Border trees of complex networks

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small-world properties of real networks were fundamental to stimulate more realistic models and to understand important dynamical processes related to network growth. However, the properties of the network borders (nodes with degree equal to 1), one of its most fragile parts, remained little investigated and understood. The border nodes may be involved in the evolution of structures such as geographical networks. Here we analyze the border trees of complex networks, which are defined as the subgraphs without cycles connected to the remainder of the network (containing cycles) and terminating into border nodes. In addition to describing an algorithm for identification of such tree subgraphs, we also consider how their topological properties can be quantified in terms of their depth and number of leaves. We investigate the properties of border trees for several theoretical models as well as real-world networks. Among the obtained results, we found that more than half of the nodes of some real-world networks belong to the border trees. A power-law with cut-off was observed for the distribution of the depth and number of leaves of the border trees. An analysis of the local role of the nodes in the border trees was also performed.

GEOCHEMISTRY AND U-PB ZIRCON AGE OF THE INTERNAL OSSA-MORENA ZONE OPHIOLITE SEQUENCES: A REMNANT OF RHEIC OCEAN IN SW IBERIA

The Early Paleozoic geodynamic evolution in SW Iberia is believed to have been dominated by the opening of the Rheic Ocean. The Rheic Ocean is generally accepted to have resulted from the drift of peri-Gondwanan terranes such as Avalonia from the northern margin of Gondwana during Late Cambrian-Early Ordovician times. The closure of the Rheic Ocean was the final result of a continent-continent collision between Gondwana and Laurussia that produced the Variscan orogen. The Ossa-Morena Zone is a peri-Gondwana terrane, which preserves spread fragments of ophiolites - the Internal Ossa-Morena Zones Ophiolite Sequences (IOMZOS). The final patchwork of the IOMZOS shows a complete oceanic lithospheric sequence with geochemical characteristics similar to the ocean-floor basalts, without any orogenic fingerprint and/or crustal contamination. The IOMZOS were obducted and imbricated with high pressure lithologies. Based on structural, petrological and whole-rock geochemical data, the authors argue that the IOMZOS represent fragments of the oceanic lithosphere from the Rheic Ocean. Zircon SHRIMP U-Pb geochronological data on metagabbros point to an age of ca. 480 Ma for IOMZOS, providing evidence of a well-developed ocean in SW Iberia during this period, reinforcing the interpretation of the Rheic Ocean as a wide ocean among the peri-Gondwanan terranes during Early Ordovician times.

Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

Examples from trees, related to discrete subsets, pseudo-radiality and omega-boundedness

We construct some examples using trees. Some of them are consistent counterexamples for the discrete reflection of certain topological properties. All the properties dealt with here were already known to be non-discretely reflexive if we assume CH and we show that the same is true assuming the existence of a Suslin tree. In some cases we actually get some ZFC results. We construct also, using a Suslin tree, a compact space that is pseudo-radial but it is not discretely generated. With a similar construction, but using an Aronszajn tree, we present a ZFC space that is first countable, omega-bounded but is not strongly w-bounded, answering a question of Peter Nyikos. (C) 2008 Elsevier B.V. All rights reserved.

Nuclear magnetic resonance characterization of metabolite disorder in orange trees caused by citrus sudden death disease

Citrus sudden death (CSD) is a new disease of sweet orange and mandarin trees grafted on Rangpur lime and Citrus volkameriana rootstocks. It was first seen in Brazil in 1999, and has since been detected in more than four million trees. The CSD causal agent is unknown and the current hypothesis involves a virus similar to Citrus tristeza virus or a new virus named Citrus sudden death-associated virus. CSD symptoms include generalized foliar discoloration, defoliation and root death, and, in most cases, it can cause tree death. One of the unique characteristics of CSD disease is the presence of a yellow stain in the rootstock bark near the bud union. This region also undergoes profound anatomical changes. In this study, we analyse the metabolic disorder caused by CSD in the bark of sweet orange grafted on Rangpur lime by nuclear magnetic resonance (NMR) spectroscopy and imaging. The imaging results show the presence of a large amount of non-functional phloem in the rootstock bark of affected plants. The spectroscopic analysis shows a high content of triacylglyceride and sucrose, which may be related to phloem blockage close to the bud union. We also propose that, without knowing the causal CSD agent, the determination of oil content in rootstock bark by low-resolution NMR can be used as a complementary method for CSD diagnosis, screening about 300 samples per hour.

Vedegenskaper i härskande och behärskade granar vid Remingstorp : Wood properties in dominant and sub-dominant trees of Norway spruce at Remingstorp

Variation in wood properties for Picea abies trees and logs of different dimensions has been studied at two sites in southern Sweden of different site quality class. Trees have been classified as dominant or sub-dominant, according to their height. Log and board grades were classified and strength grade of boards, basic density and annual ring width measured. A similar study made on four northern sites was used as reference material.Sub-dominant trees were of superior quality in comparison to dominant trees, when classified by log and board grades or strength grading. Differences were accentuated for the second log where the sub-dominant trees had superior strength and low amount of boards with coarse branches. The results correspond well to those from the northern region, Jämtland. The classifica¬tion of boards as well as bending strength indicated superior properties on timber from northern sites even though the basic density was similar.

Predictive models for chronic renal disease using decision trees, naïve bayes and case-based methods

Data mining can be used in healthcare industry to “mine” clinical data to discover hidden information for intelligent and affective decision making. Discovery of hidden patterns and relationships often goes intact, yet advanced data mining techniques can be helpful as remedy to this scenario. This thesis mainly deals with Intelligent Prediction of Chronic Renal Disease (IPCRD). Data covers blood, urine test, and external symptoms applied to predict chronic renal disease. Data from the database is initially transformed to Weka (3.6) and Chi-Square method is used for features section. After normalizing data, three classifiers were applied and efficiency of output is evaluated. Mainly, three classifiers are analyzed: Decision Tree, Naïve Bayes, K-Nearest Neighbour algorithm. Results show that each technique has its unique strength in realizing the objectives of the defined mining goals. Efficiency of Decision Tree and KNN was almost same but Naïve Bayes proved a comparative edge over others. Further sensitivity and specificity tests are used as statistical measures to examine the performance of a binary classification. Sensitivity (also called recall rate in some fields) measures the proportion of actual positives which are correctly identified while Specificity measures the proportion of negatives which are correctly identified. CRISP-DM methodology is applied to build the mining models. It consists of six major phases: business understanding, data understanding, data preparation, modeling, evaluation, and deployment.

Campus Life: In Perkins Arboretum there are birds of all feathers, trees that tell a story, and even romance (especially if you're a frog)

To the uninitiated, Perkins Arboretum is the edge of campus. For those familiar with its flora and fauna, the arboretum is a wondrous classroom and refuge.

Operações booleanas entre objetos delimitados por surfels usando constrained BSP-trees

As áreas de visualização e modelagem baseados em pontos têm sido pesquisadas ativamente na computação gráfica. Pontos com atributos (por exemplo, normais) são geralmente chamados de surfels e existem vários algoritmos para a manipulação e visualização eficiente deles. Um ponto chave para a eficiência de muitos métodos é o uso de estruturas de particionamento do espaço. Geralmente octrees e KD-trees, por utilizarem cortes alinhados com os eixos são preferidas em vez das BSP-trees, mais genéricas. Neste trabalho, apresenta-se uma estrutura chamada Constrained BSP-tree (CBSP-tree), que pode ser vista como uma estrutura intermediárias entre KD-trees e BSP-trees. A CBSP-tree se caracteriza por permitir cortes arbitrários desde que seja satisfeito um critério de validade dos cortes. Esse critério pode ser redefinido de acordo com a aplicação. Isso permite uma aproximação melhor de regões curvas. Apresentam-se algoritmos para construir CBSP-trees, valendo-se da flexibilidade que a estrutura oferece, e para realizar operações booleanas usando uma nova classificação de interior/exterior.

Occurrence of Quesada gigas on Schizolobium amazonicum trees in Maranhão and Pará States, Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)