By reconstructing the history of water impoundment in the world's artificial reservoirs, we show that a total of ∼10,800 cubic kilometers of water has been impounded on land to date, reducing the… Expand

We show that the minimax mean-square error is within the universal multiplicative constant factors of (k/n log k)2 t log2 k/n if n exceeds a constant factor of (K/log k).Expand

We consider the problem of estimating the support size of a discrete distribution whose minimum non-zero mass is at least $ \frac{1}{k}$. Under the independent sampling model, we show that the sample… Expand

Significance Many scientific applications ranging from ecology to genetics use a small sample to estimate the number of distinct elements, known as ”species,” in a population. Classical results have… Expand

We show that the semidefinite programming relaxation of the maximum likelihood estimator achieves the optimal threshold for exactly recovering the partition from the graph with probability tending to one, resolving a conjecture of Abbe et al.Expand

Resolving a conjecture of Abbe, Bandeira, and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp threshold for exactly recovering the community structure under the binary stochastic block model of two equal-sized clusters.Expand

Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form.Expand

The data-processing inequality, that is, I(U; Y) for a Markov chain U → X → Y, has been the method of choice for proving impossibility (converse) results in information theory and many other disciplines.Expand