Tootfinder

Transposing cartesian and other structure in double categories
Evan Patterson
https://arxiv.org/abs/2404.08835 https://arxiv.org/pdf/…

Transposing cartesian and other structure in double categories
The cartesian structure possessed by morphisms like relations, spans, and profunctors is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program of cartesian bicategories, the precise relationship between the double-categorical and bicategorical approaches has so far remained mysterious, except in special cases. We provide a formal connection by showing that every double category with iso-strong finite produ…

This https://arxiv.org/abs/2306.00537 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Stable developmental patterns of gene expression without morphogen gradients
Gene expression patterns (GEPs) are established by cross-regulating target genes that interpret morphogen gradients. However, as development progresses, morphogen activity is reduced, leaving the emergent GEP without stabilizing positional cues. The GEP then can be deteriorated by the intrinsically noisy biochemical processes acting at the cellular level. However, the established GEPs remain spatio-temporally stable in many biological systems. Here we combine spatial-stochastic simulations with…