This work provides a general framework for the analysis and synthesis of a class of linear networked dynamic systems (NDS). We focus our attention on NDS where the underlying connection topology couples the agents at their outputs. A distinction is made between NDS with homogeneous agent dynamics and NDS with heterogeneous agent dynamics. In the homogeneous setting, the H2 norm expression reduc...

We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with high probability, it satisfies a form of restricted strong convexity with respect to weighted Frobenius norm. Using this property, we obtain as corollaries ...

We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assump tion for the in nite Frobenius elements in the class groups of these orders

Consider the map from the real symmetric matrices of Frobenius norm one to themselves given by matrix cubing followed by rescaling. We show that this is a gradient dynamical system with potential

We present a generalization bound for feedforward neural networks in terms of the product of the spectral norms of the layers and the Frobenius norm of the weights. The generalization bound is derived using a PAC-Bayes analysis.

We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assumption for the infinite Frobenius elements in the class groups of these orders.