Search results for "complex"
showing 10 items of 5889 documents
An Image Segmentation Algorithm based on Community Detection
2016
International audience; With the recent advances in complex networks, image segmentation becomes one of the most appropriate application areas. In this context, we propose in this paper a new perspective of image segmentation by applying two efficient community detection algorithms. By considering regions as communities, these methods can give an over-segmented image that has many small regions. So, the proposed algorithms are improved to automatically merge those neighboring regions agglomerative to achieve the highest modularity/stability. To produce sizable regions and detect homogeneous communities, we use the combination of a feature based on the Histogram of Oriented Gradients of the …
User and group networks on YouTube: A comparative analysis
2015
International audience; YouTube is the largest video-sharing social network where users (aka channels) can create links to any other users. Moreover, initially, users were allowed to create and join special groups of interest. Therefore, two types of online social networks can be defined. First, a user network where the nodes represent the users and the edges represent the social ties (friendship) between users. Second, a group network where the nodes represent the groups and the edges represent the social ties between groups, due to shared users. As the group network can be apprehended as the ground-truth overlapping community graph (where the nodes are the discovered communities and the l…
Camera-based measurement of relative image contrast in projection displays
2013
International audience; This research investigated the measured contrast of projection displays based on pictures taken by un-calibrated digital cameras under typical viewing conditions. A high-end radiometer was employed as a reference to the physical response of projection luminance. Checkerboard, gray scale and color complex test images with a range of the projector's brightness and contrast settings were projected. Two local and two global contrast metrics were evaluated on the acquired pictures. We used contrast surface plots and Pearson correlation to investigate the measured contrast versus the projector's brightness and contrast settings. The results suggested, as expected, the proj…
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…
Bifurcations in the elementary Desboves family
2017
International audience; We give an example of a family of endomorphisms of $\mathbb{P}^2(\mathbb{C})$ whose Julia set depends continuously on the parameter and whose bifurcation locus has non-empty interior.
Automatic detection of P, QRS and T patterns in 12 leads ECG signal based on CWT
2016
International audience; In this paper, a new method based on the continuous wavelet transform is described in order to detect the QRS, P and T waves. QRS, P and T waves may be distinguished from noise, baseline drift or irregular heartbeats. The algorithm, described in this paper, has been evaluated using the Computers in Cardiology (CinC) Challenge 2011 database and also applied on the MIT-BIH Arrhythmia database (MITDB). The data from the CinC Challenge 2011 are standard 12 ECG leads recordings with full diagnostic bandwidth compared to the MITDB which only includes two leads for each ECG signal. Firstly, our algorithm is validated using fifty 12 leads ECG samples from the CinC collection…
IRREDUCIBLE COXETER GROUPS
2004
We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that an indefinite irreducible Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly) indecomposable. Let W be a Coxeter group. Write W = WX1 × ⋯ × WXb × WZ3, where WX1, … , WXb are non-spherical irreducible Coxeter groups and WZ3 is a finite one. By a classical result, known as the Krull–Remak–Schmidt theorem, the group WZ3 has a decomposition WZ3 = H1 × ⋯ × Hq as a direct product of indecomposable groups, which is unique up to a central automorphism and a permutation of the factors. Now, W = WX1 × ⋯ × WXb × H1 × ⋯ × Hq is a decomposition of W as a dir…
A note on the Lawrence-Krammer-Bigelow representation
2002
A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.
On the classification of mapping class actions on Thurston's asymmetric metric
2011
AbstractWe study the action of the elements of the mapping class group of a surface of finite type on the Teichmüller space of that surface equipped with Thurston's asymmetric metric. We classify such actions as elliptic, parabolic, hyperbolic and pseudo-hyperbolic, depending on whether the translation distance of such an element is zero or positive and whether the value of this translation distance is attained or not, and we relate these four types to Thurston's classification of mapping class elements. The study is parallel to the one made by Bers in the setting of Teichmüller space equipped with Teichmüller's metric, and to the one made by Daskalopoulos and Wentworth in the setting of Te…
$PT$-symmetry and Schrödinger operators. The double well case
2016
International audience; We study a class of $PT$-symmetric semiclassical Schrodinger operators, which are perturbations of a selfadjoint one. Here, we treat the case where the unperturbed operator has a double-well potential. In the simple well case, two of the authors have proved in [6] that, when the potential is analytic, the eigenvalues stay real for a perturbation of size $O(1)$. We show here, in the double-well case, that the eigenvalues stay real only for exponentially small perturbations, then bifurcate into the complex domain when the perturbation increases and we get precise asymptotic expansions. The proof uses complex WKB-analysis, leading to a fairly explicit quantization condi…