Renewal/repair effect on network robustness

Aging increases heterogeneity.  Renewal and repair should increase network homogeneity. So, renewal/repair should increase robustness (high G).

However, Barlow&Proschan96 argues that renewal/repair also leads approximate exponential function for the pdf of mortality  (page 15 and section 3).  Exponential pdf give CDF in form of $1 - exp(- \lambda x)$, so its surviorship or viability is also exponential.  From this perspective, renewal/repair should lead to constant mortality rate and G->0.

Why are there two opposite conclusions?


Point-repair (age-based component repair)
 Heat-shock proteins
 Proteosome
 Ubiquitin?

Block-repair
 Lysosome-like vacuole, mitochondria

Random repair versus targeted repair

Limiting modules in power-law network
  For fixed decaying rate, small degree essential node -> faster earlier rates, large-degree essential node -> fat tail.