Search results for "Curve"
showing 10 items of 1693 documents
Computational approach to compact Riemann surfaces
2017
International audience; A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on…
Darboux curves on surfaces I
2017
International audience; In 1872, G. Darboux defined a family of curves on surfaces of $\mathbb{R}^3$ which are preserved by the action of the Mobius group and share many properties with geodesics. Here, we characterize these curves under the view point of Lorentz geometry and prove that they are geodesics in a 3-dimensional sub-variety of a quadric $\Lambda^4$ contained in the 5-dimensional Lorentz space $\mathbb{R}^5_1$ naturally associated to the surface. We construct a new conformal object: the Darboux plane-field $\mathcal{D}$ and give a condition depending on the conformal principal curvatures of the surface which guarantees its integrability. We show that $\mathcal{D}$ is integrable w…
Surfaces of minimal degree of tame representation type and mutations of Cohen–Macaulay modules
2017
We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands.
Arrangements de cercles sur une sphère: Algorithmes et Applications aux modèles moléculaires representés par une union de boules
2008
Since the early work of Richard et al., geometric constructions havebeen paramount for the description of macromolecules and macro-molecularassemblies. In particular, Voronoï and related constructions have beenused to describe the packing properties of atoms, to compute molecularsurfaces, to find cavities. This thesis falls in this realm, andafter a brief introduction to protein structure, makes fourcontributions.First, using the sweep line paradigm of Bentley and Ottmann, wepresent the first effective algorithm able to construct the exactarrangement of circles on a sphere. Moreover, assuming the circlesstem from the intersection between spheres, we present a strategy to reportthe covering …
Extrapolation des inventaires de biodiversité incomplets : comment estimer au mieux le nombre d’espèces manquantes et prévoir l’effort additionnel d’…
2016
While approaching or even reaching total completeness remains the idealgoal of any species inventory, incomplete samplings are deemed to become more often the rule, that are significantly more difficult to cope with (such as (micro-) invertebrates, for example).However, once post-operated appropriately, incomplete samplings may provide farmore data than it would seem and it is indeed possible to obtain valuable extra information froma reliable mode of extrapolation of the so-called Species Accumulation Curve.In fact, numerous tools designed for the exploitation of incomplete samplings havealready been proposed in the literature but the concern, with these numerous different tools, isprecise…
Road Signs Detection and Reconstruction using Gielis Curves
2012
International audience; Road signs are among the most important navigation tools in transportation systems. The identification of road signs in images is usually based on first detecting road signs location using color and shape information. In this paper, we introduce such a two-stage detection method. Road signs are located in images based on color segmentation, and their corresponding shape is retrieved using a unified shape representation based on Gielis curves. The contribution of our approach is the shape reconstruction method which permits to detect any common road sign shape, i.e. circle, triangle, rectangle and octagon, by a single algorithm without any training phase. Experimental…
A NEW POTENTIAL FUNCTION FOR SELF INTERSECTING GIELIS CURVES WITH RATIONAL SYMMETRIES
2009
International audience; We present a new potential field equation for self-intersecting Gielis curves with rational rotational symmetries. In the literature, potential field equations for these curves, and their extensions to surfaces, impose the rotational symmetries to be integers in order to guarantee the unicity of the intersection between the curve/surface and any ray starting from its center. Although the representation with natural symmetries has been applied to mechanical parts modeling and reconstruction, the lack of a potential function for Rational symmetry Gielis Curves (RGC) remains a major problem for natural object representation, such as flowers and phyllotaxis. We overcome thi…
Modelling analysis of centroid curves of olfactory habituation in humans
2020
Indexation en cours.; International audience; Previously published experiments established the time-course of olfactory habituation in humans, and extracted 3 centroid curves from clustering analysis that reflected high, middle and low habituation. The aim of the current theoretical study was to further analyse these previous experimental data by developing a mathematical modelling analysis designed for fitting the 3 curves from a general equation. After adjusting equation parameters for each curve, fitting equation outcomes on experimental data yielded high correlation coefficients of 0.9997 – 0.9995 – 0.9962, respectively. A model-based interpretation of olfactory-habituation centroid cur…
Extrapolation of the Species Accumulation Curve for Incomplete Species Samplings: A New Nonparametric Approach to Estimate the Degree of Sample Compl…
2015
9 pages; International audience; Incomplete species samplings are deemed to remain the common practice in those groups of animals, such as small or micro- invertebrates, with numerous species that often are more or less difficult to detect in the field. Thus, extrapolating the Species Accumulation Curve as far as possible beyond the actual sample size may thus serve as a useful (although imperfect) surrogate to the desired, but practically inaccessible, complete samplings. In this context, several kinds of theoretical or empirical models for the Species Accumulation Curve and also a lot of estimators of the asymptotic limit of the Curve (i.e. total species richness) have been proposed. The …
Scritti scelti di Antonino Mineo
2011
Questo volume presenta una selezione ragionata degli scritti di Antonino Mineo (1936-2008), di cui mantiene la veste tipografica originale. La raccolta di scritti è preceduta dai lavori di Giuseppe Burgio, Marcello Chiodi e Vittorio Frosini, presentati in occasione della “Giornata in ricordo di Antonino Mineo”, tenuta il 22 maggio 2009 presso la Facoltà di Economia di Palermo ed al termine della quale è stata intitolata ad Antonino Mineo un'aula del dipartimento di Scienze Statistiche e Matematiche “Silvio Vianelli”. I lavori di Giuseppe Burgio e Vittorio Frosini sono due contributi originali presentati in quella giornata di studio, sul tema delle curve normali di ordine p, che è stato uno …