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.

Considerations in the design of a mixed-method cluster evaluation of a community programme for 'at-risk' young people

This article discusses the design of a comprehensive evaluation of a community development programme for young people 'at-risk' of self-harming behaviour. It outlines considerations in the design of the evaluation and focuses on the complexities and difficulties associated with the evaluation of a community development programme. The challenge was to fulfil the needs of the funding body for a broad, outcome-focused evaluation while remaining close enough to the programme to accurately represent its activities and potential effects at a community level. Specifically, the strengths and limitations of a mixed-method evaluation plan are discussed with recommendations for future evaluation practice.

An in vitro study of non-axial forces upon the retention of an O-ring attachment

Objective The purpose of this study was to evaluate the retention force of an O-ring attachment system in different inclinations to the ideal path of insertion, using devices to compensate angulations. Material and methods Two implants were inserted into an aluminum base, and ball attachments were screwed to implants. Cylinders with O-rings were placed on ball attachments and connected to the test device using positioners to compensate implant angulations (0 degrees, 7 degrees, and 14 degrees). Plexiglass bases were used to simulate implant angulations. The base and the test device were positioned in a testing apparatus, which simulated insertion/removal of an overdenture. A total of 2900 cycles, simulating 2 years of overdenture use, were performed and 36 O-rings were tested. The force required for each cycle was recorded with computer software. Longitudinal sections of ball attachment-positioner-cylinder with O-rings of each angulation were obtained to analyze the relationship among them, and O-ring sections tested in each angulation were compared with an unused counterpart. A mixed linear model was used to analyze the data, and the comparison was performed by orthogonal contrasts (alpha=0.05). Results At 0 degrees, the retention force decreased significantly over time, and the retention force was significantly different in all comparisons, except from 12 to 18 months. When the implants were positioned at 7 degrees, the retention force was statistically different at 0 and 24 months. At 14 degrees, significant differences were found from 6 and 12 to 24 months. Conclusions Within the limitations of this study, it was concluded that O-rings for implant/attachments perpendicular to the occlusal plane were adequately retentive over the first year and that the retentive capacity of O-ring was affected by implant inclinations despite the proposed positioners. To cite this article:Rodrigues RCS, Faria ACL, Macedo AP, Sartori IAM, de Mattos MGC, Ribeiro RF. An in vitro study of non-axial forces upon the retention of an O-ring attachment.Clin. Oral Impl. Res. 20, 2009; 1314-1319.doi: 10.1111/j.1600-0501.2009.01742.x.

Ni(II)-doped CsCdBrCl2: Variation of spectral and structural properties via mixed-halide coordination

A new addition to the family of single-molecule magnets is reported: an Fete cage stabilized with benzoate and pyridonate ligands. Monte Carlo methods have been used to derive exchange parameters within the cage, and hence model susceptibility behavior.

X-ray scattering studies of mixed langmuir monolayers and Langmuir-Blodgett films of a noncentrosymmetric porphyrin with cadmium arachidate

The structures of mixed Langmuir (floating) monolayers and Langmuir-Blodgett (LB) films of a phenanthroline-porphyrin with cadmium arachidate (PhenPor + CdAr) have been investigated by synchrotron X-ray grazing incidence diffraction (GIXD) and specular X-ray reflectivity (SXR). GIXD measurements of the floating monolayers showed only one peak, arising from the CdAr domains in the films, at a scattering angle of 21.5 degrees. This is consistent with a hexagonal structure (alpha = 4.77 Angstrom). The correlation length in these domains is 250 Angstrom. GMD measurements of the LB films, however, show two sets of diffraction features: one arises from CdAr domains with a rectangular in-plane structure (alpha = 7.44 Angstrom and b = 4.90 Angstrom) and a correlation length of 85 Angstrom; the other is from porphyrin domains with an oblique in-plane structure (alpha (p) 15.2 Angstrom, b(p) = 8.86 Angstrom, and gamma (p) = 80 degrees) and a correlation length of 105 Angstrom. These dimensions are consistent with the surface pressure-area isotherm measurements and indicate that the two components are immiscible. The thickness of the bilayer is 57 Angstrom, and there is no correlation between the bilayers. Introduction of a trigger compound does not alter the structure of the films but slightly increases the bilayer thickness. The SXR measurements of the floating monolayers also support the suggested immiscibility of the two components in the films.

A methodology for analysis of sugarcane productivity trends - I. Analysis across districts

Historically, few articles have addressed the use of district level mill production data for analysing the effect of varietal change on sugarcane productivity trends. This appears to be due to lack of compiled district data sets and appropriate methods by which to analyse these data. Recently, varietal data on tonnes of sugarcane per hectare (TCH), sugar content (CCS), and their product, tonnes of sugar content per hectare (TSH) on a district basis, have been compiled. This study was conducted to develop a methodology for regular analysis of such data from mill districts to assess productivity trends over time, accounting for variety and variety x environment interaction effects for 3 mill districts (Mulgrave, Babinda, and Tully) from 1958 to 1995. Restricted maximum likelihood methodology was used to analyse the district level data and best linear unbiased predictors for random effects, and best linear unbiased estimates for fixed effects were computed in a mixed model analysis. In the combined analysis over districts, Q124 was the top ranking variety for TCH, and Q120 was top ranking for both CCS and TSH. Overall production for TCH increased over the 38-year period investigated. Some of this increase can be attributed to varietal improvement, although the predictors for TCH have shown little progress since the introduction of Q99 in 1976. Although smaller gains have been made in varietal improvement for CCS, overall production for CCS decreased over the 38 years due to non-varietal factors. Varietal improvement in TSH appears to have peaked in the mid-1980s. Overall production for TSH remained stable over time due to the varietal increase in TCH and the non-varietal decrease in CCS.

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.

Non-Markovian homodyne-mediated feedback on a two-level atom: a quantum trajectory treatment

Quantum feedback can stabilize a two-level atom against decoherence (spontaneous emission), putting it into an arbitrary (specified) pure state. This requires perfect homodyne detection of the atomic emission, and instantaneous feedback. Inefficient detection was considered previously by two of us. Here we allow for a non-zero delay time tau in the feedback circuit. Because a two-level atom is a non-linear optical system, an analytical solution is not possible. However, quantum trajectories allow a simple numerical simulation of the resulting non-Markovian process. We find the effect of the time delay to be qualitatively similar to chat of inefficient detection. The solution of the non-Markovian quantum trajectory will not remain fixed, so that the time-averaged state will be mixed, not pure. In the case where one tries to stabilize the atom in the excited state, an approximate analytical solution to the quantum trajectory is possible. The result, that the purity (P = 2Tr[rho (2)] - 1) of the average state is given by P = 1 - 4y tau (where gamma is the spontaneous emission rate) is found to agree very well with the numerical results. (C) 2001 Elsevier Science B.V. All rights reserved.

Power of the joint segregation analysis method for testing mixed major-gene and polygene inheritance models of quantitative traits

Understanding the genetic architecture of quantitative traits can greatly assist the design of strategies for their manipulation in plant-breeding programs. For a number of traits, genetic variation can be the result of segregation of a few major genes and many polygenes (minor genes). The joint segregation analysis (JSA) is a maximum-likelihood approach for fitting segregation models through the simultaneous use of phenotypic information from multiple generations. Our objective in this paper was to use computer simulation to quantify the power of the JSA method for testing the mixed-inheritance model for quantitative traits when it was applied to the six basic generations: both parents (P-1 and P-2), F-1, F-2, and both backcross generations (B-1 and B-2) derived from crossing the F-1 to each parent. A total of 1968 genetic model-experiment scenarios were considered in the simulation study to quantify the power of the method. Factors that interacted to influence the power of the JSA method to correctly detect genetic models were: (1) whether there were one or two major genes in combination with polygenes, (2) the heritability of the major genes and polygenes, (3) the level of dispersion of the major genes and polygenes between the two parents, and (4) the number of individuals examined in each generation (population size). The greatest levels of power were observed for the genetic models defined with simple inheritance; e.g., the power was greater than 90% for the one major gene model, regardless of the population size and major-gene heritability. Lower levels of power were observed for the genetic models with complex inheritance (major genes and polygenes), low heritability, small population sizes and a large dispersion of favourable genes among the two parents; e.g., the power was less than 5% for the two major-gene model with a heritability value of 0.3 and population sizes of 100 individuals. The JSA methodology was then applied to a previously studied sorghum data-set to investigate the genetic control of the putative drought resistance-trait osmotic adjustment in three crosses. The previous study concluded that there were two major genes segregating for osmotic adjustment in the three crosses. Application of the JSA method resulted in a change in the proposed genetic model. The presence of the two major genes was confirmed with the addition of an unspecified number of polygenes.

Determination of breeding strategies for beef cattle bull breeders selling bulls into two competing markets on a non-linear price grid

Computer simulation was used to suggest potential selection strategies for beef cattle breeders with different mixes of clients between two potential markets. The traditional market paid on the basis of carcass weight (CWT), while a new market considered marbling grade in addition to CWT as a basis for payment. Both markets instituted discounts for CWT in excess of 340 kg and light carcasses below 300 kg. Herds were simulated for each price category on the carcass weight grid for the new market. This enabled the establishment of phenotypic relationships among the traits examined [CWT, percent intramuscular fat (IMF), carcass value in the traditional market, carcass value in the new market, and the expected proportion of progeny in elite price cells in the new market pricing grid]. The appropriateness of breeding goals was assessed on the basis of client satisfaction. Satisfaction was determined by the equitable distribution of available stock between markets combined with the assessment of the utility of the animal within the market to which it was assigned. The best goal for breeders with predominantly traditional clients was a CWT in excess of 330 kg, while that for breeders with predominantly new market clients was a CWT of between 310 and 329 kg and with a marbling grade of AAA in the Ontario carcass pricing system. For breeders who wished to satisfy both new and traditional clients, the optimal CWT was 310-329 kg and the optimal marbling grade was AA-AAA. This combination resulted in satisfaction levels of greater than 75% among clients, regardless of the distribution of the clients between the traditional and new marketplaces.