Accurate computation of quaternions from rotation matrices

The final publication is available at link.springer.comThe main non-singular alternative to 3×3 proper orthogonal matrices, for representing rotations in R3, is quaternions. Thus, it is important to have reliable methods to pass from one representation to the other. While passing from a quaternion to the corresponding rotation matrix is given by Euler-Rodrigues formula, the other way round can be performed in many different ways. Although all of them are algebraically equivalent, their numerical behavior can be quite different. In 1978, Shepperd proposed a method for computing the quaternion corresponding to a rotation matrix which is considered the most reliable method to date. Shepperd’s method, thanks to a voting scheme between four possible solutions, always works far from formulation singularities. In this paper, we propose a new method which outperforms Shepperd’s method without increasing the computational cost.Peer ReviewedPostprint (author's final draft

Readmission Rates of Patients Discharged against Medical Advice: A Matched Cohort Study

OBJECTIVE: We compared the readmission rates and the pattern of readmission among patients discharged against medical advice (AMA) to control patients discharged with approval over a one-year follow-up period. METHODS: A retrospective matched-cohort study of 656 patients(328 were discharged AMA) who were followed for one year after their initial hospitalization at an urban university-affiliated teaching hospital in Vancouver, Canada that serves a population with high prevalence of addiction and psychiatric disorders. Multivariate conditional logistic regression was used to examine the independent association of discharge AMA on 14-day related diagnosis hospital readmission. We fit a multivariate conditional negative binomial regression model to examine the readmission frequency ratio between the AMA and non-AMA group. PRINCIPAL FINDINGS: AMA patients were more likely to be homeless (32.3% vs. 11%) and have co-morbid conditions such as psychiatric illnesses, injection drug use, HIV, hepatitis C and previous gastrointestinal bleeding. Patients discharged AMA were more likely to be readmitted: 25.6% vs. 3.4%, p<0.001 by day 14. The AMA group were more likely to be readmitted within 14 days with a related diagnosis than the non-AMA group (Adjusted Odds Ratio 12.0; 95% Confidence Interval [CI]: 3.7-38.9). Patients who left AMA were more likely to be readmitted multiple times at one year compared to the non-AMA group (adjusted frequency ratio 1.6; 95% CI: 1.3-2.0). There was also higher all-cause in-hospital mortality during the 12-month follow-up in the AMA group compared to non-AMA group (6.7% vs. 2.4%, p = 0.01). CONCLUSIONS: Patients discharged AMA were more likely to be homeless and have multiple co-morbid conditions. At one year follow-up, the AMA group had higher readmission rates, were predisposed to multiple readmissions and had a higher in-hospital mortality. Interventions to reduce discharges AMA in high-risk groups need to be developed and tested

Cap integration in spectral gravity forward modelling: near- and far-zone gravity effects via Molodensky’s truncation coefficients

Spectral gravity forward modelling is a technique that converts a band-limited topography into its implied gravitational field. This conversion implicitly relies on global integration of topographic masses. In this paper, a modification of the spectral technique is presented that provides gravity effects induced only by the masses located inside or outside a spherical cap centred at the evaluation point. This is achieved by altitude-dependent Molodensky’s truncation coefficients, for which we provide infinite series expansions and recurrence relations with a fixed number of terms. Both representations are generalized for an arbitrary integer power of the topography and arbitrary radial derivative. Because of the altitude-dependency of the truncation coefficients, a straightforward synthesis of the near- and far-zone gravity effects at dense grids on irregular surfaces (e.g. the Earth’s topography) is computationally extremely demanding. However, we show that this task can be efficiently performed using an analytical continuation based on the gradient approach, provided that formulae for radial derivatives of the truncation coefficients are available. To demonstrate the new cap-modified spectral technique, we forward model the Earth’s degree-360 topography, obtaining near- and far-zone effects on gravity disturbances expanded up to degree 3600. The computation is carried out on the Earth’s surface and the results are validated against an independent spatial-domain Newtonian integration ((Formula presented.) RMS agreement). The new technique is expected to assist in mitigating the spectral filter problem of residual terrain modelling and in the efficient construction of full-scale global gravity maps of highest spatial resolution

Dying Safely

The burden of deaths due to noncommunicable disease, particularly in the elderly, is projected to rise from 59% in 2002 to 69% in 2030. The ageing population has increased the use of medical technology and life support systems for the support of elderly complex cases—the so-called “sick elderly.” Public expectations believe modern medicine and its associated miracles can prolong life almost indefinitely. Sophisticated technology and the way media portrays the latest miracles generates unrealistic expectations by relatives and often causes potential conflict at the end of life (EoL). The medicalization of death and dying, despite its inevitability has contributed to the disappearance of the concept of a dignified natural death. Dying and death are seen as the ultimate challenge for successful ageing or as a failure of medicine if doctors cannot offer hope of recovery. Unfortunately, in many terminal cases, efforts are made to prolong life under pressure from families as well as the culture of acute hospitals and their concentration on “curing.” Clinicians are often reluctant to recommend limitations of treatment and instead, often administer inappropriate treatment in the face of futility. This chapter is not about assisted dying, euthanasia, nor about the “right to die.” It is about recognition of dying by clinicians; acceptance of death as a natural part of the cycle of life; understanding what constitutes a “good death”; considering the ethical aspects of futile interventions; and reviewing best practice in providing quality of EoL. We discuss the role of doctors, nurses, and the health system in supporting patients and family through the transition

The genetic correlation between height and IQ: shared genes or assortative mating?

Traits that are attractive to the opposite sex are often positively correlated when scaled such that scores increase with attractiveness, and this correlation typically has a genetic component. Such traits can be genetically correlated due to genes that affect both traits ("pleiotropy") and/or because assortative mating causes statistical correlations to develop between selected alleles across the traits ("gametic phase disequilibrium"). In this study, we modeled the covariation between monozygotic and dizygotic twins, their siblings, and their parents (total N = 7,905) to elucidate the nature of the correlation between two potentially sexually selected traits in humans: height and IQ. Unlike previous designs used to investigate the nature of the height-IQ correlation, the present design accounts for the effects of assortative mating and provides much less biased estimates of additive genetic, non-additive genetic, and shared environmental influences. Both traits were highly heritable, although there was greater evidence for non-additive genetic effects in males. After accounting for assortative mating, the correlation between height and IQ was found to be almost entirely genetic in nature. Model fits indicate that both pleiotropy and assortative mating contribute significantly and about equally to this genetic correlation