Noah Olsman | Searcharxiv

arXiv2019

Antithetic integral feedback for the robust control of monostable and oscillatory biomolecular circuits

Biomolecular feedback systems are now a central application area of interest within control theory. While classical control techniques provide invaluable insight into the function and design of both natural and synthetic biomolecular systems, there are certain aspects of biological control that have proven difficult to analyze with traditional methods. To this end, we describe here how the recently developed tools of dominance analysis can be used to gain insight into the nonlinear behavior of the antithetic integral feedback circuit, a recently discovered control architecture which implements integral control of arbitrary biomolecular processes using a simple feedback mechanism. We show that dominance theory can predict both monostability and periodic oscillations in the circuit, depending on the corresponding parameters and architecture. We then use the theory to characterize the robustness of the asymptotic behavior of the circuit in a nonlinear setting.

eess.SY↗

arXiv2016

Efficient Bayesian Learning in Social Networks with Gaussian Estimators

We consider a group of Bayesian agents who try to estimate a state of the world $θ$ through interaction on a social network. Each agent $v$ initially receives a private measurement of $θ$: a number $S_v$ picked from a Gaussian distribution with mean $θ$ and standard deviation one. Then, in each discrete time iteration, each reveals its estimate of $θ$ to its neighbors, and, observing its neighbors' actions, updates its belief using Bayes' Law. This process aggregates information efficiently, in the sense that all the agents converge to the belief that they would have, had they access to all the private measurements. We show that this process is computationally efficient, so that each agent's calculation can be easily carried out. We also show that on any graph the process converges after at most $2N \cdot D$ steps, where $N$ is the number of agents and $D$ is the diameter of the network. Finally, we show that on trees and on distance transitive-graphs the process converges after $D$ steps, and that it preserves privacy, so that agents learn very little about the private signal of most other agents, despite the efficient aggregation of information. Our results extend those in an unpublished manuscript of the first and last authors.

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