From symmetry breaking to Poisson Point Process in 2D Voronoi Tessellations: the generic nature of hexagons

We bridge the properties of the regular triangular, square, and hexagonal honeycomb Voronoi tessellations of the plane to the Poisson-Voronoi case, thus analyzing in a common framework symmetry breaking processes and the approach to uniform random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise, whose variance is given by the parameter α2 times the square of the inverse of the average density of points. We analyze the number of sides, the area, and the perimeter of the Voronoi cells. For all valuesα >0, hexagons constitute the most common class of cells, and 2-parameter gamma distributions provide an efficient description of the statistical properties of the analyzed geometrical characteristics. The introduction of noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α = 0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise withα <0.12. For all tessellations and for small values of α, we observe a linear dependence on α of the ensemble mean of the standard deviation of the area and perimeter of the cells. Already for a moderate amount of Gaussian noise (α >0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α >2, results converge to those of Poisson-Voronoi tessellations. The geometrical properties of n-sided cells change with α until the Poisson- Voronoi limit is reached for α > 2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established. This law allows for an easy link to the Lewis law for areas and agrees with exact asymptotic results. Finally, for α >1, the ensemble mean of the cells area and perimeter restricted to the hexagonal cells agree remarkably well with the full ensemble mean; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be interpreted as typical polygons in 2D Voronoi tessellations.

Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces.

Identification of lattices from genus of compact surface

In this work we propose procedures for the identification of structure of group associate lattices from fundamental region F4g of regular tessellations {4g; 4g} in the Euclidian plane and hyperbolic plane, where g denote genus of compact surface. © 2006 SBrT.

The relationship between physical aspects of quality of life and extreme levels of regular physical activity in adults

This study aimed to check for any significant differences in perceived quality of life, specifically aspects of a physical nature, among volunteers who are more physically active and those less physically active in a university community. The sample consisted of 1,966 volunteers in a university community in Brazil. To assess physical activity levels, volunteers responded to the International Physical Activity Questionnaire (IPAQ), and to analyse the perception of quality of life they responded to WHOQOL-bref, which is classified into three groups according to level of physical activity, taking into account the metabolic equivalent index (MET) over a full week. For comparison, consideration was given to the first and third tertiles, respectively, namely groups of more and less active students. The results indicated that individuals who engaged in more physical activity had a more positive perception of quality of life compared to those who were less active in physical aspects related to the ability to work, energy for day-to-day activities and locomotion.

O aluno portador de visão subnormal na escola regular: desafio para o professor?

Purpose:1) To check self-knowledge and needs for orientation among regular class teachers working with low vision students; 2) To gather information to assist the training on visual deficiency of regular class teachers. Methods: A survey was conducted for the academic year of 1999 among those teachers working in public schools, Campinas/SP/Brazil, of which 11 were municipal and 9 state schools, respectively 79.0% and 90.0% of these schools. A self-administered questionnaire was used as data collection instrument. Results: The sample was composed of 50 teachers with a regular class experience averaging 20 years. Most of them, 94.0%, said that they had no specific preparation in the area of low vision. Only 18 teachers declared to have received some kind of information/orientation in order to work with their low vision students and of those only 15 teachers mentioned the kind of orientation received. The whole group of 50 declared interest in receiving information. From the information/orientation requested 66.0% mentioned extended working class materials, 50.0% visual performance and eye disease of their students and 46.0% visual acuity/visual field. Conclusion: It was detected that teachers of regular classes received none or little information about their low vision students but demonstrated interest in its obtention. It was also shown that those teachers are not prepared to work with visually impaired children.

A inclusão da criança com Síndrome de Down na rede regular de ensino: desafios e possibilidades

O estudo teve como objetivo buscar evidências na literatura acerca da inclusão de crianças com Síndrome de Down na rede regular de ensino. Elaboraram-se revisão da literatura e busca dos artigos nas bases de dados PubMed e PsycINFO, utilizando as palavras-chave Down syndrome, schools, mainstreaming (education), education, infant, newborn, adolescent, child e preschool, no período de 1994 a 2007. Selecionaram-se oito artigos e sua análise permitiu a identificação do tema: experiências e recomendações para a inclusão. Os dados desta revisão, em sua maioria provenientes de relatos de experiências, indicaram que os fatores que colaboraram ou dificultaram o processo de inclusão da criança com síndrome de Down na rede regular de ensino relacionaram-se à escola, aos pais e ao professor. Os resultados deste estudo oferecem possibilidades para melhorar o processo de inclusão, apresentam os desafios e ainda apontam a necessidade do desenvolvimento de novas pesquisas, cujos resultados possam ser aplicados na prática.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

EVOLUTION OF DISPARITY BETWEEN THE REGULAR AND VARIANT PHLOEM IN BIGNONIEAE (BIGNONIACEAE)

Premise of the study: The phloem is a plant tissue with a critical role in plant nutrition and signaling. However, little is still known about the evolution of this tissue. In lianas of the Bignoniaceae, two distinct types of phloem coexist: a regular and a variant phloem. The cells associated with these two phloem types are known to be anatomically different; however, it is still unclear what steps were involved in the evolution of such differences. Methods: Here we studied the anatomical development of the regular and variant phloem in representatives of all 21 genera of Bignonieae and used a phylogenetic framework to investigate the timing of changes associated with the evolution of each phloem type. Key results: We found that the variant phloem always appears in a determinate location, between the leaf orthostichies. Furthermore, the variant phloem was mostly occupied by very wide sieve tubes and generally included a higher concentration of fibers, indicating an increase in conduction and mechanical support. On the other hand, the regular phloem included much more parenchyma, more and wider rays, and tiny sieve tubes that resembled terminal sieve tubes from plants with seasonal formation of vascular tissues; these findings suggest reduced conduction and higher storage capacity in the regular phloem. Conclusions: Overall, differences between the regular and variant phloem increased over time, leading to further specialization in conduction in the variant phloem and an increase in storage specialization in the regular phloem.

Treatment of vitamin D deficiency increases lower limb muscle strength in institutionalized older people independently of regular physical activity: a randomized double-blind controlled trial

Aims: To investigate the effects of a 6-month supplementation with calcium and cholecalciferol on biochemical parameters and muscle strength of institutionalized elderly. Methods: This prospective, double-blind, placebo-controlled, randomized trial included Brazilian institutionalized people 6 60 years of age receiving a 6-month supplementation ( December to May) of daily calcium plus monthly placebo (calcium/placebo group) or daily calcium plus oral cholecalciferol (150,000 IU once a month during the first 2 months, followed by 90,000 IU once a month for the last 4 months; calcium/vitamin D group). Fasting blood samples for 25-(OH) D, PTH and calcium determination were collected (n = 56) and muscle tests were performed ( n = 46) to measure the strength of hip flexors (SHF) and knee extensors (SKE) before ( baseline) and after the 6-month intervention ( 6 months). Results: Due to seasonal variations, serum 25( OH) D significantly enhanced in both groups after treatment, but the calcium/vitamin D group had significantly higher 25-(OH) D levels than the calcium/placebo group (84 vs. 33%, respectively; p < 0.0001). No cases of hypercalcemia were observed. While the calcium/placebo group showed no improvement in SHF and SKE at 6 months (p = 0.93 and p = 0.61, respectively), SHF was increased in the calcium/vitamin D group by 16.4% (p = 0.0001) and SKE by 24.6% (p = 0.0007). Conclusions: The suggested cholecalciferol supplementation was safe and efficient in enhancing 25(OH)D levels and lower limb muscle strength in the elderly, in the absence of any regular physical exercise practice. Copyright (C) 2009 S. Karger AG, Basel

Concentration inequalities and laws of large numbers under epistemic and regular irrelevance

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance that are expressed using lower and upper expectations. The results build upon De Cooman and Miranda`s recent inequalities and laws of large numbers. The proofs indicate connections between the theory of martingales and concepts of epistemic and regular irrelevance. (C) 2010 Elsevier Inc. All rights reserved.

Adsorption hysteresis and criticality in regular mesoporous materials

In the present work, various theories predicting the critical diameter for the absence of capillary condensation and hysteresis are applied to experimental adsorption isotherms of vapors on regular mesoporous materials. Among the various theories studied, the tensile strength approximation proposed by the authors was found to be the most successful. Reversibility of nitrogen adsorption at 77.4 K was studied on pure MCM-41 of various pore sizes, as well as mixtures of pure MCM-41 samples in a 1:1 ratio. The results of PSD and hysteresis on MCM-41 mixtures are close to that expected from studies of the pure materials. The estimates of hysteresis critical temperature and diameter of MCM-41, HMS, FSM and KIT materials are also provided.

Children's cooperative behavior and interactions in trained and untrained work groups in regular classrooms

This study examined group and individual factors that facilitate changes in cooperation and learning outcomes in trained and untrained work groups of elementary school-age children. The study had two foci. The first was to determine if the cooperative behaviors and interactions of children in classroom groups who were trained in cooperative learning skins were different from those of children who were given no training, and the second was to investigate small group interactions and achievement in these groups over time. The results showed that there were observable differences between student interactions in the two conditions and these differences were maintained over time. Compared with children in the untrained groups, those in the trained groups were consistently more cooperative and helpful to each other; they actively tried to involve each other in the learning task by using language which was more inclusive (e.g., frequent use of ''we''), and they gave more explanations to assist each other as they worked together. It appeared that as the children worked together over time, they became more responsive to the learning needs of each other. Furthermore, the children in the trained groups performed significantly better on the learning outcomes questionnaire than those in the untrained groups. (C) 1997 Society for the Study of School Psychology. Published by Elsevier Science Ltd.