The lifespan method as a tool to study criticality in absorbing-state phase transitions

In a recent work, a new numerical method (the lifespan method) has been introduced to study the critical properties of epidemic processes on complex networks [Phys. Rev. Lett. \textbf{111}, 068701 (2013)]. Here, we present a detailed analysis of the viability of this method for the study of the critical properties of generic absorbing-state phase transitions in lattices. Focusing on the well understood case of the contact process, we develop a finite-size scaling theory to measure the critical point and its associated critical exponents. We show the validity of the method by studying numerically the contact process on a one-dimensional lattice and comparing the findings of the lifespan method with the standard quasi-stationary method. We find that the lifespan method gives results that are perfectly compatible with those of quasi-stationary simulations and with analytical results. Our observations confirm that the lifespan method is a fully legitimate tool for the study of the critical properties of absorbing phase transitions in regular lattices

Slow dynamics and rare-region effects in the contact process on weighted tree networks

We show that generic, slow dynamics can occur in the contact process on complex networks with a tree-like structure and a superimposed weight pattern, in the absence of additional (non-topological) sources of quenched disorder. The slow dynamics is induced by rare-region effects occurring on correlated subspaces of vertices connected by large weight edges, and manifests in the form of a smeared phase transition. We conjecture that more sophisticated network motifs could be able to induce Griffiths phases, as a consequence of purely topological disorder.Comment: 12 pages, 10 figures, final version appeared in PR

The Husain-Kuchar Model: Time Variables and Non-degenerate Metrics

We study the Husain-Kuchar model by introducing a new action principle similar to the self-dual action used in the Ashtekar variables approach to Quantum Gravity. This new action has several interesting features; among them, the presence of a scalar time variable that allows the definition of geometric observables without adding new degrees of freedom, the appearance of a natural non-degenerate four-metric and the possibility of coupling ordinary matter.Comment: LaTeX, 22 pages, accepted for publication in Phys. Rev.

Self-organization of collaboration networks

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks. The model depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc. The simplest model defined within this framework already allows us to describe many of the main topological characteristics (degree distribution, clustering coefficient, etc.) of one-mode projections of several real collaboration networks, without parameter fitting. We explain the observed dependence of the local clustering on degree and the degree--degree correlations in terms of the ``aging'' of collaborators and their physical impossibility to participate in an unlimited number of collaborations.Comment: 10 pages, 8 figure

Morphological characterization of the Pelibuey sheep of Yucatan, Mexico

Three databases or stratums: I. The Secretariat of Agriculture, Cattle, Rural Development, Fishing and Feeding, II. Specialized Local Cattle association of sheep farmers of Mérida and, III. Local Cattle Union of Tízimin was used to characterize morphometrically the Pelibuey sheep breed of the state of Yucatan, Mexico. The sample size and producer were determined within stratum. A total of 369 animals within breed standards, males and females, and over a year of age were selected and classified by stratum and coat color: coffee, white, and pinto. Five phaneroptical and 11 morphostructural characteristics in addition to the body weight were registered by animals. All animals presented coffee eyes, tongue without pigmentation dominates for the coffee (20%) and white (24%) coat colors, whereas for the pinto dominates the pigmented tongue (66%). Black hooves dominate in the coffee coat color individuals (57%), faulty colored hooves in the white (68%), and marbled hooves in the pinto (75%). Wooly (30%) and wattled (2%) individuals were common among coat colors. Differences among stratums of live weight, head length, length of the neck, length of hip, and the longitudinal diameter in males; and neck length, wither height, length of the hip, the width of the hip, and thorax perimeter in the females were not significant (P>0.05). Whereas, hip-width in males and head width in females differed significantly among coat colors (P<0.05). The highest correlations for males (0.92) and females (0.87) were for hip height and wither height. Differences found among stratums are associated with differences in the production system. The minimum variation among coat colors indicates that animals come from a common trunk

Diffusion-annihilation processes in complex networks

We present a detailed analytical study of the $A+A\to\emptyset$ diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of $A$ particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e. a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power-law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free networks with different degree exponents.Comment: 9 pages, 5 EPS figure

Diffusion-annihilation processes in complex networks

We present a detailed analytical study of the $A+A\to\emptyset$ diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of $A$ particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e. a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power-law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free networks with different degree exponents.Comment: 9 pages, 5 EPS figure

Epidemic dynamics in finite size scale-free networks

Many real networks present a bounded scale-free behavior with a connectivity cut-off due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cut-offs. The finite size effects introduced by the cut-off induce an epidemic threshold that approaches zero at increasing sizes. The induced epidemic threshold is very small even at a relatively small cut-off, showing that the neglection of connectivity fluctuations in bounded scale-free networks leads to a strong over-estimation of the epidemic threshold. We provide the expression for the infection prevalence and discuss its finite size corrections. The present work shows that the highly heterogeneous nature of scale-free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes.Comment: 4 pages, 2 eps figure

Produção de mudas de caramboleiras 'B-10' e 'Golden Star': II. Marcha de absorção e acúmulo de nutrientes.

A participação do Brasil no mercado externo de frutas tem aumentado consideravelmente e com potencial para crescer ainda mais. A constante ascensão dos dados de exportação brasileira é resultado da combinação de avanços tecnológicos do setor produtivo e de acesso a novos mercados consumidores. A caramboleira apresenta-se como uma excelente opção de cultivo de frutas exóticas, com grande potencial para atender ao mercado interno e às exportações. Assim, objetivou-se avaliar a marcha de absorção e de acúmulo de nutrientes em mudas de caramboleiras cultivadas em solução nutritiva. O experimento foi realizado em parcelas subdivididas, sendo utilizadas como parcela as duas cultivares de caramboleira (?B-10? e ?Golden Star?) e, como subparcelas, cinco épocas de coleta de plantas, realizadas aos 208; 233; 258; 283 e 308 dias após o transplantio para a solução nutritiva. O delineamento foi inteiramente casualizado, com três repetições. As mudas foram cultivadas em vasos (8L) com solução nutritiva (pH=5,5 ± 0,5), com aeração. O experimento iniciou-se em 24-08-2005. Nos diferentes órgãos das mudas (folhas, caule e raízes), determinaram-se a marcha de absorção, o acúmulo de nutrientes e os índices nutricionais. Não houve diferenças no acúmulo de nutrientes entre as mudas de caramboleira de ambas as cultivares, sendo a ordem decrescente dos nutrientes em cada muda de ?B-10?, no final do período experimental: N > K > Ca > Mg > S > P > Fe > Mn > B > Cu > Zn. Para a ?Golden Star?, a ordem foi: N > K > Ca > Mg > P > S > Fe > Mn > B > Cu > Zn. Para as duas cultivares, o acúmulo médio foi maior nas folhas > caule > raízes. O período de maior exigência para ?B-10? foi entre 208 ? 233 e, para ?Golden Star?, entre 233 ? 283 dias após o transplantio. As diferentes taxas de acumulação líquida dos nutrientes, nos diferentes órgãos da caramboleira, nem sempre acompanharam a taxa de acumulação de nutrientes do respectivo órgão. Production of star fruit ?B-10? and ?Golden Star? seedlings: II ? Absorption rate and acumulation of nutrients. Abstract ? Brazil?s participation in the external market of fruits has increased considerably with the potential to grow further. The constant rise of the Brazilian exportation data is the result of a combination of technological advances in the productive sector and access to new markets. The star fruit is presented as an excellent option for cultivation of exotic fruits, with great potential to attend the domestic market and exportation. Thus, the objective was to assess absorption rate and accumulation of nutrients in star fruit seedlings, grown in nutrient solution. The experiment was conducted in split plots being used as part of the two cultivars of star fruit (?B-10? and ?Golden Star?) and as subplots, five plant collecting periods, realized at 208, 233, 258, 283 and 308 days after transplanting to the nutrient solution. The experimental design was completely randomized with three replications. The seedlings were grown in pots (8L) with nutrient solution (pH = 5.5 ± 0.5) with aeration. The experiment started on 08.24.2005. In different plant organs (leaves, stems and roots), absorption rate, accumulation of nutrients and nutritional indices were determined. It did not have differences in the accumulation of nutrients in the star fruit seedlings for both cultivars, the decreasing order of the nutrients in each ?B-10?seedlings, in the end of the experimental period, was: N > K > Ca > Mg > S > P > Fe > Mn > B > Cu > Zn. For ?Golden Star? the decreasing order was: N > K > Ca > Mg > P > S > Fe > Mn > B > Cu > Zn. For the two cultivars, the average accumulation was bigger in leaves > stem > roots. The period of bigger requirement for ?B-10? was between 208 - 233 and, for ?Golden Star?, between 233 - 283 days after the transplantation. The different rates of nutrient liquid accumulation, in the different organs of star fruit trees, not always followed the nutrient accumulation rate of the respective organ

Produção de mudas de caramboleiras 'B-10' e 'Golden Star': I. Parâmetros biológicos.

O Brasil é um dos maiores produtores de carambola do mundo, entretanto há poucas informações científicas, especialmente estudos de nutrição mineral com mudas dessa frutífera. Objetivando contribuir com o conhecimento desse importante aspecto, desenvolveu-se estudo que permitisse avaliar o crescimento e o acúmulo de nutrientes em mudas de caramboleiras, cultivadas em solução nutritiva. O experimento foi realizado em parcelas subdivididas, sendo utilizadas como parcela as duas cultivares de caramboleira ('B-10' e 'Golden Star') e, como subparcelas, as cinco épocas de coleta de plantas, realizadas aos 208; 233; 258; 283 e 308 dias após o transplantio para a solução nutritiva. O delineamento foi inteiramente casualizado, com três repetições. As mudas foram cultivadas em vasos (8L) com solução nutritiva (pH=5,5 ± 0,5), com aeração. O experimento iniciou-se em 24-08-2005. Nos diferentes órgãos das mudas (folhas, caule e raízes), avaliaram-se o crescimento e o acúmulo de nutrientes, e os índices nutricionais. Não houve diferenças no crescimento e, em geral, no acúmulo da massa da matéria seca entre as duas cultivares. Houve acúmulo linear da massa da matéria seca das mudas de caramboleira com o tempo de cultivo, sendo maior nas folhas > caule > raízes. O período de maior acúmulo da massa de matéria seca e da taxa de crescimento relativo na planta inteira esteve compreendido entre 208 ? 233 e 233 258 dias após o transplantio para a 'B-10' e a 'Golden Star', respectivamente. Production of seedlings of star fruit 'B-10' and 'Golden Star': I biological parameters. Abstract ? Brazil is one of the greatest producer of star fruit in the world, however, there are few scientific information, especially studies of mineral nutrition with seedlings of this fruitful. In order to contribute with the knowledge of this important aspect, it was developed a study that allowed evaluating the growth and the accumulation of nutrients in seedlings of star fruits trees, cultivated in nutritional solution. The experiment was realize in split plot, with two cultivars ('B-10' and 'Golden Star') and as subplots, five collecting periods of plants, realized in 208, 233, 258, 283 and 308 days after the transplantation to nutritional solution, with 3 repetitions. The seedlings had been cultivated in pots (8L) with nutritional solution (pH=5.5 ± 0.5), with aeration. The experiment started on 08-24-2005. In the different parts of the seedlings (leaves, stem and roots), it was evaluated the growth and the accumulation of nutrients and nutritional ratios. It did not have differences in the growth and, in general, in the accumulation of the dry matter between the two cultivars. There was linear accumulation of the dry matter of the seedlings of star fruit trees with the cultivation period, it was bigger in leaves > stem > roots. The period of greater accumulation of dry matter and the tax of relative growth in the entire plant was between 208 - 233 and 233 - 258 days after the transplantation for 'B-10' and 'Golden Star' respectively