We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitraryâ€¦ (More)

The spatial distribution of people exhibits clustering across a wide range of scales, from household (âˆ¼10(-2) km) to continental (âˆ¼10(4) km) scales. Empirical data indicate simple power-law scalingsâ€¦ (More)

The spatial distribution of people exhibits clustering across a wide range of scales, from household (âˆ¼ 10âˆ’2 km) to continental (âˆ¼ 10 km) scales. Empirical data indicates simple power-law scalingsâ€¦ (More)

We show that although many important data sequences â€” from texts in different languages to melodies and genomes â€” exhibit critical behavior, where the mutual information between symbols decaysâ€¦ (More)

We present first results on the cooling properties derived from Chandra X-ray observations of 83 high-redshift (0.3 < z < 1.2) massive galaxy clusters selected by their Sunyaevâ€“Zelâ€™dovich signatureâ€¦ (More)

We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a powerâ€¦ (More)

Sunyaevâ€“Zelâ€™dovich (SZ) surveys find massive clusters of galaxies by measuring the inverse Compton scattering of cosmic microwave background off of intra-cluster gas. The cluster selection functionâ€¦ (More)

P/2011 S1 (Gibbs) is an outer solar system comet or active Centaur with a similar orbit to that of the famous 29P/Schwassmann-Wachmann 1. P/2011 S1 (Gibbs) has been observed by the Pan-STARRS 1 (PS1)â€¦ (More)