Elaheh Fata

Haotian Zhang, Elaheh Fata, Shreyas Sundaram

We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph properties such as connectivity and minimum degree in that one can construct graphs with high connectivity and minimum degree but low robustness. However, we show that the notions of connectivity and robustness coincide on common random graph models for complex networks (Erdos-Renyi, geometric random, and preferential attachment graphs). More specifically, the properties share the same threshold function in the Erdos-Renyi model, and have the same values in one-dimensional geometric graphs and preferential attachment networks. This indicates that a variety of purely local diffusion dynamics will be effective at spreading information in such networks. Although graphs generated according to the above constructions are inherently robust, we also show that it is coNP-complete to determine whether any given graph is robust to a specified extent.

Elaheh Fata, Igor Kadota, Ian Schneider

Electricity is bought and sold in wholesale markets at prices that fluctuate significantly. Short-term forecasting of electricity prices is an important endeavor because it helps electric utilities control risk and because it influences competitive strategy for generators. As the "smart grid" grows, short-term price forecasts are becoming an important input to bidding and control algorithms for battery operators and demand response aggregators. While the statistics and machine learning literature offers many proposed methods for electricity price prediction, there is no consensus supporting a single best approach. We test two contrasting machine learning approaches for predicting electricity prices, regression decision trees and recurrent neural networks (RNNs), and compare them to a more traditional ARIMA implementation. We conduct the analysis on a challenging dataset of electricity prices from ERCOT, in Texas, where price fluctuation is especially high. We find that regression decision trees in particular achieves high performance compared to the other methods, suggesting that regression trees should be more carefully considered for electricity price forecasting.