b-coloring is NP-hard on co-bipartite graphs and polytime solvable on tree-cographs

A b-coloring of a graph is a proper coloring such that every color class contains a vertex that is adjacent to all other color classes. The b-chromatic number of a graph G, denoted by \chi_b(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is called b-continuous if it admits a b-coloring with t colors, for every t = \chi(G),\ldots,\chi_b(G), and b-monotonic if \chi_b(H_1) \geq \chi_b(H_2) for every induced subgraph H_1 of G, and every induced subgraph H_2 of H_1. We investigate the b-chromatic number of graphs with stability number two. These are exactly the complements of triangle-free graphs, thus including all complements of bipartite graphs. The main results of this work are the following: - We characterize the b-colorings of a graph with stability number two in terms of matchings with no augmenting paths of length one or three. We derive that graphs with stability number two are b-continuous and b-monotonic. - We prove that it is NP-complete to decide whether the b-chromatic number of co-bipartite graph is at most a given threshold. - We describe a polynomial time dynamic programming algorithm to compute the b-chromatic number of co-trees. - Extending several previous results, we show that there is a polynomial time dynamic programming algorithm for computing the b-chromatic number of tree-cographs. Moreover, we show that tree-cographs are b-continuous and b-monotonic

Etude Clinique des niveaux de perturbation de la metacognition, de la cognition sociale et du contrôle exécutif dans la pathologie frontale

Recent and convergent studies in neuropsychology have suggested the importance of frontal regions to the integrity of a number of functions such as metamemory capacities, executive functions, and social skills (Theory of Mind : ToM). In this original work, following Stuss et Anderson (2004), we assume a link between disturbances of these functions. We proposed to 16 frontal patients and 20 matched healthy subjects a protocol designed to test metamemory, ToM and executive functions in order to analyze the relations between disturbances of self-awareness (metamemory) and awareness of others (ToM), and cognitive control (executive functions). Our results confirm the importance of frontal lobes on these capacities. No correlation was found between measures of metamemory, measures of ToM and executive scores. The observation of individual profiles emphasizes the existence of dissociations between self awareness and consciousness of the others, and between these two forms of metacognitive control and the executive functioning. These results confirm the importance to engage more studies combining aspects of ToM, metacognition and executive control, to better understand the organization and architecture of the functions supported by frontal lobe

Nonlinear Rheology of Unentangled Polymer Melts Reinforced with High Concentration of Rigid Nanoparticles

A scaling model is presented to analyze the nonlinear rheology of unentangled polymer melts filled with high concentration of small spherical particles. Assuming the majority of chains to be reversibly adsorbed to the surface of the particles, we show that the emergence of nonlinearity in the viscoelastic response of the composite system subjected to a 2D shear flow results from stretching of the adsorbed chains and increasing desorption rate of the adsorbed segments due to the imposed deformation. The steady-state shear viscosity of the mixture in nonlinear shear thinning regime follows the power lawwhereis the applied shear rate. At large strain amplitude γ 0, the storage and loss moduli in strain sweep tests scale asandrespectively

Contraception and screening for cervical and breast cancer in neuromuscular disease: A retrospective study of 50 patients monitored at a clinical reference centre

AbstractObjectiveTo analyse contraceptive methods and the extent of screening for breast and cervical cancer in women with neuromuscular disease, compare these results with data and guidelines for the general population and determine the environmental and attitudinal barriers encountered.Patients and methodsA retrospective, descriptive study in a population of female neuromuscular disease patients (aged 20 to 74) monitored at a clinical reference centre.ResultsComplete datasets were available for 49 patients. Seventy percent used contraception (hormonal contraception in most cases). Sixty-eight percent had undergone screening for cervical cancer at some time in the previous 3 years and 100% of the patients over 50 had undergone a mammography. Architectural accessibility and practical problems were the most common barriers to care and were more frequently encountered by wheelchair-bound, ventilated patients.ConclusionsIn general, the patients had good access to contraceptive care and cervical and breast cancer screening. However, specific measures may be useful for the most severely disabled patients

Bilingualism and adult differences in inhibitory mechanisms: Evidence from a bilingual stroop task

The present investigation examined the functioning of inhibitory mechanisms in younger and older bilinguals using a bilingual version of the Stroop test. The study predicted different patterns of age related decline in inhibitory mechanisms (inter- and intralingual interference) in bilinguals depending on their level of proficiency. Consistent with expectations, older bilinguals were slower when they responded in their non-dominant language. Furthermore, older unbalanced bilinguals showed greater interlingual interference when they responded with their second language to visual stimuli written in their dominant language. Balanced bilinguals showed equivalent interference effects between all conditions. These findings suggest that manipulating two languages may enhance the efficiency of inhibitory mechanisms

Surgical care for the direct and indirect victims of violence in the eastern Democratic Republic of Congo

ABSTRACT: BACKGROUND: The provision of surgical assistance in conflict is often associated with care for victims of violence. However, there is an increasing appreciation that surgical care is needed for non-traumatic morbidities. In this paper we report on surgical interventions carried out by Medecins sans Frontieres in Masisi, North Kivu, Democratic Republic of Congo to contribute to the scarce evidence base on surgical needs in conflict. METHODS: We analysed data on all surgical interventions done at Masisi district hospital between September 2007 to December 2009. Types of interventions are described, and logistic regression used to model associations with violence-related injury. RESULTS: 2869 operations were performed on 2441 patients. Obstetric emergencies accounted for over half (675, 57%) of all surgical pathology and infections for another quarter (160, 14%). Trauma-related injuries accounted for only one quarter (681, 24%) of all interventions; among these, 363 (13%) were violence-related. Male gender (adjusted odds ratio (AOR)=20.0, p<0.001), military status (AOR=4.1, p<0.001), and age less than 20 years (AOR=2.1, p<0.001) were associated with violence-related injury. Immediate peri-operative mortality was 0.2%. CONCLUSIONS: In this study, most surgical interventions were unrelated to violent trauma and rather reflected the general surgical needs of a low-income tropical country. Programs in conflict zones in low-income countries need to be prepared to treat both the war-wounded and non-trauma related life-threatening surgical needs of the general population. Given the limited surgical workforce in these areas, training of local staff and task shifting is recommended to support broad availability of essential surgical care. Further studies into the surgical needs of the population are warranted, including population-based surveys to improve program planning and resource allocation and the effectiveness of the humanitarian response

A Unified Approach to Distance-Two Colouring of Graphs on Surfaces

In this paper we introduce the notion of $\Sigma$-colouring of a graph $G$: For given subsets $\Sigma(v)$ of neighbours of $v$, for every $v\in V(G)$, this is a proper colouring of the vertices of $G$ such that, in addition, vertices that appear together in some $\Sigma(v)$ receive different colours. This concept generalises the notion of colouring the square of graphs and of cyclic colouring of graphs embedded in a surface. We prove a general result for graphs embeddable in a fixed surface, which implies asymptotic versions of Wegner's and Borodin's Conjecture on the planar version of these two colourings. Using a recent approach of Havet et al., we reduce the problem to edge-colouring of multigraphs, and then use Kahn's result that the list chromatic index is close to the fractional chromatic index. Our results are based on a strong structural lemma for graphs embeddable in a fixed surface, which also implies that the size of a clique in the square of a graph of maximum degree $\Delta$ embeddable in some fixed surface is at most $\frac32\,\Delta$ plus a constant.Comment: 36 page

Nonrepetitive Colouring via Entropy Compression

A vertex colouring of a graph is \emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\Delta$ is $c\Delta^2$-choosable, for some constant $c$. We prove this result with $c=1$ (ignoring lower order terms). We then prove that every subdivision of a graph with sufficiently many division vertices per edge is nonrepetitively 5-choosable. The proofs of both these results are based on the Moser-Tardos entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek for the nonrepetitive choosability of paths. Finally, we prove that every graph with pathwidth $k$ is nonrepetitively $O(k^{2})$-colourable.Comment: v4: Minor changes made following helpful comments by the referee