Abstract: We investigate algorithms to find the first vertex in large trees generated by either the uniform attachment or preferential attachment model. We require the algorithm to output a set of K vertices, such that, with probability at least 1−e, the first vertex is in this set. We show that for any e, there exist such algorithms with K independent of the size of the input tree. Moreover, we provide almost tight bounds for the best value of K as a function of e. In the uniform attachment case we show that the optimal K is subpolynomial in 1/e, and that it has to be at least superpolylogarithmic. On the other hand, the preferential attachment case is exponentially harder, as we prove that the best K is polynomial in 1/e. We conclude the paper with several open problems. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016

Abstract: What is the probability that the number of triangles in Gn,p, the Erdi¾?s-Renyi random graph with edge density p, is at least twice its mean? Writing it as exp[-rn,p], already the order of the rate function rn, p was a longstanding open problem when p=o1, finally settled in 2012 by Chatterjee and by DeMarco and Kahn, who independently showed that rn,pi¾?n2p2log1/p for pi¾?lognn; the exact asymptotics of rn, p remained unknown. The following variational problem can be related to this large deviation question at pi¾?lognn: for i¾?>0 fixed, what is the minimum asymptotic p-relative entropy of a weighted graph on n vertices with triangle density at least 1+i¾?p3? A beautiful large deviation framework of Chatterjee and Varadhan 2011 reduces upper tails for triangles to a limiting version of this problem for fixed p. A very recent breakthrough of Chatterjee and Dembo extended its validity to n-αi¾?pi¾?1 for an explicit α>0, and plausibly it holds in all of the above sparse regime.

Abstract: This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges in distribution to a finite random variable R* that can be written as a linear combination of i.i.d. copies of the attracting endogenous solution to a stochastic fixed-point equation of the form R=D∑i=1NCiRi+Q, where (Q,N,{Ci}) is a real-valued vector with N∈{0,1,2,…}, P(|Q|>0)>0, and the {Ri} are i.i.d. copies of R, independent of (Q,N,{Ci}). Moreover, we provide precise asymptotics for the limit R*, which when the in-degree distribution in the directed configuration model has a power law imply a power law distribution for R* with the same exponent. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 237–274, 2017

Abstract: A random spherical polytope Pn in a spherically convex set inline image as considered here is the spherical convex hull of n independent, uniformly distributed random points in K. The behaviour of Pn for a spherically convex set K contained in an open halfsphere is quite similar to that of a similarly generated random convex polytope in a Euclidean space, but the case when K is a halfsphere is different. This is what we investigate here, establishing the asymptotic behaviour, as n tends to infinity, of the expectation of several characteristics of Pn, such as facet and vertex number, volume and surface area. For the Hausdorff distance from the halfsphere, we obtain also some almost sure asymptotic estimates.

Abstract: We compute the homology of random Cech complexes over a homogeneous Poisson process on the d-dimensional torus, and show that there are, coarsely, two phase transitions. The first transition is analogous to the Erdi¾?s -Renyi phase transition, where the Cech complex becomes connected. The second transition is where all the other homology groups are computed correctly almost simultaneously. Our calculations also suggest a finer measurement of scales, where there is a further refinement to this picture and separation between different homology groups. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 14-51, 2017

Abstract: O balanco hidrico climatologico (BHC) e uma das formas de monitorar o armazenamento de agua no solo, sendo ferramenta essencial no planejamento estrategico agricola. Objetivou-se com este estudo desenvolver o BHC de acordo com a metodologia proposta por Thornthwaite e Mather (1955), para o municipio de Balsas-MA e a classificacao climatica segundo Thornthwaite (1948). Nesse estudo foi utilizada uma serie de dados historicos entre os anos de 1976 (inicio de operacoes da estacao meteorologica no municipio) a 2015, contendo a precipitacao pluvial media mensal e temperatura. Foram desconsiderados dados que, por alguma razao, nao foram registrados. Para o calculo do BHC foi adotado o valor de 100 mm para a capacidade de agua disponivel (CAD). A classificacao climatica foi obtida por meio dos valores do indice hidrico (Ih), indice de aridez (Ia) e indice de umidade (Iu). A evapotranspiracao real atingiu 1099 mm e verificou-se um deficit hidrico anual de 621 mm, distribuido em sua totalidade entre os meses de abril e novembro, indicando a necessidade de irrigacao nessa epoca para os cultivos agricolas. O codigo climatico da regiao pela metodologia de Thornthwaite foi C 1 dA’a’.

Abstract: A graph H is Ks-saturated if it is a maximal Ks-free graph, i.e., H contains no clique on s vertices, but the addition of any missing edge creates one. The minimum number of edges in a Ks-saturated graph was determined over 50 years ago by Zykov and independently by Erdi¾?s, Hajnal and Moon. In this paper, we study the random analog of this problem: minimizing the number of edges in a maximal Ks-free subgraph of the Erdi¾?s-Renyi random graph Gn, p. We give asymptotically tight estimates on this minimum, and also provide exact bounds for the related notion of weak saturation in random graphs. Our results reveal some surprising behavior of these parameters. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 169-181, 2017

Abstract: La “crise de la pilule” de 2012-2013 a contribue a remettre en cause la predominance de la pilule contraceptive en France, sans pour autant que l’imputation aux femmes de leur responsabilite en matiere de controle des naissances ne soit remise en cause Cet article s’interesse aux mecanismes de domination, en particulier medicaux et de genre, qui fondent et maintiennent les differentes dimensions ordinaires et invisibilisees du travail qui decoule de cette responsabilite Il s’agit d’abord de montrer comment, du fait de la medicalisation de la contraception, la responsabilite du controle des naissances est progressivement devenue feminine et comment, dans le meme temps, le travail lie a cette responsabilite est demeure cache Cette invisibilisation du travail feminin passe par la naturalisation de la contrainte que represente l’observance contraceptive, et en particulier de la charge mentale afferente C’est aussi de la contradiction entre une injonction au choix et un panel limite de methodes effectivement disponibles pour les femmes que nait la necessite d’une autre forme de travail contraceptif : un travail cognitif Enfin, l’utilisation d’une methode de controle de la fecondite implique, en particulier s’il s’agit d’une methode hormonale, de faire face a des effets secondaires minores voire nies La encore, c’est une for­me de travail invisible – un travail sur soi – que cet article vise a devoiler

Abstract: Suppose that are independent identically distributed Bernoulli random variables with mean p, so and . Any estimate of p has relative error . This paper builds a new estimate of p with the remarkable property that the relative error of the estimate does not depend in any way on the value of p. This allows the easy construction of exact confidence intervals for p of any desired level without needing any sort of limit or approximation. In addition, is unbiased. For ∊ and δ in (0, 1), to obtain an estimate where , the new algorithm takes on average at most samples. It is also shown that any such algorithm that applies whenever requires at least samples on average. The same algorithm can also be applied to estimate the mean of any random variable that falls in . The used here employs randomness external to the sample, and has a small (but nonzero) chance of being above 1. It is shown that any nontrivial where the relative error is independent of p must also have these properties. Applications of this methodology include finding exact p-values and randomized approximation algorithms for # P complete problems. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016

Abstract: Recently, in [Random Struct Algorithm 41 2012, 441-450] we adapted exploration and martingale arguments of Nachmias and Peres [ALEA Lat Am J Probab Math Stat 3 2007, 133-142], in turn based on ideas of Martin-Lof [J Appl Probab 23 1986, 265-282], Karp [Random Struct Alg 1 1990, 73-93] and Aldous [Ann Probab 25 1997, 812-854], to prove asymptotic normality of the number L1 of vertices in the largest component L1 of the random r-uniform hypergraph in the supercritical regime. In this paper we take these arguments further to prove two new results: strong tail bounds on the distribution of L1, and joint asymptotic normality of L1 and the number M1 of edges of L1 in the sparsely supercritical case. These results are used in [Combin Probab Comput 25 2016, 21-75], where we enumerate sparsely connected hypergraphs asymptotically. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 325-352, 2017

Abstract: We analyse the size of an independent set in a random graph on n vertices with specified vertex degrees, constructed via a simple greedy algorithm: order the vertices arbitrarily, and, for each vertex in turn, place it in the independent set unless it is adjacent to some vertex already chosen. We find the limit of the expected proportion of vertices in the greedy independent set as n→∞, expressed as an integral whose upper limit is defined implicitly, valid whenever the second moment of a random vertex degree is uniformly bounded. We further show that the random proportion of vertices in the independent set converges to the jamming constant as n→∞. The results hold under weaker assumptions in a random multigraph with given degrees constructed via the configuration model.

Abstract: The theory of dense graph limits comes with a natural sampling process which yields an inhomogeneous variant math formula of the Erdős–Renyi random graph. Here we study the clique number of these random graphs. We establish the concentration of the clique number of math formula for each fixed n, and give examples of graphons for which math formula exhibits wild long-term behavior. Our main result is an asymptotic formula which gives the almost sure clique number of these random graphs. We obtain a similar result for the bipartite version of the problem. We also make an observation that might be of independent interest: Every graphon avoiding a fixed graph is countably-partite. © The Authors Random Structures & Algorithms Published byWiley Periodicals, Inc. Random Struct. Alg., 2016

Abstract: A recuperacao de ecossistemas que ja foram degradados podem nao ocorrer da maneira desejada se houver carencia nutricional ou suprimento insuficiente de nutrientes durante o estadio inicial de desenvolvimento, sendo, portanto, a materia orgânica um dos meios de grande influencia nesta etapa inicial. O objetivo desse trabalho foi avaliar o desenvolvimento e a qualidade de mudas de aroeira em funcao de substratos contendo diferentes fontes de materia orgânica. O experimento foi realizado em casa de vegetacao localizada no IFES Campus Itapina utilizando-se o delineamento de blocos casualizados com sete tratamentos, sendo eles compostos com diferentes fontes de materia orgânica (lodo de curtume, residuo de torrefacao de cafe, esterco bovino curtido, residuo de laticinio e composto de lixo urbano), sempre na mesma proporcao de 20%, alem dos tratamentos sem uso de materia orgânica (terra pura com e sem adubacao). Foram avaliadas caracteristicas de desenvolvimento e de qualidade das mudas, observando-se que todas as fontes de materia orgânica utilizadas favoreceram o desenvolvimento das mudas de aroeira em relacao as mudas que nao receberam as dosagens de materia orgânica. A mistura terra com composto urbano e esterco bovino mostrou-se superior na maioria das caracteristicas avaliadas gerando mudas de melhor qualidade.

Abstract: In 2002, Bollobas and Scott posed the following problem: for an integer k≥2 and a graph G of m edges, what is the smallest f(k, m) such that V(G) can be partitioned into V 1,…,Vk in which e(Vi∪Vj)≤f(k,m) for all 1≤i≠j≤k, where e(Vi∪Vj) denotes the number of edges with both ends in Vi∪Vj? In this paper, we solve this problem asymptotically by showing that f(k,m)≤m/(k−1)+o(m). We also show that V(G) can be partitioned into V1,…,Vk such that e(Vi∪Vj)≤4m/k2+4Δ/k+o(m) for 1≤i≠j≤k, where Δ denotes the maximum degree of G. This confirms a conjecture of Bollobas and Scott. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 59–70, 2017

Abstract: Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded-degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G? Our main results are: We show that if every t-vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum-weight spanning tree algorithm. We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3-regular graphs of high girth, in which every t-vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016

Abstract: Let H be a fixed graph and G a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in G of order n, chosen uniformly at random, follows a normal limiting distribution with linear expectation and variance. The main ingredient in our proof is the analytic framework developed by Drmota, Gittenberger and Morgenbesser to deal with infinite systems of functional equations [Drmota, Gittenberger, and Morgenbesser, Submitted]. As a case study, we obtain explicit expressions for the number of triangles and cycles of length 4 in the family of series-parallel graphs. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 2017

Abstract: We consider random sub-graphs of a fixed graph G=(V,E) with large minimum degree. We fix a positive integer k and let Gk be the random sub-graph where each v∈V independently chooses k random neighbors, making kn edges in all. When the minimum degree δ(G)≥(12+ϵ)n,n=|V| then Gk is k-connected w.h.p. for k=O(1); Hamiltonian for ksufficiently large. When δ(G)≥m, then Gk has a cycle of length (1−ϵ)m for k≥kϵ. By w.h.p. we mean that the probability of non-occurrence can be bounded by a function ϕ(n) (or ϕ(m)) where limn→∞ϕ(n)=0.

Abstract: We consider two competing first passage percolation processes started from uniformly chosen subsets of a random regular graph on N vertices. The processes are allowed to spread with different rates, start from vertex subsets of different sizes or at different times. We obtain tight results regarding the sizes of the vertex sets occupied by each process, showing that in the generic situation one process will occupy i¾?1Nα vertices, for some 0<α<1. The value of α is calculated in terms of the relative rates of the processes, as well as the sizes of the initial vertex sets and the possible time advantage of one process. The motivation for this work comes from the study of viral marketing on social networks. The described processes can be viewed as two competing products spreading through a social network random regular graph. Considering the processes which grow at different rates corresponding to different attraction levels of the two products or starting at different times the first to market advantage allows to model aspects of real competition. The results obtained can be interpreted as one of the two products taking the lion share of the market. We compare these results to the same process run on d dimensional grids where we show that in the generic situation the two products will have a linear fraction of the market each. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 534-583, 2017

Abstract: O manejo de bovinos em sistemas integrados de producao agropecuaria reduz a biomassa, podendo alterar a dinâmica dos atributos do solo. O objetivo desse trabalho foi avaliar os efeitos relacionados a altura de manejo do pasto, na cobertura, umidade e temperatura do solo, durante o pastejo e o cultivo de soja. A altura de manejo do pasto foi de 10, 20, 30, 40 cm e sem pastejo. Os atributos de solo foram determinados nas camadas 0-5, 5-10 e 10-20 cm, sendo; caracterizacao fisica, umidade do solo e temperatura do solo no periodo noturno e diurno. A biomassa sobre o solo, no ciclo de pasto, foi determinada coletando amostras a cada mes. As diferentes intensidades de pastejo reduziram a biomassa sobre o solo, sendo que no mes de setembro a biomassa residual foi de 0,48 Mg ha -1 no pasto mantido a 10 cm de altura e 5,81 Mg ha -1 no sem pastejo. A umidade do solo foi pouco alterada, sendo esse resultado relacionado a precipitacao regular e acima da media regional. A maior temperatura do solo no inicio do cultivo do pasto e da soja foi observada nas areas com maior intensidade de pastejo. A reducao da biomassa do pasto, em funcao do pastejo, proporcionou maior temperatura do solo durante o dia e menor durante a noite, fato que aumentou a amplitude de temperatura, especialmente no pasto mantido a 10 e 20 cm de altura.

Abstract: A utilizacao de residuos industriais, como o lodo de curtume, em substratos para producao de mudas e uma alternativa para reducao de custos de producao, e para destinacao dos residuos industriais. O cultivo de pimentas tem ganhado espaco no mercado brasileiro favorecendo principalmente a agricultura familiar, onde um dos desafios e diminuir o custo de producao. O objetivo do trabalho foi avaliar o efeito de diferentes concentracoes de lodo de curtume bovino adicionado ao substrato comercial na germinacao, desenvolvimento e qualidade de mudas de pimenta biquinho. O experimento foi conduzido em delineamento de blocos casualizados com 7 tratamentos, sendo dois substratos comerciais: Provaso ® (TP) e Bioplant ® (TL0); e cinco diferentes proporcoes de lodo desidratado (10, 30, 50, 70 e 90%) misturados ao substrato Bioplant®. Avaliou-se nesse experimento o percentual de germinacao, caracteristicas de desenvolvimento e Indice de Qualidade de mudas de Dickson (IQD). O potencial germinativo foi maior para os tratamentos com adicao de lodo de curtume ao substrato comercial Bioplant ® . Os melhores resultados para as caracteristicas de desenvolvimento das mudas ocorreram com a adicao de lodo desidratado ao substrato Bioplant ® nos intervalos de 30 a 70% de lodo no substrato. O indice de qualidade de mudas foi maior para a mistura de 30% de lodo de curtume desidratado com Bioplant ® .

Abstract: Piper umbellatum L. (Piperaceae) e um subarbusto perene com atividades anti-inflamatorias, analgesicas, antimicrobianas, antitumorais, antioxidantes e dermoprotetoras. A obtencao da materia-prima para estes fins e restrita ao extrativismo e as pequenas areas de cultivo devido ao limitado conhecimento agronomico sobre a especie. Neste sentido, sao necessarias investigacoes referentes a praticas agronomicas, especialmente tecnicas adequadas de propagacao. O objetivo do presente trabalho foi avaliar diferentes comprimentos de estaca e tipos de substrato na estaquia de P. umbellatum . Para isso, estacas caulinares de 10, 15 e 20 cm de comprimento e diâmetro medio de um centimetro foram preparadas com corte em bisel na base e reto no apice, sem folhas e contendo ao menos uma gema. Os propagulos foram estaqueados em tubetes com substrato Plantmax ® e vermiculita de granulometria fina, e mantidas em casa de vegetacao. Apos 50 dias da instalacao do experimento foi avaliada a porcentagem de estacas enraizadas, mortas, com calos, com brotacoes, numero medio de raizes, comprimento das tres maiores raizes, massa fresca de raizes e de brotacoes. O enraizamento variou de 37,5% a 60,0% e nao foi verificado interacao entre substratos e comprimento das estacas, exceto para massa fresca de raizes e brotacoes, para as quais, estacas de maior comprimento apresentaram melhor desempenho. O substrato Plantmax ® apresentou menor mortalidade, maior porcentagem de estacas com calo, massa fresca de raizes e numero de brotacoes. Neste sentido sao indicadas estacas de 20 cm e utilizacao de substrato Plantmax ® para obtencao de mudas de melhor qualidade.

Abstract: O sistema de gerenciamento automatico de marchas permite ao trator, na rotacao de trabalho estabelecida no motor, extrair o maximo de desempenho de tracao do trator. Neste trabalho, os beneficios de gerenciamento automatico de marchas foram comprovados atraves da comparacao da velocidade, patinagem, consumo horario de combustivel, rendimento e potencia na barra de tracao, forca e consumo especifico durante deslocamento do trator nas condicoes manual e automatica de gerenciamento de marcha. O experimento foi conduzido em delineamento em faixas, com dois tratamentos (marchas selecionadas manualmente e automaticamente) e cinco repeticoes. Os parâmetros foram determinados pelo metodo de comboio composto por dois tratores conduzidos em pavimento de concreto a velocidade de 8,0 km h -1 e o segundo trator simulando carga de 40 kN na barra de tracao. O gerenciamento automatico e manual das marchas nao resultou em diferenca significativa na forca e patinagem. Contudo, o gerenciamento automatico de marchas permitiu que o trator atingisse maior velocidade com menor consumo especifico e horario de combustivel, com respectivo aumento na potencia e rendimento na barra de tracao. Palavras–chave: Tratores agricolas; caixa de câmbio; eficiencia tratativa.

Abstract: Graph bootstrap percolation, introduced by Bollobas in 1968, is a cellular automaton defined as follows. Given a “small” graph H and a “large” graph G=G0⊆Kn, in consecutive steps we obtain Gt+1 from Gt by adding to it all new edges e such that Gt∪e contains a new copy of H. We say that G percolates if for some t≥0, we have Gt = Kn. For H = Kr, the question about the size of the smallest percolating graphs was independently answered by Alon, Frankl and Kalai in the 1980's. Recently, Balogh, Bollobas and Morris considered graph bootstrap percolation for G=G(n,p) and studied the critical probability pc(n,Kr), for the event that the graph percolates with high probability. In this paper, using the same setup, we determine, up to a logarithmic factor, the critical probability for percolation by time t for all 1≤t≤Cloglogn © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016

Abstract: A producao de mudas com qualidade e fundamental na exploracao das culturas agricolas, e os bioestimulantes apresentam-se como ferramentas beneficas nessa fase da planta. O estudo objetivou avaliar as diferentes concentracoes de bioestimulante composto por extrato de algas, no favorecimento da expansao radicular e desenvolvimento vegetativo inicial de mudas de uva, cultivar Crimson Seedless enxertadas em porta-enxerto SO4. O experimento foi realizado em viveiro comercial na cidade de Petrolina-PE. O delineamento experimental utilizado foi o inteiramente casualizado, com cinco tratamentos e quatro repeticoes. Os tratamentos foram: (T1) 0; (T2) 0,75; (T3) 1,12; (T4) 1,5 e (T5) 1,87 mL planta -1 do bioestimulante. Aos 45 dias apos a enxertia foram analisados o comprimento e diâmetro da brotacao do enxerto; area foliar; diâmetro, densidade, area, comprimento e materia seca das raizes e materia seca da parte aerea. Os dados foram submetidos a analise de variância e analise de regressao polinomial. Os melhores resultados foram proporcionados pela aplicacao da dose 0,75 mL planta -1 . O aumento da dose causou efeito fitotoxico. Conclui-se que o bioestimulante e uma ferramenta importante na producao de mudas com qualidade.

Abstract: O presente estudo teve como objetivo analisar as fracoes da materia orgânica, o indice de manejo do carbono e os atributos fisicos de um Latossolo Vermelho sob diferentes sistemas de uso. Quatro areas distintas de uso do solo foram avaliadas: Lavoura de culturas anuais sob sistema plantio direto ha mais de 5 anos (LAV-PD); Pastagem com grama estrela (PAST); Plantio florestal de eucaliptos com 10 anos de idade (EUC); Floresta Ombrofila Mista em estagio medio de regeneracao (MATA). Amostras de solo foram coletadas nas camadas de 0,00-0,05, 0,05-0,10, 0,10-0,20 e 0,20-0,40 m para a determinacao do teor de carbono orgânico total (COT), do carbono orgânico particulado (COP), do carbono orgânico associado aos minerais (CAM), do diâmetro medio geometrico de agregados (DMG), da densidade do solo (Ds), da macroporosidade (Ma), da microporosidade (Mi) e da porosidade total (Pt). O estudo mostrou a importância de se realizar avaliacoes quali-quantitativas do teor de carbono do solo (COT, COP e CAM), no intuito de se avaliar de uma forma mais precisa a contribuicao dos sistemas de uso sobre a dinâmica do carbono no ambiente e nos atributos fisicos do solo. O tratamento MATA mostrou-se ser o sistema mais equilibrado, considerando todas as camadas de solo avaliadas, pois apresentou a maior estabilidade dos agregados, menor Ds e maior percentual de Pt e Ma em relacao aos demais tratamentos

Abstract: We discuss a new algorithmic type of problem in random graphs studying the minimum number of queries one has to ask about adjacency between pairs of vertices of a random graph G∼G(n,p) in order to find a subgraph which possesses some target property with high probability. In this paper we focus on finding long paths in G∼G(n,p) when p=1+en for some fixed constant e>0 . This random graph is known to have typically linearly long paths. To have l edges with high probability in G∼G(n,p) one clearly needs to query at least Ω(lp) pairs of vertices. Can we find a path of length l economically, i.e., by querying roughly that many pairs? We argue that this is not possible and one needs to query significantly more pairs. We prove that any randomised algorithm which finds a path of length l=Ω(log(1e)e) with at least constant probability in G∼G(n,p) with p=1+en must query at least Ω(lpelog(1e)) pairs of vertices. This is tight up to the log(1e) factor. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016

Abstract: For a martingale Xn converging almost surely to a random variable X, the sequence Xn- X is called martingale tail sum. Recently, Neininger Random Structures Algorithms 46 2015, 346-361 proved a central limit theorem for the martingale tail sum of Regnier's martingale for the path length in random binary search trees. Grubel and Kabluchko in press gave an alternative proof also conjecturing a corresponding law of the iterated logarithm. We prove the central limit theorem with convergence of higher moments and the law of the iterated logarithm for a family of trees containing binary search trees, recursive trees and plane-oriented recursive trees. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 493-508, 2017

Abstract: We consider the adjacency operator of the Linial-Meshulam model for random simplicial complexes on n vertices, where each d-cell is added independently with probability p to the complete (d−1) -skeleton. Under the assumption np(1−p)≫log4n, we prove that the spectral gap between the (n−1d) smallest eigenvalues and the remaining (n−1d−1) eigenvalues is np−2dnp(1−p)(1+o(1)) with high probability. This estimate follows from a more general result on eigenvalue confinement. In addition, we prove that the global distribution of the eigenvalues is asymptotically given by the semicircle law. The main ingredient of the proof is a Furedi-Komlos-type argument for random simplicial complexes, which may be regarded as sparse random matrix models with dependent entries. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 2017

Abstract: A regiao do MATOPIBA representa 10,83% da area cultivada com soja no pais e 7,8% da producao nacional dessa oleaginosa, e apesar do fosforo ser o decimo segundo elemento quimico mais abundante na crosta terrestre, e o segundo elemento que mais limita a produtividade nos solos tropicais. Mediante a importância da fertilizacao fosfatada de solos com grande potencial agricola para o pais, o presente trabalho tem como objetivo avaliar o efeito de fertilizante fosfatado na soja e o comportamento do fosforo residual na regiao do MATOPIBA em tres safras consecutivas. O ensaio foi realizado durante tres anos, utilizando o delineamento experimental de blocos casualizados, com cinco repeticoes e tres replicatas. Durante as tres safras de cultivo, a pesquisa foi conduzida com adubacao fosfatada usando-se o fertilizante TOP-PHOS ® , atraves de cinco tratamentos nas doses de 0; 357; 714; 1071 e 1428 kg ha -1 (0, 100, 200, 300 e 400 kg ha -1 de P 2 O 5 , respectivamente). Na segunda e terceira safra, foi acrescido o tratamento padrao fazenda, composto pela aplicacao de 96 kg ha -1 de P 2 O 5 , obtidos com a aplicacao de 200 kg ha -1 da fonte MAP. Nas safras 13/14 e 14/15 a utilizacao do fertilizante TOP-PHOS ® proporcionou resultados 29% e 27% superiores a ausencia de adubacao fosfatada para produtividade da soja. Na safra 15/16 a baixa precipitacao durante a fase reprodutiva da soja prejudicou os parâmetros avaliados, produzindo plantas altas, mas prejudicando as estruturas reprodutivas da soja.