Minimum feedback vertex set and acyclic coloring

International audienceIn the feedback vertex set problem, the aim is to minimize, in a connected graph G =(V,E), the cardinality of the set overline(V) (G) \subseteq V , whose removal induces an acyclic subgraph. In this paper, we show an interesting relationship between the minimum feedback vertex set problem and the acyclic coloring problem (which consists in coloring vertices of a graph G such that no two colors induce a cycle in G). Then, using results from acyclic coloring, as well as other techniques, we are able to derive new lower and upper bounds on the cardinality of a minimum feedback vertex set in large families of graphs, such as graphs of maximum degree 3, of maximum degree 4, planar graphs, outerplanar graphs, 1-planar graphs, k-trees, etc. Some of these bounds are tight (outerplanar graphs, k-trees), all the others differ by a multiplicative constant never exceeding 2

Minimum feedback vertex set and acyclic coloring

International audienceIn the feedback vertex set problem, the aim is to minimize, in a connected graph G =(V,E), the cardinality of the set overline(V) (G) \subseteq V , whose removal induces an acyclic subgraph. In this paper, we show an interesting relationship between the minimum feedback vertex set problem and the acyclic coloring problem (which consists in coloring vertices of a graph G such that no two colors induce a cycle in G). Then, using results from acyclic coloring, as well as other techniques, we are able to derive new lower and upper bounds on the cardinality of a minimum feedback vertex set in large families of graphs, such as graphs of maximum degree 3, of maximum degree 4, planar graphs, outerplanar graphs, 1-planar graphs, k-trees, etc. Some of these bounds are tight (outerplanar graphs, k-trees), all the others differ by a multiplicative constant never exceeding 2

Machine learning techniques to identify putative genes involved in nitrogen catabolite repression in the yeast Saccharomyces cerevisiae

Nitrogen is an essential nutrient for all life forms. Like most unicellular organisms, the yeast Saccharomyces cerevisiae transports and catabolizes good nitrogen sources in preference to poor ones. Nitrogen catabolite repression (NCR) refers to this selection mechanism. All known nitrogen catabolite pathways are regulated by four regulators. The ultimate goal is to infer the complete nitrogen catabolite pathways. Bioinformatics approaches offer the possibility to identify putative NCR genes and to discard uninteresting genes.Journal Articleinfo:eu-repo/semantics/publishe

The Cult Statues of the Pantheon

This article reconsiders the possible statuary of the Pantheon in Rome, both in its original Augustan form and in its later phases. It argues that the so-called ‘Algiers Relief’ has wrongly been connected with the Temple of Mars Ultor and is in fact evidence of the association of the Divus Julius with Mars and Venus in the Pantheon of Agrippa, a juxtaposition which reflects the direction of Augustan ideology in the 20s b.c. and the building's celestial purpose. This triple statue group became the focus of the later Pantheon, and its importance is highlighted by the hierarchized system of architectural ornament of the present building

Genomic Relationships, Novel Loci, and Pleiotropic Mechanisms across Eight Psychiatric Disorders

Genetic influences on psychiatric disorders transcend diagnostic boundaries, suggesting substantial pleiotropy of contributing loci. However, the nature and mechanisms of these pleiotropic effects remain unclear. We performed analyses of 232,964 cases and 494,162 controls from genome-wide studies of anorexia nervosa, attention-deficit/hyper-activity disorder, autism spectrum disorder, bipolar disorder, major depression, obsessive-compulsive disorder, schizophrenia, and Tourette syndrome. Genetic correlation analyses revealed a meaningful structure within the eight disorders, identifying three groups of inter-related disorders. Meta-analysis across these eight disorders detected 109 loci associated with at least two psychiatric disorders, including 23 loci with pleiotropic effects on four or more disorders and 11 loci with antagonistic effects on multiple disorders. The pleiotropic loci are located within genes that show heightened expression in the brain throughout the lifespan, beginning prenatally in the second trimester, and play prominent roles in neurodevelopmental processes. These findings have important implications for psychiatric nosology, drug development, and risk prediction.Peer reviewe

Randomized feasibility trial of the Scleroderma patient-centered intervention network hand exercise program (SPIN-HAND): Study protocol

BACKGOUND: Significant functional impairment of the hands is nearly universal in systemic sclerosis (SSc, scleroderma). Hand exercises may improve hand function, but developing, testing and disseminating rehabilitation interventions in SSc is challenging. The Scleroderma Patient-centered Intervention Network (SPIN) was established to address this issue and has developed an online hand exercise program to improve hand function for SSc patients (SPIN-HAND). The aim of the proposed feasibility trial is to evaluate the feasibility of conducting a full-scale randomized controlled trial (RCT) of the SPIN-HAND intervention. DESIGN AND METHODS: The SPIN-HAND feasibility trial will be conducted via the SPIN Cohort. The SPIN Cohort was developed as a framework for embedded pragmatic trials using the cohort multiple RCT design. In total, 40 English-speaking SPIN Cohort participants with at least mild hand function limitations (Cochin Hand Function Scale ≥3) and an indicated interest in using an online hand-exercise intervention will be randomized with a 1:1 ratio to be offered to use the SPIN-HAND program or usual care for 3 months. The primary aim is to evaluate the trial implementation processes, required resources and management, scientific aspects, and participant acceptability and usage of the SPIN-HAND program. DISCUSSION: The SPIN-HAND exercise program is a self-help tool that may improve hand function in patients with SSc. The SPIN-HAND feasibility trial will ensure that trial methodology is robust, feasible, and consistent with trial participant expectations. The results will guide adjustments that need to be implemented before undertaking a full-scale RCT of the SPIN-HAND program. TRIAL REGISTRATION: ClinicalTrials.gov IDENTIFIER: NCT03092024

Acyclic and k-distance coloring of the grid

International audienceIn this paper, we give a relatively simple though very efficient way to color the d-dimensional grid G(n1, n2, . . . , nd ) (with ni vertices in each dimension 1 \leq i \leq d), for two different types of vertex colorings: (1) acyclic coloring of graphs, in which we color the vertices such that (i) no two neighbors are assigned the same color and (ii) for any two colors i and j, the subgraph induced by the vertices colored i or j is acyclic; and (2) k-distance coloring of graphs, in which every vertex must be colored in such a way that two vertices lying at distance less than or equal to k must be assigned different colors. The minimum number of colors needed to acyclically color (respectively k-distance color) a graph G is called acyclic chromatic number of G (respectively k-distance chromatic number), and denoted a(G) (respectively k(G)). The method we propose for coloring the d-dimensional grid in those two variants relies on the representation of the vertices of Gd (n1, . . . , nd ) thanks to its coordinates in each dimension; this gives us upper bounds on a(Gd (n1, . . . , nd )) and k(Gd (n1, . . . , nd )). We also give lower bounds on a(Gd (n1, . . . , nd )) and k(Gd (n1, . . . , nd )). In particular, we give a lower bound on a(G) for any graph G; surprisingly, as far as we know this result was never mentioned before. Applied to the d-dimensional grid Gd (n1, . . . , nd ), the lower and upper bounds for a(Gd (n1, . . . , nd )) match (and thus give an optimal result) when the lengths in each dimension are “sufficiently large” (more precisely, if sum_{i=1}^{d} (1/ni)\leq 1). If this is not the case, then these bounds differ by an additive constant at most equal to 1−⌊sum_{i=1}^{d} (1/ni)⌋. Concerning k(Gd (n1, . . . , nd )), we give exact results on its value for (1) k = 2 and any d \geq 1, and (2) d = 2 and any k \geq 1. In the case of acyclic coloring, we also apply our results to hypercubes of dimension d, Hd , which are a particular case of Gd (n1, . . . , nd ) in which there are only 2 vertices in each dimension. In that case, the bounds we obtain differ by a multiplicative constant equal to 2

Scattering by a two-dimensional doped photonic crystal presenting an optical Kerr-effect

International audienceThe purpose of this paper is to discuss two-dimensional electromagnetic diffraction by a finite set of parallel nonlinear rods (optical Kerr-effect). A new route for obtaining the scattered field by nonlinear obstacles is proposed