Fast Bayesian identification of a class of elastic weakly nonlinear systems using backbone curves

This paper introduces a method for the identification of the parameters of nonlinear structures using a probabilistic Bayesian framework, employing a Markov chain Monte Carlo algorithm. This approach uses analytical models to describe the unforced, undamped dynamic responses of structures in the frequency–amplitude domain, known as the backbone curves. The analytical models describing these backbone curves are then fitted to measured responses, found using the resonant-decay method. To investigate the proposed identification method, a nonlinear two-degree-of-freedom example structure is simulated numerically and analytical expressions describing the backbone curves are found. These expressions are then used, in conjunction with the backbone curve data found through simulated experiment, to estimate the system parameters. It is shown that the use of these computationally-cheap analytical expressions allows for an extremely efficient method for modelling the dynamic behaviour, providing an identification procedure that is both fast and accurate. Furthermore, for the example structure, it is shown that the estimated parameters may be used to accurately predict the existence of dynamic behaviours that are well-away from the backbone curve data provided; specifically the existence of an isola is predicted

Comparing the direct normal form and multiple scales methods through frequency detuning

Approximate analytical methods, such as the multiple scales (MS) and direct normal form (DNF) techniques, have been used extensively for investigating nonlinear mechanical structures, due to their ability to offer insight into the system dynamics. A comparison of their accuracy has not previously been undertaken, so is addressed in this paper. This is achieved by computing the backbone curves of two systems: the single-degree-of-freedom Duffing oscillator and a non-symmetric, two-degree-of-freedom oscillator. The DNF method includes an inherent detuning, which can be physically interpreted as a series expansion about the natural frequencies of the underlying linear system and has previously been shown to increase its accuracy. In contrast, there is no such inbuilt detuning for MS, although one may be, and usually is, included. This paper investigates the use of the DNF detuning as the chosen detuning in the MS method as a way of equating the two techniques, demonstrating that the two can be made to give identical results up to ε2 order. For the examples considered here, the resulting predictions are more accurate than those provided by the standard MS technique. Wolfram Mathematica scripts implementing these methods have been provided to be used in conjunction with this paper to illustrate their practicality

ε^2-Order normal form analysis for a two-degree-of-freedom nonlinear coupled oscillator

In this paper, we describe an ε^2-order normal form decomposition for a two-degree-of-freedom oscillator system that has a mass supported with horizontal and vertical support springs. This system has nonlinear terms that are not necessarily ε^1-order small when compared to the linear terms. As a result, analytical approximate methods based on an ε expansion would typically need to include higher-order components in order to capture the nonlinear dynamic behaviour. In this paper we show how this can be achieved using a direct normal form transformation up to order ε^2. However, we will show that the requirement for including ε^2 components is primarily due to the way the direct normal form method deals with quadratic coupling terms rather than the relative size of the coefficients

Suspected idiopathic sclerosing orbital inflammation presenting as immunoglobulin G4-related disease: a case report

<p>Abstract</p> <p>Introduction</p> <p>Idiopathic sclerosing orbital inflammation is a rare and ill-defined heterogeneous entity, and a distinct subset of orbital inflammation. Recently, attention has been focused on immunoglobulin G4-related disease complicated with fibrotic changes in some other organs with high serum immunoglobulin G4 levels. This report presents a case of suspected idiopathic sclerosing orbital inflammation complicated with high serum immunoglobulin G4 levels.</p> <p>Case presentation</p> <p>An 82-year-old Japanese woman had a 30-year history of chronic thyroiditis. She experienced right ptosis and eyelid swelling. These symptoms gradually developed over five years. The clinical and radiographic findings suggested that our patient had idiopathic sclerosing orbital inflammation. We were unable to obtain our patient's consent to perform a biopsy. While the serum immunoglobulin G level was within the normal limits, the serum immunoglobulin G4 level was significantly elevated. The serum immunoglobulin G4 levels decreased after the administration of oral prednisolone at a daily dose of 20 mg. In addition, the swelling and ptosis of the right upper eyelid disappeared gradually after four weeks. Our patient was then suspected to have idiopathic sclerosing orbital inflammation complicated with immunoglobulin G4-related disease and chronic thyroiditis.</p> <p>Conclusion</p> <p>An orbital pseudotumor of this type is indicative of idiopathic sclerosing orbital inflammation immunoglobulin G4-related disease. Immunoglobulin G4 may thus be considered a subclass of immunoglobulin G when the serum immunoglobulin G level is within normal limits.</p

N-1 modal interactions of a three-degree-of-freedom system with cubic elastic nonlinearities

In this paper the (Formula presented.) nonlinear modal interactions that occur in a nonlinear three-degree-of-freedom lumped mass system, where (Formula presented.), are considered. The nonlinearity comes from springs with weakly nonlinear cubic terms. Here, the case where all the natural frequencies of the underlying linear system are close (i.e. (Formula presented.)) is considered. However, due to the symmetries of the system under consideration, only (Formula presented.) modes interact. Depending on the sign and magnitude of the nonlinear stiffness parameters, the subsequent responses can be classified using backbone curves that represent the resonances of the underlying undamped, unforced system. These backbone curves, which we estimate analytically, are then related to the forced response of the system around resonance in the frequency domain. The forced responses are computed using the continuation software AUTO-07p. A comparison of the results gives insights into the multi-modal interactions and shows how the frequency response of the system is related to those branches of the backbone curves that represent such interactions

Multi-centre parallel arm randomised controlled trial to assess the effectiveness and cost-effectiveness of a group-based cognitive behavioural approach to managing fatigue in people with multiple sclerosis

Abstract (provisional) Background Fatigue is one of the most commonly reported and debilitating symptoms of multiple sclerosis (MS); approximately two-thirds of people with MS consider it to be one of their three most troubling symptoms. It may limit or prevent participation in everyday activities, work, leisure, and social pursuits, reduce psychological well-being and is one of the key precipitants of early retirement. Energy effectiveness approaches have been shown to be effective in reducing MS-fatigue, increasing self-efficacy and improving quality of life. Cognitive behavioural approaches have been found to be effective for managing fatigue in other conditions, such as chronic fatigue syndrome, and more recently, in MS. The aim of this pragmatic trial is to evaluate the clinical and cost-effectiveness of a recently developed group-based fatigue management intervention (that blends cognitive behavioural and energy effectiveness approaches) compared with current local practice. Methods This is a multi-centre parallel arm block-randomised controlled trial (RCT) of a six session group-based fatigue management intervention, delivered by health professionals, compared with current local practice. 180 consenting adults with a confirmed diagnosis of MS and significant fatigue levels, recruited via secondary/primary care or newsletters/websites, will be randomised to receive the fatigue management intervention or current local practice. An economic evaluation will be undertaken alongside the trial. Primary outcomes are fatigue severity, self-efficacy and disease-specific quality of life. Secondary outcomes include fatigue impact, general quality of life, mood, activity patterns, and cost-effectiveness. Outcomes in those receiving the fatigue management intervention will be measured 1 week prior to, and 1, 4, and 12 months after the intervention (and at equivalent times in those receiving current local practice). A qualitative component will examine what aspects of the fatigue management intervention participants found helpful/unhelpful and barriers to change. Discussion This trial is the fourth stage of a research programme that has followed the Medical Research Council guidance for developing and evaluating complex interventions. What makes the intervention unique is that it blends cognitive behavioural and energy effectiveness approaches. A potential strength of the intervention is that it could be integrated into existing service delivery models as it has been designed to be delivered by staff already working with people with MS. Service users will be involved throughout this research. Trial registration: Current Controlled Trials ISRCTN7651747

The impact of ambient temperature on mortality among the urban population in Skopje, Macedonia during the period 1996–2000

BACKGROUND: This study assesses the relationship between daily numbers of deaths and variations in ambient temperature within the city of Skopje, R. Macedonia. METHODS: The daily number of deaths from all causes, during the period 1996–2000, as well as those deaths from cardiovascular diseases, occurring within the city of Skopje were related to the average daily temperature on the same day using Multiple Regression statistical analyses. Temperature was measured within the regression model as two complementary variables: 'Warm' and 'Cold'. Excess winter mortality was calculated as winter deaths (deaths occurring in December to March) minus the average of non-winter deaths (April to July of the current year and August to November of the previous year). RESULTS: In this study the average daily total of deaths was 7% and 13% greater in the cold when compared to the whole period and warm period respectively. The same relationship was noticed for deaths caused by cardiovascular diseases. The Regression Beta Coefficient (b = -0.19) for the total mortality as a function of the temperature in Skopje during the period 1996–2000 was statistically significant with negative connotation as was the circulatory mortality due to average temperature (statistically significant regression Beta coefficient (b = -0.24)). A measure of this increase is provided, on an annual basis, in the form of the excess winter mortality figure. CONCLUSION: Mortality with in the city of Skopje displayed a marked seasonality, with peaks in the winter and relative troughs in the summer

Successful treatment of pediatric IgG4 related systemic disease with mycophenolate mofetil: case report and a review of the pediatric autoimmune pancreatitis literature

Autoimmune pancreatitis is frequently associated with elevated serum and tissue IgG4 levels in the adult population, but there are few reports of pediatric autoimmune pancreatitis, and even fewer reports of IgG4 related systemic disease in a pediatric population. The standard of care treatment in adults is systemic corticosteroids with resolution of symptoms in most cases; however, multiple courses of corticosteroids are occasionally required and some patients require long term corticosteroids. In these instances, steroid sparing disease modify treatments are in demand. We describe a 13-year-old girl with IgG4 related systemic disease who presented with chronic recurrent autoimmune pancreatitis resulting in surgical intervention for obstructive hyperbilirubinemia and chronic corticosteroid treatment. In addition, she developed fibrosing medianstinitis as part of her IgG4 related systemic disease. She was eventually successfully treated with mycophenolate mofetil allowing for discontinuation of corticosteroids. This is the first reported use of mycophenolate mofetil for IgG4 related pancreatitis. Although autoimmune pancreatitis as part of IgG4 related systemic disease is rarely reported in pediatrics, autoimmune pancreatitis is also characterized as idiopathic fibrosing pancreatitis. All pediatric autoimmune pancreatitis cases reported in the world medical literature were identified via a PUBMED search and are reviewed herein. Twelve reports of pediatric autoimmune pancreatitis were identified, most of which were treated with corticosteroids or surgical approaches. Most case reports failed to report IgG4 levels, so it remains unclear how commonly IgG4 related autoimmune pancreatitis occurs during childhood. Increased evaluation of IgG4 levels in patients with autoimmune pancreatitis may shed further light on the association of IgG4 with pancreatitis and the underlying pathophysiology