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.

Interaction between polymorphisms of the Human Leukocyte Antigen and HPV-16 Variants on the risk of invasive cervical cancer

Background: Persistent infection with oncogenic types of human papillomavirus (HPV) is the major risk factor for invasive cervical cancer (ICC), and non-European variants of HPV-16 are associated with an increased risk of persistence and ICC. HLA class II polymorphisms are also associated with genetic susceptibility to ICC. Our aim is to verify if these associations are influenced by HPV-16 variability. Methods: We characterized HPV-16 variants by PCR in 107 ICC cases, which were typed for HLA-DQA1, DRB1 and DQB1 genes and compared to 257 controls. We measured the magnitude of associations by logistic regression analysis. Results: European ( E), Asian-American ( AA) and African (Af) variants were identified. Here we show that inverse association between DQB1*05 ( adjusted odds ratio [ OR] = 0.66; 95% confidence interval [CI]: 0.39-1.12]) and HPV-16 positive ICC in our previous report was mostly attributable to AA variant carriers ( OR = 0.27; 95% CI: 0.10-0.75). We observed similar proportions of HLA DRB1*1302 carriers in E-P positive cases and controls, but interestingly, this allele was not found in AA cases ( p = 0.03, Fisher exact test). A positive association with DRB1*15 was observed in both groups of women harboring either E ( OR = 2.99; 95% CI: 1.13-7.86) or AA variants ( OR = 2.34; 95% CI: 1.00-5.46). There was an inverse association between DRB1*04 and ICC among women with HPV-16 carrying the 350T [83L] single nucleotide polymorphism in the E6 gene ( OR = 0.27; 95% CI: 0.08-0.96). An inverse association between DQB1*05 and cases carrying 350G (83V) variants was also found ( OR = 0.37; 95% CI: 0.15-0.89). Conclusion: Our results suggest that the association between HLA polymorphism and risk of ICC might be influenced by the distribution of HPV-16 variants.

Excitation energies from ground-state density-functionals by means of generator coordinates

The generator-coordinate method is a flexible and powerful reformulation of the variational principle. Here we show that by introducing a generator coordinate in the Kohn-Sham equation of density-functional theory, excitation energies can be obtained from ground-state density functionals. As a viability test, the method is applied to ground-state energies and various types of excited-state energies of atoms and ions from the He and the Li isoelectronic series. Results are compared to a variety of alternative DFT-based approaches to excited states, in particular time-dependent density-functional theory with exact and approximate potentials.

Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

Stress and coping in older people with Alzheimer`s disease

To investigate stress intensity and coping style in older people with mild Alzheimer`s disease. The potential risk assessment of a stress event and the devising of coping strategies are dependent on cognitive function. Although older individuals with Alzheimer`s disease present significant cognitive impairment, little is known about how these individuals experience stress events and select coping strategies in stress situations. Survey. A convenient sample of 30 cognitively healthy older people and 30 individuals with mild Alzheimer`s disease were given an assessment battery of stress indicators (Symptom Stress List, Cornell Scale for Depression in Dementia, State-Trait Anxiety Inventory), coping style (Jalowiec Coping Scale) and cognitive performance (mini-mental state exam) were applied in both groups. Statistical analysis of the data employed the Mann-Whitney test to compare medians of stress indicators and coping style, Fischer`s exact test to compare proportions when expected frequencies were lower than five, and Spearman`s correlation coefficient to verify correlation between coping style and cognitive performance. Both groups suffered from the same stress intensity (p = 0.254). Regarding coping styles, although differences were not statistically significant (p = 0.124), emotion-oriented coping was predominant in the patients with Alzheimer`s disease. However, those individuals displaying better cognitive performance in the Alzheimer`s disease group had selected coping strategies focused on problem solving (p = 0.0074). Despite a tendency for older people with Alzheimer`s disease to select escape strategies and emotional control, rather than attempting to resolve or lesser the consequences arising from a problem, coping ultimately depends on cognitive performance of the individual. The findings of this study provide information and data to assist planning of appropriate support care for individuals with Alzheimer`s disease who experience stress situations, based on their cognitive performance.

Use of Hyaluronidase to Prevent Perineal Trauma During Spontaneous Births: A Randomized, Placebo-Controlled, Double-blind, Clinical Trial

Introduction: The purpose of this study was to compare the frequency and severity of perineal trauma during spontaneous birth with or without perineal injections of hyaluronidase (HAase). Methods: A randomized, placebo-controlled, double-blind clinical trial was conducted in a midwife-led, in-hospital birth center in Sao Paulo, Brazil. Primiparous women (N = 160) were randomly assigned to an experimental (n = 80) or control (n = 80) group. During the second stage of labor, women in the experimental group received an injection of 20.000 turbidity-reducing units of HAase in the posterior region of the perineum, and those in the control group received a placebo injection. The assessment of perineal outcome was performed by 2 independent nurse-midwives. A 1-tailed Fisher exact test was performed, and a P value < .025 was considered statistically significant. Results: Perineal integrity occurred in 34.2% of the experimental group and in 32.5% of the control group, which was not a statistically significant difference (P = .477). First-degree laceration was the most common trauma in the posterior region of the perineum in women in both groups (experimental = 56%, control = 42.6%). Severe perineal trauma occurred in 28.9% of the experimental group and 38.8% of the control group, which also was not a statistically significant difference (P =. 131). The depth of second-degree perineal lacerations in the experimental and control groups, measured by the Peri-Rule, was 1.9 cm and 2.3 cm, respectively. An episiotomy was performed in 11 women (experimental group = 3, control group = 8), and 4 (all in control group) had third-degree lacerations. Discussion: The use of injectable HAase did not increase the proportion of intact perineum and did not reduce the proportion of severe perineal trauma in our sample. J Midwifery Womens Health 2011; 56: 436-445 (C) 2011 by the American College of Nurse-Midwives.

Identification and Validation of Brazilian Chronic Pain Descriptors

Appropriate pain assessment is very important for managing chronic pain. Given the cultural differences in verbally expressing pain and in psychosocial problems, specific tools are needed. The goal of this study was to identify and validate Brazilian pain descriptors. A purposive sample of health professionals and chronic pain patients was recruited. Four studies were conducted using direct and indirect psychophysical methods: category estimation, magnitude estimation, and magnitude estimation and tine-length. Results showed the descriptors which best describe chronic pain in Brazilian culture and demonstrated that there is not a significant correlation between patients and health professionals and that the psychophysical scale of judgment of pain descriptors is valid, stable, and consistent. Results reinforced that the translations of word descriptors and research tools into another language may be inappropriate, owing to differences in perception and communication and the inadequacy of exact translations to reflect the intended meaning. Given the complexity of the chronic pain, personal suffering involved, and the need for accurate assessment of chronic pain using descriptors stemming from Brazilian culture and language, it is essential to investigate the most adequate words to describe chronic pain. Although it requires more refinement, the Brazilian chronic pain descriptors can be used further to develop a multidimensional pain assessment tool that is culturally sensitive. (C) 2009 by the American Society for Pain Management Nursing

Classification of normal swallowing and oropharyngeal dysphagia using wavelet

Oropharyngeal dysphagia is characterized by any alteration in swallowing dynamics which may lead to malnutrition and aspiration pneumonia. Early diagnosis is crucial for the prognosis of patients with dysphagia, and the best method for swallowing dynamics assessment is swallowing videofluoroscopy, an exam performed with X-rays. Because it exposes patients to radiation, videofluoroscopy should not be performed frequently nor should it be prolonged. This study presents a non-invasive method for the pre-diagnosis of dysphagia based on the analysis of the swallowing acoustics, where the discrete wavelet transform plays an important role to increase sensitivity and specificity in the identification of dysphagic patients. (C) 2008 Elsevier Inc. All rights reserved.

Gait Pattern Adaptation for an Active Lower-Limb Orthosis Based on Neural Networks

This work deals with neural network (NN)-based gait pattern adaptation algorithms for an active lower-limb orthosis. Stable trajectories with different walking speeds are generated during an optimization process considering the zero-moment point (ZMP) criterion and the inverse dynamic of the orthosis-patient model. Additionally, a set of NNs is used to decrease the time-consuming analytical computation of the model and ZMP. The first NN approximates the inverse dynamics including the ZMP computation, while the second NN works in the optimization procedure, giving an adapted desired trajectory according to orthosis-patient interaction. This trajectory adaptation is added directly to the trajectory generator, also reproduced by a set of NNs. With this strategy, it is possible to adapt the trajectory during the walking cycle in an on-line procedure, instead of changing the trajectory parameter after each step. The dynamic model of the actual exoskeleton, with interaction forces included, is used to generate simulation results. Also, an experimental test is performed with an active ankle-foot orthosis, where the dynamic variables of this joint are replaced in the simulator by actual values provided by the device. It is shown that the final adapted trajectory follows the patient intention of increasing the walking speed, so changing the gait pattern. (C) Koninklijke Brill NV, Leiden, 2011

Hybrid modeling of convective laminar flow in a permeable tube associated with the cross-flow process

The confined flows in tubes with permeable surfaces arc associated to tangential filtration processes (microfiltration or ultrafiltration). The complexity of the phenomena do not allow for the development of exact analytical solutions, however, approximate solutions are of great interest for the calculation of the transmembrane outflow and estimate of the concentration, polarization phenomenon. In the present work, the generalized integral transform technique (GITT) was employed in solving the laminar and permanent flow in permeable tubes of Newtonian and incompressible fluid. The mathematical formulation employed the parabolic differential equation of chemical species conservation (convective-diffusive equation). The velocity profiles for the entrance region flow, which are found in the connective terms of the equation, were assessed by solutions obtained from literature. The velocity at the permeable wall was considered uniform, with the concentration at the tube wall regarded as variable with an axial position. A computational methodology using global error control was applied to determine the concentration in the wall and concentration boundary layer thickness. The results obtained for the local transmembrane flux and the concentration boundary layer thickness were compared against others in literature. (C) 2007 Elsevier B.V. All rights reserved.

Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

Chaos-Galerkin solution of stochastic Timoshenko bending problems

This paper presents an accurate and efficient solution for the random transverse and angular displacement fields of uncertain Timoshenko beams. Approximate, numerical solutions are obtained using the Galerkin method and chaos polynomials. The Chaos-Galerkin scheme is constructed by respecting the theoretical conditions for existence and uniqueness of the solution. Numerical results show fast convergence to the exact solution, at excellent accuracies. The developed Chaos-Galerkin scheme accurately approximates the complete cumulative distribution function of the displacement responses. The Chaos-Galerkin scheme developed herein is a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2011 Elsevier Ltd. All rights reserved.

A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematics description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant-Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad`s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. (C) 2010 Elsevier B.V. All rights reserved.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier Inc. All rights reserved.