29-2014d0949.svg"

Note that complex adaptive systems are often represented as networks, and these networks happen to have small-world scale-free properties

Possible metrics
-simple metrics: number of edges, mean path length, power law degree, and clustering coefficient
-Potential metrics: degree entropy, search entropy, Bianconi energy and entropy of network network ensembles,  pearson correlation with power law degree distribution, fractal dimension 
-Other possibly interesting metrics: road entropy, target entropy, heirarchical degree, rs-clustering coefficient, convergence ratio, divergence ratio, Meyer-Ortmanns complexity, off-diagonal complexity, rich-club coefficient, some of the modularity measures possibly
-some of my favorites
{
-Search information entropy
-"temperature or energy" of graph
}
-many of these metrics (if not all of them) are listed in the following paper: [Characterization of complex networks: A survey of measurements]
-also consider comparing networks mentioned in other papers
--variation of each element (gene) in a non-network form ([Increased cell-to-cell variation in gene expression in ageing mouse heart])
--differential network entropy as discussed in this paper (I think it's like looking at the entropy of a random walk on a network): "Differential network entropy reveals cancer system hallmarks"

-[Some literature review for optimal health of a complex adaptive system 11-11-2014d1154]

[Graph Analysis code 06-18-2014d1719]

Table comparing a variety of networks with several metrics 06-26-2014d0008
table of metric values of networks
table of many (all) networks
-"C:\Users\kurtw_000\Documents\kurt\storage\pDR\2014\06-26-2014d0006\Table comparing a variety of networks with several metrics 06-26-2014d0008.xlsx"

-[Possible sources of data to compare healthy and disease or aged networks 09-26-2014d1648]
-[How to transform gene expression data into a network 10-18-2014d1301]

Hypothesis about what nature or complex adaptive systems may be trying to optimize
-From some brief investigations, search information entropy seems to be higher for real world networks than random networks.  This implies that there are more decisions that need to be made (more yes and no questions that need to be answered) when travelling between any two nodes in a real world network.  However, real world networks are also sparse networks.  Therefore, maybe complex adaptive systems are trying to maximize options with the fewest edges.
--Perhaps this hypothesis could be investigated by generating every single possible network with 20 nodes and any number of edges from 1 to the number of edges required to connect every node to every other node.  I could calculate the search information entropy, power law degree, and clustering coefficient for all of the networks.  Perhaps the network most similar to a real world network with a characteristic power law degree and clustering coefficient will also be the network with the highest search information entropy with the fewest edges.

-[to do list for optimal cas metric portal 03-23-2014d1543]

Some questions
-If I remove edges and nodes from a network in order to keep the proportions of nodes and edges the same, and the proportion of degrees the same, will a scale free network remain scale free?

Work on project
-[how to get a subgraph of a graph that is representative of the whole graph 03-06-2015d1051]
-[ram processor storage and time info for characterizing networks 03-04-2015d1621]
-[searched Is there some feature of overall gene co-expression networks that changes with age]
-searched network analsis of healthy and unhealthy networks
--I didn't really see anything relevant; 11-10-2014d1515
-[started analyzing some data related to age calorie restriction and resveratrol study June 2008 11-10-2014d0955]
-[searched what is nature trying to optimize in scale free small world networks 10-21-2014d1034]
-searched [transform gene expression data into a network 10-18-2014d1218]
-wondered about question: how to model protein network structure changes with time?
--came across this paper: http://www.ncbi.nlm.nih.gov/pubmed/18304007 (Analyzing protein interaction networks using structural information)
-[work testing approximation of search information entropy 04-26-2014d1827]
-[work testing random numbers of node pairs with airport network 4-17-14]
-[work on optimal cas metric verifying se results 03-26-2014d2210]
-[work on optimal cas metric developing power law exponent 03-23-2014d1541]
-[work on optimal cas metric to fix clustering coefficient 03-21-2014d1524]
-[work on optimal cas metric 03-09-2014d1315]
-[work on optimal cas metric 03-03-2014d1123]

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See also
-[Network metrics portal 03-07-2014d1503]

azim58wiki: