On the clustering behavior of sliding windows

Things can go spectacularly wrong when clustering timeseries data that has been preprocessed with a sliding window. We highlight three surprising failures that emerge depending on how the window size compares with the timeseries length. In addition to computational examples, we present theoretical explanations for each of these failure modes.

Combining GHOST and Casper

We present "Gasper," a proof-of-stake-based consensus protocol, which is an idealized version of the proposed Ethereum 2.0 beacon chain. The protocol combines Casper FFG, a finality tool, with LMD GHOST, a fork-choice rule. We prove safety, plausible liveness, and probabilistic liveness under different sets of assumptions.