Chaotic planar piecewise smooth vector fields with non-trivial minimal sets

In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is introduced. Some relations between minimality and orientable minimality are also investigated and the existence of new kinds of non-trivial minimal sets in chaotic systems is observed. The approach is geometrical and involves the ordinary techniques of non-smooth systems.

Description of the attainable sets of one-dimensional differential inclusions

The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a description of the attainable sets of differential inclusions. In particular, we obtain an exact delineation of the attainable set for a large class of nonlinear differential inclusions.

Zero sets of bivariate Hermite polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The evolution of phylogeographic data sets

Empirical phylogeographic studies have progressively sampled greater numbers of loci over time, in part motivated by theoretical papers showing that estimates of key demographic parameters improve as the number of loci increases. Recently, next-generation sequencing has been applied to questions about organismal history, with the promise of revolutionizing the field. However, no systematic assessment of how phylogeographic data sets have changed over time with respect to overall size and information content has been performed. Here, we quantify the changing nature of these genetic data sets over the past 20years, focusing on papers published in Molecular Ecology. We found that the number of independent loci, the total number of alleles sampled and the total number of single nucleotide polymorphisms (SNPs) per data set has improved over time, with particularly dramatic increases within the past 5years. Interestingly, uniparentally inherited organellar markers (e.g. animal mitochondrial and plant chloroplast DNA) continue to represent an important component of phylogeographic data. Single-species studies (cf. comparative studies) that focus on vertebrates (particularly fish and to some extent, birds) represent the gold standard of phylogeographic data collection. Based on the current trajectory seen in our survey data, forecast modelling indicates that the median number of SNPs per data set for studies published by the end of the year 2016 may approach similar to 20000. This survey provides baseline information for understanding the evolution of phylogeographic data sets and underscores the fact that development of analytical methods for handling very large genetic data sets will be critical for facilitating growth of the field.

Early loading of 6-mm-short implants with a moderately rough surface supporting single crowns: a prospective 5-year cohort study

AimTo evaluate prospectively the clinical and radiographic outcomes after 5years of early loading of 6-mm implants with a moderately rough (SLActive((R))) surface supporting single crowns in the posterior regions.Material and methodsThirty-five consecutive patients received 40 SLActive((R)) (Straumann) 6-mm implants with a diameter of 4.1mm (n=19) or 4.8mm (n=21). Insertion torque and resonance frequency analysis (RFA) were measured at implant installation. RFA was also measured at abutment connection. SynOcta abutments were tightened with 35Ncm after 6weeks of healing, and single porcelain fuse to metal crowns was cemented within 1week. Implant survival rate and marginal bone loss were evaluated at various time intervals until 5years after loading. The clinical crown/implant ratio was calculated as well.ResultsTwo of 40 implants were lost before loading (incorporation rate 95%), and no further implant loss or technical complications were encountered during the 5-year follow-up period. A mean marginal bone loss of 0.70.6mm was found after 5years of function. The clinical crown/implant ratio increased with time from 1.6 at the delivery of the prosthesis to 2 after 5years of loading.ConclusionSix millimeter implants with a SLActive((R)) moderately rough surface supporting single crowns in the posterior region and loaded after 6-7weeks maintained full function for at least 5year with low marginal bone resorption.

Histomorphometric analysis of pure titanium implants with porous surface versus rough surface

The purpose of this study was to analyze the bone repair around commercially pure titanium implants with rough and porous surface, fabricated using powder metallurgy technique, after their insertion in tibiae of rabbits. Seven male rabbits were used. Each animal received 3 porous-surface implants in the left tibia and 3 rough-surface implants in the right tibia. The rabbits were sacrificed 4 weeks after surgery and fragments of the tibiae containing the implants were submitted to histological and histomorphometric analyses to evaluate new bone formation at the implant-bone interface. Means (%) of bone neoformation obtained in the histomorphometric analysis were compared by Student's t-test for paired samples at 5% significance level.. The results of the histological analysis showed that osseointegration occurred for both types of implants with similar quality of bone tissue. The histomorphometric analysis revealed means of new bone formation at implant-bone interface of 79.69 ± 1.00% and 65.05 ± 1.23% for the porous- and rough-surface implants, respectively. Statistically significant difference was observed between the two types of implants with respect to the amount new bone formation (p<0.05). In conclusion, the porous-surface implants contributed to the osseointegration because they provide a larger contact area at implant-bone interface.

A support system that delineates location-choice sets for firms seeking office space

Factors influencing the location decisions of offices include traffic, accessibility, employment conditions, economic prospects and land-use policies. Hence tools for supporting real-estate managers and urban planners in such multidimensional decisions may be useful. Accordingly, the objective of this study is to develop a GIS-based tool to support firms who seek office accommodation within a given regional or national study area. The tool relies on a matching approach, in which a firm's characteristics (demand) on the one hand, and environmental conditions and available office spaces (supply) on the other, are analyzed separately in a first step, after which a match is sought. That is, a suitability score is obtained for every firm and for every available office space by applying some value judgments (satisfaction, utility etc.). The latter are powered by a focus on location aspects and expert knowledge about the location decisions of firms/organizations with respect to office accommodation as acquired from a group of real-estate advisers; it is stored in decision tables, and they constitute the core of the model. Apart from the delineation of choice sets for any firm seeking a location, the tool supports two additional types of queries. Firstly, it supports the more generic problem of optimally allocating firms to a set of vacant locations. Secondly, the tool allows users to find firms which meet the characteristics of any given location. Moreover, as a GIS-based tool, its results can be visualized using GIS features which, in turn, facilitate several types of analyses.