Variational based analysis and modelling using B-splines

The use of energy methods and variational principles is widespread in many fields of engineering of which structural mechanics and curve and surface design are two prominent examples. In principle many different types of function can be used as possible trial solutions to a given variational problem but where piecewise polynomial behaviour and user controlled cross segment continuity is either required or desirable, B-splines serve as a natural choice. Although there are many examples of the use of B-splines in such situations there is no common thread running through existing formulations that generalises from the one dimensional case through to two and three dimensions. We develop a unified approach to the representation of the minimisation equations for B-spline based functionals in tensor product form and apply these results to solving specific problems in geometric smoothing and finite element analysis using the Rayleigh-Ritz method. We focus on the development of algorithms for the exact computation of the minimisation matrices generated by finding stationary values of functionals involving integrals of squares and products of derivatives, and then use these to seek new variational based solutions to problems in the above fields. By using tensor notation we are able to generalise the methods and the algorithms from curves through to surfaces and volumes. The algorithms developed can be applied to other fields where a variational form of the problem exists and where such tensor product B-spline functions can be specified as potential solutions.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Moderate to vigorous physical activity and sedentary time and cardiometabolic risk factors in children and adolescents.

CONTEXT: Sparse data exist on the combined associations between physical activity and sedentary time with cardiometabolic risk factors in healthy children. OBJECTIVE: To examine the independent and combined associations between objectively measured time in moderate- to vigorous-intensity physical activity (MVPA) and sedentary time with cardiometabolic risk factors. DESIGN, SETTING, AND PARTICIPANTS: Pooled data from 14 studies between 1998 and 2009 comprising 20 871 children (aged 4-18 years) from the International Children's Accelerometry Database. Time spent in MVPA and sedentary time were measured using accelerometry after reanalyzing raw data. The independent associations between time in MVPA and sedentary time, with outcomes, were examined using meta-analysis. Participants were stratified by tertiles of MVPA and sedentary time. MAIN OUTCOME MEASURES: Waist circumference, systolic blood pressure, fasting triglycerides, high-density lipoprotein cholesterol, and insulin. RESULTS: Times (mean [SD] min/d) accumulated by children in MVPA and being sedentary were 30 (21) and 354 (96), respectively. Time in MVPA was significantly associated with all cardiometabolic outcomes independent of sex, age, monitor wear time, time spent sedentary, and waist circumference (when not the outcome). Sedentary time was not associated with any outcome independent of time in MVPA. In the combined analyses, higher levels of MVPA were associated with better cardiometabolic risk factors across tertiles of sedentary time. The differences in outcomes between higher and lower MVPA were greater with lower sedentary time. Mean differences in waist circumference between the bottom and top tertiles of MVPA were 5.6 cm (95% CI, 4.8-6.4 cm) for high sedentary time and 3.6 cm (95% CI, 2.8-4.3 cm) for low sedentary time. Mean differences in systolic blood pressure for high and low sedentary time were 0.7 mm Hg (95% CI, -0.07 to 1.6) and 2.5 mm Hg (95% CI, 1.7-3.3), and for high-density lipoprotein cholesterol, differences were -2.6 mg/dL (95% CI, -1.4 to -3.9) and -4.5 mg/dL (95% CI, -3.3 to -5.6), respectively. Geometric mean differences for insulin and triglycerides showed similar variation. Those in the top tertile of MVPA accumulated more than 35 minutes per day in this intensity level compared with fewer than 18 minutes per day for those in the bottom tertile. In prospective analyses (N = 6413 at 2.1 years' follow-up), MVPA and sedentary time were not associated with waist circumference at follow-up, but a higher waist circumference at baseline was associated with higher amounts of sedentary time at follow-up. CONCLUSION: Higher MVPA time by children and adolescents was associated with better cardiometabolic risk factors regardless of the amount of sedentary time

Maturity associated variance in physical activity and health-related quality of life in adolescent females. A mediated effects model

BACKGROUND. This study tested a mediated effects model of psychological and behavioral adaptation to puberty within the context of physical activity (PA). METHODS. Biological maturity status, physical self-concept, PA, and health-related quality of life (HRQoL) were assessed in 222 female British year 7 to 9 pupils (mean age = 12.7 years, SD = .8). RESULTS. Structural equation modeling using maximum likelihood estimation and bootstrapping procedures supported the hypothesized model. Maturation status was inversely related to perceptions of sport competence, body attractiveness, and physical condition; and indirectly and inversely related to physical self-worth, PA, and HRQoL. Examination of the bootstrap-generated bias-corrected confidence intervals representing the direct and indirect paths between suggested that physical self-concept partially mediated the relations between maturity status and PA, and maturity status and HRQoL. CONCLUSIONS. Evidence supports the contention that perceptions of the physical self partially mediate relations maturity, PA, and HRQoL in adolescent females

Variable and changing trajectories in youth athlete development: further verification in advocating a long-term inclusive tracking approach.

Athlete development through adolescence can vary greatly because of maturational processes. For example, variation can be observed in anthropometric and fitness measures with later maturing individuals "catching up" their earlier maturing peers at later time points. This study examined a methodological issue concerning how best to assess anthropometric and fitness change (i.e., "across age categories" or "per year") relative to an age and skill-matched population (N = 1,172). Furthermore, it examined changes in anthropometric and fitness characteristics in 3 cases of youth rugby league players (aged 13-15) across a 2-year period. Findings identified the "per year" method as generating less deviated z-scores across anthropometric and fitness measures (e.g., mean change p < 0.001), suggesting less substantial change in case players relative to the population. When applied to additional players, z-score and radar graphs showed developmental variability and longitudinal change. The possibility of a "later maturing player" increasing anthropometric (e.g., height: player 4 = 3.3 cm; player 5 = 13.2 cm; and player 6 = 15.7 cm) and fitness (e.g., 30-m sprint: player 4 = -0.18 s, player 5 = -0.46 s, and player 6 = -0.59 s) characteristics compared with early maturing players was confirmed. Findings affirm the potential for variable and changing trajectories in adolescent athletes. Practical implications advocate a long-term inclusive tracking approach of athletes, the avoidance of (de)selection, and the reduction of a performance emphasis in adolescent stages of sport systems

Concurrent and prospective associations among biological maturation, and physical activity at 11 and 13 years of age

This study examined concurrent and prospective associations between objective measures of biological maturation, body composition and physical activity (PA) in adolescent males (n=671) and females (n=680). Participants born to women recruited to the Avon Longitudinal Study of Parents and Children birth cohort study were assessed at 11 and 13 years. Percentage of predicted adult stature was used as an estimate of biological maturation. PA and time sedentary was assessed over 7 consecutive days using Actigraph accelerometers. Body composition was assessed using whole-body DXA scans. At 11 and 13 years, maturity in males was inversely associated with accelerometer counts-per-minute (CPM) and time engaged in light PA, and positively associated with time sedentary. In females, maturity was inversely associated with accelerometer (CPM) at 11 but not 13 years. Adjusting for accelerometer wear times and corresponding activity levels at 11 years, maturity and percentage fat mass at 11 years did not predict any indices of PA or sedentary behavior in males or females at 13 years. Whereas advanced maturation in males is associated with less PA and more sedentary behavior at 11 and 13 years, maturity at 11 does not predict PA or sedentary behavior at 13 years in either sex

Resistance to data loss from the Freestyle Libre:Impact on glucose variability indices and recommendations for data analysis

Like many wearables, flash glucose monitoring relies on user compliance and is subject to missing data. As recent research is beginning to utilise glucose technologies as behaviour change tools, it is important to understand whether missing data is tolerable. Complete Freestyle Libre data files were amputed to remove 1-6 hours of data both at random and over mealtimes (breakfast, lunch and dinner). Absolute percent errors (MAPE) and intraclass correlation coefficients (ICC) were calculated to evaluate agreement and reliability. Thirty-two (91%) participants provided at least one complete day (24-hours) of data (age: 44.8±8.6 years, female: 18 (56%); mean fasting glucose: 5.0±0.6 mmol/L). Mean and CONGA (60 minutes) were robust to data loss (MAPE ≤3%). Larger errors were calculated for standard deviation, coefficient of variation (CV) and MAGE at increasing missingness (MAPE 2-10%, 2-9% and 4-18%, respectively). ICC decreased as missing data increased, with most indicating excellent reliability (>0.9) apart from certain MAGE ICC, which indicated good reliability (0.84-0.9). Researchers and clinicians should be aware of the potential for larger errors when reporting standard deviation, CV and MAGE at higher rates of data loss in nondiabetic populations. But where mean and CONGA are of interest, data loss is less of a concern. Novelty: As research now utilises flash glucose monitoring as behavioural change tools in nondiabetic populations, it is important to consider the influence of missing data. Glycaemic variability indices of mean and CONGA are robust to data loss, but standard deviation, CV and MAGE are influenced at higher rates of missingness

The mediating role of physical self-concept on relations between biological maturity status and physical activity in adolescent females

The current study examined the mediating role of physical self-concept on relations between biological maturity status and self-reported physical activity in adolescent British females. Biological maturity status, physical self-concept and physical activity were assessed in 407 female British year 7-9 pupils (M age = 13.2 years, SD = 1.0). Participants completed the Physical Activity Questionnaire for Adolescents (Kowalski, Crocker, & Donen, 2004) and the Children and Youth Physical Self-Perceptions Profile (Whitehead, 1995). Percentage of predicted adult height attained at measurement was used as an estimate of biological maturity status. Structural equation modelling using maximum likelihood estimation and bootstrapping procedures revealed that perceptions of sports competence, body attractiveness and physical self-worth mediated an inverse relation between maturity status and physical activity. The results provide partial support for Petersen and Taylor's (1980) Mediated Effects Model of Psychological and Behavioural Adaptation to Puberty within the context of physical activity