Entry and Return times distribution

This is a review article on the distributions of entry and return times in dynamical systems which discusses recent results for systems of positive entropy.Comment: To appear in "Dynamical Systems: An International Journal dedicated to the Statistical Properties of Dynamical Systems

Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems

We show that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. We also provide error terms which are powers of logarithm of the radius. In order to get those uniform rates of convergence the balls centres have to avoid a set whose size is estimated to be of similar order. This result can be applied to non-uniformly hyperbolic maps and to any invariant measure that satisfies a weak regularity condition. In particular it shows that the return times to balls is Poissonian for SRB measures on attractors.Comment: 28 page

Allele-Specific HLA Loss and Immune Escape in Lung Cancer Evolution

Immune evasion is a hallmark of cancer. Losing the ability to present neoantigens through human leukocyte antigen (HLA) loss may facilitate immune evasion. However, the polymorphic nature of the locus has precluded accurate HLA copy-number analysis. Here, we present loss of heterozygosity in human leukocyte antigen (LOHHLA), a computational tool to determine HLA allele-specific copy number from sequencing data. Using LOHHLA, we find that HLA LOH occurs in 40% of non-small-cell lung cancers (NSCLCs) and is associated with a high subclonal neoantigen burden, APOBEC-mediated mutagenesis, upregulation of cytolytic activity, and PD-L1 positivity. The focal nature of HLA LOH alterations, their subclonal frequencies, enrichment in metastatic sites, and occurrence as parallel events suggests that HLA LOH is an immune escape mechanism that is subject to strong microenvironmental selection pressures later in tumor evolution. Characterizing HLA LOH with LOHHLA refines neoantigen prediction and may have implications for our understanding of resistance mechanisms and immunotherapeutic approaches targeting neoantigens. Video Abstract [Figure presented] Development of the bioinformatics tool LOHHLA allows precise measurement of allele-specific HLA copy number, improves the accuracy in neoantigen prediction, and uncovers insights into how immune escape contributes to tumor evolution in non-small-cell lung cancer