A Generic Sample Splitting Approach for Refined Community Recovery in Stochastic Block Models

We propose and analyze a generic method for community recovery in stochastic block models and degree corrected block models. This approach can exactly recover the hidden communities with high probability when the expected node degrees are of order $\log n$ or higher. Starting from a roughly correct community partition given by some conventional community recovery algorithm, this method refines the partition in a cross clustering step. Our results simplify and extend some of the previous work on exact community recovery, discovering the key role played by sample splitting. The proposed method is simple and can be implemented with many practical community recovery algorithms.Comment: 19 page

Aptamers as theranostic agents: modifications, serum stability and functionalisation

Aptamers, and the selection process known as Systematic Evolution of Ligands by Exponential Enrichment (SELEX) used to generate them, were first described more than twenty years ago. Since then, there have been numerous modifications to the selectionprocedures. This review discusses the use of modified bases as a means of enhancing serum stability and producing effective therapeutic tools, as well as functionalising these nucleic acids to be used as potential diagnostic agents