Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

Association of Streptococcus mutans Infection and Oral Developmental Nodules in Pre-dentate Infants

Since dental caries may present soon after tooth eruption, we hypothesized that colonization of Streptococcus mutans can occur in the predentate stages. In this study, we examined S. mutans colonization and its association with oral developmental nodules (Bohn's nodules) in 60 pre-term and 128 full-term, three-month-old infants. Overall, S. mutans was cultured from 30% (56/188) of the infants, and oral developmental nodules were noted in 55% (103/188). Compared with the pre-term, full-term infants showed a higher prevalence of S. mutans (34% vs. 20%, p < 0.02) as well as developmental nodules (61% vs. 42%, p < 0.05). In both groups, S. mutans was positively associated with numbers of developmental nodules in a dose-response relationship (p < 0,001), and with maternal salivary levels of the bacteria (p = 0.03). The permanence of S. mutans infection was confirmed by repeat saliva sampling at 6 months of age. Our results thus showed that many infants have already acquired S. mutans at 3 months of age, prior to tooth eruption.

A parent-completed developmental questionnaire: Follow up of ex-premature infants

Objective: premature infants are at increased risk of developmental disability. Early identification of problems allows intervention to ameliorate or attenuate problems. A reliable screening tool allows triage of children in this high-risk population by identifying those unlikely to need full developmental assessment. To explore the test characteristics of an established parent-completed developmental assessment questionnaire 'Ages and Stages Questionnaire' (ASQ) in follow up of an Australian population of premature infants. Methodology: One hundred and sixty-seven children born prematurely with corrected ages 12- to 48-months attending the Growth and Development Clinic at the Mater Children's Hospital in Brisbane, Queensland, Australia; 136 questionnaires 'ASQ' were returned completed (81%) and were compared to formal psychometric assessment (Griffith Mental Development Scales for 12- and 24-months, Bayley Mental Development Intelligence Scale for 18-months, McCarthy General Cognitive Intelligence Scale for 18-months). Developmental delay was considered to be present if any of the above psychometric assessments fell below 1.0 standard deviations (SD). The ASQ cut-off used was 2.0 SD (US data derived means and SD). Results: Aggregate results for all age groups comparing ASQ to psychometric assessments as 'gold standards' found the ASQ to have the following test characteristics: sensitivity (90%); specificity (77%); positive predictive value (40%); negative predictive value (98%): % over-referred (20%); % under-referred (1%); % agreement (79%). likelihood ratio for children failing the ASQ was 3.8 and for passing the ASQ was 0.13. Twenty-one children with known disabilities were included in the study and in 14 of these, the ASQ overall score agreed with the psychometric assessment (67%). Conclusion: The high negative predictive value of the ASQ supports its use as a screening tool for cognitive and motor delays in the follow up of ex-premature infants. This would need to be combined with other strategies as part of a comprehensive follow up program for ex-premature infants.

The acquisition of movement skills: Practice enhances the dynamic stability of bimanual coordination

During bimanual movements, two relatively stable inherent patterns of coordination (in-phase and anti-phase) are displayed (e.g., Kelso, Am. J. Physiol. 246 (1984) R1000). Recent research has shown that new patterns of coordination can be learned. For example, following practice a 90 degrees out-of-phase pattern can emerge as an additional, relatively stable, state (e.g., Zanone & Kelso, J. Exp. Psychol.: Human Performance and Perception 18 (1992) 403). On this basis, it has been concluded that practice leads to the evolution and stabilisation of the newly learned pattern and that this process of learning changes the entire attractor layout of the dynamic system. A general feature of such research has been to observe the changes of the targeted pattern's stability characteristics during training at a single movement frequency. The present study was designed to examine how practice affects the maintenance of a coordinated pattern as the movement frequency is scaled. Eleven volunteers were asked to perform a bimanual forearm pronation-supination task. Time to transition onset was used as an index of the subjects' ability to maintain two symmetrically opposite coordinated patterns (target task - 90 degrees out-of-phase - transfer task - 270 degrees out-of-phase). Their ability to maintain the target task and the transfer task were examined again after five practice sessions each consisting of 15 trials of only the 90 degrees out-of-phase pattern. Concurrent performance feedback (a Lissajous figure) was available to the participants during each practice trial. A comparison of the time to transition onset showed that the target task was more stable after practice (p = 0.025). These changes were still observed one week (p = 0.05) and two months (p = 0.075) after the practice period. Changes in the stability of the transfer task were not observed until two months after practice (p = 0.025). Notably, following practice, transitions from the 90 degrees pattern were generally to the anti-phase (180 degrees) pattern, whereas, transitions from the 270 degrees pattern were to the 90 degrees pattern. These results suggest that practice does improve the stability of a 90 degrees pattern, and that such improvements are transferable to the performance of the unpractised 270 degrees pattern. In addition, the anti-phase pattern remained more stable than the practised 90 degrees pattern throughout. (C) 2001 Elsevier Science B.V. All rights reserved.

Let your feet do the walking: constraints on the stability of bipedal coordination

In this paper we consider whether the behaviour of the neural circuitry that controls lower limb movements in humans is shaped primarily by the spatiotemporal characteristics of bipedal gait patterns, or by selective pressures that are sensitive to considerations of balance and energetics. During the course of normal locomotion, the full dynamics of the neural circuitry are masked by the inertial properties of the limbs. In the present study, participants executed bipedal movements in conditions in which their feet were either unloaded or subject to additional inertial loads. Two patterns of rhythmic coordination were examined. In the in-phase mode, participants were required to flex their ankles and extend their ankles in synchrony. In the out-of-phase mode, the participants flexed one ankle while extending the other and vice versa. The frequency of movement was increased systematically throughout each experimental trial. All participants were able to maintain both the in-phase and the out-of-phase mode of coordination, to the point at which they could no longer increase their frequency of movement. Transitions between the two modes were not observed, and the stability of the out-of-phase and in-phase modes of coordination was equivalent at all movement frequencies. These findings indicate that, in humans, the behaviour of the neural circuitry underlying coordinated movements of the lower limbs is not constrained strongly by the spatiotemporal symmetries of bipedal gait patterns.