Search results for "abstract"
showing 10 items of 1959 documents
Computing Euclidean Steiner trees over segments
2020
In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superse…
A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter
2021
The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalueλβwith negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer forλβand the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.
The project scheduling polyhedron: Dimension, facets and lifting theorems
1993
Abstract The Project scheduling with resource constraints can be formulated as follows: given a graph G with node set N, a set H of directed arcs corresponding to precedence relations, and a set H′ of disjunctive arcs reflecting the resource incompatibilities, find among the subsets of H′ satisfying the resource constraints the set S that minimizes the longest path in graph (N, H ∪ S). We define the project scheduling polyhedron Qs as the convex hull of the feasible solutions. We investigate several classes of inequalities with respect to their facet-defining properties for the associated polyhedron. The dimension of Qs is calculated and several inequalities are shown to define facets. For …
Graph cut-based method for segmenting the left ventricle from MRI or echocardiographic images
2017
International audience; In this paper, we present a fast and interactive graph cut method for 3D segmentation of the endocardial wall of the left ventricle (LV) adapted to work on two of the most widely used modalities: magnetic resonance imaging (MRI) and echocardiography. Our method accounts for the fundamentally different nature of both modalities: 3D echocardiographic images have a low contrast, a poor signal-to-noise ratio and frequent signal drop, while MR images are more detailed but also cluttered and contain highly anisotropic voxels. The main characteristic of our method is to work in a 3D Bezier coordinate system instead of the original Euclidean space. This comes with several ad…
Elementary Integration of Superelliptic Integrals
2021
Consider a superelliptic integral $I=\int P/(Q S^{1/k}) dx$ with $\mathbb{K}=\mathbb{Q}(\xi)$, $\xi$ a primitive $k$th root of unity, $P,Q,S\in\mathbb{K}[x]$ and $S$ has simple roots and degree coprime with $k$. Note $d$ the maximum of the degree of $P,Q,S$, $h$ the logarithmic height of the coefficients and $g$ the genus of $y^k-S(x)$. We present an algorithm which solves the elementary integration problem of $I$ generically in $O((kd)^{\omega+2g+1} h^{g+1})$ operations.
Set Descriptors for Visual Evaluation of Human Corneal Endothelia
2001
Images of corneal endothelium obtained from specular microscopy are of great importance in the evaluation of the corneal endothelium status. Several commercial tools provide some numerical descriptors to characterize these images in terms of cell density, hexagonality, and some descriptive statistics of the cell areas. However, it is a too simple analysis that only detects severe abnormal endothelia with many irregular and large cells. Detection of subtle abnormalities needs a more refined analysis. This paper proposes a shape-size descriptor based on some modified versions of the geometric covariogram. This descriptor is presented as a valid alternative to the classical analysis that provi…
Set-valued consensus for distributed clock synchronization
2009
This paper addresses the clock synchronization problem in a wireless sensor network (WSN) and proposes a distributed solution that consists of a form of consensus, where agents are able to exchange data representing intervals or sets. The solution is based on a centralized algorithm for clock synchronization, proposed by Marzullo, that determines the smallest interval that is in common with the maximum number of measured intervals. We first show how to convert such an algorithm into a problem involving only operations on sets, and then we convert it into a set–valued consensus. The solution is valid for more general scenarios where agents have uncertain measures of e.g. the position of an o…
Improving protein secondary structure predictions by prediction fusion
2009
Protein secondary structure prediction is still a challenging problem at today. Even if a number of prediction methods have been presented in the literature, the various prediction tools that are available on-line produce results whose quality is not always fully satisfactory. Therefore, a user has to know which predictor to use for a given protein to be analyzed. In this paper, we propose a server implementing a method to improve the accuracy in protein secondary structure prediction. The method is based on integrating the prediction results computed by some available on-line prediction tools to obtain a combined prediction of higher quality. Given an input protein p whose secondary struct…
A note on correlation and local dimensions
2015
Abstract Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.
One-Counter Verifiers for Decidable Languages
2013
Condon and Lipton (FOCS 1989) showed that the class of languages having a space-bounded interactive proof system (IPS) is a proper subset of decidable languages, where the verifier is a probabilistic Turing machine. In this paper, we show that if we use architecturally restricted verifiers instead of restricting the working memory, i.e. replacing the working tape(s) with a single counter, we can define some IPS’s for each decidable language. Such verifiers are called two-way probabilistic one-counter automata (2pca’s). Then, we show that by adding a fixed-size quantum memory to a 2pca, called a two-way one-counter automaton with quantum and classical states (2qcca), the protocol can be spac…