Cannon-Thurston Maps for Kleinian Groups

We show that Cannon-Thurston maps exist for degenerate free groups without parabolics, i.e. for handlebody groups. Combining these techniques with earlier work proving the existence of Cannon-Thurston maps for surface groups, we show that Cannon-Thurston maps exist for arbitrary finitely generated Kleinian groups without parabolics, proving conjectures of Thurston and McMullen. We also show that point pre-images under Cannon-Thurston maps for degenerate free groups without parabolics correspond to end-points of leaves of an ending lamination in the Masur domain, whenever a point has more than one pre-image. This proves a conjecture of Otal. We also prove a similar result for point pre-images under Cannon-Thurston maps for arbitrary finitely generated Kleinian groups without parabolics.Comment: 39 pgs 1 fig. Final version incorporating referee comments. To appear in Forum of Mathematics, P

Identifying Real Estate Opportunities using Machine Learning

The real estate market is exposed to many fluctuations in prices because of existing correlations with many variables, some of which cannot be controlled or might even be unknown. Housing prices can increase rapidly (or in some cases, also drop very fast), yet the numerous listings available online where houses are sold or rented are not likely to be updated that often. In some cases, individuals interested in selling a house (or apartment) might include it in some online listing, and forget about updating the price. In other cases, some individuals might be interested in deliberately setting a price below the market price in order to sell the home faster, for various reasons. In this paper, we aim at developing a machine learning application that identifies opportunities in the real estate market in real time, i.e., houses that are listed with a price substantially below the market price. This program can be useful for investors interested in the housing market. We have focused in a use case considering real estate assets located in the Salamanca district in Madrid (Spain) and listed in the most relevant Spanish online site for home sales and rentals. The application is formally implemented as a regression problem that tries to estimate the market price of a house given features retrieved from public online listings. For building this application, we have performed a feature engineering stage in order to discover relevant features that allows for attaining a high predictive performance. Several machine learning algorithms have been tested, including regression trees, k-nearest neighbors, support vector machines and neural networks, identifying advantages and handicaps of each of them.Comment: 24 pages, 13 figures, 5 table