Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Semantic Approach in Image Change Detection

International audienceChange detection is a main issue in various domains, and especially for remote sensing purposes. Indeed, plethora of geospatial images are available and can be used to update geographical databases. In this paper, we propose a classification-based method to detect changes between a database and a more recent image. It is based both on an efficient training point selection and a hierarchical decision process. This allows to take into account the intrinsic heterogeneity of the objects and themes composing a database while limiting false detection rates. The reliability of the designed framework method is first assessed on simulated data, and then successfully applied on very high resolution satellite images and two land-cover databases

Data mining with neural networks and support vector machines using the R/rminer tool

We present rminer, our open source library for the R tool that facilitates the use of data mining (DM) algorithms, such as neural Networks (NNs) and support vector machines (SVMs), in classification and regression tasks. Tutorial examples with real-world problems (i.e. satellite image analysis and prediction of car prices) were used to demonstrate the rminer capabilities and NN/SVM advantages. Additional experiments were also held to test the rminer predictive capabilities, revealing competitive performances.Fundação para a Ciência e a Tecnologia (FCT) - PTDC/EIA/64541/200

Emergence of Skyrme crystal in Gross-Neveu and 't Hooft models at finite density

We study two-dimensional, large $N$ field theoretic models (Gross-Neveu model, 't Hooft model) at finite baryon density near the chiral limit. The same mechanism which leads to massless baryons in these models induces a breakdown of translational invariance at any finite density. In the chiral limit baryonic matter is characterized by a spatially varying chiral angle with a wave number depending only on the density. For small bare quark masses a sine-Gordon kink chain is obtained which may be regarded as simplest realization of the Skyrme crystal for nuclear matter. Characteristic differences between confining and non-confining models are pointed out.Comment: 27 pages, 11 figures, added reference, corrected sig

Topology Control in Cooperative Ad Hoc Wireless Networks

AbstractCooperative communication (CC) is a technique that exploits spatial diversity allowing multiple nodes to cooperatively relay signals to the receiver so that it can combine the received signals to obtain the original message. CC can be combined with topology control to increase connectivity at the cost of a small increase in energy consumption. This work focuses on exploring CC to improve the connectivity with a sink node in ad hoc wireless networks. More precisely, this work proposes a new technique, named CoopSink, that combines CC and topology control techniques to increase connectivity to a sink node while ensuring energy-efficient routes. Simulation results show that connectivity and routing to the sink cost can be improved up to 6.8 and 2.3 times, respectively, when compared with other similar strategies

Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category

A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Adapting Decision DAGs for Multipartite Ranking

European Conference, ECML PKDD 2010, Barcelona, Spain, September 20-24, 2010Multipartite ranking is a special kind of ranking for problems in which classes exhibit an order. Many applications require its use, for instance, granting loans in a bank, reviewing papers in a conference or just grading exercises in an education environment. Several methods have been proposed for this purpose. The simplest ones resort to regression schemes with a pre- and post-process of the classes, what makes them barely useful. Other alternatives make use of class order information or they perform a pairwise classi cation together with an aggregation function. In this paper we present and discuss two methods based on building a Decision Directed Acyclic Graph (DDAG). Their performance is evaluated over a set of ordinal benchmark data sets according to the C-Index measure. Both yield competitive results with regard to stateof- the-art methods, specially the one based on a probabilistic approach, called PR-DDA

Evidence for a narrow dip structure at 1.9 GeV/c2^2 in 3π+3π−3\pi^+ 3\pi^- diffractive photoproduction

A narrow dip structure has been observed at 1.9 GeV/c$^2$ in a study of diffractive photoproduction of the $~3\pi^+3\pi^-$ final state performed by the Fermilab experiment E687.Comment: The data of Figure 6 can be obtained by downloading the raw data file e687_6pi.txt. v5 (2nov2018): added Fig. 7, the 6 pion energy distribution as requested by a reade

Search for a strongly decaying neutral charmed pentaquark

We present a search for a charmed pentaquark decaying strongly to $D^{(*)-}p$. Finding no evidence for such a state, we set limits on the cross section times branching ratio relative to $D^{*-}$ and $D^-$ under particular assumptions about the production mechanism.Comment: To be published in Physics Letters