30 research outputs found
Robustness of force and stress inference in an epithelial tissue
During morphogenesis, the shape of a tissue emerges from collective cellular
behaviors, which are in part regulated by mechanical and biochemical
interactions between cells. Quantification of force and stress is therefore
necessary to analyze the mechanisms controlling tissue morphogenesis. Recently,
a mechanical measurement method based on force inference from cell shapes and
connectivity has been developed. It is non-invasive, and can provide space-time
maps of force and stress within an epithelial tissue, up to prefactors. We
previously performed a comparative study of three force-inference methods,
which differ in their approach of treating indefiniteness in an inverse problem
between cell shapes and forces. In the present study, to further validate and
compare the three force inference methods, we tested their robustness by
measuring temporal fluctuation of estimated forces. Quantitative data of
cell-level dynamics in a developing tissue suggests that variation of forces
and stress will remain small within a short period of time (minutes).
Here, we showed that cell-junction tensions and global stress inferred by the
Bayesian force inference method varied less with time than those inferred by
the method that estimates only tension. In contrast, the amplitude of temporal
fluctuations of estimated cell pressures differs less between different
methods. Altogether, the present study strengthens the validity and robustness
of the Bayesian force-inference method.Comment: 4 pages, 4 figure
Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry
We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry
Critical slope p-adic L-functions of CM modular forms
For ordinary modular forms, there are two constructions of a p-adic
L-function attached to the non-unit root of the Hecke polynomial, which are
conjectured but not known to coincide. We prove this conjecture for modular
forms of CM type, by calculating the the critical-slope L-function arising from
Kato's Euler system and comparing this with results of Bellaiche on the
critical-slope L-function defined using overconvergent modular symbols.Comment: 14 page
Comparative study of non-invasive force and stress inference methods in tissue
In the course of animal development, the shape of tissue emerges in part from
mechanical and biochemical interactions between cells. Measuring stress in
tissue is essential for studying morphogenesis and its physical constraints.
Experimental measurements of stress reported thus far have been invasive,
indirect, or local. One theoretical approach is force inference from cell
shapes and connectivity, which is non-invasive, can provide a space-time map of
stress and relies on prefactors. Here, to validate force- inference methods, we
performed a comparative study of them. Three force-inference methods, which
differ in their approach of treating indefiniteness in an inverse problem
between cell shapes and forces, were tested by using two artificial and two
experimental data sets. Our results using different datasets consistently
indicate that our Bayesian force inference, by which cell-junction tensions and
cell pressures are simultaneously estimated, performs best in terms of accuracy
and robustness. Moreover, by measuring the stress anisotropy and relaxation, we
cross-validated the force inference and the global annular ablation of tissue,
each of which relies on different prefactors. A practical choice of
force-inference methods in distinct systems of interest is discussed.Comment: 12 pages, 8 figures, EPJ E: Topical issue on "Physical constraints on
morphogenesis and evolution
Quantitative fractographic analysis of impact fracture surfaces of steel R73
Macroscopic images offracture surfaces of Charpy test specimens of steel R73 were studied, where bright spots in images represent cleavage facets or ductile dimples, respectively, both in special orientations. Within image analysis, they may be taken for the most significant textural element. Being the brightest patches in the image, they can be extracted by thresholding. Their counts and area distribution are closely related to temperature and impact energy.Выполнены исследования макроизображений поверхностей разрушений образцов Шарпи из стали R73. При специальных условиях ориентации поверхностей разрушения видны яркие участки на изображениях, соответствующие граням скола или ямкам вязкого разрушения. Эти участки могут быть использованы в качестве основного элемента текстуры для обработки изображения. Поскольку эти участки на изображениях являются наиболее яркими, их можно отсеять путем настройки порогового уровня освещенности. Результаты расчета относительной доли их площади тесно коррелируют с температурой и энергией ударного разрушения
Unified quantitative characterization of epithelial tissue development.
Understanding the mechanisms regulating development requires a quantitative characterization of cell divisions, rearrangements, cell size and shape changes, and apoptoses. We developed a multiscale formalism that relates the characterizations of each cell process to tissue growth and morphogenesis. Having validated the formalism on computer simulations, we quantified separately all morphogenetic events in the Drosophila dorsal thorax and wing pupal epithelia to obtain comprehensive statistical maps linking cell and tissue scale dynamics. While globally cell shape changes, rearrangements and divisions all significantly participate in tissue morphogenesis, locally, their relative participations display major variations in space and time. By blocking division we analyzed the impact of division on rearrangements, cell shape changes and tissue morphogenesis. Finally, by combining the formalism with mechanical stress measurement, we evidenced unexpected interplays between patterns of tissue elongation, cell division and stress. Our formalism provides a novel and rigorous approach to uncover mechanisms governing tissue development
OVERCONVERGENT MODULAR SYMBOLS
The theory of overconvergent modular symbols was created by Glenn Stevens over 20 years ago, and since then the subject has had many generalizations and applications central to modern number theory (e.g. overconvergent cohomology, eigenvarieties of reductive groups, families of p-adic L-functions, just to name