Chebyshev approximation of a point set by a straight line

The problem of calculating the best approximating straight line—in the sense of Chebyshev—to a finite set of points inRn is considered. First-and second-order optimality conditions are derived and analysed. Lipschitz optimization techniques can be used to find a global minimizer

The Chebyshev Hyperplane Optimization Problem

We consider the following problem. Given a finite set of pointsyj inR n we want to determine a hyperplane H such that the maximum Euclidean distance betweenH and the pointsyj is minimized. This problem(CHOP) is a non-convex optimization problem with a special structure. Forexample, all local minima can be shown to be strongly unique. We present agenericity analysis of the problem. Two different global optimizationapproaches are considered for solving (CHOP). The first is a Lipschitzoptimization method; the other a cutting plane method for concaveoptimization. The local structure of the problem is elucidated by analysingthe relation between (CHOP) and certain associated linear optimizationproblems. We report on numerical experiments

Supporting Device Discovery and Spontaneous Interaction with Spatial References

The RELATE interaction model is designed to support spontaneous interaction of mobile users with devices and services in their environment. The model is based on spatial references that capture the spatial relationship of a user’s device with other co-located devices. Spatial references are obtained by relative position sensing and integrated in the mobile user interface to spatially visualize the arrangement of discovered devices, and to provide direct access for interaction across devices. In this paper we discuss two prototype systems demonstrating the utility of the model in collaborative and mobile settings, and present a study on usability of spatial list and map representations for device selection

Exploring views on satisfaction with life in young children with chronic illness: an innovative approach to the collection of self-report data from children under 11

The objective of this study was to explore young children’s views on the impact of chronic illness on their life in order to inform future development of a patient-based self-report health outcome measure. We describe an approach to facilitating self-report views from young children with chronic illness. A board game was designed in order to obtain qualitative data from 39 children with a range of chronic illness conditions and 38 healthy controls ranging in age from 3 to 11 years. The format was effective in engaging young children in a self-report process of determining satisfaction with life and identified nine domains. The board game enabled children aged 5–11 years with chronic illness to describe the effects of living with illness on home, family, friends, school and life in general. It generated direct, non-interpreted material from children who, because of their age, may have been considered unable or limited their ability to discuss and describe how they feel. Obtaining this information for children aged 4 and under continues to be a challenge

Hypoxia exposure and B-type natriuretic peptide release from Langendorff heart of rats

AimWe studied whether available oxygen without induced mechanical stretch regulates the release of the biologically active B-type natriuretic peptide (BNP) from Langendorff heart.MethodsRat hearts were isolated and perfused with a physiological Krebs-Henseleit solution at a constant hydrostatic pressure in Langendorff set-up. The basal O-2 level of perfusate (24.40.04mgL(-1)) was gradually lowered to 3.00.01mgL(-1) over 20min using N-2 gas (n=7). BNP and O-2 level were measured from coronary flow. During control perfusions (n=5), the O-2 concentration was kept at 26.6 +/- 0.3mgL(-1).ResultsA low oxygen concentration in the perfusate was associated with a significant increase in BNP release (F=40.4, P<0.001). Heart rate decreased when the oxygen concentration in the perfusate reached 9.1 +/- 0.02mgL(-1) and continued to fall in lower oxygen concentrations (F=14.8, P<0.001). There was also a significant but inverse correlation between BNP and oxygen in the coronary flow (R-2=0.27, P<0.001).ConclusionIn the spontaneously beating Langendorff rat heart, a decreasing concentration of oxygen in the ingoing perfusion increased the secretion of BNP. The effect of oxygen was independent of mechanical stretch of the heart as it occurred even when the heart rate decreased but the pressure conditions remained constant. The difference in the oxygen capacitance of blood and Krebs-Henseleit solution appears to be a major factor affecting secretion of BNP, which is correlated with the oxygen tension of myocardial cells and affected both by the oxygen concentration and capacitance of solution perfusing the heart and by the coronary flow

Azimuthal correlation in DIS

We introduce the azimuthal correlation for the deep inelastic scattering process. We present the QCD prediction to the level of next-to-leading log resummation, matching to the fixed order prediction. We also estimate the leading non-perturbative power correction. The observable is compared with the energy-energy correlation in e+e- annihilation, on which it is modelled. The effects of the resummation and of the leading power correction are both quite large. It would therefore be particularly instructive to study this observable experimentally.Comment: 33 pages, 4 figures, JHEP class included. One figure and some clarifications adde

QCD: Quantum Chromodynamic Diffraction

The first measurements of the diffractive structure function $F_2^{D(3)}$ at HERA are discussed. A factorisable interpretation in which a partonic structure is assigned to the pomeron is investigated through QCD analyses in which both the quark and gluon densities are permitted to vary freely. A method of measuring the longitudinal structure function of the pomeron without changing the $ep$ centre of mass energy is presented. The possibility that the pomeron structure may receive a large contribution from gluons, relative to quarks, at high $\beta$ is highlighted, and the experimental signatures which may support such a structure are reviewed.Comment: 8 Latex pages, 4 figures, from talks given by the authors at the Workshop on Proton, Photon and Pomeron Structure, Durham, September 199