No-splitting property and boundaries of random groups

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.Comment: 20 page

An algorithm to identify automorphisms which arise from self-induced interval exchange transformations

We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The algorithm effectively yields the interval exchange transformation in case of success.Comment: 26 pages, 8 figures. v2: the article has been reorganized to make for a more linear read. A few paragraphs have been added for clarit

Centriole splitting caused by loss of the centrosomal linker protein C-NAP1 reduces centriolar satellite density and impedes centrosome amplification

Duplication of the centrosomes is a tightly regulated process. Abnormal centrosome numbers can impair cell division and cause changes in how cells migrate. Duplicated centrosomes are held together by a proteinaceous linker made up of rootletin filaments anchored to the centrioles by C-NAP1. This linker is removed in a NEK2A kinase-dependent manner as mitosis begins. To explore C-NAP1 activities in regulating centrosome activities, we used genome editing to ablate it. C-NAP1–null cells were viable and had an increased frequency of premature centriole separation, accompanied by reduced density of the centriolar satellites, with reexpression of C-NAP1 rescuing both phenotypes. We found that the primary cilium, a signaling structure that arises from the mother centriole docked to the cell membrane, was intact in the absence of C-NAP1, although components of the ciliary rootlet were aberrantly localized away from the base of the cilium. C-NAP1–deficient cells were capable of signaling through the cilium, as determined by gene expression analysis after fluid flow–induced shear stress and the relocalization of components of the Hedgehog pathway. Centrosome amplification induced by DNA damage or by PLK4 or CDK2 overexpression was markedly reduced in the absence of C-NAP1. We conclude that centriole splitting reduces the local density of key centriolar precursors to impede overduplication

Stabilizers of R\mathbb R-trees with free isometric actions of FNF_N

We prove that if $T$ is an $\mathbb R$-tree with a minimal free isometric action of $F_N$, then the $Out(F_N)$-stabilizer of the projective class $[T]$ is virtually cyclic. For the special case where $T=T_+(\phi)$ is the forward limit tree of an atoroidal iwip element $\phi\in Out(F_N)$ this is a consequence of the results of Bestvina, Feighn and Handel, via very different methods. We also derive a new proof of the Tits alternative for subgroups of $Out(F_N)$ containing an iwip (not necessarily atoroidal): we prove that every such subgroup $G\le Out(F_N)$ is either virtually cyclic or contains a free subgroup of rank two. The general case of the Tits alternative for subgroups of $Out(F_N)$ is due to Bestvina, Feighn and Handel.Comment: corrected the proof of Proposition 4.1, plus several minor fixes and updates; to appear in Journal of Group Theor

Orbit equivalence rigidity for ergodic actions of the mapping class group

We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher complexity. We prove similar rigidity results for a finite direct product of mapping class groups as well.Comment: 11 pages, title changed, a part of contents remove

Live imaging of alveologenesis in precision-cut lung slices reveals dynamic epithelial cell behaviour

Damage to alveoli, the gas-exchanging region of the lungs, is a component of many chronic and acute lung diseases. In addition, insufficient generation of alveoli results in bronchopulmonary dysplasia, a disease of prematurity. Therefore visualising the process of alveolar development (alveologenesis) is critical for our understanding of lung homeostasis and for the development of treatments to repair and regenerate lung tissue. Using long-term, time-lapse imaging of precision-cut lung slices, we show alveologenesis for the first time. We reveal that during this process, epithelial cells are highly mobile and we identify specific cell behaviours that contribute to alveologenesis: cell clustering, hollowing and cell extension. Using the cytoskeleton inhibitors blebbistatin and cytochalasin D, we showed that cell migration is a key driver of alveologenesis. This study reveals important novel information about lung biology and provides a new system in which to manipulate alveologenesis genetically and pharmacologically

Converging and diverging burn rates in North American boreal forests from the Little Ice Age to the present

Warning. This article contains terms, descriptions, and opinions used for historical context that may be culturally sensitive for some readers. Background. Understanding drivers of boreal forest dynamics supports adaptation strategies in the context of climate change. Aims. We aimed to understand how burn rates varied since the early 1700s in North American boreal forests. Methods. We used 16 fire-history study sites distributed across such forests and investigated variation in burn rates for the historical period spanning 1700-1990. These were benchmarked against recent burn rates estimated for the modern period spanning 1980-2020 using various data sources. Key results. Burn rates during the historical period for most sites showed a declining trend, particularly during the early to mid 1900s. Compared to the historical period, the modern period showed less variable and lower burn rates across sites. Mean burn rates during the modern period presented divergent trends among eastern versus northwestern sites, with increasing trends in mean burn rates in most northwestern North American sites. Conclusions. The synchronicity of trends suggests that large spatial patterns of atmospheric conditions drove burn rates in addition to regional changes in land use like fire exclusion and suppression. Implications. Low burn rates in eastern Canadian boreal forests may continue unless climate change overrides the capacity to suppress fire.Peer reviewe

Content-aware frame interpolation (CAFI): deep learning-based temporal super-resolution for fast bioimaging

The development of high-resolution microscopes has made it possible to investigate cellular processes in 3D and over time. However, observing fast cellular dynamics remains challenging because of photobleaching and phototoxicity. Here we report the implementation of two content-aware frame interpolation (CAFI) deep learning networks, Zooming SlowMo and Depth-Aware Video Frame Interpolation, that are highly suited for accurately predicting images in between image pairs, therefore improving the temporal resolution of image series post-acquisition. We show that CAFI is capable of understanding the motion context of biological structures and can perform better than standard interpolation methods. We benchmark CAFI’s performance on 12 different datasets, obtained from four different microscopy modalities, and demonstrate its capabilities for single-particle tracking and nuclear segmentation. CAFI potentially allows for reduced light exposure and phototoxicity on the sample for improved long-term live-cell imaging. The models and the training and testing data are available via the ZeroCostDL4Mic platform

Phase Transitions on Nonamenable Graphs

We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees

Group measure space decomposition of II_1 factors and W*-superrigidity

We prove a "unique crossed product decomposition" result for group measure space II_1 factors arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups \Gamma in a fairly large family G, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products over an amenable subgroup. We deduce that if T_n denotes the group of upper triangular matrices in PSL(n,Z), then any free, mixing p.m.p. action of the amalgamated free product of PSL(n,Z) with itself over T_n, is W*-superrigid, i.e. any isomorphism between L^\infty(X) \rtimes \Gamma and an arbitrary group measure space factor L^\infty(Y) \rtimes \Lambda, comes from a conjugacy of the actions. We also prove that for many groups \Gamma in the family G, the Bernoulli actions of \Gamma are W*-superrigid.Comment: Final version. Some extra details have been added to improve the expositio