Random @math -intersection graphs have recently received much interest in a wide range of application areas. Broadly speaking, a random @math -intersection graph is constructed by first assigning each vertex a set of items in some random manner, and then putting an undirected edge between all pairs of vertices that share at least @math items (the graph is called a random intersection graph when @math ). A special case of particular interest is a uniform random @math -intersection graph, where each vertex independently selects the same number of items uniformly at random from a common item pool. Another important case is a binomial random @math -intersection graph, where each item from a pool is independently assigned to each vertex with the same probability. Both models have found numerous applications thus far including cryptanalysis, and the modeling of recommender systems, secure sensor networks, online social networks, trust networks and small-world networks (uniform random @math -intersection graphs), as well as clustering analysis, classification, and the design of integrated circuits (binomial random @math -intersection graphs). In this paper, for binomial uniform random @math -intersection graphs, we present results related to @math -connectivity and minimum vertex degree. Specifically, we derive the asymptotically exact probabilities and zero-one laws for the following three properties: (i) @math -vertex-connectivity, (ii) @math -edge-connectivity and (iii) the property of minimum vertex degree being at least @math .
& 3 * -1.5pt @math -1.5pt & 2 * & 2 * -1.5pt exact probabilities -1.5pt & -1.5pt 5-5 & & & & 3-5 & & & -1.5pt exact probabilities & 2-5 & 4 * -1.5pt @math -1.5pt & 2 * & -1.5pt exact probabilities -1.5pt & -1.5pt @cite_22 4-5 & & & -1.5pt zero--one laws & -1.5pt @cite_35 @cite_5 3-5 & & 2 * & -1.5pt exact probabilities -1.5pt & -1.5pt @cite_18 4-5 & & & -1.5pt zero--one laws & -1.5pt @cite_16 @cite_29 8 * & 4 * -1.5pt @math -1.5pt & 2 * & -1.5pt exact probabilities -1.5pt & 4 * -1.5pt -1.5pt 4-4 & & & -1.5pt zero--one laws & 3-4 & & 2 * & -1.5pt exact probabilities -1.5pt & 4-4 & & & -1.5pt zero--one laws & 2-5 & 4 * -1.5pt @math -1.5pt & 2 * & -1.5pt exact probabilities -1.5pt & -1.5pt @cite_22 4-5 & & & -1.5pt zero--one laws -1.5pt & -1.5pt @cite_35 3-5 & & 2 * & -1.5pt exact probabilities -1.5pt & -1.5pt @cite_10 4-5 & & & -1.5pt zero--one laws & -1.5pt @cite_8 @cite_39 2.5
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Pour des echantillons aleatoires independants: X 1 X 2 …X n1 distribue selon f(x) et Y 1 Y 2 …Y n2 distribue selon g(x) on presente un test qui possede les proprietes suivantes: la probabilite d'erreur de premiere espece ne depend pas de f; lorsque min (n 1 , n 2 )→∞, la statistique de test est asymptotiquement independante de la distribution sous Ho et la distribution limite est connue; le test est consistant contre des alternatives generales Soit Ω un domaine borne dans R n , n≥3 avec une frontiere C 1,1 . On considere l'operateur Lγ(u)=⊇•(γ⊇u) ou γ(x) est une fonction a valeur reelle dans C 1,1 (Ω) avec une borne superieure positive. On definit la forme quadratique Qγ sur H 1 2 (∂Ω) par Qγ(f)=∫ Ω γ(x)|⊇u(x)| 2 dx ou u∈H 1 (Ω) est la solution unique a Lγu=0 dans Ω, u| ∂Ω =f. On etudie la reconstruction de γ a partir de Qγ Considerons une marche aleatoire branchante surcritique a temps discret. Nous nous interessons a la probabilite qu'il existe un rayon infini du support de la marche aleatoire branchante, le long duquel elle croit plus vite qu'une fonction lineaire de pente y - e, ou γ designe la vitesse asymptotique de la position de la particule la plus a droite dans la marche aleatoire branchante. Sous des hypotheses generales peu restrictives, nous prouvons que, lorsque e → 0, cette probabilite decroit comme exp —β+o(1) e 1 2 , ou β est une constante strictement positive dont la valeur depend de la loi de la marche aleatoire branchante. Dans le cas special ou des variables aleatoires i.i.d. de Bernoulli(p) (avec 0 < p < 1 2 ) sont placees sur les aretes d'un arbre binaire enracine, ceci repond a une question ouverte de Robin Pemantle (Ann. Appl. Probab. 19 (2009) 1273-1291). On presente un algorithme polynomial permettant de determiner un sous-graphe biparti d'un graphe G sans triangle ni boucle de degre maximum 3, contenant au moins 4 5 des aretes de G. On caracterise le dodecaedre et le graphe de Petersen comme les seuls graphes connexes 3-reguliers sans triangle ni boucle pour lesquels il n'existe pas de sous graphe biparti ayant un nombre d'aretes superieur a cette proportion 3 Voting 17 3.1 Voting Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1.1 Scoring Rules . . . . . . . . . . . . . . . . . . . . . . . . 18 3.1.2 Condorcet Extensions . . . . . . . . . . . . . . . . . . . 19 3.1.3 Other Rules . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.1 The Gibbard-Satterthwaite Impossibility . . . . . . . . . . 24 3.2.2 Restricted Domains of Preferences . . . . . . . . . . . . . 24 3.2.3 Computational Hardness of Manipulation . . . . . . . . . 26 3.2.4 Probabilistic Voting Rules . . . . . . . . . . . . . . . . . 29 3.2.5 Irresolute Voting Rules . . . . . . . . . . . . . . . . . . . 30 3.3 Possible and Necessary Winners . . . . . . . . . . . . . . . . . . 31 Let f be a random Boolean formula that is an instance of 3-SAT. We consider the problem of computing the least real number k such that if the ratio of the number of clauses over the number of variables of f strictly exceeds k , then f is almost certainly unsatisfiable. By a well-known and more or less straightforward argument, it can be shown that kF5.191. This upper bound was improved by to 4.758 by first providing new improved bounds for the occupancy problem. There is strong experimental evidence that the value of k is around 4.2. In this work, we define, in terms of the random formula f, a decreasing sequence of random variables such that, if the expected value of any one of them converges to zero, then f is almost certainly unsatisfiable. By letting the expected value of the first term of the sequence converge to zero, we obtain, by simple and elementary computations, an upper bound for k equal to 4.667. From the expected value of the second term of the sequence, we get the value 4.601q . In general, by letting the U This work was performed while the first author was visiting the School of Computer Science, Carleton Ž University, and was partially supported by NSERC Natural Sciences and Engineering Research Council . of Canada , and by a grant from the University of Patras for sabbatical leaves. The second and third Ž authors were supported in part by grants from NSERC Natural Sciences and Engineering Research . Council of Canada . During the last stages of this research, the first and last authors were also partially Ž . supported by EU ESPRIT Long-Term Research Project ALCOM-IT Project No. 20244 . †An extended abstract of this paper was published in the Proceedings of the Fourth Annual European Ž Symposium on Algorithms, ESA’96, September 25]27, 1996, Barcelona, Spain Springer-Verlag, LNCS, . pp. 27]38 . That extended abstract was coauthored by the first three authors of the present paper. Correspondence to: L. M. Kirousis Q 1998 John Wiley & Sons, Inc. CCC 1042-9832r98r030253-17 253 In this paper we study a fundamental open problem in the area of probabilistic checkable proofs: What is the smallest s such that NP ⊆ naPCP1,s[O(log n),3]? In the language of hardness of approximation, this problem is equivalent to determining the smallest s such that getting an s-approximation for satisfiable 3-bit constraint satisfaction problems ("3-CSPs") is NP-hard. The previous best upper bound and lower bound for s are 20 27+µ by Khot and Saket [KS06], and 5 8 (assuming NP subseteq BPP) by Zwick [Zwi98]. In this paper we close the gap assuming Khot's d-to-1 Conjecture. Formally, we prove that if Khot's d-to-1 Conjecture holds for any finite constant integer d, then NP naPCP1,5 8+ µ[O(log n),3] for any constant µ > 0. Our conditional result also solves Hastad's open question [Has01] on determining the inapproximability of satisfiable Max-NTW ("Not Two") instances and confirms Zwick's conjecture [Zwi98] that the 5 8-approximation algorithm for satisfiable 3-CSPs is optimal. Dans cette Note on determine deux fonctions x et y, uniformes et continues d’une variable (reelle) t, qui, lorsque t varie dans l’intervalle (0, 1), prennent toutes les couples de valeurs telles que 0≤x≤1, 0≤y≤1. Si l’on appelle, suivant l’usage, courbe continue le lieu des points dont les coordonnees sont des fonctions continues d’une variable, on a ainsi un arc de courbe qui passe par tous les points d’un carre. Donc, etant donne un arc de courbe continue, sans faire d’autres hypotheses, il n’est pas toujours possible de le renfermer dans une aire arbitrairement petite. Les principes de l'ethique biomedicale constituent, par leur influence, l’ouvrage majeur de l’ethique medicale contemporaine. Au-dela de son contexte nord-americain d’elaboration, de la deontologie medicale traditionnelle et des theories morales classiques, la reflexion proposee a reconfigure l’analyse des questions ethiques liees a la relation de soin et au monde de la sante. Depuis la premiere edition de ce texte (1979), les auteurs n’ont eu de cesse de le remanier et d’en presenter des versions integrant toujours davantage leurs reponses aux objections et critiques qu’ils recevaient ou se formulaient eux-memes. C’est la 5e edition (dans l’attente de la 6e), datant de 2001, qui est ici traduite pour la premiere fois. Livre en debat, ne lui-meme des discussions engagees aux Etats-Unis dans les annees 1970, notamment sur l’ethique des essais cliniques, il vise a determiner des principes-reperes susceptibles d’eclairer les pratiques medicales et les argumentations qui les accompagnent des lors qu’elles engagent un rapport aux normes et aux valeurs : le principe d’autonomie, le principe de non-malfaisance, le principe de bienfaisance et le principe de justice. Le statut de la theorie dans la vie morale, les rapports entre les principes et les elements factuels, les rapports des differents principes entre eux sont les problemes qui structurent continument la reflexion des auteurs. Ainsi s’edifie une approche se voulant fine, souple et rigoureuse de ce qui peut justifier et guider le raisonnement ethique dans les prestations de sante et les relations de soin.