Structured total least norm and approximate GCDs of inexact polynomials

The determination of an approximate greatest common divisor (GCD) of two inexact polynomials f=f(y) and g=g(y) arises in several applications, including signal processing and control. This approximate GCD can be obtained by computing a structured low rank approximation S*(f,g) of the Sylvester resultant matrix S(f,g). In this paper, the method of structured total least norm (STLN) is used to compute a low rank approximation of S(f,g), and it is shown that important issues that have a considerable effect on the approximate GCD have not been considered. For example, the established works only yield one matrix S*(f,g), and therefore one approximate GCD, but it is shown in this paper that a family of structured low rank approximations can be computed, each member of which yields a different approximate GCD. Examples that illustrate the importance of these and other issues are presented

Shuttle time and frequency transfer experiment

A proposed space shuttle experiment to demonstrate techniques for global high precision comparison of clocks and primary frequency standards is described. The experiment, using transmitted microwave and pulsed laser signals, compared a hydrogen maser clock onboard the space shuttle with a clock in a ground station in order to demonstrate time transfer with accuracies of 1 nsec or better and frequency comparison at the 10 to the -14th power accuracy level

Activity-composition relations in the system CaCO3-MgCO3 predicted from static structure energy calculations and Monte Carlo simulations

Thermodynamic mixing properties and subsolidus phase relations of the rhombohedral carbonate system, (1 - x) CaCO3 - x MgCO3, were modelled in the temperature range of 623-2023 K with static structure energy calculations based on well-parameterised empirical interatomic potentials. Relaxed static structure energies of a large set of randomly varied structures in a 4 x 4 x 1 supercell of R3c calcite (a = 19.952A , c = 17.061A ) were calculated with the General Utility Lattice Program (GULP). These energies were cluster expanded in a basis set of 12 pair-wise effective interactions. Temperature-dependent enthalpies of mixing were calculated by the Monte Carlo method. Free energies of mixing were obtained by thermodynamic integration of the Monte Carlo results. The calculated phase diagram is in good agreement with experimental phase boundaries

High-accuracy global time and frequency transfer with a space-borne hydrogen maser clock

A proposed system for high-accuracy global time and frequency transfer using a hydrogen maser clock in a space vehicle is discussed. Direct frequency transfer with a accuracy of 10 to the minus 14th power and time transfer with an estimated accuracy of 1 nsec are provided by a 3-link microwave system. A short pulse laser system is included for subnanosecond time transfer and system calibration. The results of studies including operational aspects, error sources, data flow, system configuration, and implementation requirements for an initial demonstration experiment using the Space Shuttle are discussed

Scoring rules in probability assessment and evaluation

The purpose of this paper is to briefly discuss some important current questions and problems related to the use of scoring rules (SRs) both in connection with the actual assessment of probabilities and with the evaluation of probability forecasts and probability assessors. With regard to the assessment process, we consider both the case in which the assessor's utility function is linear and the case in which his utility function is nonlinear. Under linear utility, important problems of concern are the sensitivity of SRs to deviations from optimality (with a strictly proper SR, optimality consists of the assessor making his statements correspond to his judgments) and the effect of psychological considerations arising from the use of different SRs. Under nonlinear utility, SRs should be modified to allow for the nonlinearity in such a manner that for a specific utility function, the modified SRs are strictly proper. This introduces the difficult question of the assessment of the assessor's utility function. With regard to the evaluation process (as opposed to the assessment process), we consider the process from an inferential viewpoint and from a decision-theoretic viewpoint. From an inferential viewpoint, attributes such as validity may be of interest, and in certain circumstances these attributes may be related to SRs. The attributes of interest, of course, depend on the framework within which the evaluation process is undertaken. From a decision-theoretic viewpoint, SRs may be related to a decision maker's utilities or expected utilities (under uncertainty about the utilities) if the decision maker uses the assessed probabilities in an actual decision situation.In summary, there are many important questions and problems related to SRs, and the need for future research on these problems seems clear. Such research should lead to a greatly improved understanding of the processes of probability assessment and evaluation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32842/1/0000218.pd

Fourteen degrees of latitude and a continent apart: comparison of lichen activity over two years at continental and maritime Antarctic sites

There are marked declines in precipitation, mean temperatures and the number of lichen species with increasing latitude in Antarctica. However, it is not known which factors are the predominant controllers of biodiversity changes. Results are presented from over two years of almost continuous monitoring of both microclimate and activity in lichens at Livingston Island, South Shetland Islands, 62°S, and Botany Bay, Ross Sea region, 77°S. Lichen activity was evident over a much longer period at Livingston Island, (3694 versus 897 hours) and could occur in any month whereas it was almost completely confined to the period November–February at Botany Bay. Mean air temperatures were much lower at Botany Bay (-18° compared to -1.5°C at Livingston Island), but the temperatures at which the lichens were active were almost identical at around 2°C at both sites. When the lichens were active incident light at Botany Bay was very much higher. The differences are related to the availability of meltwater which only occurs at times of high light and warm temperatures at Botany Bay. Temperature as a direct effect does not seem to explain the differences in biodiversity between the sites, but an indirect effect through active hours is much more probable. In addition there are negative effects of stresses such as high light and extreme winter cold at Botany Bay

Computational studies of light acceptance and propagation in straight and curved multimodal active fibres

A Monte Carlo simulation has been performed to track light rays in cylindrical multimode fibres by ray optics. The trapping efficiencies for skew and meridional rays in active fibres and distributions of characteristic quantities for all trapped light rays have been calculated. The simulation provides new results for curved fibres, where the analytical expressions are too complex to be solved. The light losses due to sharp bending of fibres are presented as a function of the ratio of curvature to fibre radius and bending angle. It is shown that a radius of curvature to fibre radius ratio of greater than 65 results in a light loss of less than 10% with the loss occurring in a transition region at bending angles of pi/8 rad.Comment: 21 pages, 13 figure

Associations between self-reported sleep quality and white matter in community-dwelling older adults: A prospective cohort study.

Both sleep disturbances and decline in white matter microstructure are commonly observed in ageing populations, as well as in age-related psychiatric and neurological illnesses. A relationship between sleep and white matter microstructure may underlie such relationships, but few imaging studies have directly examined this hypothesis. In a study of 448 community-dwelling members of the Whitehall II Imaging Sub-Study aged between 60 and 82 years (90 female, mean age 69.2 ± 5.1 years), we used the magnetic resonance imaging technique diffusion tensor imaging to examine the relationship between self-reported sleep quality and white matter microstructure. Poor sleep quality at the time of the diffusion tensor imaging scan was associated with reduced global fractional anisotropy and increased global axial diffusivity and radial diffusivity values, with small effect sizes. Voxel-wise analysis showed that widespread frontal-subcortical tracts, encompassing regions previously reported as altered in insomnia, were affected. Radial diffusivity findings remained significant after additional correction for demographics, general cognition, health, and lifestyle measures. No significant differences in general cognitive function, executive function, memory, or processing speed were detected between good and poor sleep quality groups. The number of times participants reported poor sleep quality over five time-points spanning a 16-year period was not associated with white matter measures. In conclusion, these data demonstrate that current sleep quality is linked to white matter microstructure. Small effect sizes may limit the extent to which poor sleep is a promising modifiable factor that may maintain, or even improve, white matter microstructure in ageing. Hum Brain Mapp 38:5465-5473, 2017. © 2017 Wiley Periodicals, Inc