Anatoly Dymarsky

Oleg O. Khamisov, Janusz W. Bialek, Anatoly Dymarsky

Introduction of renewable generation leads to significant reduction of inertia in power system, which deteriorates the quality of frequency control. This paper suggests a new control scheme utilizing controllable load to deal with low inertia systems. Optimization problem is formulated to minimize the systems deviations from the last economically optimal operating point. The proposed scheme combines frequency control with congestion management and maintaining inter-area flows. The proposed distributed control scheme requires only local measurements and communication with neighbors or between buses participating in inter-area flows. Global asymptotic stability is proved for arbitrary network. Numerical simulations confirm that proposed algorithm can rebalance power and perform congestion management after disturbance with transient performance significantly improved in comparison with the traditional control scheme.

Anatoly Dymarsky, Kirill Pavlenko

How many different ways are there to handwrite digit 3? To quantify this question imagine extending a dataset of handwritten digits MNIST by sampling additional images until they start repeating. We call the collection of all resulting images of digit 3 the "full set." To study the properties of the full set we introduce a tensor network architecture which simultaneously accomplishes both classification (discrimination) and sampling tasks. Qualitatively, our trained network represents the indicator function of the full set. It therefore can be used to characterize the data itself. We illustrate that by studying the full sets associated with the digits of MNIST. Using quantum mechanical interpretation of our network we characterize the full set by calculating its entanglement entropy. We also study its geometric properties such as mean Hamming distance, effective dimension, and size. The latter answers the question above -- the total number of black and white threes written MNIST style is $2^{72}$.