Existence of solutions to some equilibrium problems

The concept of a monotone family of functions, which need not be countable, and the solution of an equilibrium problem associated with the family are introduced. A fixed-point theorem is applied to prove the existence of solutions to the problem.

Accelerating, hyperaccelerating, and decelerating networks

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyperaccelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.

Levels of physical activity for colon cancer prevention compared with generic public health recommendations: Population prevalence and sociodemographic correlates

Background: The proportion of Australian adults achieving physical activity levels believed to be sufficient for colon cancer prevention was estimated, and sociodemographic correlates (age, gender, educational attainment, occupation, marital status, and children in household) of meeting these levels of activity were analyzed. Methods: Data from the 2000 National Physical Activity Survey were used to estimate the prevalence of participation in physical activity in relation to three criteria: generic public health recommendations, weekly amount of at least moderate-intensity physical activity currently believed to reduce risk of colon cancer, and weekly amount of vigorous-intensity physical activity believed to reduce risk of colon cancer. Results: Overall, 46% of adults met the generic public health criterion, 26% met the colon cancer criterion based on participation in at least moderate-intensity physical activity, and 10% met the colon cancer criterion based on vigorous-intensity physical activity. Women were less likely than men to meet the colon cancer criteria. Younger and more educated persons were more likely to meet all three criteria. The most pronounced differences between gender, age, and educational attainment groups were found for meeting the amount of vigorous-intensity physical activity believed to reduce risk of colon cancer. Conclusions: The population prevalence for meeting proposed physical activity criteria for colon cancer prevention is low and much lower than that related to the more generic public health recommendations. If further epidemiologic studies confirm that high volumes and intensities of activity are required, the public health challenges for colon cancer will be significant.

Effect of Australia's walk to work day campaign on adults' active commuting and physical activity behavior

Purpose. To determine whether Australia's Walk to Work Day media campaign resulted in behavioural change among targeted groups. Methods. Pre- and postcampaign telephone surveys of a cohort of adults aged 18 to 65 years (n = 1100, 55% response rate) were randomly sampled from Australian major melropolitan areas. Tests for dependent samples were applied (McNemax chi(2) or paired t-test). Results. Among participants who did not usually actively commute to work was a significant decrease in car only use an increase in walking combined with public transport. Among those who were employed was a significant increase in total time walking (+16 min/wk; t [780] = 2.04, p < .05) and in other moderate physical activity (+120 min/wk; t [1087] = 4.76, p < .005), resulting in a significant decrease in the proportion who were inactive (chi(2) (1) = 6.1, p < .05). Conclusion. Although nonexperimental, the Walk to Work Day initiative elicited short-term changes in targeted behaviors among target groups. Reinforcement by integrating worksite health promotion strategies may be required for sustained effects.

Piloting the feasibility and effectiveness of print- and telephone-mediated interventions for promoting the adoption of physical activity in Australian adults

This study examined the feasibility and effectiveness for increasing physical activity of a print-based intervention, and a print- plus telephone-mediated intervention among mid-life and older Australian adults. A randomised controlled trial study design was used. In mid-2002, 66 adults (18 men, 48 women) aged 45-78 years, who identified themselves as under-active, were recruited through advertisements and word-of-mouth at two sites (Melbourne and Brisbane), and randomised to either the print or print-plus-telephone mediated intervention group. Participants in both groups attended an initial briefing session, and over the 12-week intervention period received an instructional newsletter and use of a pedometer (both groups), and individualised telephone calls (print- plus-telephone group only). Self-reported physical activity data were collected at baseline, 12 and 16 weeks. Measures of self-reported global physical activity, moderate-vigorous intensity activity and walking all showed increases between baseline and 12 weeks for both intervention groups. These increases were generally maintained by 16 weeks, although participants in the print-plus-telephone group maintained slightly higher levels of global reported activity and walking (by approximately 30 mins/wk) than those in the print group. These interventions show potential for promoting initial increases in physical activity among mid-life and older Australian adults, and should be evaluated across more extended time periods.

Physical and psychological factors maintain long-term predictive capacity post-whiplash injury

Higher initial levels of pain and disability, older age, cold hyperalgesia, impaired sympathetic vasoconstriction and moderate post-traumatic stress symptoms have been shown to be associated with poor outcome 6 months following whiplash injury. This study prospectively investigated the predictive capacity of these variables at a long-term follow-up. Sixty-five of an initial cohort of 76 acutely injured whiplash participants were followed to 2-3 years post-accident. Motor function (ROM; kinaesthetic sense; activity of the superficial neck flexors (EMG) during cranio-cervical flexion), quantitative sensory testing (pressure, thermal pain thresholds and brachial plexus provocation test), sympathetic vasoconstrictor responses and psychological distress (GHQ-28, TSK and IES) were measured. The outcome measure was Neck Disability Index (NDI) scores. Participants with ongoing moderate/severe symptoms at 2-3 years continued to manifest decreased ROM, increased EMG during cranio-cervical flexion, sensory hypersensitivity and elevated levels of psychological distress when compared to recovered participants and those with milder symptoms. The latter two groups showed only persistent deficits in cervical muscle recruitment patterns. Higher initial NDI scores (OR 1.00-1.1), older age (OR 1.00-1.13), cold hyperalgesia (OR 1.1-1.13) and post-traumatic stress symptoms (OR 1.03-1.2) remained significant predictors of poor outcome at long-term follow-up (r(2) = 0.56). The robustness of these physical and psychological factors suggests that their assessment in the acute stage following whiplash injury will be important. (c) 2006 International Association for the Study of Pain. Published by Elsevier B.V. All rights reserved.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Physical activity and strength of the femoral neck during the adolescent growth spurt: A longitudinal analysis

Loading of the femoral neck (FN) is dominated by bending and compressive stresses. We hypothesize that adaptation of the FN to physical activity would be manifested in the cross-sectional area (CSA) and section modulus (Z) of bone, indices of axial and bending strength, respectively. We investigated the influence of physical activity on bone strength during adolescence using 7 years of longitudinal data from 109 boys and 121 girls from the Saskatchewan Paediatric Bone and Mineral Accrual Study (PBMAS). Physical activity data (PAC-Q physical activity inventory) and anthropometric measurements were taken every 6 months and DXA bone scans were measured annually (Hologic QDR2000, array mode). We applied hip structural analysis to derive strength and geometric indices of the femoral neck using DXA scans. To control for maturation, we determined a biological maturity age defined as years from age at peak height velocity (APHV). To account for the repeated measures within individual nature of longitudinal data, multilevel random effects regression analyses were used to analyze the data. When biological maturity age and body size (height and weight) were controlled, in both boys and girls, physical activity was a significant positive independent predictor of CSA and Z of the narrow region of the femoral neck (P < 0.05). There was no independent effect of physical activity on the subperiosteal width of the femoral neck. When leg length and leg lean mass were introduced into the random effects models to control for size and muscle mass of the leg (instead of height and weight), all significant effects of physical activity disappeared. Even among adolescents engaged in normal levels of physical activity, the statistically significant relationship between physical activity and indices of bone strength demonstrate that modifiable lifestyle factors like exercise play an important role in optimizing bone strength during the growing years. Physical activity differences were explained by the interdependence between activity and lean mass considerations. Physical activity is important for optimal development of bone strength. (c) 2005 Elsevier Inc. All rights reserved.

Using Rasch modeling to re-evaluate three scales related to physical activity: Enjoyment, perceived benefits and perceived barriers

Studies suggest that enjoyment, perceived benefits and perceived barriers may be important mediators of physical activity. However, the psychometric properties of these scales have not been assessed using Rasch modeling. The purpose of this study was to use Rasch modeling to evaluate the properties of three scales commonly used in physical activity studies: the Physical Activity Enjoyment Scale, the Benefits of Physical Activity Scale and the Barriers to Physical Activity Scale. The scales were administered to 378 healthy adults, aged 25–75 years (50% women, 62% Whites), at the baseline assessment for a lifestyle physical activity intervention trial. The ConQuest software was used to assess model fit, item difficulty, item functioning and standard error of measurement. For all scales, the partial credit model fit the data. Item content of one scale did not adequately cover all respondents. Response options of each scale were not targeting respondents appropriately, and standard error of measurement varied across the total score continuum of each scale. These findings indicate that each scale's effectiveness at detecting differences among individuals may be limited unless changes in scale content and response format are made.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.