The growth of the rank of Abelian varieties upon extensions

Number theory, Algebra and Geometr

Effects of Ionospheric Asymmetry on Electron Density Standard Inversion Algorithm Applicable to Radio Occultation (RO) Data Using Best-suited Ionospheric Model

The "Onion-peeling" algorithm is a very common technique used to invert Radio Occultation (RO) data in the ionosphere. Because of the implicit assumption of spherical symmetry for the electron density (Ne) distribution in the ionosphere, the standard Onion-peeling algorithm could give erroneous concentration values in the retrieved electron density vertical profile Ne(h). In particular, this happens when strong horizontal ionospheric electron density gradients are present, like for example in the Equatorial Ionization Anomaly (EIA) region during high solar activity periods. Using simulated RO Total Electron Content (TEC) data computed by means of the best-suited ionospheric model and ideal RO geometries, we evaluated the asymmetry level index for quasi-horizontal TEC observations. This asymmetry index is based on the Ne variations that a signal may experience along its ray-path (satellite to satellite link) during a RO event. The index is strictly dependent on RO geometry and azimuth of the occultation plane and is able to provide us indication of the errors (in particular those concerning the peak electron density NmF2 and the vertical TEC) expected in the retrieval of Ne(h) using standard Onion-peeling algorithm. On the basis of the outcomes of our work, and using best-suited ionospheric model, we will try to investigate the possibility to predict the ionospheric asymmetry expected for the particular RO geometry considered. We could also try to evaluate, in advance, its impact on the inverted electron density profile, providing an indication of the product qualit

A Fast, Memory-Efficient Alpha-Tree Algorithm using Flooding and Tree Size Estimation

The alpha-tree represents an image as hierarchical set of alpha-connected components. Computation of alpha-trees suffers from high computational and memory requirements compared with similar component tree algorithms such as max-tree. Here we introduce a novel alpha-tree algorithm using 1) a flooding algorithm for computational efficiency and 2) tree size estimation (TSE) for memory efficiency. In TSE, an exponential decay model was fitted to normalized tree sizes as a function of the normalized root mean squared deviation (NRMSD) of edge-dissimilarity distributions, and the model was used to estimate the optimum memory allocation size for alpha-tree construction. An experiment on 1256 images shows that our algorithm runs 2.27 times faster than Ouzounis and Soille's thanks to the flooding algorithm, and TSE reduced the average memory allocation of the proposed algorithm by 40.4%, eliminating unused allocated memory by 86.0% with a negligible computational cost

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

Impulsive noise removal from color images with morphological filtering

This paper deals with impulse noise removal from color images. The proposed noise removal algorithm employs a novel approach with morphological filtering for color image denoising; that is, detection of corrupted pixels and removal of the detected noise by means of morphological filtering. With the help of computer simulation we show that the proposed algorithm can effectively remove impulse noise. The performance of the proposed algorithm is compared in terms of image restoration metrics and processing speed with that of common successful algorithms.Comment: The 6th international conference on analysis of images, social networks, and texts (AIST 2017), 27-29 July, 2017, Moscow, Russi

Generating and Adding Flows on Locally Complete Metric Spaces

As a generalization of a vector field on a manifold, the notion of an arc field on a locally complete metric space was introduced in \cite{BC}. In that paper, the authors proved an analogue of the Cauchy-Lipschitz Theorem i.e they showed the existence and uniqueness of solution curves for a time independent arc field. In this paper, we extend the result to the time dependent case, namely we show the existence and uniqueness of solution curves for a time dependent arc field. We also introduce the notion of the sum of two time dependent arc fields and show existence and uniqueness of solution curves for this sum.Comment: 29 pages,6 figure

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

Dating of the oldest continental sediments from the Himalayan foreland basin

A detailed knowledge of Himalayan development is important for our wider understanding of several global processes, ranging from models of plateau uplift to changes in oceanic chemistry and climate(1-4). Continental sediments 55 Myr old found in a foreland basin in Pakistan(5) are, by more than 20 Myr, the oldest deposits thought to have been eroded from the Himalayan metamorphic mountain belt. This constraint on when erosion began has influenced models of the timing and diachrony of the India-Eurasia collision(6-8), timing and mechanisms of exhumation(9,10) and uplift(11), as well as our general understanding of foreland basin dynamics(12). But the depositional age of these basin sediments was based on biostratigraphy from four intercalated marl units(5). Here we present dates of 257 detrital grains of white mica from this succession, using the Ar-40-(39) Ar method, and find that the largest concentration of ages are at 36-40 Myr. These dates are incompatible with the biostratigraphy unless the mineral ages have been reset, a possibility that we reject on the basis of a number of lines of evidence. A more detailed mapping of this formation suggests that the marl units are structurally intercalated with the continental sediments and accordingly that biostratigraphy cannot be used to date the clastic succession. The oldest continental foreland basin sediments containing metamorphic detritus eroded from the Himalaya orogeny therefore seem to be at least 15-20 Myr younger than previously believed, and models based on the older age must be re-evaluated

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

On making nD images well-composed by a self-dual local interpolation

International audienceNatural and synthetic discrete images are generally not well-composed, leading to many topological issues: connectivities in binary images are not equivalent, the Jordan Separation theorem is not true anymore, and so on. Conversely, making images well-composed solves those problems and then gives access to many powerful tools already known in mathematical morphology as the Tree of Shapes which is of our principal interest. In this paper, we present two main results: a characterization of 3D well-composed gray-valued images; and a counter-example showing that no local self-dual interpolation satisfying a classical set of properties makes well-composed images with one subdivision in 3D, as soon as we choose the mean operator to interpolate in 1D. Then, we briefly discuss various constraints that could be interesting to change to make the problem solvable in nD