Almost spanning subgraphs of random graphs after adversarial edge removal

Let Delta>1 be a fixed integer. We show that the random graph G(n,p) with p>>(log n/n)^{1/Delta} is robust with respect to the containment of almost spanning bipartite graphs H with maximum degree Delta and sublinear bandwidth in the following sense: asymptotically almost surely, if an adversary deletes arbitrary edges in G(n,p) such that each vertex loses less than half of its neighbours, then the resulting graph still contains a copy of all such H.Comment: 46 pages, 6 figure

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996)

Local resilience and Hamiltonicity Maker-Breaker games in random-regular graphs

For an increasing monotone graph property \mP the \emph{local resilience} of a graph $G$ with respect to \mP is the minimal $r$ for which there exists of a subgraph $H\subseteq G$ with all degrees at most $r$ such that the removal of the edges of $H$ from $G$ creates a graph that does not possesses \mP. This notion, which was implicitly studied for some ad-hoc properties, was recently treated in a more systematic way in a paper by Sudakov and Vu. Most research conducted with respect to this distance notion focused on the Binomial random graph model \GNP and some families of pseudo-random graphs with respect to several graph properties such as containing a perfect matching and being Hamiltonian, to name a few. In this paper we continue to explore the local resilience notion, but turn our attention to random and pseudo-random \emph{regular} graphs of constant degree. We investigate the local resilience of the typical random $d$-regular graph with respect to edge and vertex connectivity, containing a perfect matching, and being Hamiltonian. In particular we prove that for every positive $\epsilon$ and large enough values of $d$ with high probability the local resilience of the random $d$-regular graph, \GND, with respect to being Hamiltonian is at least $(1-\epsilon)d/6$. We also prove that for the Binomial random graph model \GNP, for every positive $\epsilon>0$ and large enough values of $K$, if $p>\frac{K\ln n}{n}$ then with high probability the local resilience of \GNP with respect to being Hamiltonian is at least $(1-\epsilon)np/6$. Finally, we apply similar techniques to Positional Games and prove that if $d$ is large enough then with high probability a typical random $d$-regular graph $G$ is such that in the unbiased Maker-Breaker game played on the edges of $G$, Maker has a winning strategy to create a Hamilton cycle.Comment: 34 pages. 1 figur

Variations du volume pulmonaire au cours de la ventilation mécanique (modes ventilatoires et manœuvres positionnelles)

Le Syndrome de détresse respiratoire aiguë (SDRA) est une pathologie fréquente et grave. Son traitement fait appel à la ventilation mécanique qui est indispensable pour maintenir une oxygénation suffisante mais elle peut induire des lésions pulmonaires responsables d'une morbidité importante. Le volume pulmonaire est diminué au cours du SDRA ; sa mesure a longtemps été du domaine de la recherche clinique mais une technique de mesure au lit du patient a récemment été proposée : le lavage de l'azote. Ce travail avait pour but de tester la mesure du volume pulmonaire par la technique du lavage de l'azote dans des conditions d'utilisation comparables à celles du SDRA c'est à dire avec des niveaux de pression expiratoire positive (PEP) et de FiO2 élevés. Une fois cette étape préliminaire validée, nous avons utilisé la mesure du volume pulmonaire pour évaluer le recrutement induit par des réglages de PEP différents et lors de changements de position.Nous avons montré dans l'étude n1 que les mesures étaient suffisamment précises et reproductibles pour une utilisation clinique. La PEP et le niveau d'oxygénation influençaient peu les mesures. Dans l'étude n2, le recrutement induit par une PEP de type recrutement maximal réglée pour obtenir une pression de plateau (Pplat) entre 28 et 32 cmH2O, a été estimé à partir des mesures de volume pulmonaire comparées à l'augmentation minimale prédite du volume pulmonaire. Une bonne corrélation avec le recrutement mesuré par la technique des courbes pression - volume était trouvée sous réserve d'une élimination des mesures incohérentes.Parallèlement, la mesure du volume pulmonaire et l'oxygénation de patients en SDRA et Acute Lung Injury (ALI) ont été analysées lors de changements de position (Position demi-assise puis assise). Cette étude montre que le volume pulmonaire est augmenté lors de la verticalisation et particulièrement chez les patients augmentant leur oxygénation > 20%. Les patients ne répondant pas au positionnement avaient des volumes pulmonaires plus élevés et qui variaient peu.Les différents travaux réalisés ont permis de montrer la simplicité d'utilisation de la technique. Ceci offre des perspectives de recherche au lit du patient plus accessibles qu'avec les techniques de référence (scanner et dilution de l'hélium), et également des perspectives cliniques. Une approche de la déformation pulmonaire induite par la ventilation (strain) et potentiellement des lésions induites par la ventilation mécanique est rendue possible par la mise à disposition en clinique de cette technique.The acute respiratory distress syndrome (ARDS) is a frequent and severe form of acute respiratory failure. Mechanical ventilation is the cornerstone of treatment but it may induce a specific form of lung injury (Ventilator induced Lung Injury) responsible for superimposed morbidity and mortality. Lung volume is dramatically decreased during ARDS. Lung volume measurements remained limited to clinical research until recently when the nitrogen washout/washin technique has been adapted for bedside use and implemented in an intensive care ventilator. The aim of this work was to test the nitrogen washout/washin method in clinical conditions of ARDS treatment with high Positive End Expiratory Pressure (PEEP) and high oxygen fraction (FiO2). Once this preliminary validation study was realised, we used the technique to assess the amount of lung recruitment induced by PEEP and positioning.We showed in the first study that accuracy and reproducibility of the technique were acceptable. PEEP and FiO2 had a minor influence on measurements. In the second study, the recruitment induced by a maximal recruitment PEEP set to obtain a plateau pressure between 28-32 cmH2O has been estimated using end-expiratory lung volume (EELV) measurements. A significant correlation was found between the recruitment measured on Pressure/Volume curves and the recruitment estimated comparing the predicted minimal increase in lung volume and the true increase in EELV.In a third study, we have evaluated the concomitant effects of verticalization on EELV and oxygenation following a change from supine to semi recumbent, seated and back to supine position. In this third study, verticalization (seated position) resulted in a significant concomitant increase in lung volume and oxygenation. Interestingly, patients responding to verticalization had lower EELV at baseline than non-responders. Only the group of patients increasing their PaO2/FiO2>20% during verticalization had a significant increase in their EELV compared to non-responders.These three studies confirmed the feasibility of the technique, easier than the gold standard techniques (helium dilution or CT scan), and offering both research and clinical perspectives. This technique should also allow an easier approach of the strain induced by ventilation and assess the risk of ventilation induced lung injury.PARIS-EST-Université (770839901) / SudocPARIS12-Bib. électronique (940280011) / SudocSudocFranceF

Intrapulmonary percussive ventilation superimposed on spontaneous breathing: a physiological study in patients at risk for extubation failure

Purpose: Intrapulmonary percussive ventilation (IPV) is a high-frequency ventilation modality that can be superimposed on spontaneous breathing. IPV may diminish respiratory muscle loading and help to mobilize secretions. The aim of this prospective study was to assess the short-term effects of IPV in patients at high risk for extubation failure who were receiving preventive non-invasive ventilation (NIV) after extubation. Methods: Respiratory rate, work of breathing, and gas exchange were evaluated in 17 extubated patients during 20min of IPV and 20min of NIV delivered via a facial mask, separated by periods of spontaneous breathing. The pressure-support level during NIV was adjusted until tidal volume reached 6-8ml/kg and positive end-expiratory pressure (PEEP) 4-5cmH2O. For IPV, the pressurisation frequency was set at 250cycles/min and driving pressure at 1.2bar. The pressure-time product of the diaphragm (PTPdi/min) was measured using an oesophageal and gastric double-balloon catheter. Results: Transdiaphragmatic pressure and PTPdi/min improved significantly (p<0.01), from a median [25th-75th percentiles] of 264 [190-300] to 192 [152-221]cmH2Os/min with IPV and from 273 [212-397] to 176 [120-216]cmH2Os/min with NIV. Respiratory rate decreased significantly from 23 [19-27] to 22 [17-24] breaths/min for IPV and from 25 [19-28] to 20 [18-22] breaths/min for NIV (p<0.01). Mean PaCO2 decreased after NIV (from 46 [42-48] to 41 [36-42]mmHg, p<0.01) but not after IPV. There was no noticeable effect on oxygenation. Conclusions: IPV is an interesting alternative to NIV in patients at risk for post-extubation respiratory failure. Both NIV and IPV diminished the respiratory rate and work of breathing, but IPV was less effective in improving alveolar ventilatio

Powers of Hamilton cycles in pseudorandom graphs

We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph $G$ is $(\varepsilon,p,k,\ell)$-pseudorandom if for all disjoint $X$ and $Y\subset V(G)$ with $|X|\ge\varepsilon p^kn$ and $|Y|\ge\varepsilon p^\ell n$ we have $e(X,Y)=(1\pm\varepsilon)p|X||Y|$. We prove that for all $\beta>0$ there is an $\varepsilon>0$ such that an $(\varepsilon,p,1,2)$-pseudorandom graph on $n$ vertices with minimum degree at least $\beta pn$ contains the square of a Hamilton cycle. In particular, this implies that $(n,d,\lambda)$-graphs with $\lambda\ll d^{5/2 }n^{-3/2}$ contain the square of a Hamilton cycle, and thus a triangle factor if $n$ is a multiple of $3$. This improves on a result of Krivelevich, Sudakov and Szab\'o [Triangle factors in sparse pseudo-random graphs, Combinatorica 24 (2004), no. 3, 403--426]. We also extend our result to higher powers of Hamilton cycles and establish corresponding counting versions.Comment: 30 pages, 1 figur

UM NOVO OLHAR SOBRE AS ESCOLAS DE EDUCAÇÃO INFANTIL EM TEMPO INTEGRAL: EXPERIÊNCIAS DE GESTÃO PARTICIPATIVA EM UM SISTEMA MUNICIPAL

Relata-se uma experiência de gestão educacional em um sistema municipal, relacionada à educação infantil em tempo integral. A partir da escuta sensível das crianças, percebeu-se a necessidade de uma abordagem gestionária que levasse em conta as peculiaridades e responsabilidades sociais da escola e das famílias envolvidas. Os dados disponíveis foram obtidos por pesquisa documental e pela observação informal praticada pelos autores. A permanência da criança na escola por mais de dez horas diárias, além de não garantir o direito à convivência familiar, não corresponderia necessariamente à qualidade na educação integral. Por isso, foi proposto um modelo de redução da carga horária nas escolas, sem ferir a legislação ou prejudicar as demandas familiares. Os resultados proporcionaram conquistas para alunos, famílias e as escolas municipais. Palavras-chave: Educação Infantil. Gestão escolar. Educação em tempo integral