Dynamics of a charged particle in a dissipative Fermi-Ulam model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Factors associated with recurrence of venous leg ulcers : a survey and retrospective chart review

Background: Chronic venous leg ulcers have a significant impact on older individuals’ well-being and health care resources. Unfortunately after healing, up to 70% recur. ----- Objective: To examine the relationships between leg ulcer recurrence and physical activity, compression, nutrition, health, psychosocial indicators and self-care activities in order to provide information for preventive strategies. ----- Design: Survey and retrospective chart review Settings: Two metropolitan hospital and three community-based leg ulcer clinics. ----- Subjects: A sample of 122 community living patients with leg ulcer of venous aetiology which had healed between 12 and 36 months prior to the survey. ---- Methods: Data were collected from medical records on demographics, medical history and previous ulcer history and treatments; and from self-report questionnaires on physical activity, nutrition, psychosocial measures, ulcer recurrences and history, compression and other self-care activities. All variables significantly associated with recurrence at the bivariate level were entered into a logistic regression model to determine their independent influences on recurrence. ----- Results: Median follow-up time was 24 months (range 12–40 months). Sixty-eight percent of participants had recurred. Bivariate analysis found recurrence was positively associated with ulcer duration, cardiac disease, a Body Mass Index ≤20, scoring as at-risk of malnutrition and depression; and negatively associated with increased physical activity, leg elevation, wearing Class 2 (20–25mmHg) or Class 3 (30–40mmHg) compression hosiery, and higher self-efficacy scores. After adjusting for all variables, an hour/day of leg elevation (OR=0.04, 95% CI=0.01–0.17), days/week in Class 2 or 3 compression hosiery (OR=0.53, 95% CI=0.34–0.81), Yale Physical Activity Survey score (OR=0.95, 95% CI=0.92–0.98), cardiac disease (OR=5.03, 95% CI=1.01–24.93) and General Self-Efficacy scores (OR=0.83, 95% CI=0.72–0.94) remained significantly associated (p<0.05) with recurrence. ----- Conclusions: Results indicate a history of cardiac disease is a risk factor for recurrence; while leg elevation, physical activity, compression hosiery and strategies to improve self-efficacy are likely to prevent recurrence.

Compression for preventing recurrence of venous ulcers

Background: Up to 1% of adults will suffer from leg ulceration at some time. The majority of leg ulcers are venous in origin and are caused by high pressure in the veins due to blockage or weakness of the valves in the veins of the leg. Prevention and treatment of venous ulcers is aimed at reducing the pressure either by removing / repairing the veins, or by applying compression bandages / stockings to reduce the pressure in the veins. The vast majority of venous ulcers are healed using compression bandages. Once healed they often recur and so it is customary to continue applying compression in the form of bandages, tights, stockings or socks in order to prevent recurrence. Compression bandages or hosiery (tights, stockings, socks) are often applied for ulcer prevention. Objectives To assess the effects of compression hosiery (socks, stockings, tights) or bandages in preventing the recurrence of venous ulcers. To determine whether there is an optimum pressure/type of compression to prevent recurrence of venous ulcers. Search methods The searches for the review were first undertaken in 2000. For this update we searched the Cochrane Wounds Group Specialised Register (October 2007), The Cochrane Central Register of Controlled Trials (CENTRAL) - The Cochrane Library 2007 Issue 3, Ovid MEDLINE - 1950 to September Week 4 2007, Ovid EMBASE - 1980 to 2007 Week 40 and Ovid CINAHL - 1982 to October Week 1 2007. Selection criteria Randomised controlled trials evaluating compression bandages or hosiery for preventing venous leg ulcers. Data collection and analysis Data extraction and assessment of study quality were undertaken by two authors independently. Results No trials compared recurrence rates with and without compression. One trial (300 patients) compared high (UK Class 3) compression hosiery with moderate (UK Class 2) compression hosiery. A intention to treat analysis found no significant reduction in recurrence at five years follow up associated with high compression hosiery compared with moderate compression hosiery (relative risk of recurrence 0.82, 95% confidence interval 0.61 to 1.12). This analysis would tend to underestimate the effectiveness of the high compression hosiery because a significant proportion of people changed from high compression to medium compression hosiery. Compliance rates were significantly higher with medium compression than with high compression hosiery. One trial (166 patients) found no statistically significant difference in recurrence between two types of medium (UK Class 2) compression hosiery (relative risk of recurrence with Medi was 0.74, 95% confidence interval 0.45 to 1.2). Both trials reported that not wearing compression hosiery was strongly associated with ulcer recurrence and this is circumstantial evidence that compression reduces ulcer recurrence. No trials were found which evaluated compression bandages for preventing ulcer recurrence. Authors' conclusions No trials compared compression with vs no compression for prevention of ulcer recurrence. Not wearing compression was associated with recurrence in both studies identified in this review. This is circumstantial evidence of the benefit of compression in reducing recurrence. Recurrence rates may be lower in high compression hosiery than in medium compression hosiery and therefore patients should be offered the strongest compression with which they can comply. Further trials are needed to determine the effectiveness of hosiery prescribed in other settings, i.e. in the UK community, in countries other than the UK.

The impact of psychosocial factors on adherence to compression therapy to prevent recurrence of venous leg ulcers

Aims To identify self-care activities undertaken and determine relationships between self-efficacy, depression, quality of life, social support and adherence to compression therapy in a sample of patients with chronic venous insufficiency. Background Up to 70% of venous leg ulcers recur after healing. Compression hosiery is a primary strategy to prevent recurrence, however, problems with adherence to this strategy are well documented and an improved understanding of how psychosocial factors influence patients with chronic venous insufficiency will help guide effective preventive strategies. Design Cross-sectional survey and retrospective medical record review. Method All patients previously diagnosed with a venous leg ulcer which healed between 12–36 months prior to the study were invited to participate. Data on health, psychosocial variables and self-care activities were obtained from a self-report survey and data on medical and previous ulcer history were obtained from medical records. Multiple linear regression modelling was used to determine the independent influences of psychosocial factors on adherence to compression therapy. Results In a sample of 122 participants, the most frequently identified self-care activities were application of topical skin treatments, wearing compression hosiery and covering legs to prevent trauma. Compression hosiery was worn for a median of 4 days/week (range 0–7). After adjustment for all variables and potential confounders in a multivariable regression model, wearing compression hosiery was found to be significantly positively associated with participants’ knowledge of the cause of their condition (p=0.002), higher self-efficacy scores (p=0.026) and lower depression scores (p=0.009). Conclusion In this sample, depression, self-efficacy and knowledge were found to be significantly related to adherence to compression therapy. Relevance to clinical practice These findings support the need to screen for and treat depression in this population. In addition, strategies to improve patient knowledge and self-efficacy may positively influence adherence to compression therapy.

Identification of factors contributing to recurrence of venous leg ulcers

Background and Significance Venous leg ulcers are a significant cause of chronic ill-health for 1–3% of those aged over 60 years, increasing in incidence with age. The condition is difficult and costly to heal, consuming 1–2.5% of total health budgets in developed countries and up to 50% of community nursing time. Unfortunately after healing, there is a recurrence rate of 60 to 70%, frequently within the first 12 months after heaing. Although some risk factors associated with higher recurrence rates have been identified (e.g. prolonged ulcer duration, deep vein thrombosis), in general there is limited evidence on treatments to effectively prevent recurrence. Patients are generally advised to undertake activities which aim to improve the impaired venous return (e.g. compression therapy, leg elevation, exercise). However, only compression therapy has some evidence to support its effectiveness in prevention and problems with adherence to this strategy are well documented. Aim The aim of this research was to identify factors associated with recurrence by determining relationships between recurrence and demographic factors, health, physical activity, psychosocial factors and self-care activities to prevent recurrence. Methods Two studies were undertaken: a retrospective study of participants diagnosed with a venous leg ulcer which healed 12 to 36 months prior to the study (n=122); and a prospective longitudinal study of participants recruited as their ulcer healed and data collected for 12 months following healing (n=80). Data were collected from medical records on demographics, medical history and ulcer history and treatments; and from self-report questionnaires on physical activity, nutrition, psychosocial measures, ulcer history, compression and other self-care activities. Follow-up data for the prospective study were collected every three months for 12 months after healing. For the retrospective study, a logistic regression model determined the independent influences of variables on recurrence. For the prospective study, median time to recurrence was calculated using the Kaplan-Meier method and a Cox proportional-hazards regression model was used to adjust for potential confounders and determine effects of preventive strategies and psychosocial factors on recurrence. Results In total, 68% of participants in the retrospective study and 44% of participants in the prospective study suffered a recurrence. After mutual adjustment for all variables in multivariable regression models, leg elevation, compression therapy, self efficacy and physical activity were found to be consistently related to recurrence in both studies. In the retrospective study, leg elevation, wearing Class 2 or 3 compression hosiery, the level of physical activity, cardiac disease and self efficacy scores remained significantly associated (p<0.05) with recurrence. The model was significant (p <0.001); with a R2 equivalent of 0.62. Examination of relationships between psychosocial factors and adherence to wearing compression hosiery found wearing compression hosiery was significantly positively associated with participants’ knowledge of the cause of their condition (p=0.002), higher self-efficacy scores (p=0.026) and lower depression scores (p=0.009). Analysis of data from the prospective study found there were 35 recurrences (44%) in the 12 months following healing and median time to recurrence was 27 weeks. After adjustment for potential confounders, a Cox proportional hazards regression model found that at least an hour/day of leg elevation, six or more days/week in Class 2 (20–25mmHg) or 3 (30–40mmHg) compression hosiery, higher social support scale scores and higher General Self-Efficacy scores remained significantly associated (p<0.05) with a lower risk of recurrence, while male gender and a history of DVT remained significant risk factors for recurrence. Overall the model was significant (p <0.001); with an R2 equivalent 0.72. Conclusions The high rates of recurrence found in the studies highlight the urgent need for further information in this area to support development of effective strategies for prevention. Overall, results indicate leg elevation, physical activity, compression hosiery and strategies to improve self-efficacy are likely to prevent recurrence. In addition, optimal management of depression and strategies to improve patient knowledge and self-efficacy may positively influence adherence to compression therapy. This research provides important information for development of strategies to prevent recurrence of venous leg ulcers, with the potential to improve health and decrease health care costs in this population.

Relationships between preventive activities, psychosocial factors and recurrence of venous leg ulcers : a prospective study

Aim To identify relationships between preventive activities, psychosocial factors and leg ulcer recurrence in patients with chronic venous leg ulcers. Background Chronic venous leg ulcers are slow to heal and frequently recur, resulting in years of suffering and intensive use of health care resources. Methods A prospective longitudinal study was undertaken with a sample of 80 patients with a venous leg ulcer recruited when their ulcer healed. Data were collected from 2006–2009 from medical records on demographics, medical history and ulcer history; and from self-report questionnaires on physical activity, nutrition, preventive activities and psychosocial measures. Follow-up data were collected via questionnaires every three months for 12 months after healing. Median time to recurrence was calculated using the Kaplan-Meier method. A Cox proportional-hazards regression model was used to adjust for potential confounders and determine effects of preventive strategies and psychosocial factors on recurrence. Results: There were 35 recurrences in a sample of 80 participants. Median time to recurrence was 27 weeks. After adjustment for potential confounders, a Cox proportional hazards regression model found that at least an hour/day of leg elevation, six or more days/week in Class 2 (20–25mmHg) or 3 (30–40mmHg) compression hosiery, higher social support scale scores and higher General Self-Efficacy scores remained significantly associated (p<0.05) with a lower risk of recurrence, while male gender and a history of DVT remained significant risk factors for recurrence. Conclusion Results indicate that leg elevation, compression hosiery, high levels of self-efficacy and strong social support will help prevent recurrence.

Application of a new discreet form of Gauss’ theorem for measuring volume

Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a triangular mesh. In this paper we describe and evaluate a new discreet form of Gauss’ theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference ± one standard deviation were 1.2 ± 2.3, 5.5 ± 4.7, 3.0 ± 3.2 and −1.2 ± 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition.

The role of neuromuscular inhibition in hamstring strain injury recurrence

Hamstring strain injuries are amongst the most common and problematic injuries in a wide range of sports that involve high speed running. The comparatively high rate of hamstring injury recurrence is arguably the most concerning aspect of these injuries. A number of modifiable and nonmodifiable risk factors are proposed to predispose athletes to hamstring strains. Potentially, the persistence of risk factors and the development of maladaptations following injury may explain injury recurrence. Here, the role of neuromuscular inhibition following injury is discussed as a potential mechanism for several maladaptations associated with hamstring re-injury. These maladaptations include eccentric hamstring weakness, selective hamstring atrophy and shifts in the knee flexor torque-joint angle relationship. Current evidence indicates that athletes return to competition after hamstring injury having developed maladaptations that predispose them to further injury. When rehabilitating athletes to return to competition following hamstring strain injury, the role of neuromuscular inhibition in re-injury should be considered.