On the cohomology rings of tree braid groups

Let $\Gamma$ be a finite connected graph. The (unlabelled) configuration space $UC^n \Gamma$ of $n$ points on $\Gamma$ is the space of $n$-element subsets of $\Gamma$. The $n$-strand braid group of $\Gamma$, denoted $B_n\Gamma$, is the fundamental group of $UC^n \Gamma$. We use the methods and results of our paper "Discrete Morse theory and graph braid groups" to get a partial description of the cohomology rings $H^*(B_n T)$, where $T$ is a tree. Our results are then used to prove that $B_n T$ is a right-angled Artin group if and only if $T$ is linear or $n<4$. This gives a large number of counterexamples to Ghrist's conjecture that braid groups of planar graphs are right-angled Artin groups.Comment: 25 pages, 7 figures. Revised version, accepted by the Journal of Pure and Applied Algebr

De novo human genome assemblies reveal spectrum of alternative haplotypes in diverse populations.

The human reference genome is used extensively in modern biological research. However, a single consensus representation is inadequate to provide a universal reference structure because it is a haplotype among many in the human population. Using 10×&nbsp;Genomics (10×G) "Linked-Read" technology, we perform whole genome sequencing (WGS) and de novo assembly on 17 individuals across five populations. We identify 1842 breakpoint-resolved non-reference unique insertions (NUIs) that, in aggregate, add up to 2.1 Mb of so far undescribed genomic content. Among these, 64% are considered ancestral to humans since they are found in non-human primate genomes. Furthermore, 37% of the NUIs can be found in the human transcriptome and 14% likely arose from Alu-recombination-mediated deletion. Our results underline the need of a set of human reference genomes that includes a comprehensive list of alternative haplotypes to depict the complete spectrum of genetic diversity across populations

Systematic identification of functional plant modules through the integration of complementary data sources

A major challenge is to unravel how genes interact and are regulated to exert specific biological functions. The integration of genome-wide functional genomics data, followed by the construction of gene networks, provides a powerful approach to identify functional gene modules. Large-scale expression data, functional gene annotations, experimental protein-protein interactions, and transcription factor-target interactions were integrated to delineate modules in Arabidopsis (Arabidopsis thaliana). The different experimental input data sets showed little overlap, demonstrating the advantage of combining multiple data types to study gene function and regulation. In the set of 1,563 modules covering 13,142 genes, most modules displayed strong coexpression, but functional and cis-regulatory coherence was less prevalent. Highly connected hub genes showed a significant enrichment toward embryo lethality and evidence for cross talk between different biological processes. Comparative analysis revealed that 58% of the modules showed conserved coexpression across multiple plants. Using module-based functional predictions, 5,562 genes were annotated, and an evaluation experiment disclosed that, based on 197 recently experimentally characterized genes, 38.1% of these functions could be inferred through the module context. Examples of confirmed genes of unknown function related to cell wall biogenesis, xylem and phloem pattern formation, cell cycle, hormone stimulus, and circadian rhythm highlight the potential to identify new gene functions. The module-based predictions offer new biological hypotheses for functionally unknown genes in Arabidopsis (1,701 genes) and six other plant species (43,621 genes). Furthermore, the inferred modules provide new insights into the conservation of coexpression and coregulation as well as a starting point for comparative functional annotation

Fast computation of Tukey trimmed regions and median in dimension p>2p>2

Given data in $\mathbb{R}^{p}$, a Tukey $\kappa$-trimmed region is the set of all points that have at least Tukey depth $\kappa$ w.r.t. the data. As they are visual, affine equivariant and robust, Tukey regions are useful tools in nonparametric multivariate analysis. While these regions are easily defined and interpreted, their practical use in applications has been impeded so far by the lack of efficient computational procedures in dimension $p > 2$. We construct two novel algorithms to compute a Tukey $\kappa$-trimmed region, a na\"{i}ve one and a more sophisticated one that is much faster than known algorithms. Further, a strict bound on the number of facets of a Tukey region is derived. In a large simulation study the novel fast algorithm is compared with the na\"{i}ve one, which is slower and by construction exact, yielding in every case the same correct results. Finally, the approach is extended to an algorithm that calculates the innermost Tukey region and its barycenter, the Tukey median