On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio

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

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

Bioreactor analyses of tissue ingrowth, ongrowth and remodelling around implants: an alternative to live animal testing

Introduction: Preclinical assessment of bone remodelling onto, into or around novel implant technologies is underpinned by a large live animal testing burden. The aim of this study was to explore whether a lab-based bioreactor model could provide similar insight. Method: Twelve ex vivo trabecular bone cylinders were extracted from porcine femora and were implanted with additively manufactured stochastic porous titanium implants. Half were cultured dynamically, in a bioreactor with continuous fluid flow and daily cyclic loading, and half in static well plates. Tissue ongrowth, ingrowth and remodelling around the implants were evaluated with imaging and mechanical testing. Results: For both culture conditions, scanning electron microscopy (SEM) revealed bone ongrowth; widefield, backscatter SEM, micro computed tomography scanning, and histology revealed mineralisation inside the implant pores; and histology revealed woven bone formation and bone resorption around the implant. The imaging evidence of this tissue ongrowth, ingrowth and remodelling around the implant was greater for the dynamically cultured samples, and the mechanical testing revealed that the dynamically cultured samples had approximately three times greater push-through fixation strength (p < 0.05). Discussion: Ex vivo bone models enable the analysis of tissue remodelling onto, into and around porous implants in the lab. While static culture conditions exhibited some characteristics of bony adaptation to implantation, simulating physiological conditions with a bioreactor led to an accelerated response

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

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

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

ID-HALL, a new double stage Hall thruster design. I. Principle and hybrid model of ID-HALL

International audienceIn Hall thrusters, ions are extracted from a quasineutral plasma by the electric field induced by the local drop of electron conductivity associated with the presence of a magnetic barrier. Since the electric field is used both to extract and accelerate ions and to generate the plasma, thrust and specific impulse are not independent in a Hall thruster. There is a need for versatile thrusters that can be used for a variety of maneuvers, i.e., that can operate either at high thrust or at high specific impulse for a given power. The double stage Hall thruster (DSHT) design could allow a separate control of ionization and acceleration, and hence separate control of thrust and specific impulse. In the DSHT configuration, a supplementary plasma source (ionization stage), independent of the applied voltage, is added and placed upstream of the magnetic barrier (acceleration stage). The DSHT concept is also well adapted to the use of alternative propellants, lighter and with a less efficient ionization than xenon. Several designs of double stage Hall thrusters have been proposed in the past, but these attempts were not really successful. In this paper, we present a brief review of the main DSHT designs described in the literature, we discuss the relevance of the DSHT concept, and, on the basis of simple physics arguments and simulation results, we propose a new design, called ID-HALL (Inductive Double stage HALL thruster). In this design, the ionization stage is a magnetized inductively coupled RF plasma. The inductive coil is inside the central cylinder of the thruster and located nearby the acceleration stage. Preliminary modeling results of this DSHT are described. Published by AIP Publishing. https://doi

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