Abstract: We compute the probability of satisfiability of a class of random Horn-SAT formulae, motivated by a connection with the nonemptiness problem of finite tree automata. In particular, when the maximum clause length is three, this model displays a curve in its parameter space, along which the probability of satisfiability is discontinuous, ending in a second-order phase transition where it is continuous but its derivative diverges. This is the first case in which a phase transition of this type has been rigorously established for a random constraint satisfaction problem. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Abstract: Let K be a graph on r vertices and let G = (V,E) be another graph on mV m = n vertices. Denote the set of all copies of K in G by K. A non-negative real-valued function f : K→ R+ is called a fractional K-factor if ∑ K:v∈K∈Kf(K) ≤ 1 for every v ∈ V and ∑ K∈Kf(K) = n/r. For a non-empty graph K let d(K) = e(K)/v(K) and d(1)(K) = e(K)/(v(K) - 1). We say that K is strictly K1-balanced if for every proper subgraph K′ s K, d(1)(K′) d(K). Considering a random graph process $\widetilde{G}$ on n vertices, we show that if K is strictly K1-balanced, then with probability tending to 1 as n →∞, at the first moment τ0 when every vertex is covered by a copy of K, the graph ${\widetilde{G}}_{\tau_0}$ has a fractional K-factor. This result is the best possible. As a consequence, if K is K1-balanced, we derive the threshold probability function for a random graph to have a fractional K-factor. On the other hand, we show that if K is an imbalanced graph, then for asymptotically almost every graph process there is a gap between τ0 and the appearance of a fractional K-factor. We also introduce and apply a criteria for perfect fractional matchings in hypergraphs in terms of expansion properties. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Abstract: Let G = (V,E) be an undirected weighted graph on |V | = n vertices and |E| = m edges. A t-spanner of the graph G, for any t ≥ 1, is a subgraph (V,ES), ES ⊆ E, such that the distance between any pair of vertices in the subgraph is at most t times the distance between them in the graph G. Computing a t-spanner of minimum size (number of edges) has been a widely studied and well-motivated problem in computer science. In this paper we present the first linear time randomized algorithm that computes a t-spanner of a given weighted graph. Moreover, the size of the t-spanner computed essentially matches the worst case lower bound implied by a 43-year old girth lower bound conjecture made independently by Erdos, Bollobas, and Bondy & Simonovits. Our algorithm uses a novel clustering approach that avoids any distance computation altogether. This feature is somewhat surprising since all the previously existing algorithms employ computation of some sort of local or global distance information, which involves growing either breadth first search trees up to t(t)-levels or full shortest path trees on a large fraction of vertices. The truly local approach of our algorithm also leads to equally simple and efficient algorithms for computing spanners in other important computational environments like distributed, parallel, and external memory. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 Preliminary version of this work appeared in the 30th International Colloquium on Automata, Languages and Programming, pages 384–396, 2003.

Abstract: We consider Nash equilibria in 2-player random games and analyze a simple Las Vegas algorithm for finding an equilibrium. The algorithm is combinatorial and always finds a Nash equilibrium; on m × n payoff matrices, it runs in time O(m2nloglog n + n2mloglog m) with high probability. Our result follows from showing that a 2-player random game has a Nash equilibrium with supports of size two with high probability, at least 1 - O(1/log n). Our main tool is a polytope formulation of equilibria. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Abstract: We study the k‐core of a random (multi)graph on n vertices with a given degree sequence. We let n →∞. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the degree sequence that imply that with high probability the k‐core is empty and other conditions that imply that with high probability the k‐core is non‐empty and the sizes of its vertex and edge sets satisfy a law of large numbers; under suitable assumptions these are the only two possibilities. In particular, we recover the result by Pittel, Spencer, and Wormald (J Combinator Theory 67 (1996), 111–151) on the existence and size of a k‐core in G(n,p) and G(n,m), see also Molloy (Random Struct Algor 27 (2005), 124–135) and Cooper (Random Struct Algor 25 (2004), 353–375). Our method is based on the properties of empirical distributions of independent random variables and leads to simple proofs. © 2006 Wiley Periodicals, Inc. Random Struct. Alg.,, 2007

Abstract: We study the k-core of a random (multi)graph on n vertices with a given degree sequence. We let n →∞. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the degree sequence that imply that with high probability the k-core is empty and other conditions that imply that with high probability the k-core is non-empty and the sizes of its vertex and edge sets satisfy a law of large numbers; under suitable assumptions these are the only two possibilities. In particular, we recover the result by Pittel, Spencer, and Wormald (J Combinator Theory 67 (1996), 111151) on the existence and size of a k-core in G(n,p) and G(n,m), see also Molloy (Random Struct Algor 27 (2005), 124135) and Cooper (Random Struct Algor 25 (2004), 353375). Our method is based on the properties of empirical distributions of independent random variables and leads to simple proofs. © 2006 Wiley Periodicals, Inc. Random Struct. Alg.,, 2007

Abstract: Simply generated families of trees are described by the equation T(z) = φ(T(z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label e {1,…,n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are especially important: recursive trees, heap ordered trees, and binary increasing trees. They belong to the subclass of very simple families of increasing trees, which can be characterized in 3 different ways. This paper contains results about these families as well as about polynomial families (the function φ(u) is just a polynomial). The random variable of interest is the level of the node (labelled) j, in random trees of size n≥ j. For very simple families, this is independent of n, and the limiting distribution is Gaussian. For polynomial families, we can prove this as well for j,n ➝ ∞ such that n - j is fixed. Additional results are also given. These results follow from the study of certain trivariate generating functions and Hwang's quasi power theorem. They unify and extend earlier results by Devroye, Mahmoud, and others. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Abstract: The classical random graph models, in particular G(n,p), are homogeneous, in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the real...

Abstract: We study the cover time of a random walk on graphs G e Gn,p when $p={c\log n \over n}, c>1$. We prove that whp, the cover time, is asymptotic to $c\log({c \over c-1})n\log n$. ©Wiley Periodicals, Inc. Random Struct. Alg., 2007

Abstract: We study the problem of counting and randomly sampling binary contingency tables. For given row and column sums, we are interested in approximately counting (or sampling) 0/1 n x m matrices with the specified row/column sums. We present a simulated annealing algorithm with running time O((nm)2D3d max log 5(n + m)) for any row/column sums, where D is the number of nonzero entries and dmax is the maximum row/column sum. In the worst case, the running time of the algorithm is O(n11 log 5n) for an n x n matrix. This is the first algorithm to directly solve binary contingency tables for all row/column sums. Previous work reduced the problem to the permanent, or restricted attention to row/column sums that are close to regular. The interesting aspect of our simulated annealing algorithm is that it starts at a nontrivial instance, whose solution relies on the existence of short alternating paths in the graph constructed by a particular Greedy algorithm.© 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Abstract: Let ℋ be a family of graphs. A graph T is ℋ-universal if it contains a copy of each Heℋ as a subgraph. Let ℋ(k,n) denote the family of graphs on n vertices with maximum degree at most k. For all positive integers k and n, we construct an ℋ(k,n)-universal graph T with Ok(n2-2/klog4/kn) edges and exactly n vertices. The number of edges is almost as small as possible, as Ω(n2-2/k) is a lower bound for the number of edges in any such graph. The construction of T is explicit, whereas the proof of universality is probabilistic and is based on a novel graph decomposition result and on the properties of random walks on expanders. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Abstract: We present a novel analysis of a random sampling approach for four clustering problems in metric spaces: k-median, k-means, min-sum k-clustering, and balanced k-median. For all these problems, we consider the following simple sampling scheme: select a small sample set of input points uniformly at random and then run some approximation algorithm on this sample set to compute an approximation of the best possible clustering of this set. Our main technical contribution is a significantly strengthened analysis of the approximation guarantee by this scheme for the clustering problems.The main motivation behind our analyses was to design sublinear-time algorithms for clustering problems. Our second contribution is the development of new approximation algorithms for the aforementioned clustering problems. Using our random sampling approach, we obtain for these problems the first time approximation algorithms that have running time independent of the input size, and depending on k and the diameter of the metric space only. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006A preliminary extended abstract of this work appeared in Proceedings of the 31st Annual International Colloquium on Automata, Languages and Programming (ICALP), pp. 396-407, 2004.

Abstract: The use of germplasm in breeding programs is related to the availability of information on the accessions of a collection or germplasm bank. The characterization and the quantification of genetic and phenotypic divergence among accessions were already studied, including many vegetables species. Aiming to quantify the phenotypic divergence among 29 Capsicum spp. accessions, based on morphological and agronomic traits, 37 descriptors were analyzed using principal components, cluster analysis and multicategorical variables. The experiment was carried out in field conditions, at Campos dos Goytacazes, RJ, from March to December, 2004. The data were analyzed using GENES software. The clusters formed using Tocher and nearest neighbor clustering methods showed partial agreement. The use of multicategorical analysis was efficient to quantify the phenotypic divergence.

Abstract: This objective in this work went identify the arboreal species that compound the tree planting in the downtown area of Pato Branco-PR and a critical discussion about the utilization of exotic species. The trees with were identified individually by the use of a spread sheet to write down the cientific name of the specie, common name, name of the street and the name of the closest common grounds. For the identification of the species they were collected fertile samples that were herborized. Besides, each species was photographed. The data were collected from May to November of 2005. Hey were traveled 31,5 km in thirty four streets. Were identified 3191 arboreal specimens, understanding 47 different species The inventoried area presents the predominance of the specie Ligustrum lucidum W. T. Aiton (62,4%). This specie is not native and it is on the list of invader plants. In the sequence appear Lagerstroemia indica L. (11,4%), Schinus molle L. (6,3%), Bauhinia variegata L. (3,8%), and others (16,1%). From the most abundant species only one is from Brazil ( Schinus molle ). Framed ad "others" are found varied species but with a very individual frequence lower to 2,95%. From these species, twenty-two are native and twenty-five are exotic. The result demonstrates that the downtown area doesn´t have a peculiar local bioma identity, because, besides there being prevalence of species, more than 60% of the specimens is exotic.

Abstract: The main aim of this article is to understand how men living in couples with young children construct their roles and identities as fathers in the context of different types of family functioning. To explore this issue, our analytical framework examines the dynamics of fathering and of family functioning, thereby focusing on the interrelationships between men as fathers, partners and breadwinners. Drawing on data from a qualitative study carried out in 2005-2006 in Portugal, the article shows a diversity of fatherhood patterns. Joint and supportive fatherhood emerge within the framework of fusional dynamics, while disengaged fatherhood is connected to gender-differentiated autonomy. Four other patterns were found to be linked to the various forms of the modern “associative” family identified in this study. Equal fatherhood emerges in couples whose practices closely match the ideals of gender equality and individual autonomy, whereas appropriative, time-condensed and stay-at-home patterns of fatherhood are connected to different forms of “gender unequal” associative couples.

Abstract: While it is exponentially unlikely that a sparse random graph or hypergraph is connected, with probability 1 - o(1) such a graph has a “giant component” that, given its numbers of edges and vertices, is a uniformly distributed connected graph. This simple observation allows us to estimate the number of connected graphs, and more generally the number of connected d-uniform hypergraphs, on n vertices with ((d - 1)-1 + e)n ≤ m = o(nlnn) edges, where e > 0 is arbitrarily small but independent of n. We also estimate the probability that a binomial random hypergraph Hd(n,p) is connected, and determine the expected number of edges of Hd(n,p) given that it is connected. This extends prior work of Bender et al. (Random Struct Algorithm 1 (1990), 127–169) on the number of connected graphs. While Bender et al. (1990) is based on a recursion relation satisfied by the number of connected graphs, so that the argument is to some extent enumerative, we present a purely probabilistic approach. © 2007 Wiley Periodicals, Inc. Random Struct., 2007

Abstract: Comment definir et analyser sociologiquement la gestion ? C’est a cette interrogation que cet article propose des reponses. Dans cette perspective, les auteurs rappellent que la plupart des activites sociales sont dorenavant concernees par des dispositifs de gestion ou, a tout le moins, par des raisonnements qui empruntent a cette discipline. Aussi, en rendre compte avec les categories de la sociologie, dans une visee de connaissance, et non d’aide a l’action gestionnaire, constitue-t-il un objectif legitime. C’est pourquoi, les auteurs construisent un programme detaille de recherche, en trois axes, tenant compte aussi bien des acteurs, des visees, que des principes et dispositifs. Ils y voient un moyen d’apprecier les dynamiques a l’œuvre dans la gestionnarisation de la societe et, peut-etre, d’envisager des conceptions alternatives.

Abstract: The inexistence of one method of vegetative propagation for erva-mate of efficient form difficult the silvicultural advances of this species. The experiment was carried in the Embrapa Florestas, with the objective of evaluating the effect of initial environment and substratum compositions in the survival, rooting and development of minicuttings of erva-mate. Shoots had been collected of ministumps produced for seed and cultivated in minigarden in semi-hydroponic system. The work was conducted in the delineation blocks in the bifactorial arrangement, with six substratum compositions: S1 - substratum for rooting with base of rind of Pinus , S2 - substratum for rooting with base of rind of Pinus and vermiculite, S3 - carbonized rind of rice + fine vermiculite + substratum for rooting with base of rind of Pinus and vermiculite (1:1:1 v/v), S4 - carbonized rind of rice + substratum for rooting with base of rind of Pinus and vermiculite (1:1 v/v), S5 - carbonized rind of rice + fine vermiculite (1:1 v/v) and S6 - coconut fiber and, two environments of rooting: automatized greenhouse and simple greenhouse. The results indicated that independent of the analyzed variable, the greenhouse with control oh humidity and temperature was superior to the environment without control and that the substratum formed by the mixture of carbonized rind of rice + substratum for rooting with base of rind of Pinus and vermiculite (1:1 v/v) is advised to be used in two environments for the rooting of juvenile minicuttings of erva-mate.

Abstract: We model noisy clustering data using random graphs: Clusters correspond to disjoint sets of vertices. Two vertices from the same set (resp., different sets) share an edge with probability p (resp., r < p). We give algorithms that reconstruct the clusters from the graph with high probability. Compared to previous studies, our algorithms have lower time complexity and apply under wider parameter range. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007 A preliminary version containing some of the results has been published in the Proceedings of the Eighth Scandinavian Workshop on Algorithm Theory (SWAT 02).

Abstract: The central observation of this paper is that if en random arcs are added to any n-node strongly connected digraph with bounded degree then the resulting graph has diameter O(lnn) with high probability. We apply this to smoothed analysis of algorithms and property testing. Smoothed Analysis: Recognizing strongly connected digraphs is a basic computational task in graph theory. Even for digraphs with bounded degree, it is NL-complete. By XORing an arbitrary bounded degree digraph with a sparse random digraph R ∼ Dn,e/n we obtain a “smoothed” instance. We show that, with high probability, a log-space algorithm will correctly determine if a smoothed instance is strongly connected. We also show that if NL n almost-L then no heuristic can recognize similarly perturbed instances of (s,t)-connectivity. Property Testing: A digraph is called k-linked if, for every choice of 2k distinct vertices s1,…,sk,t1,…,tk, the graph contains k vertex disjoint paths joining sr to tr for r = 1,…,k. Recognizing k-linked digraphs is NP-complete for k ≥ 2. We describe a polynomial time algorithm for bounded degree digraphs, which accepts k-linked graphs with high probability, and rejects all graphs that are at least en arcs away from being k-linked. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Abstract: As sementes de diferentes especies apresentam comportamento variavel para a temperatura e o substrato no processo de germinacao, o que pode fornecer informacoes de interesse biologico e ecologico. Com relacao as especies tropicais, muito pouco se conhece sobre as exigencias das sementes quanto aos diversos fatores envolvidos na germinacao, sendo assim o objetivo do trabalho foi avaliar a influencia da temperatura e substrato na germinacao de sementes de Melocactus bahiensis . As germinacoes f oram analisadas nas temperaturas constantes de 20, 25 e 30 o C e alternada de 20-30 o C nos substratos areia e papel de filtro. As variaveis avaliadas foram o indice de velocidade de germinacao, a porcentagem de germinacao e a altura da parte aerea da plântula. A maior germinacao e indice de velocidade de germinacao foram a 25 o C nao havendo diferenca entre os substratos testados. Para altura da parte aerea da plântula, os resultados mostraram que nao houve variacao em funcao da temperatura para o substrato areia, sendo as medias superiores ao substrato papel. As melhores condicoes para conducao do teste de germinacao em sementes de Melocactus bahiensis sao o substrato areia e a temperatura de 25 o C.

Abstract: With the aim of determine the rate and the time of ethyl-trinexapac application in wheat cultivars experiments was established at the UEPG School Farm in Ponta Grossa, PR, in 2005. The experimental design was a complete randomized blocks, in a factorial scheme 2 x 2 x 6, with three repetitions for each wheat cultivars. The treatments consisted of nitrogen rates (50 and 240 kg ha -1 ), time of trinexapac-ethyl application (between first and second node and between second and third perceivable node) and trinexapac-ethyl rates (0; 31,2; 62,5; 93,7; 125,0 and 156,2 g ha -1 ). It was evaluated agronomical characteristics, diseases severity and yield. The increase of the nitrogen rate resulted in the increase of the yield for CEP-24 cultivar; the most delayed time of application of trinexapac-ethyl affects positively the yield of CD-104 and CEP-24 cultivars; trinexapac-ethyl reduced the plants height of all the cultivars; for all the cultivars the equation of the yield in relation to the trinexapac-ethyl rates was quadratic, occurring an increase of the yield with the increase of the reducer rate, until a limit (since 63,8 to 132,5 g ha -1 ) , variable with the cultivar.

Abstract: We derive several limit results for the profile of random plane-oriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximation to the expected width, and the correlation coefficients of two level sizes. Most of our proofs are based on a method of moments. We also discover an unexpected connection between the profile of plane-oriented recursive trees (with logarithmic height) and that of random binary trees (with height proportional to the square root of tree size). © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 An extended abstract of this paper appears in a special issue (DMTCS Proceedings Volume AD, 2005, pp. 193–200) of Discrete Mathematics and Theoretical Computer Science for the 2005 International Conference on the Analysis of Algorithms, Barcelona, June 6–10, 2005.

Abstract: La difficile mise en œuvre des politiques publiques d’education en Belgique francophone conduit l’auteur a s’interroger sur la problematique de la legitimation politique. Celle-ci est abordee sous l’angle du travail de construction de la legitimite de reformes pedagogiques opere par des conseillers pedagogiques aupres des enseignants. L’analyse montre qu’aux yeux des enseignants, la legitimite meme des conseillers pedagogiques fait initialement defaut. La position intermediaire des conseillers pedagogiques, entre la figure du pair et celle de l’expert, s’avere profondement inconfortable et explique en grande partie la difficulte de leurs relations avec les enseignants. Une bonne part de leur activite consiste donc a fonder d’abord leur propre legitimite afin de construire ensuite la legitimite des reformes. Au final, l’epreuve de legitimite des reformes pedagogiques s’avere largement incertaine et fragile.

Abstract: The aim of this research was to verify the grafting compatibility between pear cultivars Cascatense, Carrick and Seleta and the quince rootstock ´EMC‘, with three-years old plants. The orchard was growing in field conditions in an high/density system (2000 trees ha -1 ) and pruned in form of central leader and irrigated with a drip irrigation system (2 L h -1 emitters per tree). The analyzed parameters were: 1) Compatibility of grafting, verified through the diameter of the trunk and visual evaluation; 2) Height of plant and 3) Canopy Volume. The diameter of the trunk was similar for all the treatments, except when compared with the grafting point, which had presented a higher diameter in all rootstock/cultivar combinations. By the visual observation of the grafting point, it was verified that only in the interation Cascatense/EMC the rootstock presented a reduced development in relation to cultivar canopy, besides presenting an extreme developed hipertrofia the grafting point. The cultivars Carrick and Seleta had presented smaller differences, which can be considered normal even if a light hipertrofia was observed. The cv. Cascatense presented greater development with 84.67 cm and 0.144 m 3 , for height and canopy volume, respectively. On the other hand, the cv. Select showed the lowest development (70.13 cm and 0.022 m 3 , respectively). The cultivars Carrick and Seleta presented a good grafting compatibility with the EMC quince roostock.

Abstract: Patchouli ( Pogostemon cablin ) belongs to Lamiaceae family and has great comercial interest due the essential oil production in leaves which is used mainly in the perfumary industry. The objective of this work was to evaluate the root formation of patchouli according to leaf and stem cutting positions. The plant material was obtained from Joinville (SC). Two experiments were carried out using a complete randomized design with five replications. The first experiment investigated the effect of leaves on stem cuttings (stems without leaves and with one and two leaves) obtained from medium region of the stems. The second experiment compared the effect of the region of the stem as a source of cuttings and the treatments included basal, medium and apical regions. The stems from apical and medium region had one pair of leaves and the stem from basal region had no leaves. After 30 days the experiment results were evaluated. Stem cuttings collected from the apical and medium regions of the stem showed no statistical difference of rooting percentage (93,7% and 83,7%, respectively) and the length of the three great roots of the cuttings (11,1 cm and 10,2 cm, respectively), being superior than the basal stem cuttings. The root number on cuttings decreased from apical (35,5) to basal (7,3) region. Stems cuttings with two leaves and with one leaf showed higher root percentage (71,7% and 51,7%, respectively) and stem formation (78,4% and 44,9%, respectively) than the basal stems without leaves. The root number on stems decreased from stem with two leaves (25,7) than with one leaf (15,6) and withou leaves (2,7). Based on the obtained results, it is recommended the use of stem cuttings from apical and medium regions containing two leaves.

Abstract: A rainbow subgraph of an edge-colored graph has all edges of distinct colors. A random d-regular graph with d even, and having edges colored randomly with d/2 of each of n colors, has a rainbow Hamilton cycle with probability tending to 1 as n →∞, for fixed d ≥ 8. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Abstract: With the objective of evalulating the effect of water-retaining polymers on the infiltration capacity and the depth reached by the wet front in two different porous media, one of a clay nature and the other of a beach sand, experiments in laboratory were performed. The polymer concentrations used were 0; 4 and 8 kg m -3 . The results showed that the polymers did not affect either the infiltration capacity or the depth reached by the wet front when the infiltration times were relatively short and the polymers were dry at time zero. For long periods of infiltration, when the polymers were completely hydrated, the rate of infiltration was reduced 13-fold, but only in the clay-based porous medium. The absence of effects in the sandy medium could not be explained.

Abstract: Cet article interroge la mise en œuvre et le suivi des politiques europeennes d’employabilite en Belgique a la lumiere de la sociologie de Norbert Elias, en reliant les dimensions sociogenetiques et psychogenetiques de la construction europeenne. Le traitement clinique des chomeurs, qui repose principalement sur la construction professionnelle de troubles de l’employabilite, contribue a l’interiorisation de normes a grande echelle, a la socialisation de la population active au marche du travail et renforce la concurrence entre les actifs occupes et les actifs inoccupes (principale condition de stabilite de la monnaie unique). Parallelement, le traitement statistique du chomage, qui consiste en un jeu rationnel entre Etats (et Regions) de maximisation des indicateurs de resultats, renforce la competition territoriale pour attirer les investisseurs et encadre, legitime, dynamise ce mouvement incertain d’harmonisation ou d’integration des systemes de protection sociale en Europe.