Two-dimensional volume-frozen percolation: deconcentration and prevalence of mesoscopic clusters

Frozen percolation on the binary tree was introduced by Aldous [1], inspired by sol-gel transitions. We investigate a version of the model on the triangular lattice, where connected components stop growing (freeze) as soon as they contain at least N vertices, where N is a (typically large) parameter. For the process in certain +nite domains, we show a Òseparation of scalesÓ and use this to prove a deconcentration property. Then, for the full-plane process, we prove an accurate comparison to the process in suitable +nite domains, and obtain that, with high probability (as N→), the origin belongs in the nal con+guration to a mesoscopic cluster, i.e., a cluster which contains many, but much fewer than N, vertices (and hence is non-frozen). For this work we develop new interesting properties for near-critical percolation, including asymp-totic formulas involving the percolation probability θ(p) and the characteristic length L(p) as p → pc

Hybrid Capture and Next-Generation Sequencing Identify Viral Integration Sites from Formalin-Fixed, Paraffin-Embedded Tissue

Although next-generation sequencing (NGS) has been the domain of large genome centers, it is quickly becoming more accessible to general pathology laboratories. In addition to finding single-base changes, NGS allows for the detection of larger structural variants, including insertions/deletions, translocations, and viral insertions. We describe the use of targeted NGS on DNA extracted from formalin-fixed, paraffin-embedded (FFPE) tissue, and show that the short read lengths of NGS are ideally suited to fragmented DNA obtained from FFPE tissue. Further, we describe a novel method for performing hybrid-capture target enrichment using PCR-generated capture probes. As a model, we captured the 5.3-kb Merkel cell polyomavirus (MCPyV) genome in FFPE cases of Merkel cell carcinoma using inexpensive, PCR-derived capture probes, and achieved up to 37,000-fold coverage of the MCPyV genome without prior virus-specific PCR amplification. This depth of coverage made it possible to reproducibly detect viral genome deletions and insertion sites anywhere within the human genome. Out of four cases sequenced, we identified the 5′ insertion sites in four of four cases and the 3′ sites in three of four cases. These findings demonstrate the potential for an inexpensive gene targeting and NGS method that can be easily adapted for use with FFPE tissue to identify large structural rearrangements, opening up the possibility for further discovery from archival tissue