Complete set of invariants for a Bykov attractor

In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behaviour and, from the asymptotic properties of these non-converging time averages, we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. These invariants are determined by the quotient of the real parts of the eigenvalues of the equilibria, a linear combination of their imaginary components and also the transition maps between two cross sections on the separatrices.Comment: 23 pages, 4 figure

Moduli of stability for heteroclinic cycles of periodic solutions

We consider $C^2$ vector fields in the three dimensional sphere with an attracting heteroclinic cycle between two periodic hyperbolic solutions with real Floquet multipliers. The proper basin of this attracting set exhibits historic behavior and from the asymptotic properties of its orbits we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. As expected, this set contains the periods of the orbits involved in the cycle, a combination of their angular speeds, the rates of expansion and contraction in linearizing neighborhoods of them, besides information regarding the transition maps and the transition times between these neighborhoods. We conclude with an application of this result to a class of cycles obtained by the lifting of an example of R. Bowen.Comment: 23 pages, 6 figure

The role of the saddle-foci on the structure of a Bykov attractor

We consider a one-parameter family ( fλ)λ 0 of symmetric vector fields on the three-dimensional sphere whose flows exhibit a heteroclinic network between two saddle-foci inside a global attracting set. More precisely, when λ = 0, there is an attracting heteroclinic cycle between the two equilibria which is made of two 1- dimensional connections together with a 2-dimensional sphere which is both the stable manifold of one saddle-focus and the unstable manifold of the other. After slightly increasing the parameter while keeping the 1-dimensional connections unaltered, the two-dimensional invariant manifolds of the equilibria become transversal, and thereby create homoclinic and heteroclinic tangles. It is known that these newborn structures are the source of a countable union of topological horseshoes, which prompt the coexistence of infinitely many sinks and saddle-type invariant sets for many values of λ. We show that, for every small enough positive parameter λ, the stable and unstable manifolds of the saddle-foci and those infinitely many horseshoes are contained in the global attracting set of fλ; moreover, the horseshoes belong to the heteroclinic class of the equilibria. In addition, we show that the set of chain-accessible points from either of the saddle-foci is chain-stable and contains the closure of the invariant manifolds of the two equilibria.info:eu-repo/semantics/publishedVersio

Recurrent pneumonias in patient with antibody deficiency and normal immunoglobulins

The authors report the case of a 7-year-old girl, with a history of recurrent respiratory infections since five months of age. Immunological evaluation at four years of age revealed a normal level of total serum immunoglobulins, but a deficient humoral response to Streptococcus pneumoniae. Although having all normal IgG subclasses, the patient had inadequate antibody levels to all serotypes tested (1, 3, 5, 6, 9, and 14). Concurrent radiological evaluation showed diffuse atelectasis and bronchiectasis. Patient was started on IVIG, and subsequent chest CT scan revealed resolution of the above-mentioned lesions. To prevent irreversible damage to lung parenchyma, due to recurrent lower respiratory infections, it is important to identify immunocompromised individuals and treat them accordingly.É relatado o caso de uma menina de sete anos de idade com infecções de vias aéreas de repetição (otites, pneumonias e sinusites) desde os cinco meses de vida. A avaliação imunológica demonstrou produção inadequada de anticorpos ao Streptococcus pneumoniae após imunização para todos os sorotipos (1, 3, 5, 6, 9 e 14) testados, embora a paciente apresentasse níveis normais de imunoglobulinas. A avaliação radiológica, no momento da admissão, demonstrou presença de atelectasias difusas associadas a bronquiectasias. Após início do tratamento com imunoglobulina endovenosa e fisioterapia respiratória houve esvaecimento gradual até reversão das alterações radiológicas. Demonstrou-se, assim, a importância de um diagnóstico preciso para início de tratamento específico, com melhora gradual do quadro clínico e radiológico, evitando seqüelas pulmonares irreversíveis.UNIFESP-EPM Departamento de PediatriaUNIFESP-EPM Departamento de Diagnóstico por ImagemUNIFESP-EPMUniversidade de São Paulo Instituto de Ciências Biomédicas Departamento de ImunologiaUNIFESP, EPM, Depto. de PediatriaUNIFESP, EPM Depto. de Diagnóstico por ImagemUNIFESP, EPMSciEL

A note on reversibility and Pell equations

Esta nota é sobre automorfismos hiperbólicos do toro que são reversíveis relativamente a uma involução linear conservativa. Por estarmos em dimensão dois, será possível associar à reversibilidade uma equação de Pell generalizada de cujo conjunto de soluções retiraremos informação adi- cional sobre aquela propriedade. Provaremos ainda que a reversibilidade é uma propriedade rara neste contexto e descreveremos o caso genérico

Pathogens in ornamental waters: a follow up study

Ornamental waters of easy access and populated with animals are quite attractive and can hide threats to human health. Here we evaluated the microbiota of ornamental waters in a Lisbon park. Water and biofilm samples where collected, in 2 lakes (L1-L2) and ornamental fountains (L3-L4) in February/2015. In May/2015 and monthly during a year (starting March/2016) samples from L4 where collected. Microbiota identification was performed as described previouslya. Biofilm assembly was monitored by crystal violet assay and SEMb and antibiotic susceptibility was performed by conventional methods. The results of the first water sampling (Feb/2015) revealed the presence of Enterobactereaceae and non-fermentative oxidase-positive bacteria. Fountains and lakes presented different microbota being the highest diversity found in L1 hosting a duck population. This result suggested the existence of an interplay between animal inhabitants and microbiota which was confirmed by the second sampling of L4 (May/2015). Between the 2 sampling events a fish population was introduced and the microbiota was completely altered with the appearance of a typical fish pathogen (Aeromonas spp). This tendency was also confirmed over 2016. K. pneumoniae and Aeromonas spp., present as planktonic and biofilm organized bacteria in 2015 showed an enhanced ability to assemble biofilms in vitro at 25 °C than at 37 °C. Bacteria recovered from biofilm showed an increased antibiotic resistance compared to planktonic counterparts. The pilot study conducted during 2015 and the follow up study (still in progress) support a periodic control of ornamental water microbiota as simple preventive measure to avoid potential health issues.Fundação para a Ciência e Tecnologia for the grant PEst-OE/CTM/UI0084/2011N/

AUTOMATIC METHOD FOR GLAUCOMA CLASSIFICATION USING TEXTURE ANALYSIS, XGBOOST AND GRID SEARCH

Glaucoma is an irreversible pathology, generated by increased intraocular pressure. Early detection is critical and can pre- vent total vision loss. Clinical examinations are commonly used to detect the disease. Still, the time and cost of identi- fication is quite high. This paper presents a computational methodology that aims to assist specialists in the discov- ery of glaucoma through Computer Vision techniques. The proposed methodology consists in the application of several texture descriptors combined with a parameter optimiza- tion done through Grid search with the XGBoost classifier. A result was obtained with accuracy of 82.37% and ROC of 82.08%

Sleep and diet quality in adolescents

Background: Inability to sleep increases the vulnerability of overeating in particular high calorie density foods considering the current obesogenic environment. In addition, scientific research has shown that a healthy and balanced diet positively influences sleep quality. Objectives: This study aimed to evaluate the quality of sleep of adolescents in the county of Bragança and its association with diet quality. Methods: It was carry out the study in a population of 345 high school students. The data was collected in May 2017 through a questionnaire that included the Pittsburgh Sleep Quality Index (PSQI), by Ramalho (2008). Results: Throughout the study and following PSQI analysis, it was concluded that 39.71% (n=137) of participants showed poor quality of sleep (PSQI >5 points). The correlation between sleep quality and diet quality was assessed and a statistically significant association was found between the quality of sleep and the intake of snacks (X2=17.144; p≤0.001), sugary products (X2=18.603; p=0.000), fast-food (X2=12.353; p=0.002) and ready meals (X2=14.852; p≤0.001). The risk of suffering from poor sleep quality is higher in young populations who frequently eat snacks ([OR]: 2.811; 99%), sugary products ([OR]: 1.901; 95%), fast-food ([OR]: 4.000; 99%) and ready meals ([OR]: 5.621; 95%) in comparison with young populations who rarely eat this sort of food. The sleep quality is also significantly related to the number of correct eating habits (test t = 4.857, p≤0.001). Adolescents with good sleep quality presented a greater number of correct eating habits (mean: 7.85) compared to students with poor sleep quality (mean: 6.55). Conclusions: Through the analysis of the results, the correlation between sleep quality and dietary quality is evident. The risk of having poor quality of sleep is higher in students who frequently eat a high calorie diet and also in students who have fewer healthy eating habits.info:eu-repo/semantics/publishedVersio