An optimal architecture for poset-causal systems | Computable Bounds on Sparsity Recovery

Title: Computable Bounds on Sparsity Recovery

Abstract:
The performance of sparsity recovery depends on the structures of the sensing matrices. The quality of these matrices in the context of signal recovery is usually quantified by the restricted isometry constant and its variants. However, the restricted isometry constant and its variants are extremely difficult to compute. We present a framework for numerically assessing the performance of sparsity recovery. We define a family of incoherence measures to quantify the goodness of arbitrary sensing matrices. Our primary contribution is computing the exact values of these incoherence measures using a series of linear programs and second order cone programs. We also analyze the typical behavior of the proposed incoherence measures for random sensing matrices.

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Pari’s talk:

Title: An optimal architecture for poset-causal systems

Abstract:
Partially ordered sets (posets) provide a natural way of modeling problems where communication constraints between subsystems have a hierarchical or causal structure. In this talk, we consider general poset-causal decentralized decision-making problems, and describe a simple and natural controller architecture based on the Moebius transform of the poset. This architecture possesses simple and appealing separation properties, that I will discuss.