Flexible Priors to Predict the Number of Unseen Features
How many species in our ecosystem have not been discovered? How many words did Williams Shakespeare know but not include in his written works? The unseen species problem has applications in both sciences and humanities, and it has been studied since the 1940s. This classical problem is recently generalized to the unseen features problem. In genomic applications, a feature is a genetic variant compared to a reference genome, and the scientific goal is to estimate the number of new genetic variants to be observed if we were to collect more samples.
A solid which floats in every orientation: An answer to a problem from the Scottish Book
If a solid object floats in water in every position, is it necessarily a sphere? In a paper published this year in the Annals of Mathematics, Dmitry Ryabogin proves the answer is “no”.
The Stellahedral Geometry of Matroids
Some of the hardest questions to answer in math are the simplest to state. For example “when does a sequence of numbers $a_1, a_2, a_3, \ldots$ have the property that $a_{i}^2 \geq a_{i-1}a_{i+1}?” A sequence having this property is called “log-concave”. To get familiar with log-concavity, let’s consider the most famous log-concave sequence: the sequence found by specifying a row of Pascal’s triangle