Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\Omega\left( \frac{n \log h}{\log \log h}\right)}$. This rules out the existence of a single-exponential algorithm and shows that the trivial upper bound $2^{{\mathcal O}(n\log{h})}$ is almost asymptotically tight. We also investigate what properties of graphs $G$ and $H$ make it difficult to solve HOM$(G,H)$. An easy observation is that an ${\mathcal O}(h^n)$ upper bound can be improved to ${\mathcal O}(h^{\operatorname{vc}(G)})$ where $\operatorname{vc}(G)$ is the minimum size of a vertex cover of $G$. The second lower bound $h^{\Omega(\operatorname{vc}(G))}$ shows that the upper bound is asymptotically tight. As to the properties of the "right-hand side" graph $H$, it is known that HOM$(G,H)$ can be solved in time $(f(\Delta(H)))^n$ and $(f(\operatorname{tw}(H)))^n$ where $\Delta(H)$ is the maximum degree of $H$ and $\operatorname{tw}(H)$ is the treewidth of $H$. This gives single-exponential algorithms for graphs of bounded maximum degree or bounded treewidth. Since the chromatic number $\chi(H)$ does not exceed $\operatorname{tw}(H)$ and $\Delta(H)+1$, it is natural to ask whether similar upper bounds with respect to $\chi(H)$ can be obtained. We provide a negative answer to this question by establishing a lower bound $(f(\chi(H)))^n$ for any function $f$. We also observe that similar lower bounds can be obtained for locally injective homomorphisms.Comment: 19 page

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

Contrôle exécutif, cognition sociale, émotions et métacognition

Cette synthèse aborde la question de la cognition sociale (théorie de l’esprit en particulier), du traitement des émotions et de la métacognition dans une perspective de neuropsychologie clinique. Nous nous attardons sur les études examinant les relations qu’entretiennent ces différents aspects du comportement humain avec les fonctions exécutives et les structures frontales. Les résultats rapportés montrent que les liens potentiels entre la théorie de l’esprit et le fonctionnement exécutif font encore beaucoup débat, et que l’étude des relations entre théorie de l’esprit et lobe frontal mérite d’être affinée. Les lésions frontales perturbent le traitement des émotions, mais les relations entre perturbation des fonctions exécutives et troubles du traitement des émotions restent inexplorées. La métacognition a été peu étudiée chez les patients dysexécutifs par lésions frontales, si ce n’est au travers de quelques études sur la métamémoire qui montrent que les patients frontaux ont globalement tendance à surestimer leurs performances. Cette surestimation ne semble pas nécessairement procéder d’un déficit exécutif, d’une incapacité de jugement, ni d’une méconnaissance du fonctionnement mnésique normal et pathologique. Il ne s’agit pas non plus d’une difficulté d’utilisation de connaissances. De plus, les différentes mesures métamnésiques obtenues chez les patients frontaux corrèlent peu entre elles, indiquant qu’elles engagent probablement des processus du contrôle métamnésique relativement indépendants qu’il conviendrait de spécifier. Enfin, il faudra aussi vérifier, avec des malades porteurs de lésions frontales et/ou de syndromes dysexécutifs, les propositions théoriques les plus récentes voulant que les concepts de théorie de l’esprit et de métacognition soient finalement assez proches

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

Pandemic Preparedness in the Live Performing Arts: Lessons to Learn from COVID-19 in the G7 Countries: Project Report

This is the final versionThis report publishes the findings of the British Academy-funded Pandemic Preparedness: Lessons to Learn from Covid-19 across the G7 project. Between April 2023 - January 2024, a UK-led research team with Co-Investigators in the USA, Canada and Germany and Research Associates in France, Italy and Japan examined the lessons learned from the responses of the live performing arts sector and governments to COVID-19 in the G7 countries. We focused our attention on policy interventions by governments and funders alongside the individual responses by workers in the live performing arts as well as organisations and their audiences. We further considered the impact of the pandemic on digital modes of working and disseminating creative content; how the pandemic affected communities, places and how ‘cultural value’ is understood; and what the pandemic revealed about systems and structures in the sector. The aim was to support sector preparedness for future crises, whether caused by new pandemics, climate-related disasters, demographic changes, economic pressures or the impacts on the live performing arts of national and international politics. This full report consists of detailed literature reviews of how the pandemic affected the performing arts sector in the United Kingdom, the USA, Canada and Germany; it also contains shorter literature reviews which focus on France, Italy and Japan. This research underpins the policy recommendations which are published in separate reports.British Academ

Prognostic significance of cortactin levels in head and neck squamous cell carcinoma: comparison with epidermal growth factor receptor status

Cortactin is an actin-binding Src substrate involved in cell motility and invasion. In this study, we sought to examine the prognostic importance of cortactin protein expression in head and neck squamous cell carcinoma (HNSCC). To do so, cortactin and EGF receptor (EGFR) expression was retrospectively evaluated by immunohistochemistry in a tissue microarray composed of 176 HNSCCs with a mean follow-up time of 5 years. Cortactin immunoreactivity was weak to absent in normal epithelial tissue. Overexpression of the protein in 77 out of 176 tumours (44%) was associated with more advanced tumour-node-metastasis stage and higher histologic grade. Cortactin overexpression was associated with significantly increased local recurrence rates (49 vs 28% for high and low expressing carcinomas, respectively), decreased disease-free survival (17 vs 61%), and decreased the 5-year overall survival of (21 vs 58%), independently of the EGFR status. In multivariate analysis, cortactin expression status remained an independent prognostic factor for local recurrence, disease-free survival, and overall survival. Importantly, we identified a subset of patients with cortactin-overexpressing tumours that displayed low EGFR levels and a survival rate that equalled that of patients with tumoral overexpression of both EGFR and cortactin. These findings identify cortactin as a relevant prognostic marker and may have implications for targeted therapies in patients with HNSCC

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