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.

Resting energy expenditure of children attending a rehabilitation programme following head injury

Statement of purpose: Increased resting energy expenditure following head injury is well documented, but whether this increase extends into rehabilitation and whether this is affected by changes in body composition have not been studied. The aim of this study was to determine whether children attending a rehabilitation program following head injury had altered energy expenditure and body composition. Methods: Measurements of resting energy expenditure by indirect calorimetry were performed in 21 head injured children (mean age 10.2±3.8 years). Measurement of body composition was performed using total body potassium. Results: Measured resting energy expenditure values were widely distributed, ranging from 52.3-156.4% of predicted values, yet the mean percentage predicted using Schofield weight, Schofield weight and height and World Health Organization predictive equations were 97.5%, 97.4% and 98.6%, respectively. Mean percentage of expected total body potassium for weight, height and age for head injured children were 85.1 ± 15.5%, 89.1 ± 14.1% and 86.9 ± 15.9%, thus all showed significant depletion. Conclusions: During rehabilitation, using predictive equations to estimate resting energy expenditure in this group revealed a small bias on average but very large bias at the individual level. Head injured children had altered resting energy expenditure and body composition.

Energy expenditure during 2nd week of an ultra-endurance run around Australia

Purpose: For ultra-endurance athletes, whose energy expenditure is likely to be at the extremes of human tolerance for sustained periods of time, there is increased concern regarding meeting energy needs. Due to the lack of data outlining the energy requirements of such athletes, it is possible that those participating in ultra-endurance exercise are compromising performance, as well as health, as a result of inadequate nutrition and energy intake. To provide insight into this dilemma, we have presented a case study of a 37-yr-old ultra-marathon runner as he runs around the coast of Australia. Methods: Total energy expenditure was measured over a 2-wk period using the doubly labeled water technique. Results: The average total energy expenditure of the case subject was 6321 kcal.d(-1). Based on the expected accuracy and precision of the doubly labeled water technique the subject's total energy expenditure might range between 6095 and 6550 kcal.d(-1). The subject's average daily water turnover was 6.083 L over the 14-d period and might range between 5.9 L and 6.3 L.d(-1). Conclusions: This information will provide a guide to the energy requirements of ultra-endurance running and enable athletes, nutritionists, and coaches to optimize performance without compromising the health of the participant.

Energy expenditure and the body cell mass in cystic fibrosis

Poor nutritional status in patients with cystic fibrosis (CF) is associated with severe lung disease, and possible causative factors include inadequate intake, malabsorption, and increased energy requirements. Body cell mass (which can be quantified by measurement of total body potassium) provides an ideal standard for measurements of energy expenditure. The aim of this study was to compare resting energy expenditure (REE) in patients with CF with both predicted values and age-matched healthy children and to determine whether REE was related to either nutritional status or pulmonary function. REE was measured by indirect calorimetry and body cell mass by scanning with total body potassium in 30 patients with CF(12 male, mean age = 13.07 +/- 0.55 y) and 18 healthy children (six male, mean age = 12.56 +/- 1.25 y). Nutritional status was expressed as a percentage of predicted total body potassium; Lung function was measured in the CF group by spirometry and expressed as the percentage of predicted forced expiratory volume in 1 s. Mean REE was significantly increased in the patients with CF compared with healthy children (119.3 +/- 3.1% predicted versus 103.6 +/- 5% predicted, P < 0.001) and, using multiple regression techniques, REE for total body potassium was significantly increased in patients with CF (P = 0.0001). There was no relation between REE and nutritional status or pulmonary disease status in the CF group. In conclusion, REE is increased in children and adolescents with CF but is not directly related to nutritional status or pulmonary disease. Nutrition 2001;17:22-25. (C)Elsevier Science Inc. 2001.

The validity of self-reported energy intake as determined using the doubly labelled water technique

In the 1980s the development of the doubly labelled water (DLW) technique made it possible to determine the validity of dietary assessment methods using external, independent markers of intake in free-living populations. Since then, the accuracy of self-reported energy intake (EI) has been questioned on a number of occasions as under-reporting has been found to be prevalent in many different populations. This paper is a review of investigations using the DLW technique in conjunction with self-reported EI measures in groups including adults, children and adolescents, obese persons, athletes, military personnel and trekking explorers. In studies where a person other than the subject is responsible for recording dietary intake, such as parents of young children, EI generally corresponds to DLW determined energy expenditure. However, in instances where the subjects themselves report their intake, EI is generally under-reported when compared with energy expenditure. It was originally believed that this phenomenon of under-reporting was linked to increased adiposity and body size, however, it is now apparent that other factors, such as dietary restraint and socio-economic status, are also involved. This paper therefore aims to present a more comprehensive picture of under-reporting by tying in the findings of many DLW studies with other studies focusing particularly on the characteristics and mechanisms for under-reporting. Awareness of these characteristics and mechanisms will enable researchers to obtain more accurate self-reports of EI using all dietary recording techniques.

Photoinduced electron transfer and electronic energy transfer in naphthyl-appended cyclams

A series of novel macrocyclic tetraaza ligands that incorporate a naphthalene moiety as a photoactive chromophore have been prepared and structurally characterized as their Cu(II) complexes. Variable-temperature photophysical studies have concluded that the luminescence quenching evident in the Cu(H) complexes is due to intramolecular electronic energy transfer (EET). In their free-base forms, these ligands undergo reductive luminescence quenching via photoinduced electron transfer (PET) reactions, with proximate amine lone pairs acting as electron donors. Consequently, the emission behavior can be modulated by variations in pH and/or the presence of other Lewis acids such as Zn(H).

Hydraulic Performances of Minimum Energy Loss Culverts in Australia

Culverts are among the most common hydraulic structures. Modern designs do not differ from ancient structures and are often characterised by significant afflux at design flows. A significant advance was the development of the Minimum Energy Loss (MEL) culverts in the late 1950s. The design technique allows a drastic reduction in upstream flooding associated with lower costs. The development and operational performances of this type of structure is presented. The successful operation of MEL culverts for more than 40 years is documented with first-hand records during and after floods. The experiences demonstrate the design soundness while highlighting the importance of the hydraulic expertise of the design engineers.

Incubation temperature, energy expenditure and hatchling size in the green turtle (Chelonia mydas), a species with temperature-sensitive sex determination

Eggs from the Heron Island, Great Barrier Reef, nesting population of green turtles (Chelonia mydas) were incubated at all-male-determining (26 degreesC) and all-female-determining (30 degreesC) temperatures. Oxygen consumption and embryonic growth were monitored throughout incubation, and hatchling masses and body dimensions were measured from both temperatures. Eggs hatched after 79 and 53 days incubation at 26 degreesC and 30 degreesC respectively. Oxygen consumption at both temperatures increased to a peak several days before hatching, a pattern typical of turtle embryos, and the rate of oxygen was higher at 30 degreesC than 26 degreesC. The total amount of energy consumed during incubation, and hatchling dimensions, were similar at both temperatures, but hatchlings from 26 degreesC had larger mass, larger yolk-free mass and smaller residual yolks than hatchlings from 30 degreesC. Because of the difference in mass of hatchlings, hatchlings from 30 degreesC had a higher production cost.

Measurement of energy expenditure of daily tasks among mothers of young children

There is currently some debate about whether the energy expenditure of domestic tasks is sufficient to confer health benefits. The aim of this study was therefore to measure the energy cost of five activities commonly undertaken by mothers of young children. Seven women with at least one child younger than five years of age spent 15 minutes in each of the following activities: sitting quietly, vacuum cleaning, washing windows, walking at moderate pace (approx 5km/hour), walking with a stroller and grocery shopping in a super-market. Each of the six 'trials' was completed on the same day, in random order. A carefully calibrated portable gas analyser was used to measure oxygen uptake during each activity, and data were converted to units of energy expenditure (METS). Vacuum cleaning, washing windows and walking with and without a stroller were found to be 'moderate intensity activities' (3 to 6 METs), but supermarket shopping did not reach this criterion. The MET values for these activities were similar to those reported in the Compendium of Physical Activities (Ainsworth et al., 2000). However, the energy expenditures of walking, both with and without a stroller, were higher than those reported in the Compendium. The findings suggest that some of the tasks associated with domestic caring duties are conducted at an intensity which is sufficient to confer some health benefit. Such benefits will only accrue however if the daily duration of these activities is sufficient to meet current guidelines.

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the ill and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.

Linear models of simple cells: Correspondence to real cell responses and space spanning properties

Despite their limitations, linear filter models continue to be used to simulate the receptive field properties of cortical simple cells. For theoreticians interested in large scale models of visual cortex, a family of self-similar filters represents a convenient way in which to characterise simple cells in one basic model. This paper reviews research on the suitability of such models, and goes on to advance biologically motivated reasons for adopting a particular group of models in preference to all others. In particular, the paper describes why the Gabor model, so often used in network simulations, should be dropped in favour of a Cauchy model, both on the grounds of frequency response and mutual filter orthogonality.

Self-reported calcium intake and bone mineral content in children and adolescents

Objective: We examined the relationship between self-reported calcium (Cal intake and bone mineral content (BMC) in children and adolescents. We hypothesized that an expression of Ca adjusted for energy intake (El), i.e., Ca density, would be a better predictor of BMC than unadjusted Ca because of underreporting of EI. Methods: Data were obtained on dietary intakes (repeated 24-hour recalls) and BMC (by DEXA) in a cross-section of 227 children aged 8 to 17 years. Bivariate and multivariate analyses were used to examine die relationship between Ca, Ca density, and the dependent variables total body BMC and lumbar spine BMC. Covariates included were height, weight, bone area, maturity age, activity score and El. Results: Reported El compared to estimated basal metabolic rate suggested underreporting of El. Total body and lumbar spine BMC were significantly associated with El, but not Ca or Ca density, in bivariate analyses. After controlling for size and maturity, multiple linear regression analysis revealed unadjusted Ca to be a predictor of BMC in males in the total body (p = 0.08) and lumbar spine (p = 0.01). Unadjusted Ca was not a predictor of BMC at either site in females. Ca density was not a better predictor of BMC at either site in males or females. Conclusions: The relationship observed in male adolescents in this study between Ca intake and BMC is similar to that seen in clinical trials. Ca density did not enable us to see a relationship between Ca intake and BMC in females, which may reflect systematic reporting errors or that diet is not a limiting factor in this group of healthy adolescents.