Phase transitions in gene networks evolved under different selection rules

Mathematical models of gene regulation are a powerful tool for understanding the complex features of genetic control. While various modeling efforts have been successful at explaining gene expression dynamics, much less is known about how evolution shapes the structure of these networks. An important feature of gene regulatory networks is their stability in response to environmental perturbations. Regulatory systems are thought to have evolved to exist near the transition between stability and instability, in order to have the required stability to environmental fluctuations while also being able to achieve a wide variety of functions (corresponding to different dynamical patterns). We study a simplified model of gene network evolution in which links are added via different selection rules. These growth models are inspired by recent work on `explosive' percolation which shows that when network links are added through competitive rather than random processes, the connectivity phase transition can be significantly delayed, and when it is reached, it appears to be first order (discontinuous, e.g., going from no failure at all to large expected failure) instead of second order (continuous, e.g., going from no failure at all to very small expected failure). We find that by modifying the traditional framework for networks grown via competitive link addition to capture how gene networks evolve to avoid damage propagation, we also see significant delays in the transition that depend on the selection rules, but the transitions always appear continuous rather than `explosive'.

RESILIENCE OF NETWORKED INFRASTRUCTURE WITH EVOLVING COMPONENT CONDITIONS: A PAVEMENT NETWORK APPLICATION

This thesis deals with quantifying the resilience of a network of pavements. Calculations were carried out by modeling network performance under a set of possible damage-meteorological scenarios with known probability of occurrence. Resilience evaluation was performed a priori while accounting for optimal preparedness decisions and additional response actions that can be taken under each of the scenarios. Unlike the common assumption that the pre-event condition of all system components is uniform, fixed, and pristine, component condition evolution was incorporated herein. For this purpose, the health of the individual system components immediately prior to hazard event impact, under all considered scenarios, was associated with a serviceability rating. This rating was projected to reflect both natural deterioration and any intermittent improvements due to maintenance. The scheme was demonstrated for a hypothetical case study involving Laguardia Airport. Results show that resilience can be impacted by the condition of the infrastructure elements, their natural deterioration processes, and prevailing maintenance plans. The findings imply that, in general, upper bound values are reported in ordinary resilience work, and that including evolving component conditions is of value.