50 research outputs found
The integral monodromy of hyperelliptic and trielliptic curves
We compute the \integ/\ell and \integ_\ell monodromy of every irreducible
component of the moduli spaces of hyperelliptic and trielliptic curves. In
particular, we provide a proof that the \integ/\ell monodromy of the moduli
space of hyperelliptic curves of genus is the symplectic group
\sp_{2g}(\integ/\ell). We prove that the \integ/\ell monodromy of the
moduli space of trielliptic curves with signature is the special
unitary group \su_{(r,s)}(\integ/\ell\tensor\integ[\zeta_3])
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
Modulation of junction tension by tumor suppressors and proto-oncogenes regulates cell-cell contacts
International audienceTumor suppressors and proto-oncogenes play crucial roles in tissue proliferation. Furthermore, de-regulation of their functions is deleterious to tissue architecture and can result in the sorting of somatic rounded clones minimizing their contact with surrounding wild-type (wt) cells. Defects in the shape of somatic clones correlate with defects in proliferation, cell affinity, cell-cell adhesion, oriented cell division and cortical contractility. Combining genetics, live-imaging, laser ablation and computer simulations, we aim to analyze whether distinct or similar mechanisms can account for the common role of tumor suppressors and proto-oncogenes in cell-cell contact regulation. In Drosophila epithelia, the tumor suppressors Fat (Ft) and Dachsous (Ds) regulate cell proliferation, tissue morphogenesis, planar cell polarity and junction tension. By analyzing the evolution over time of ft mutant cells and clones, we show that ft clones reduce their cell-cell contacts with the surrounding wt tissue in the absence of concomitant cell divisions and over-proliferation. This contact reduction depends on opposed changes of junction tensions in the clone bulk and its boundary with neighboring wt tissue. More generally, either clone bulk or boundary junction tension is modulated by the activation of Yorkie, Myc and Ras, yielding similar contact reductions with wt cells. Together, our data highlight mechanical roles for proto-oncogene and tumor suppressor pathways in cell-cell interactions
The Structure of Reachable Sets and Geometric Optimality of Singular Trajectories for Certain Affine Control Systems in ℝ3. The Sub-Lorentzian Approach
Hausdorff measures and dimensions in non equiregular sub-Riemannian manifolds
This paper is a starting point towards computing the Hausdorff dimension of
submanifolds and the Hausdorff volume of small balls in a sub-Riemannian
manifold with singular points. We first consider the case of a strongly
equiregular submanifold, i.e., a smooth submanifold N for which the growth
vector of the distribution D and the growth vector of the intersection of D
with TN are constant on N. In this case, we generalize the result in [12],
which relates the Hausdorff dimension to the growth vector of the distribution.
We then consider analytic sub-Riemannian manifolds and, under the assumption
that the singular point p is typical, we state a theorem which characterizes
the Hausdorff dimension of the manifold and the finiteness of the Hausdorff
volume of small balls B(p,\rho) in terms of the growth vector of both the
distribution and the intersection of the distribution with the singular locus,
and of the nonholonomic order at p of the volume form on M evaluated along some
families of vector fields