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Register a new userGenerating Series for Networks of Chen-Fliess Series
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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.
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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 given pair of nodes has a locally convergent Chen-Fliess series representation. Second, sufficient conditions are given under which the input-output map between a pair of nodes has a well defined relative degree as defined by its generating series. This analysis leads to the conclusion that this relative degree property is generic in a certain sense.
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 unique synthetic profiles on demand, based on the season and type of load required. Extensive testing of the generative model is performed to verify that the synthetic data fully captures the characteristics of real loads and that it can be used for downstream power system and/or machine learning applications.
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-level time-series load data for transmission networks. The model is trained on a real dataset of over 70 Terabytes of synchrophasor measurements spanning multiple years. Leveraging a combination of principal component analysis and conditional generative adversarial network models, the scheme we developed allows for the generation of data at varying sampling rates (up to a maximum of 30 samples per second) and ranging in length from seconds to years. The generative models are tested extensively to verify that they correctly capture the diverse characteristics of real loads. Finally, we develop an open-source tool called LoadGAN which gives researchers access to the fully trained generative models via a graphical interface.
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 distance between distributions on feasible paths. When the prior is reversible, it shown that solutions to this discrete time and space steering problem are reversible as well. A notion of temperature is defined for Boltzmann distributions on networks, and problems analogous to cooling (in this case, for evolutions in discrete space and time) are discussed.
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 Z(T) in S, of codimension nd_+, indexed by totally positive semi-definite matrices with coefficients in the ring of integers O_F. The generating series for the classes of these cycles in the cohomology group H^{2nd_+}(S) are Hilbert-Siegel modular forms of parallel weight m/2+1. One can form analogous generating series for the classes of the special cycles in the Chow group CH^{nd_+}(S). For d_+=1 and n=1, the modularity of these series was proved by Yuan-Zhang-Zhang. In this note we prove the following: Assume the Bloch-Beilinson conjecture on the injectivity of Abel-Jacobi maps. Then the Chow group valued generating series for special cycles of codimension nd_+ on S is modular for all n with 1le nle m.
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