This review concerns recent results on the quantitative study of convergence towards stationary state for spatially inhomogeneous kinetic equations. We focus analytical obtained by means certain probabilistic techniques from ergodic theory Markov processes. These are sometimes referred to as Harris-type theorems. They provide constructive proofs in $L^1$ (or total variation) setting a large cla...

We introduce the main definitions and structural theorems from Goodwillie Calculus. Most of the material in these notes is taken from [3, §§6.1.1–6.1.4]. These notes are rough — use at own risk! Corrections welcome.

Structural variation (SV) encompasses diverse types of genomic variants including deletions, duplications, inversions, transpositions, translocations, and complex rearrangements, and is now recognized to be an abundant class of genetic variation in mammals. Different individuals, or strains, of a given species can differ by thousands of variants. However, despite a large number of studies over ...

African trypanosomes are lethal human and animal parasites that use antigenic variation for evasion of host adaptive immunity. To facilitate antigenic variation, trypanosomes dedicate approximately one third of their nuclear genome, including many minichromosomes, and possibly all sub-telomeres, to variant surface glycoprotein (VSG) genes and associated sequences. Antigenic variation requires t...

Genomic structural variations are an important source of genetic diversity. Copy number variations (CNVs), gains and losses of large regions of genomic sequence between individuals of a species, have been associated with a wide variety of phenotypic traits. However, in cattle, as well as many other species, relatively little is understood about CNV, including frequency of CNVs in the genome, si...