Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.

Closures of positive braids and the Morton-Franks-Williams inequality

We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is an orthonormal basis for the inner product of the Hecke algebra of the braid group defined by Kálmán, who first obtained this result by using an interesting connection with Contact Topology. We also introduce a new technique to study the Homflypt polynomial for closures of positive braids, namely resolution trees whose leaves are simple braids. In terms of these simple resolution trees, we characterize closed positive braids for which the Morton-Franks-Williams inequality is strict. In particular, we determine explicitly the positive braid words on three strands whose closures have braid index three.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Braid groups, mapping class groups, and Torelli groups

This thesis discusses subgroups of mapping class groups of particular surfaces. First, we study the Torelli group, that is, the subgroup of the mapping class group that acts trivially on the first homology. We investigate generators of the Torelli group, and we give an algorithm that factorizes elements of the Torelli group into products of particular generators. Furthermore, we investigate normal closures of powers of standard generators of the mapping class group of a punctured sphere. By using the Jones representation, we prove that in most cases these normal closures have infinite index in the mapping class group. We prove a similar result for the hyperelliptic mapping class group, that is, the group that consists of mapping classes that commute with a fixed hyperelliptic involution. As a corollary, we recover an older theorem of Coxeter (with 2 exceptional cases), which states that the normal closure of the m-th power of standard generators of the braid group has infinite index in the braid group. Finally, we study finite index subgroups of braid groups, namely, congruence subgroups of braid groups. We discuss presentations of these groups and we provide a topological interpretation of their generating sets.

Association Between Parity, Pre-pregnancy Body Mass Index And Gestational Weight Gain.

To analyze the relationship between parity, pre-pregnancy body mass index (BMI), and gestational weight gain (GWG). This observational controlled study was conducted from November 2013 to April 2014, with postpartum women who started antenatal care up to 14 weeks and had full-term births. Data were collected from medical records and antenatal cards. Descriptive and bivariate analyses were performed. The significance level was 5%. Data were collected from 130 primiparous and 160 multiparous women. At the beginning of prenatal care, 54.62% of the primiparous were eutrophic, while the majority of multiparous were overweight or obese (62.51%). Multiparas are two times more likely to be obese at the beginning of their pregnancies, when compared to primiparas. The average pre-pregnancy weight and final pregnancy weight was significantly higher in multiparous, however, the mean GWG was higher among primiparous. We found an inverse correlation between parity and the total GWG, but initial BMI was significantly higher in multiparas. Nevertheless, monitoring of the GWG through actions that promote a healthier lifestyle is needed, regardless of parity and nutritional status, in order to prevent excessive GWG and postpartum weight retention and consequently inadequate pre-pregnancy nutritional status in future pregnancies.

Sorghum Flour Fractions: Correlations Among Polysaccharides, Phenolic Compounds, Antioxidant Activity And Glycemic Index.

Nutrients composition, phenolic compounds, antioxidant activity and estimated glycemic index (EGI) were evaluated in sorghum bran (SB) and decorticated sorghum flour (DSF), obtained by a rice-polisher, as well as whole sorghum flour (WSF). Correlation between EGI and the studied parameters were determined. SB presented the highest protein, lipid, ash, β-glucan, total and insoluble dietary fiber contents; and the lowest non-resistant and total starch contents. The highest carbohydrate and resistant starch contents were in DSF and WSF, respectively. Phenolic compounds and antioxidant activities were concentrated in SB. The EGI values were: DSF 84.5±0.41; WSF 77.2±0.33; and SB 60.3±0.78. Phenolic compounds, specific flavonoids and antioxidant activities, as well as total, insoluble and soluble dietary fiber and β-glucans of sorghum flour samples were all negatively correlated to EGI. RS content was not correlated to EGI.

Validação da Body Appreciation Scale (BAS), Life Satisfaction Index for the Third Age (LSITA) e do Aging Perception Questionnaire (APQ) para a língua portuguesa no Brasil : um estudo em idosos brasileiros

Universidade Estadual de Campinas . Faculdade de Educação Física

Association of polymorphisms at the ADIPOR1 regulatory region with type 2 diabetes and body mass index in a Brazilian population with European or African ancestry

Association studies between ADIPOR1 genetic variants and predisposition to type 2 diabetes (DM2) have provided contradictory results. We determined if two single nucleotide polymorphisms (SNP c.-8503G>A and SNP c.10225C>G) in regulatory regions of ADIPOR1 in 567 Brazilian individuals of European (EA; N = 443) or African (AfA; N = 124) ancestry from rural (quilombo remnants; N = 439) and urban (N = 567) areas. We detected a significant effect of ethnicity on the distribution of the allelic frequencies of both SNPs in these populations (EA: -8503A = 0.27; AfA: -8503A = 0.16; P = 0.001 and EA: 10225G = 0.35; AfA: 10225G = 0.51; P < 0.001). Neither of the polymorphisms were associated with DM2 in the case-control study in EA (SNP c.-8503G>A: DM2 group -8503A = 0.26; control group -8503A = 0.30; P = 0.14/SNP 10225C>G: DM2 group 10225G = 0.37; control group 10225G = 0.32; P = 0.40) and AfA populations (SNP c.-8503G>A: DM2 group -8503A = 0.16; control group -8503A = 0.15; P = 0.34/SNP 10225C>G: DM2 group 10225G = 0.51; control group 10225G = 0.52; P = 0.50). Similarly, none of the polymorphisms were associated with metabolic/anthropometric risk factors for DM2 in any of the three populations, except for HDL cholesterol, which was significantly higher in AfA heterozygotes (GC = 53.75 ± 17.26 mg/dL) than in homozygotes. We conclude that ADIPOR1 polymorphisms are unlikely to be major risk factors for DM2 or for metabolic/anthropometric measurements that represent risk factors for DM2 in populations of European and African ancestries.

Diet quality index adjusted for energy requirements in adults

This study aimed to develop a diet quality index (DQI-a) adjusted for energy requirement. Dietary intake of adults was assessed using 24-hour food recall. The DQI was developed for scores evenly distributed across ten items characterizing different aspects of diet: food groups, nutrients, and variety. The components categorized under the food groups from the Dietary Guide for Brazilians were adjusted according to the estimated energy requirements of the population studied. Index consistency and correlation with nutrients of the diet was analyzed by Cronbach's alpha. A total of 737 individuals were assessed and energy requirements ranged from 1,800 to 2,500kcal among women and 2,500 to 3,400kcal in men. The food group with greatest variation in total portions was cereals and tubers. Cronbach's alpha of the DQI-a was 0.643 and the index correlated with most of the nutrients. The DQI-a can be considered a valuable instrument for assessing diet quality of the Brazilian population.

Body Mass Index, Cigarette Smoking, and Alcohol Consumption and Cancers of the Oral Cavity, Pharynx, and Larynx: Modeling Odds Ratios in Pooled Case-Control Data

study-specific results, their findings should be interpreted with caution

Short-term nutritional counseling reduces body mass index, waist circumference, triceps skinfold and triglycerides in women with metabolic syndrome

Background: It is recognized that the growing epidemic of metabolic syndrome is related to dietary and lifestyle changes. Objective: The purpose of this study was to evaluate short-term application of nutritional counseling in women with metabolic syndrome. Methods: This follow-up study was conducted from September to November 2008 with thirty three women >= 35 years old screened clinically for nutritional counseling. Dietary intake was reported, and biochemical and body composition measures were taken at baseline and after three months of follow-up. Results: Of the 33 women evaluated, 29 patients completed the study. The prevalence of type 2 diabetes mellitus, hypertension, dyslipidemia, and obesity was high at 38%, 72.4%, 55.2%, and 75.8%, respectively. At the end of three-months of follow-up, a significant decline in body mass index, waist circumference, triceps skinfold, and triglycerides was observed, as was an increase in calcium and vitamin D intake. The multiple regression analysis showed that changes in body mass index, triceps skinfold, waist circumference and triglyceride levels after nutritional intervention were positively associated with changes in anthropometric (loss of body weight) and biochemical (decrease of TG/HDL-c ratio) parameters. Moreover, waist circumference changes were negatively associated with changes in calcium and vitamin D intake. Conclusion: Short-term nutritional counseling improved some factors of metabolic syndrome. Moreover, the increases in calcium and vitamin D consumption can be associated with the improvement in markers of metabolic syndrome.

Prognostic index expression of cyclin-D1, cerbB-2 and VEGF: metastases vs corresponding primary cancers and metastatic vs non-metastatic adenocarcinomas

The prognostic relevance of different molecular markers in lung cancer is a crucial issue still worth investigating, and the specimens collected and analyzed represent a valuable source of material. Cyclin-D1, c-erbB-2 and vascular endothelial growth factor (VEGF) have shown to be promising as prognosticators in human cancer. In this study, we sought to examine the importance of Cyclin-D1, c-erbB-2 and VEGF, and to study the quantitative relationship among these factors and disease progression in metastases vs corresponding primary cancer, and metastatic vs non metastatic cancers. Material and Methods: We used immunohistochemistry and morphometric analysis to evaluate the amount of tumour staining for Cyclin-D1, c-erbB-2 and VEGF in 52 patients with surgically excised ademocarcinoma of the lung, and the outcome for our study was survival time until death from hematogenic metastases. Results: Metastasis presented lower c-erbB-2 expression than corresponding primary cancers (p=0.02). Cyclin-D1 and VEGF expression were also lower in metastases than in corresponding primary cancers, but this difference did not achieve statistical significance. Non-metastatic cancers also presented significantly lower Cyclin-D1 and c-erbB-2 expression than metastatic cancers (p<0.01 and p<0.01, respectively). Equally significant was the difference between higher c-erbB-2 expression by metastatic cancers compared to non-metastatic cancers (p=0.02). Considering survival in Kaplan-Maier analysis, Cyclin-D1 (p=0.04), c-erbB-2 (p=0.04) and VEGF (p<0.01) were important predictors of survival in metastatic cancers.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

Validity and reliability of the Portuguese version of the Epilepsy Medication Treatment Complexity Index for Brazil

We evaluated the reliability and validity of a Brazilian-Portuguese version of the Epilepsy Medication Treatment Complexity Index (EMTCI). Interrater reliability was evaluated with the intraclass correlation coefficient (ICC), and validity was evaluated by correlation of mean EMTCI scores with the following variables: number of antiepileptic drugs (AEDs), seizure control, patients` perception of seizure control, and adherence to the therapeutic regimen as measured with the Morisky scale. We studied patients with epilepsy followed in a tertiary university-based hospital outpatient clinic setting, aged 18 years or older, independent in daily living activities, and without cognitive impairment or active psychiatric disease. ICCs ranged from 0.721 to 0.999. Mean EMTCI scores were significantly correlated with the variables assessed. Higher EMTCI scores were associated with an increasing number of AEDs, uncontrolled seizures, patients` perception of lack of seizure control, and poorer adherence to the therapeutic regimen. The results indicate that the Brazilian-Portuguese EMTCI is reliable and valid to be applied clinically in the country. The Brazilian-Portuguese EMTCI version may be a useful tool in developing strategies to minimize treatment complexity, possibly improving seizure control and quality of life in people with epilepsy in our milieu. (C) 2011 Elsevier Inc. All rights reserved.

Performance of body fat and body mass index cutoffs in elevated blood pressure screening among male children and adolescents

For percentage of body fat (%BF), there are no internationally accepted cutoffs. The primary function of body fat cutoffs should be to identify not only excessive body fatness, but also the increased risk of unhealthy outcomes, such as hypertension. The purpose of this study was to analyze the accuracy of different %BF and body mass index (BMI) cutoffs as screening measures for EBP in pediatric populations. It was a cross-sectional study with a sample of 358 male subjects from 8 to 18 years old. BP was measured by the oscilometric method, and body composition was measured by dual-energy X-ray absorptiometry (DXA). The accuracy of three reference tables used for body fat cutoffs was assessed. The three body fat reference tables were highly specific, but insensitive, for elevated BP screening. For elevated BP screening, all body fat cutoffs presented similar sensitivity (range=48.3-53.7%) and specificity (range=79.2-84.1%). The body fat cutoffs performed no better than BMI in screening of children and adolescents at risk of elevated BP (EBP). BMI seems a more attractive tool for this function, as it performed similarly and can be applied in large surveys and with lower costs. Hypertension Research (2011) 34, 963-967; doi:10.1038/hr.2011.61; published online 26 May 2011