Article verifying a conjecture of Vershik by showing that Hall’s universal countable locally finite group can be embedded as a dense subgroup in the isometry group of the Urysohn space and in the automorphism group of the random graph. It shows the same for all automorphism groups of known infinite ultraextensive spaces.

Article presented at the 8th International Conference Words 2011 in Prague, Czech Republic. This article investigates the combinatorial complexity of infinite permutations on N associated with the image of uniformly recurrent aperiodic binary words under the letter doubling map.

This article proposes a new and general goodness-of-fit (GOF) test, called TEDE (TEsting Direct Effects), applicable to both correlated and independent SNPs/IVs as commonly used in transcriptome-wide association studies (TWAS) and Mendelian randomization (MR) respectively.

In this article, the authors propose a statistical method by Testing an Optimally Weighted Combination of Multiple traits (TOW-CM) to test the association between multiple traits and multiple variants in a genomic region (a gene or pathway). They investigate the performance of the proposed method through extensive simulation studies. Their simulation studies show that the proposed method has correct type I error rates and is either the most powerful test or comparable with the most powerful tests. Additionally, they illustrate the usefulness of TOW-CM based on a COPDGene study.