Paired and semipaired domination in triangulations

A dominating set of a graph $G$ is a subset $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$. A dominating set $D$ is paired if the subgraph induced by its vertices has a perfect matching, and semipaired if every vertex in $D$ is paired with exactly one other vertex in $D$ that is within distance 2 from it. The paired domination number, denoted by $\gamma_{pr}(G)$, is the minimum cardinality of a paired dominating set of $G$, and the semipaired domination number, denoted by $\gamma_{pr2}(G)$, is the minimum cardinality of a semipaired dominating set of $G$. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that $\gamma_{pr}(G) \le 2 \lfloor \frac{n}{4} \rfloor$ for any near-triangulation $G$ of order $n\ge 4$, and that with some exceptions, $\gamma_{pr2}(G) \le \lfloor \frac{2n}{5} \rfloor$ for any near-triangulation $G$ of order $n\ge 5$

Metric Dimension of Maximal Outerplanar Graphs

In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if β(G) denotes the metric dimension of a maximal outerplanar graph G of order n, we prove that 2≤β(G)≤⌈2n5⌉ and that the bounds are tight. We also provide linear algorithms to decide whether the metric dimension of G is 2 and to build a resolving set S of size ⌈2n5⌉ for G. Moreover, we characterize all maximal outerplanar graphs with metric dimension 2

Searching edges in the overlap of two plane graphs

Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that enables efficient searches among the red-blue intersections along edges of one of the graphs. Our technique has a number of applications to geometric problems. This includes: (1) a solution to the batched red-blue search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an algorithm to compute the maximum vertical distance between a pair of 3D polyhedral terrains one of which is convex in O(n log n) time, where n is the total complexity of both terrains; (3) an algorithm to construct the Hausdorff Voronoi diagram of a family of point clusters in the plane in O((n+m) log^3 n) time and O(n+m) space, where n is the total number of points in all clusters and m is the number of crossings between all clusters; (4) an algorithm to construct the farthest-color Voronoi diagram of the corners of n axis-aligned rectangles in O(n log^2 n) time; (5) an algorithm to solve the stabbing circle problem for n parallel line segments in the plane in optimal O(n log n) time. All these results are new or improve on the best known algorithms.Comment: 22 pages, 6 figure

Neotectonic processes in marine terrace sediments near Canero (Western Asturias)

The Pleistocene sediments deposited on the emerged marine abrasion platform near Canero village (Valdés, Asturias) are truncated by reverse faults which are parallel to basement bedding. These structures imply a neotectonic activity with a NW-SE maximum compressive stress, consistent with recent fault population analysis and current seismicity studies. The described deformation corresponds to a reactivation of folds in the Palaeozoic basement through a flexural slip mechanism, with the subsequent accommodation of the unconformable Pleistocene cove

Problemes de Grafs

2012/201

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

Stabbing Segments with Rectilinear Objects

Given a set of n line segments in the plane, we say that a region R of the plane is a stabber if R contains exactly one end point of each segment of the set. In this paper we provide efficient algorithms for determining wheter or not a stabber exists for several shapes of stabbers. Specially, we consider the case in which the stabber can be described as the intersecction of isothetic halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). We provided efficient algorithms reporting all combinatorially different stabbers of the shape. The algorithms run in O(n) time (for the halfplane case), O(n logn) time (for strips and quadrants), O(n^2) (for 3-sided rectangles), or O(n^3) time (for rectangles).Postprint (published version

Clinical, methodology, and patient/carer expert advice in pediatric drug development by conect4children.

Many medicines are used "off-label" in children outside the terms of the license. Feasible pediatric clinical trials are a challenge to design. Conect4children (c4c) is an Innovative Medicines Initiative project to set up a pan-European pediatric clinical trial network aiming to facilitate the development of new medicines for children. To optimize pediatric trial development by promoting innovative trial design, c4c set up a European multidisciplinary advice service, including the voice of young patients and families, tailored to industry and academia. A network of experts was established to provide multidisciplinary advice to trial sponsors. Experts were selected to join clinical and innovative methodology expert groups. A patient and public involvement (PPI) database, to include the expert opinion of patients and parents/carers was formed. A stepwise process was developed: (1) sponsors contact c4c, (2) scoping interview takes place, (3) ad hoc advice group formed, (5) advice meeting held, and (6) advice report provided. Feedback on the process was collected. Twenty-four clinical and innovative methodology expert groups (>400 experts) and a PPI database of 135 registrants were established. As of September 30, 2022, 36 advice requests were received, with 25 requests completed. Clinical and methodology experts and PPI representatives participated in several advice requests. Sponsors appreciated the advice quality and the multidisciplinary experts from different countries, including experts not known before. Experts and PPI participants were generally satisfied with the process. The c4c project has shown successful proof of concept for a service that presents a new framework to plan innovative and feasible pediatric trials

The Positive Rhinovirus/Enterovirus Detection and SARS-CoV-2 Persistence beyond the Acute Infection Phase: An Intra-Household Surveillance Study.

We aimed to assess the duration of nasopharyngeal severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA persistence in adults self-confined at home after acute infection; and to identify the associations of SARS-CoV-2 persistence with respiratory virus co-detection and infection transmission. A cross-sectional intra-household study was conducted in metropolitan Barcelona (Spain) during the time period of April to June 2020. Every adult who was the first family member reported as SARS-CoV-2-positive by reverse transcription polymerase chain reaction (RT-PCR) as well as their household child contacts had nasopharyngeal swabs tested by a targeted SARS-CoV-2 RT-PCR and a multiplex viral respiratory panel after a 15 day minimum time lag. Four-hundred and four households (404 adults and 708 children) were enrolled. SARS-CoV-2 RNA was detected in 137 (33.9%) adults and 84 (11.9%) children. Rhinovirus/Enterovirus (RV/EV) was commonly found (83.3%) in co-infection with SARS-CoV-2 in adults. The mean duration of SARS-CoV-2 RNA presence in adults' nasopharynx was 52 days (range 26-83 days). The persistence of SARS-CoV-2 was significantly associated with RV/EV co-infection (adjusted odds ratio (aOR) 9.31; 95% CI 2.57-33.80) and SARS-CoV-2 detection in child contacts (aOR 2.08; 95% CI 1.24-3.51). Prolonged nasopharyngeal SARS-CoV-2 RNA persistence beyond the acute infection phase was frequent in adults quarantined at home during the first epidemic wave; which was associated with RV/EV co-infection and could enhance intra-household infection transmission