Predict Electric Power Demand with Extended Goal Graph and Heterogeneous Mixture Modeling

In this study, methods for predicting energy demand on hourly consumption data are established for realizing an energy management system for buildings. The methods consist of an energy prediction algorithm that automatically separates the datasets to partitions (gate) and creates a linear regression model (local expert) for each partition on the heterogeneous mixture modeling, and an extended goal graph that extracts candidates of variables both for data partitioning and for linear regression for the energy prediction algorithm. These methods were implemented as tools and applied to create the energy prediction model on two years' hourly consumption data for a building. We validated the methods by comparing accuracies with those of different machine learning algorithms applied to the same datasets.

Trees with an On-Line Degree Ramsey Number of Four

On-line Ramsey theory studies a graph-building game between two players. The player called Builder builds edges one at a time, and the player called Painter paints each new edge red or blue after it is built. The graph constructed is called the background graph. Builder's goal is to cause the background graph to contain a monochromatic copy of a given goal graph, and Painter's goal is to prevent this. In the $S_k$-game variant of the typical game, the background graph is constrained to have maximum degree no greater than $k$. The on-line degree Ramsey number $\mathring{R}_{\Delta}(G)$ of a graph $G$ is the minimum $k$ such that Builder wins an $S_k$-game in which $G$ is the goal graph. Butterfield et al. previously determined all graphs $G$ satisfying $\mathring{R}_{\Delta}(G)\le 3$. We provide a complete classification of trees $T$ satisfying $\mathring{R}_{\Delta}(T)=4$.