Natasha Blitvic | Searcharxiv

arXiv2025

Statistics on monotonically ordered non-crossing partitions

We study some combinatorial statistics defined on the set $NC^{(mton)}(n)$ of monotonically ordered non-crossing partitions of {1,...,n}, and on the set $NC_2^{(mton)}(2n)$ of monotonically ordered non-crossing pair-partitions of {1,...,2n}. Unlike in the analogous results known for unordered non-crossing partitions, the computations of expectations and variances for natural block-counting statistics on $NC^{(mton)}(n)$ and for the expectation of the area statistic on $NC_2^{(mton)}(2n)$ turn out to yield a logarithmic regime. An important role in our study is played by a nice tree structure on the disjoint union of the $NC^{(mton)}(n)$'s, which we use to streamline our arguments. As an illustration of how these ideas can be applied to calculations of cumulants in monotone probability, we discuss some combinatorial aspects of the monotonic Poisson process.

math.CO↗

arXiv2025

Fluid flow generates bacterial conjugation hotspots by increasing the rate of shear-driven cell-cell encounters

Conjugation accelerates bacterial evolution by enabling bacteria to acquire genes horizontally from their neighbors. Plasmid donors must physically encounter and connect with recipients to allow plasmid transfer, and different environments are characterized by vastly different encounter rates between cells, based on mechanisms ranging from simple diffusion to fluid flow. However, how the environment affects the conjugation rate by setting the encounter rate has been largely neglected, mostly because existing experimental setups do not allow direct control over cell encounters. Here, we describe the results of conjugation experiments in E. coli in which we systematically varied the magnitude of shear flow using a cone-and-plate rheometer to control the encounter rate. We discovered that the conjugation rate increases with shear until it peaks at an optimal shear rate (100 1/s), reaching a conjugation rate five-fold higher than the baseline set by diffusion-driven encounters. This optimum marks the transition from a regime in which shear promotes conjugation by increasing the rate of cell-cell encounters to a regime in which shear disrupts conjugation. Regions of high fluid shear are widespread in aquatic systems, in the gut of host organisms, and in soil, and our results indicate that these regions could be hotspots of bacterial conjugation in the environment.

physics.bio-ph↗