Strong Euler well-composedness

In this paper, we define a new flavour of well-composedness, called strong Euler well-composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an $$(n-1)$$ ( n - 1 ) -dimensional ball. Working in the particular setting of cubical complexes canonically associated with $$n$$ n D pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension $$n\ge 2$$ n ≥ 2 and that the converse is not true when $$n\ge 4$$ n ≥ 4 .

Different temporal requirements for the LRR transmembrane receptors Tartan and Toll-2 in the formation of contractile interfaces at compartmental boundaries

Compartmental boundaries physically separate groups of epithelial cells, a property fundamental for the organization of the body plan in both insects and vertebrates. In many examples, this physical separation has been shown to be the consequence of a regulated increase in contractility of the actomyosin cortex at boundary cell-cell interfaces, a property important in developmental morphogenesis beyond compartmental boundary formation. In this study, we took an unbiased screening approach to identify cell surface receptors required for actomyosin enrichment and polarisation at parasegmental boundaries (PSBs) in early Drosophila embryos, leading us to uncover different temporal requirements for two LRR receptors, Tartan and Toll-2. First, we find that Tartan is required during germband extension for actomyosin enrichment at PSBs, confirming an earlier report. Next, by following in real time the dynamics of loss of boundary straightness in tartan mutant embryos compared to wildtype and ftz mutant embryos, we show that Tartan is not required beyond germband extension. At this stage, actomyosin enrichment at PSBs becomes regulated by Wingless signalling. We find that Wingless signalling regulates Toll-2 expression and we show that Toll-2 is required for planar polarization of actomyosin after the completion of germ-band extension. Thus the formation of contractile interfaces at PSBs depends on a dynamic set of LRR receptors cues. Our study also suggests that the number of receptor cues is small and that the receptors are interchangeable.

The neurogenic fate of the hindbrain boundaries: a Notch-dependent behavioral switch triggers asymmetric division of boundary stem cells

The generation of cell diversity in the central nervous system occurs during embryogenesis and requires a precise balance between stem cell proliferation, neuronal commitment to specific fates, and further differentiation. Understanding the cellular and molecular mechanisms regulating this balance in the embryonic brain is challenging. Here we reveal how the neurogenic capacity in the hindbrain is differently allocated to distinct domains over time, and how the boundary cells undergo a functional transition to become neurogenic during zebrafish hindbrain segmentation. By generating a CRISPR-based knock-in transgenic line to specifically label the boundary cell population, we tracked their derivatives over time and followed their behavior, allowing us to identify how asymmetric cell divisions arise and to reconstruct the trajectories of the boundary derivatives through the progenitor and differentiated domains. The behavioral switch in boundary cells is triggered by the onset of Notch signaling, based on lateral inhibition at the dorsoventral level. Our findings reveal that distinct neurogenic phases take place during hindbrain growth and suggest that boundary cells contribute to refine the final number, identity, and proportion of neurons in the brain.

Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations

We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the wombling boundary created by some new physics. We discuss the use of Voronoi and Delaunay tessellations of the point data for estimating the local gradients and investigate methods for sharpening the boundaries by reducing the statistical noise. The outcome from traditional wombling algorithms is a set of boundary cell candidates with relatively large gradients, whose spatial properties must then be scrutinized in order to construct the boundary and evaluate its significance. Here we propose an alternative approach where we simultaneously form and evaluate the significance of all possible boundaries in terms of the total gradient flux. We illustrate our method with several toy examples of both straight and curved boundaries with varying amounts of signal present in the data.

Experimental Validation of a Direct Fiber Model for Orientation Prediction

Predicting the fiber orientation of reinforced molded components is required to improve their performance and safety. Continuum-based models for fiber orientation are computationally very efficient; however, they lack in a linked theory between fiber attrition, fiber–matrix separation and fiber alignment. This work, therefore, employs a particle level simulation which was used to simulate the fiber orientation evolution within a sliding plate rheometer. In the model, each fiber is accounted for and represented as a chain of linked rigid segments. Fibers experience hydrodynamic forces, elastic forces, and interaction forces. To validate this fundamental modeling approach, injection and compression molded reinforced polypropylene samples were subjected to a simple shear flow using a sliding plate rheometer. Microcomputed tomography was used to measure the orientation tensor up to 60 shear strain units. The fully characterized microstructure at zero shear strain was used to reproduce the initial conditions in the particle level simulation. Fibers were placed in a periodic boundary cell, and an idealized simple shear flow field was applied. The model showed a faster orientation evolution at the start of the shearing process. However, agreement with the steady-state aligned orientation for compression molded samples was found.

Actomyosin regulation by Eph receptor signaling couples boundary cell formation to border sharpness

The segregation of cells with distinct regional identity underlies formation of a sharp border, which in some tissues serves to organise a boundary signaling centre. It is unclear whether or how border sharpness is coordinated with induction of boundary-specific gene expression. We show that forward signaling of EphA4 is required for border sharpening and induction of boundary cells in the zebrafish hindbrain, which we find both require kinase-dependent signaling, with a lesser input of PDZ domain-dependent signaling. We find that boundary-specific gene expression is regulated by myosin II phosphorylation, which increases actomyosin contraction downstream of EphA4 signaling. Myosin phosphorylation leads to nuclear translocation of Taz, which together with Tead1a is required for boundary marker expression. Since actomyosin contraction maintains sharp borders, there is direct coupling of border sharpness to boundary cell induction that ensures correct organisation of signaling centres.

Actomyosin regulation by Eph receptor signaling couples boundary cell formation to border sharpness

SummaryThe segregation of cells with distinct regional identity underlies formation of a sharp border, which in some tissues serves to organise a boundary signaling centre. It is unclear whether or how border sharpness is coordinated with induction of boundary-specific gene expression. We show that forward signaling of EphA4 is required for border sharpening and induction of boundary cells in the zebrafish hindbrain, which we find both require kinase-dependent signaling, with a lesser input of PDZ domain-dependent signaling. We find that boundary-specific gene expression is regulated by myosin II phosphorylation, which increases actomyosin contraction downstream of EphA4 signaling. Myosin phosphorylation leads to nuclear translocation of Taz, which together with Tead1a is required for boundary marker expression. Since actomyosin contraction maintains sharp borders, there is direct coupling of border sharpness to boundary cell induction that ensures correct organisation of signaling centres.