Tuesday, May 7, 2013

Qin, thoughts on network aging modeling (in progress)

Decaying of essential module over time can be modeled as Markov transition, and eigen value and vectors are likely to be useful for approximation.(see Sengupta02).

Cascading model of aging in network is similar to network percolation or difussion process.

Average lifespan is probably realted to the threshold of connection, and this relationship may be different in Poission and power-law networks.

Using essential gene to model lethality was used in Sengupta, et al 2002, PNAS, Specificity and robustness in transcription control networks. Sengupta02 modeled how mutation can change TF binding sites which can lead to lethality.

For 'compensation law of mortality' to be observed, Gavrilov91 argues for varying numbers of components per blocks, and unchanged component decaying rates and chance of component be functional.  These probably can be relaxed, and I can test this by simulations.

Simulation shows that change of n leads to perfect lnR ~ G, just as GG01 argued. Maybe power-law network leads to more robust lnR ~ G ?!

In general, expected mortality rate (hazard rate) of the network is the weighted average of the module mortality rates.  See http://hongqinlab.blogspot.com/2013/06/power-law-network-and-aging.html

Stochastic network model of aging leads to heterogenous individuals in populations. This idea of heterogeneity is also reflected in Vaupel's frailty model that aims to capture heterogeneity in populations. See Vaupel, Manton, and Stallard 1979.  Frailty=1 indicates 'standard' individuals. Frailty =2 indicates twice likely to die than standards. Vaupel tends to model frailty using a gamma distribution with mean =1 and \sigmma^2 as variance.


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