Path Counting on Tree-like Graphs with a Single Entropic Trap: Critical Behavior and Finite Size Effects.

It is known that maximal entropy random walks and partition functions that count long paths on graphs tend to become localized near nodes with a high degree. Here, we revisit the simplest toy model of such a localization: a regular tree of degree with one special node ("root") that has a degree different from all the others. We present an in-depth study of the path-counting problem precisely at the localization transition.

An MSH6 germline pathogenic variant p.Gly162Ter associated with Lynch syndrome.

We identified a three-generation Russian family with Lynch syndrome with a novel germline variant of the MSH6 gene. An 84-year-old female was diagnosed with endometrial adenocarcinoma at the age of 49 years. Her son was diagnosed with colorectal tubular adenoma at the age of 32 years.