The ability to produce random numbers that are unknown any outside party is crucial for many applications. Device-independent randomness generation1–4 does not require trusted devices and therefore provides strong guarantees of the security output, but it comes at price requiring violation a Bell inequality implementation. A further challenge make bounds in proofs tight enough allow expansion w...

This paper produces an efficient semidefinite programming (SDP) solution for community detection that incorporates non-graph data, which in this context is known as side information. SDP standard on graphs. We formulate a semi-definite relaxation the maximum likelihood estimation of node labels, subject to observing both graph and data. formulation distinct from detection, but maintains its des...

The integrative analysis of multiple datasets is an important strategy in data analysis. It increasingly popular genomics, which enjoys a wealth publicly available that can be compared, contrasted, and combined order to extract novel scientific insights. This paper studies stylized example integration for classical statistical problem: leveraging side information estimate vector normal means. t...

We investigate the problem of successive refinement for Wyner-Ziv coding with degraded side information and obtain a complete characterization rate region quadratic vector Gaussian case. The achievability part is based on evaluation Tian-Diggavi inner bound that involves auxiliary random vectors. For converse part, matching outer obtained aid new extremal inequality. Herein, proof this inequali...