Search results for "Arity"
showing 10 items of 2893 documents
Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces
2014
International audience; We combine geometric and numerical techniques - the Hampath code - to compute conjugate and cut loci on Riemannian surfaces using three test bed examples: ellipsoids of revolution, general ellipsoids, and metrics with singularities on S2 associated to spin dynamics.
Minimum Time Control of the Restricted Three-Body Problem
2012
The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the control.
On some Riemannian aspects of two and three-body controlled problems
2009
The flow of the Kepler problem (motion of two mutually attracting bodies) is known to be geodesic after the work of Moser [20], extended by Belbruno and Osipov [2, 21]: Trajectories are reparameterizations of minimum length curves for some Riemannian metric. This is not true anymore in the case of the three-body problem, and there are topological obstructions as observed by McCord et al. [19]. The controlled formulations of these two problems are considered so as to model the motion of a spacecraft within the influence of one or two planets. The averaged flow of the (energy minimum) controlled Kepler problem with two controls is shown to remain geodesic. The same holds true in the case of o…
Characterization of the Clarke regularity of subanalytic sets
2017
International audience; In this note, we will show that for a closed subanalytic subset $A \subset \mathbb{R}^n$, the Clarke tangential regularity of $A$ at $x_0 \in A$ is equivalent to the coincidence of the Clarke's tangent cone to $A$ at $x_0$ with the set \\$$\mathcal{L}(A, x_0):= \bigg\{\dot{c}_+(0) \in \mathbb{R}^n: \, c:[0,1]\longrightarrow A\;\;\mbox{\it is Lipschitz}, \, c(0)=x_0\bigg\}.$$Where $\dot{c}_+(0)$ denotes the right-strict derivative of $c$ at $0$. The results obtained are used to show that the Clarke regularity of the epigraph of a function may be characterized by a new formula of the Clarke subdifferential of that function.
Morphometrics of hard structures in cuttlefish
2006
7 pages; International audience; Cuttlefishes exhibit several hard structures that have been characterised using morphometric analysis. Most of these data come from cuttlebones, although statoliths and beaks are also used. It appears that morphometric techniques are mainly used for taxonomic purposes. However, some analyses have emphasised functional morphology and macroevolution. Morphological features (including the inner shell) of cuttlefishes and their availability for study (numerous specimens, culture in the laboratory) make them a first rank model for numerous studies in life sciences that require morphometrics, and especially in the field of evolutionary biology.
On listening to atonal variants of two Piano Sonatas by Beethoven
2009
International audience; We investigated the contribution of tonal relationships to the perception of musical ideas and to the feelings of "arousal." Two excerpts of piano sonatas by Beethoven and two atonal variants were used as experimental stimuli. This manipulation destroyed the tonal relationships but preserved both the local and global temporal organization (rhythm and formal). Listeners were asked to indicate the onset of musical ideas, to estimate the arousing properties of the music in a continuous response task, and to rate the similarity of the pieces. A drastic change in the pitch structure strongly affected judgments of similarity. However, it had no effect on the segmentation o…
Multi-Domain Retrieval of Geospatial Data Sources Implementing a Semantic Catalogue
2015
International audience; Nowadays, the expertise of a user plays an important role in the search and retrieval in the information systems that usually combines general and specialized knowledge in the construction of queries. In addition, most of the queries systems are currently restricted on specific domains. Tackling these issues, we propose a methodology that implements a semantic catalogue in order to provide a smart queries system for retrieving data sources on the web by means of the extension of the user expertise. We propose the combination of a query expansion method, and the use of similarity measures and controlled vocabularies. Thus, it allows the system to recommend data source…
Architectural Reconstruction of 3D Building Objects through Semantic Knowledge Management
2010
International audience; This paper presents an ongoing research which aims at combining geometrical analysis of point clouds and semantic rules to detect 3D building objects. Firstly by applying a previous semantic formalization investigation, we propose a classification of related knowledge as definition, partial knowledge and ambiguous knowledge to facilitate the understanding and design. Secondly an empirical implementation is conducted on a simplified building prototype complying with the IFC standard. The generation of empirical knowledge rules is revealed and semantic scopes are addressed both in the bottom up manner along the line of geometry --> topology --> semantic, and a vice ver…
Whole mirror duplication-random loss model and pattern avoiding permutations
2010
International audience; In this paper we study the problem of the whole mirror duplication-random loss model in terms of pattern avoiding permutations. We prove that the class of permutations obtained with this model after a given number p of duplications of the identity is the class of permutations avoiding the alternating permutations of length p2+1. We also compute the number of duplications necessary and sufficient to obtain any permutation of length n. We provide two efficient algorithms to reconstitute a possible scenario of whole mirror duplications from identity to any permutation of length n. One of them uses the well-known binary reflected Gray code (Gray, 1953). Other relative mo…
Adding Knowledge Extracted by Association Rules into Similarity Queries
2010
International audience; In this paper, we propose new techniques to improve the quality of similarity queries over image databases performing association rule mining over textual descriptions and automatically extracted features of the image content. Based on the knowledge mined, each query posed is rewritten in order to better meet the user expectations. We propose an extension of SQL aimed at exploring mining processes over complex data, generating association rules that extract semantic information from the textual description superimposed to the extracted features, thereafter using them to rewrite the queries. As a result, the system obtains results closer to the user expectation than i…