Towards a dynamic view of genetic networks: A Kalman filtering framework for recovering temporally-rewiring stable networks from undersampled data

It is widely accepted that cellular requirements and environmental conditions dictate the architecture of genetic regulatory networks. Nonetheless, the status quo in regulatory network modeling and analysis assumes an invariant network topology over time. We refocus on a dynamic perspective of genetic networks, one that can uncover substantial topological changes in network structure during biological processes such as developmental growth and cancer progression. We propose a novel outlook on the inference of time-varying genetic networks, from a limited number of noisy observations, by formulating the networks estimation as a target tracking problem. Assuming linear dynamics, we formulate a constrained Kalman ltering framework, which recursively computes the minimum mean-square, sparse and stable estimate of the network connectivity at each time point. The sparsity constraint is enforced using the weighted l1-norm; and the stability constraint is incorporated using the Lyapounov stability condition. The proposed constrained Kalman lter is formulated to preserve the convex nature of the problem. The algorithm is applied to estimate the time-varying networks during the life cycle of the Drosophila Melanogaster (fruit fly)

Convergence Analysis of Mixed Timescale Cross-Layer Stochastic Optimization

This paper considers a cross-layer optimization problem driven by multi-timescale stochastic exogenous processes in wireless communication networks. Due to the hierarchical information structure in a wireless network, a mixed timescale stochastic iterative algorithm is proposed to track the time-varying optimal solution of the cross-layer optimization problem, where the variables are partitioned into short-term controls updated in a faster timescale, and long-term controls updated in a slower timescale. We focus on establishing a convergence analysis framework for such multi-timescale algorithms, which is difficult due to the timescale separation of the algorithm and the time-varying nature of the exogenous processes. To cope with this challenge, we model the algorithm dynamics using stochastic differential equations (SDEs) and show that the study of the algorithm convergence is equivalent to the study of the stochastic stability of a virtual stochastic dynamic system (VSDS). Leveraging the techniques of Lyapunov stability, we derive a sufficient condition for the algorithm stability and a tracking error bound in terms of the parameters of the multi-timescale exogenous processes. Based on these results, an adaptive compensation algorithm is proposed to enhance the tracking performance. Finally, we illustrate the framework by an application example in wireless heterogeneous network

Sensor Management for Tracking in Sensor Networks

We study the problem of tracking an object moving through a network of wireless sensors. In order to conserve energy, the sensors may be put into a sleep mode with a timer that determines their sleep duration. It is assumed that an asleep sensor cannot be communicated with or woken up, and hence the sleep duration needs to be determined at the time the sensor goes to sleep based on all the information available to the sensor. Having sleeping sensors in the network could result in degraded tracking performance, therefore, there is a tradeoff between energy usage and tracking performance. We design sleeping policies that attempt to optimize this tradeoff and characterize their performance. As an extension to our previous work in this area [1], we consider generalized models for object movement, object sensing, and tracking cost. For discrete state spaces and continuous Gaussian observations, we derive a lower bound on the optimal energy-tracking tradeoff. It is shown that in the low tracking error regime, the generated policies approach the derived lower bound