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

Weight management: a comparison of existing dietary approaches in a work-site setting

<b>OBJECTIVES:</b> (1) To compare the effectiveness a 2512 kJ (600 kcal) daily energy deficit diet (ED) with a 6279 kJ (1500 kcal) generalized low-calorie diet (GLC) over a 24 week period (12 weeks weight loss plus 12 weeks weight maintenance). (2) To determine if the inclusion of lean red meat at least five times per week as part of a slimming diet is compatible with weight loss in comparison with a diet that excludes lean red meat. DESIGN: Randomized controlled trial. <b>SETTING:</b> Large petrochemical work-site. <b>PARTICIPANTS:</b> One-hundred and twenty-two men aged between 18 and 55 y. <b>MAIN OUTCOME MEASURES:</b> Weight loss and maintenance of weight loss. <b>INTERVENTION:</b> Eligible volunteers were randomized to one of the four diet=meat combinations (ED meat, ED no meat, GLC meat, GLC no meat). One-third of subjects in each diet/meat combination were randomized to an initial control period prior to receiving dietary advice. All subjects attended for review every 2 weeks during the weight loss period. For the 12 week structured weight maintenance phase, individualized energy prescriptions were re-calculated for the ED group as 1.4 (activity factor)x basal metabolic rate. Healthy eating advice was reviewed with subjects in the GLC group. All subjects were contacted by electronic mail at 2 week intervals and anthropometric and dietary information requested. <b>RESULTS:</b> No difference was evident between diet groups in mean weight loss at 12 weeks (4.3 (s.d. 3.4) kg ED group vs 5.0 (s.d. 3.5) kg GLC group, P=0.34). Mean weight loss was closer to the intended weight loss in the 2512 kJ (600 kcal) ED group. The dropout rate was also lower than the GLC group. The inclusion of lean red meat in the diet on at least five occasions per week did not impair weight loss. Mean weight gain following 12 weeks weight maintenance was þ1.1 (s.d. 1.8) kg, P<0.0001. No differences were found between groups. <b>CONCLUSIONS:</b> This study has shown that the individualized 2512 kJ (600 kcal) ED approach was no more effective in terms of weight loss than the 6279 kJ (1500 kcal) GLC approach. However the ED approach might be considered preferable as compliance was better with this less demanding prescription. In terms of weight loss the elimination of red meat from the diet is unnecessary. The weight maintenance intervention was designed as a low-input approach, however weight regain was significant and weight maintenance strategies require further development

A biophysical model of cell adhesion mediated by immunoadhesin drugs and antibodies

A promising direction in drug development is to exploit the ability of natural killer cells to kill antibody-labeled target cells. Monoclonal antibodies and drugs designed to elicit this effect typically bind cell-surface epitopes that are overexpressed on target cells but also present on other cells. Thus it is important to understand adhesion of cells by antibodies and similar molecules. We present an equilibrium model of such adhesion, incorporating heterogeneity in target cell epitope density and epitope immobility. We compare with experiments on the adhesion of Jurkat T cells to bilayers containing the relevant natural killer cell receptor, with adhesion mediated by the drug alefacept. We show that a model in which all target cell epitopes are mobile and available is inconsistent with the data, suggesting that more complex mechanisms are at work. We hypothesize that the immobile epitope fraction may change with cell adhesion, and we find that such a model is more consistent with the data. We also quantitatively describe the parameter space in which binding occurs. Our results point toward mechanisms relating epitope immobility to cell adhesion and offer insight into the activity of an important class of drugs.Comment: 13 pages, 5 figure

Airborne observations of methane emissions from rice cultivation in the Sacramento Valley of California

Airborne measurements of methane (CH4) and carbon dioxide (CO2) were taken over the rice growing region of California's Sacramento Valley in the late spring of 2010 and 2011. From these and ancillary measurements, we show that CH4 mixing ratios were higher in the planetary boundary layer above the Sacramento Valley during the rice growing season than they were before it, which we attribute to emissions from rice paddies. We derive daytime emission fluxes of CH4 between 0.6 and 2.0% of the CO2 taken up by photosynthesis on a per carbon, or mole to mole, basis. We also use a mixing model to determine an average CH 4/CO2 flux ratio of -0.6% for one day early in the growing season of 2010. We conclude the CH4/CO2 flux ratio estimates from a single rice field in a previous study are representative of rice fields in the Sacramento Valley. If generally true, the California Air Resources Board (CARB) greenhouse gas inventory emission rate of 2.7×1010g CH4/yr is approximately three times lower than the range of probable CH4 emissions (7.8-9.3×10 10g CH4/yr) from rice cultivation derived in this study. We attribute this difference to decreased burning of the residual rice crop since 1991, which leads to an increase in CH4 emissions from rice paddies in succeeding years, but which is not accounted for in the CARB inventory. © 2012. American Geophysical Union. All Rights Reserved

Preadaptation of pandemic GII.4 noroviruses in unsampled virus reservoirs years before emergence

The control of re-occurring pandemic pathogens requires understanding the origins of new pandemic variants and the factors that drive their global spread. This is especially important for GII.4 norovirus, where vaccines under development offer promise to prevent hundreds of millions of annual gastroenteritis cases. Previous studies have hypothesized that new GII.4 pandemic viruses arise when previously circulating pandemic or pre-pandemic variants undergo substitutions in antigenic regions that enable evasion of host population immunity, as described by conventional models of antigenic drift. In contrast, we show here that the acquisition of new genetic and antigenic characteristics cannot be the proximal driver of new pandemics. Pandemic GII.4 viruses diversify and spread over wide geographical areas over several years prior to simultaneous pandemic emergence of multiple lineages, indicating that the necessary sequence changes must have occurred before diversification, years prior to pandemic emergence. We confirm this result through serological assays of reconstructed ancestral virus capsids, demonstrating that by 2003, the ancestral 2012 pandemic strain had already acquired the antigenic characteristics that allowed it to evade prevailing population immunity against the previous 2009 pandemic variant. These results provide strong evidence that viral genetic changes are necessary but not sufficient for GII.4 pandemic spread. Instead, we suggest that it is changes in host population immunity that enable pandemic spread of an antigenically preadapted GII.4 variant. These results indicate that predicting future GII.4 pandemic variants will require surveillance of currently unsampled reservoir populations. Furthermore, a broadly acting GII.4 vaccine will be critical to prevent future pandemics

Scaling Laws in Human Language

Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes into account the effects of finite vocabulary size. Experiments, simulations and analytical solution agree well with each other. The results show that the frequency distribution follows a power law with exponent being equal to 1, at which the corresponding Zipf's exponent diverges. Actually, the distribution obeys exponential form in the Zipf's plot. Deviating from the Heaps' law, the number of distinct words grows with the text length in three stages: It grows linearly in the beginning, then turns to a logarithmical form, and eventually saturates. This work refines previous understanding about Zipf's law and Heaps' law in language systems.Comment: 6 pages, 4 figure