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Consider a set of single-input, single-output nonlinear systems whose input-output maps are described only in terms of convergent Chen-Fliess series without any assumption that finite dimensional state space models are available. It is shown that any additive or multiplicative interconnection of such systems always has a Chen-Fliess series representation that can be computed explicitly in terms of iterated formal Lie derivatives.
Given an additive network of input-output systems where each node of the network is modeled by a locally convergent Chen-Fliess series, two basic properties of the network are established. First, it is shown that every input-output map between a give
A framework for the generation of synthetic time-series transmission-level load data is presented. Conditional generative adversarial networks are used to learn the patterns of a real dataset of hourly-sampled week-long load profiles and generate uni
The availability of large datasets is crucial for the development of new power system applications and tools; unfortunately, very few are publicly and freely available. We designed an end-to-end generative framework for the creation of synthetic bus-
We derive novel results on the ergodic theory of irreducible, aperiodic Markov chains. We show how to optimally steer the network flow to a stationary distribution over a finite or infinite time horizon. Optimality is with respect to an entropic dist
In this note, we consider special algebraic cycles on the Shimura variety S associated to a quadratic space V over a totally real field F, |F:Q|=d, of signature ((m,2)^{d_+},(m+2,0)^{d-d_+}), 1le d_+<d. For each n, 1le nle m, there are special cycles