Reputation and feedback systems in online marketplaces are often biased, making it difficult to ascertain the quality of sellers. We use post-transaction, buyer-to-seller message traffic to detect signals of unsatisfactory transactions on eBay. We posit that a message sent after the item was paid for serves as a reliable indicator that the buyer may be unhappy with that purchase, particularly when the message included words associated with a negative experience. The fraction of a seller's message traffic that was negative predicts whether a buyer who transacts with this seller will stop purchasing on eBay, implying that platforms can use these messages as an additional signal of seller quality.
We present a numerical scheme for radially symmetric solutions to curvature driven moving boundary problems governed by a local law of motion, e.g. the mean curvature flow, the surface diffusion flow, and the Willmore flow. We then present several numerical experiments for the Willmore flow. In particular, we provide numerical evidence that the Willmore flow can develop singularities in finite time.