TREEWIDTH and PATHWIDTH parameterized by vertex cover

After the number of vertices, Vertex Cover is the largest of the classical graph parameters and has more and more frequently been used as a separate parameter in parameterized problems, including problems that are not directly related to the Vertex Cover. Here we consider the TREEWIDTH and PATHWIDTH problems parameterized by k, the size of a minimum vertex cover of the input graph. We show that the PATHWIDTH and TREEWIDTH can be computed in O*(3^k) time. This complements recent polynomial kernel results for TREEWIDTH and PATHWIDTH parameterized by the Vertex Cover

Reactivity tests for supplementary cementitious materials: RILEM TC 267-TRM phase 1

A primary aim of RILEM TC 267-TRM: “Tests for Reactivity of Supplementary Cementitious Materials (SCMs)” is to compare and evaluate the performance of conventional and novel SCM reactivity test methods across a wide range of SCMs. To this purpose, a round robin campaign was organized to investigate 10 different tests for reactivity and 11 SCMs covering the main classes of materials in use, such as granulated blast furnace slag, fly ash, natural pozzolan and calcined clays. The methods were evaluated based on the correlation to the 28 days relative compressive strength of standard mortar bars containing 30% of SCM as cement replacement and the interlaboratory reproducibility of the test results. It was found that only a few test methods showed acceptable correlation to the 28 days relative strength over the whole range of SCMs. The methods that showed the best reproducibility and gave good correlations used the R3 model system of the SCM and Ca(OH)2, supplemented with alkali sulfate/carbonate. The use of this simplified model system isolates the reaction of the SCM and the reactivity can be easily quantified from the heat release or bound water content. Later age (90 days) strength results also correlated well with the results of the IS 1727 (Indian standard) reactivity test, an accelerated strength test using an SCM/Ca(OH)2-based model system. The current standardized tests did not show acceptable correlations across all SCMs, although they performed better when latently hydraulic materials (blast furnace slag) were excluded. However, the Frattini test, Chapelle and modified Chapelle test showed poor interlaboratory reproducibility, demonstrating experimental difficulties. The TC 267-TRM will pursue the development of test protocols based on the R3 model systems. Acceleration and improvement of the reproducibility of the IS 1727 test will be attempted as well

Discovery of common and rare genetic risk variants for colorectal cancer.

To further dissect the genetic architecture of colorectal cancer (CRC), we performed whole-genome sequencing of 1,439 cases and 720 controls, imputed discovered sequence variants and Haplotype Reference Consortium panel variants into genome-wide association study data, and tested for association in 34,869 cases and 29,051 controls. Findings were followed up in an additional 23,262 cases and 38,296 controls. We discovered a strongly protective 0.3% frequency variant signal at CHD1. In a combined meta-analysis of 125,478 individuals, we identified 40 new independent signals at P < 5 × 10-8, bringing the number of known independent signals for CRC to ~100. New signals implicate lower-frequency variants, Krüppel-like factors, Hedgehog signaling, Hippo-YAP signaling, long noncoding RNAs and somatic drivers, and support a role for immune function. Heritability analyses suggest that CRC risk is highly polygenic, and larger, more comprehensive studies enabling rare variant analysis will improve understanding of biology underlying this risk and influence personalized screening strategies and drug development.Goncalo R Abecasis has received compensation from 23andMe and Helix. He is currently an employee of Regeneron Pharmaceuticals. Heather Hampel performs collaborative research with Ambry Genetics, InVitae Genetics, and Myriad Genetic Laboratories, Inc., is on the scientific advisory board for InVitae Genetics and Genome Medical, and has stock in Genome Medical. Rachel Pearlman has participated in collaborative funded research with Myriad Genetics Laboratories and Invitae Genetics but has no financial competitive interest

Extracorporeal Membrane Oxygenation for Severe Acute Respiratory Distress Syndrome associated with COVID-19: An Emulated Target Trial Analysis.

RATIONALE: Whether COVID patients may benefit from extracorporeal membrane oxygenation (ECMO) compared with conventional invasive mechanical ventilation (IMV) remains unknown. OBJECTIVES: To estimate the effect of ECMO on 90-Day mortality vs IMV only Methods: Among 4,244 critically ill adult patients with COVID-19 included in a multicenter cohort study, we emulated a target trial comparing the treatment strategies of initiating ECMO vs. no ECMO within 7 days of IMV in patients with severe acute respiratory distress syndrome (PaO2/FiO2 <80 or PaCO2 ≥60 mmHg). We controlled for confounding using a multivariable Cox model based on predefined variables. MAIN RESULTS: 1,235 patients met the full eligibility criteria for the emulated trial, among whom 164 patients initiated ECMO. The ECMO strategy had a higher survival probability at Day-7 from the onset of eligibility criteria (87% vs 83%, risk difference: 4%, 95% CI 0;9%) which decreased during follow-up (survival at Day-90: 63% vs 65%, risk difference: -2%, 95% CI -10;5%). However, ECMO was associated with higher survival when performed in high-volume ECMO centers or in regions where a specific ECMO network organization was set up to handle high demand, and when initiated within the first 4 days of MV and in profoundly hypoxemic patients. CONCLUSIONS: In an emulated trial based on a nationwide COVID-19 cohort, we found differential survival over time of an ECMO compared with a no-ECMO strategy. However, ECMO was consistently associated with better outcomes when performed in high-volume centers and in regions with ECMO capacities specifically organized to handle high demand. This article is open access and distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives License 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Décompositions de graphes : quelques limites et obstructions

Graphs decompositions of small width are usually used to solve efficiently problems which are difficult in general. In this thesis, we focus on some limits of these decompositions, and the construction of some obstructions certifying a large width. First, we give a generic algorithm unifying obstructions' construction for several graph widths, in XP time when parameterized by the considered width. In particular, it gives the first algorithm computing efficiently an obstruction to tree-width in time O^{tw+4}. Secondly, we study the parameterized complexity of [Sigma,Rho]-Dominating Set, a generalization of some domination problems characterized by two sets of integers Sigma and Rho. All known studies focused only on cases where this problem is FPT when parameterized by tree-width. In this work, we show that there are some cases where the problem is no longer FPT, and become W[1]-hard instead. Finally, we study the computational complexity of a new coloration problem, named k-Additive Coloring, which combines both graph theory and number theory. We show that this new problem is NP-complete for any fixed number k >= 4, while it can be solved in polynomial time on trees for any k.Les décompositions de graphes, lorsqu'elles sont de petite largeur, sont souvent utilisées pour résoudre plus efficacement des problèmes étant difficiles dans le cas de graphes quelconques. Dans ce travail de thèse, nous nous intéressons aux limites liées à ces décompositions, et à la construction d'obstructions certifiant leur grande largeur. Dans une première partie, nous donnons un algorithme généralisant et unifiant la construction d'obstructions pour différentes largeurs de graphes, en temps XP lorsque paramétré par la largeur considérée. Nous obtenons en particulier le premier algorithme permettant de construire efficacement une obstruction à la largeur arborescente en temps O^{tw+4}. La seconde partie de notre travail porte sur l'étude du problème Ensemble [Sigma,Rho]-Dominant, une généralisation des problèmes de domination sur les graphes et caractérisée par deux ensembles d'entiers Sigma et Rho. Les diverses études de ce problème apparaissant dans la littérature concernent uniquement les cas où le problème est FPT, lorsque paramétré par la largeur arborescente. Nous montrons que ce problème ne l'est pas toujours, et que pour certains cas d'ensembles Sigma et Rho, il devient W[1]-difficile lorsque paramétré par la largeur arborescente. Dans la dernière partie, nous étudions la complexité d'un nouveau problème de coloration appelé k-Coloration Additive, combinant théorie des graphes et théorie des nombres. Nous montrons que ce nouveau problème est NP-complet pour tout k >= 4 fixé, tandis qu'il peut être résolu en temps polynomial sur les arbres pour k quelconque et non fixé

Graphs decompositions : some limits and obstructions

Les décompositions de graphes, lorsqu’elles sont de petite largeur, sont souvent utilisées pour résoudre plus efficacement des problèmes étant difficiles dans le cas de graphes quelconques. Dans ce travail de thèse, nous nous intéressons aux limites liées à ces décompositions, et à la construction d’obstructions certifiant leur grande largeur. Dans une première partie, nous donnons un algorithme généralisant et unifiant la construction d’obstructions pour différentes largeurs de graphes, en temps XP lorsque paramétré par la largeur considérée. Nous obtenons en particulier le premier algorithme permettant de construire efficacement une obstruction à la largeur arborescente en temps O(ntw+4). La seconde partie de notre travail porte sur l’étude du problème ENSEMBLE [σ, ρ]-DOMINANT, une généralisation des problèmes de domination sur les graphes et caractérisée par deux ensembles d’entiers σ et ρ. Les diverses études de ce problème apparaissant dans la littérature concernent uniquement les cas ou le problème est FPT, lorsque paramétré par la largeur arborescente. Nous montrons que ce problème ne l’est pas toujours, et que pour certains cas d’ensembles σ et ρ, il devient W[1]-difficile lorsque paramétré par la largeur arborescente. Dans la dernière partie, nous étudions la complexité d’un nouveau problème de coloration appelé k-COLORATION ADDITIVE, combinant théorie des graphes et théorie des nombres. Nous montrons que ce nouveau problème est NP-complet pour tout k ≥ 4 fixé, tandis qu’il peut être résolu en temps polynomial sur les arbres pour k quelconque et non fixé.Graphs decompositions of small width are usually used to solve efficiently problems which are difficult in general. In this thesis, we focus on some limits of these decompositions, and the construction of some obstructions certifying a large width. First, we give a generic algorithm unifying obstructions’ construction for several graph widths, in XP time when parameterized by the considered width. In particular, it gives the first algorithm computing efficiently an obstruction to tree-width in time O(ntw+4). Secondly, we study the parameterized complexity of [σ, ρ]-DOMINATING SET, a generalization of some domination problems characterized by two sets of integers σ and ρ. All known studies focused only on cases where this problem is FPT when parameterized by tree-width. In this work, we show that there are some cases where the problem is no longer FPT, and become W[1]-hard instead. Finally, we study the computational complexity of a new coloration problem, named k-ADDITIVE COLORING, which combines both graph theory and number theory. We show that this new problem is NP-complete for any fixed number k ≥ 4, while it can be solved in polynomial time on trees for any k

Décompositions de graphes (quelques limites et obstructions)

Les décompositions de graphes, lorsqu elles sont de petite largeur, sont souvent utilisées pour résoudre plus efficacement des problèmes étant difficiles dans le cas de graphes quelconques. Dans ce travail de thèse, nous nous intéressons aux limites liées à ces décompositions, et à la construction d obstructions certifiant leur grande largeur. Dans une première partie, nous donnons un algorithme généralisant et unifiant la construction d obstructions pour différentes largeurs de graphes, en temps XP lorsque paramétré par la largeur considérée. Nous obtenons en particulier le premier algorithme permettant de construire efficacement une obstruction à la largeur arborescente en temps O(ntw+4). La seconde partie de notre travail porte sur l étude du problème ENSEMBLE [ , ]-DOMINANT, une généralisation des problèmes de domination sur les graphes et caractérisée par deux ensembles d entiers et . Les diverses études de ce problème apparaissant dans la littérature concernent uniquement les cas ou le problème est FPT, lorsque paramétré par la largeur arborescente. Nous montrons que ce problème ne l est pas toujours, et que pour certains cas d ensembles et , il devient W[1]-difficile lorsque paramétré par la largeur arborescente. Dans la dernière partie, nous étudions la complexité d un nouveau problème de coloration appelé k-COLORATION ADDITIVE, combinant théorie des graphes et théorie des nombres. Nous montrons que ce nouveau problème est NP-complet pour tout k >= 4 fixé, tandis qu il peut être résolu en temps polynomial sur les arbres pour k quelconque et non fixé.Graphs decompositions of small width are usually used to solve efficiently problems which are difficult in general. In this thesis, we focus on some limits of these decompositions, and the construction of some obstructions certifying a large width. First, we give a generic algorithm unifying obstructions construction for several graph widths, in XP time when parameterized by the considered width. In particular, it gives the first algorithm computing efficiently an obstruction to tree-width in time O(ntw+4). Secondly, we study the parameterized complexity of [ , ]-DOMINATING SET, a generalization of some domination problems characterized by two sets of integers and . All known studies focused only on cases where this problem is FPT when parameterized by tree-width. In this work, we show that there are some cases where the problem is no longer FPT, and become W[1]-hard instead. Finally, we study the computational complexity of a new coloration problem, named k-ADDITIVE COLORING, which combines both graph theory and number theory. We show that this new problem is NP-complete for any fixed number k >= 4, while it can be solved in polynomial time on trees for any k.ORLEANS-SCD-Bib. electronique (452349901) / SudocSudocFranceF

Treewidth and Pathwidth parameterized by the vertex cover number

International audienc

Constructing brambles

Given an arbitrary graph G and a number k, it is well-known by a result of Seymour and Thomas [20] that G has treewidth strictly larger than k if and only if it has a bramble of order k + 2. Brambles are used in combinatorics as certi cates proving that the treewidth of a graph is large. From an algorithmic point of view there are several algorithms computing tree-decompositions of G of width at most k, if such decompositions exist and the running time is polynomial for constant k. Nevertheless, when the treewidth of the input graph is larger than k, to our knowledge there is no algorithm constructing a bramble of order k + 2. We give here such an algorithm, running in O(n k+4) time. Moreover, for classes of graphs with polynomial number of minimal separators, we de ne a notion of compact brambles and show how to compute compact brambles of order k + 2 in polynomial time, not depending on k