Showing papers in "Random Structures and Algorithms in 2007"

The phase transition in inhomogeneous random graphs

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 world do not have this property, having, for example, power-law degree distributions. Thus there has been a lot of recent interest in defining and studying “inhomogeneous” random graph models. One of the most studied properties of these new models is their “robustness”, or, equivalently, the “phase transition” as an edge density parameter is varied. For G(n,p), p = c/n, the phase transition at c = 1 has been a central topic in the study of random graphs for well over 40 years. Many of the new inhomogeneous models are rather complicated; although there are exceptions, in most cases precise questions such as determining exactly the critical point of the phase transition are approachable only when there is independence between the edges. Fortunately, some models studied have this property already, and others can be approximated by models with independence. Here we introduce a very general model of an inhomogeneous random graph with (conditional) independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p = c/n scaling for G(n,p) used to study the phase transition; also, it seems to be a property of many large real-world graphs. Our model includes as special cases many models previously studied. We show that, under one very weak assumption (that the expected number of edges is “what it should be”), many properties of the model can be determined, in particular the critical point of the phase transition, and the size of the giant component above the transition. We do this by relating our random graphs to branching processes, which are much easier to analyze. We also consider other properties of the model, showing, for example, that when there is a giant component, it is “stable”: for a typical random graph, no matter how we add or delete o(n) edges, the size of the giant component does not change by more than o(n). © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 31, 3–122, 2007

The geometry of logconcave functions and sampling algorithms

Abstract: The class of logconcave functions in Rn is a common generalization of Gaussians and of indicator functions of convex sets. Motivated by the problem of sampling from logconcave density functions, we study their geometry and introduce a technique for “smoothing” them out. These results are applied to analyze two efficient algorithms for sampling from a logconcave distribution in n dimensions, with no assumptions on the local smoothness of the density function. Both algorithms, the ball walk and the hit-and-run walk, use a random walk (Markov chain) to generate a random point. After appropriate preprocessing, they produce a point from approximately the right distribution in time Oa(n4) and in amortized time Oa(n3) if n or more sample points are needed (where the asterisk indicates that dependence on the error parameter and factors of log n are not shown). These bounds match previous bounds for the special case of sampling from the uniform distribution over a convex body.© 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 Part of this work was done while the second author was visiting Microsoft Research in Redmond, WA, and when the first author was visiting the Newton Institute in Cambridge, UK.

Bootstrap percolation on the random regular graph

Abstract: The k-parameter bootstrap percolation on a graph is a model of an interacting particle system, which can also be viewed as a variant of a cellular automaton growth process with threshold k ≥ 2. At the start, each of the graph vertices is active with probability p and inactive with probability 1 − p, independently of other vertices. Presence of active vertices triggers a bootstrap percolation process controlled by a recursive rule: an active vertex remains active forever, and a currently inactive vertex becomes active when at least k of its neighbors are active. The basic problem is to identify, for a given graph, p− and p+ such that for p p+ resp.) the probability that all vertices are eventually active is very close to 0 (1 resp.). The bootstrap percolation process is a deterministic process on the space of subsets of the vertex set, which is easy to describe but hard to analyze rigorously in general. We study the percolation on the random d-regular graph, d ≥ 3, via analysis of the process on the multigraph counterpart of the graph. Here, thanks to a “principle of deferred decisions,” the percolation dynamics is described by a surprisingly simple Markov chain. Its generic state is formed by the counts of currently active and nonactive vertices having various degrees of activation capabilities. We replace the chain by a deterministic dynamical system, and use its integrals to show—via exponential supermartingales—that the percolation process undergoes relatively small fluctuations around the deterministic trajectory. This allows us to show existence of the phase transition within an interval [p−(n),p+(n)], such that (1) p±(n) p* = 1 − miny∈(0,1)y/ℙ(Bin(d − 1,1 − y) < k); (2) p+(n) − p−(n) is of order n−1/2 for k < d − 1, and n, (en 0,en log n ∞), for k = d − 1. Note that p* is the same as the critical probability of the process on the corresponding infinite regular tree. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 30, 257–286, 2007

A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs

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.

A simple solution to the k-core problem

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

Random trees and general branching processes

Abstract: We consider a tree that grows randomly in time. Each time a new vertex appears, it chooses exactly one of the existing vertices and attaches to it. The probability that the new vertex chooses vertex x is proportional to w(deg(x)), a weight function of the actual degree of x. The weight function w : ℕ ➝ ℝ+ is the parameter of the model. In [4] and [11] the authors derive the asymptotic degree distribution for a model that is equivalent to the special case, when the weight function is linear. The proof therein strongly relies on the linear choice of w. Using well-established results from the theory of general branching processes we give the asymptotical degree distribution for a wide range of weight functions. Moreover, we provide the asymptotic distribution of the tree itself as seen from a randomly selected vertex. The latter approach gives greater insight to the limiting structure of the tree. Our proof is robust and we believe that the method may be used to answer several other questions related to the model. It relies on the fact that considering the evolution of the random tree in continuous time, the process may be viewed as a general branching process, this way classical results can be applied. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Fast mixing for independent sets, colorings, and other models on trees

Abstract: We study the mixing time of the Glauber dynamics for general spin systems on the regular tree, including the Ising model, the hard-core model (independent sets), and the antiferromagnetic Potts model at zero temperature (colorings). We generalize a framework, developed in our recent paper (Martinelli, Sinclair, and Weitz, Tech. Report UCB//CSD-03-1256, Dept. of EECS, UC Berkeley, July 2003) in the context of the Ising model, for establishing mixing time O(nlog n), which ties this property closely to phase transitions in the underlying model. We use this framework to obtain rapid mixing results for several models over a significantly wider range of parameter values than previously known, including situations in which the mixing time is strongly dependent on the boundary condition. We also discuss applications of our framework to reconstruction problems on trees. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 A preliminary version of this paper appeared in Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms, January 2004. This work was done while the author was visiting the Departments of EECS and Statistics, University of California, Berkeley, supported in part by a Miller Visiting Professorship.

The diameter of sparse random graphs

Abstract: We derive an expression of the form c ln n + o(ln n) for the diameter of a sparse random graph with a specified degree sequence. The result holds asymptotically almost surely, assuming that certain convergence and supercriticality conditions are met, and is applicable to the classical random graph Gn,p with np = Θ(1) + 1, as well as certain random power law graphs. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Material vegetal e as rotinas laboratoriais nos procedimentos químico-analíticos

Abstract: The presented text has as main purpose support students and junior researchers in their laboratory work, e. g., thesis and dissertations. This is due considering that in this case, in special, the time dispended in the laboratory is generally short and not continuous. In this sense, it is necessary to present an operational laboratory method rich in specific details that normally are not considered in the methods available in the published literature enabling the operators to be auto sufficient. The descriptions contain basic information about glassware cleaning, sample preparation and readings in different equipments. It also presents the methods of nutrient determination in a didactic way for vegetable materials, including mathematical transformations of the readings, step by step, in the different equipments to standard units. Additionally, describes methods for dry digestion – incineration; wet digestion – kjeldahl, and diluted acid extractions. For sample readings, techniques as titration, colorimetry, flame photometry, and atomic absorption spectrophotometry are described also. The bibliography cited in the text is recommended for additional readings in cases where a deeper knowledge is required. It is expected that the information, presented in the text, will be useful for the operators in conducting their analyses while utilizing the described methods.

Estimating the distance to a monotone function

Abstract: In standard property testing, the task is to distinguish between objects that have a property ℘ and those that are e-far from ℘, for some e > 0. In this setting, it is perfectly acceptable for the tester to provide a negative answer for every input object that does not satisfy ℘. This implies that property testing in and of itself cannot be expected to yield any information whatsoever about the distance from the object to the property. We address this problem in this paper, restricting our attention to monotonicity testing. A function f : {1,…,n} ➝ R is at distance ef from being monotone if it can (and must) be modified at efn places to become monotone. For any fixed δ > 0, we compute, with probability at least 2/3, an interval [(1/2 -δ)e,e] that encloses ef. The running time of our algorithm is O(ef-1 log log ef- 1 log n), which is optimal within a factor of loglog ef-1 and represents a substantial improvement over previous work. We give a second algorithm with an expected running time of O(ef-1 log nlog log log n). Finally, we extend our results to multivariate functions. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007

The cover time of sparse random graphs

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

Level of nodes in increasing trees revisited

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

Nash equilibria in random games

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

Sparse universal graphs for bounded-degree graphs

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

Sampling binary contingency tables with a greedy start

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

Random cubic planar graphs

Abstract: We show that the number of labeled cubic planar graphs on n vertices with n even is asymptotically αn-7/2ρ-nn!, where ρ-1 ... 3.13259 and α are analytic constants. We show also that the chromatic number of a random cubic planar graph that is chosen uniformly at random among all the labeled cubic planar graphs on n vertices is three with probability tending to e-ρ4/4! ... 0.999568 and four with probability tending to 1 - e-ρ4/4! as n → ∞ with n even. The proof given combines generating function techniques with probabilistic arguments. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007

Descritores qualitativos e multicategóricos na estimativa da variabilidade fenotípica entre acessos de pimentas

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.

Sublinear-time approximation algorithms for clustering via random sampling

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.

The phase transition in inhomogeneous random graphs

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...

Counting connected graphs and hypergraphs via the probabilistic method

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

Arborização de vias públicas e a utilização de espécies exóticas: o caso do bairro centro de pato branco/pr

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.

Random cubic planar graphs, Random Structures and Algorithms

Abstract: We show that the number of labeled cubic planar graphs on n vertices with n even is asymptotically αn−7/2ρ−nn!, where ρ−1 . = 3.13259 and α are analytic constants. We show also that the chromatic number of a random cubic planar graph that is chosen uniformly at random among all the labeled cubic planar graphs on n vertices is three with probability tending to e−ρ/4! . = 0.999568 and four with probability tending to 1 − e−ρ/4! as n → ∞ with n even. The proof given combines generating function techniques with probabilistic arguments. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 30, 78–94, 2007

Fatherhood, Family and Work in Men’s Lives : Negotiating New and Old Masculinities

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.

Ambiente de enraizamento e substratos na miniestaquia de erva-mate

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.

Pour une sociologie critique de la gestion

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.

The diameter of randomly perturbed digraphs and some applications

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

GERMINAÇÃO DE Melocactus bahiensis (CACTACEAE) EM DIFERENTES SUBSTRATOS E TEMPERATURAS

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.

Profiles of random trees: Plane-oriented recursive trees

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.

Rainbow Hamilton cycles in random regular graphs

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