The growth of the rank of Abelian varieties upon extensions

Number theory, Algebra and Geometr

On the equivalence between hierarchical segmentations and ultrametric watersheds

We study hierarchical segmentation in the framework of edge-weighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical segmentations. We end this paper by showing how to use the proposed framework in practice in the example of constrained connectivity; in particular it allows to compute such a hierarchy following a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.Comment: 19 pages, double-colum

Counting elliptic curves with prescribed level structures over number fields

Harron and Snowden (J. reine angew. Math. 729 (2017), 151-170) counted the number of elliptic curves over Q$\mathbb {Q}$ up to height X$X$ with torsion group G$G$ for each possible torsion group G$G$ over Q$\mathbb {Q}$. In this paper, we generalize their result to all number fields and all level structures G$G$ such that the corresponding modular curve XG$X_G$ is a weighted projective line P(w0,w1)$\mathbb {P}(w_0,w_1)$ and the morphism XG -> X(1)$X_G\rightarrow X(1)$ satisfies a certain condition. In particular, this includes all modular curves X1(m,n)$X_1(m,n)$ with coarse moduli space of genus 0. We prove our results by defining a size function on P(w0,w1)$\mathbb {P}(w_0,w_1)$ following unpublished work of Deng (Preprint, ), and working out how to count the number of points on P(w0,w1)$\mathbb {P}(w_0,w_1)$ up to size X$X$.Number theory, Algebra and Geometr

Earth's Dynamic Past Revealed by Detrital Thermochronometry

A dvances in detrital noble gas thermochronometry by Ar-40/Ar-39 and (U-Th)/He dating are improving the resolution of sedimentary provenance reconstructions and are providing new insights into the evolution of Earth's surface. Detrital thermochronometry has the ability to quantify tectonic unroofing or erosion, temporal and dynamic connections between sediment source and sink, sediment lag-times and transfer rates, the timing of deposition, and postdepositional burial heating. Hence, this technique has the unique ability to use the detrital record in sedimentary basins to reconstruct Earth's dynamic long-term landscape evolution and how basins are coupled to their hinterlands

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

Automating the measurement of physiological parameters: a case study in the image analysis of cilia motion

International audienceAs image processing and analysis techniques improve, an increasing number of procedures in bio-medical analyses can be automated. This brings many benefits, e.g improved speed and accuracy, leading to more reliable diagnoses and follow-up, ultimately improving patients outcome. Many automated procedures in bio-medical imaging are well established and typically consist of detecting and counting various types of cells (e.g. blood cells, abnormal cells in Pap smears, and so on). In this article we propose to automate a different and difficult set of measurements, which is conducted on the cilia of people suffering from a variety of respiratory tract diseases. Cilia are slender, microscopic, hair-like structures or organelles that extend from the surface of nearly all mammalian cells. Motile cilia, such as those found in the lungs and respiratory tract, present a periodic beating motion that keep the airways clear of mucus and dirt. In this paper, we propose a fully automated method that computes various measurements regarding the motion of cilia, taken with high-speed video-microscopy. The advantage of our approach is its capacity to automatically compute robust, adaptive and regionalized measurements, i.e. associated with different regions in the image. We validate the robustness of our approach, and illustrate its performance in comparison to the state-of-the-art

Constructive links between some morphological hierarchies on edge-weighted graphs

International audienceIn edge-weighted graphs, we provide a unified presentation of a family of popular morphological hierarchies such as component trees, quasi flat zones, binary partition trees, and hierarchical watersheds. For any hierarchy of this family, we show if (and how) it can be obtained from any other element of the family. In this sense, the main contribution of this paper is the study of all constructive links between these hierarchies

Freeze-out configuration properties in the 197Au + 197Au reaction at 23 AMeV

Data from the experiment on the 197Au + 197Au reaction at 23 AMeV are analyzed with an aim to find signatures of exotic nuclear configurations such as toroid-shaped objects. The experimental data are compared with predictions of the ETNA code dedicated to look for such configurations and with the QMD model. A novel criterion of selecting events possibly resulting from the formation of exotic freeze-out configurations, "the efficiency factor", is tested. Comparison between experimental data and model predictions may indicate for the formation of flat/toroidal nuclear systems