Solving eigenvalue problems on curved surfaces using the Closest Point Method

Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach

Biophysical Features of Bacillithiol, the Glutathione Surrogate of Bacillus subtilis and other Firmicutes

Bacillithiol (BSH) is the major low-molecular-weight (LMW) thiol in many low-G+C Gram-positive bacteria (Firmicutes). Evidence now emerging suggests that BSH functions as an important LMW thiol in redox regulation and xenobiotic detoxification, analogous to what is already known for glutathione and mycothiol in other microorganisms. The biophysical properties and cellular concentrations of such LMW thiols are important determinants of their biochemical efficiency both as biochemical nucleophiles and as redox buffers. Here, BSH has been characterised and compared with other LMW thiols in terms of its thiol pKa, redox potential and thiol–disulfide exchange reactivity. Both the thiol pKa and the standard thiol redox potential of BSH are shown to be significantly lower than those of glutathione whereas the reactivities of the two compounds in thiol–disulfide reactions are comparable. The cellular concentration of BSH in Bacillus subtilis varied over different growth phases and reached up to 5 mM, which is significantly greater than previously observed from single measurements taken during mid-exponential growth. These results demonstrate that the biophysical characteristics of BSH are distinctively different from those of GSH and that its cellular concentrations can reach levels much higher than previously reported

Responses to supplementation by dairy cows given low pasture allowances in different seasons 2. Milk production

Two factorial experiments were designed to determine the effects of stage of lactation, and season of the year, on cow responses to supplementary feeding. These experiments were conducted over consecutive years with 128 high genetic merit multiparous Holstein-Friesian cows in early, mid and late lactation in spring, summer, autumn and winter. At each stage of lactation, and in each season of the year, cows were offered a restricted pasture allowance (25 to 35 kg dry matter (DM) per cow per day), either unsupplemented (control) or with supplement at 50 MJ metabolizable energy (ME) per cow per day in experiment 1 and 80 MJ ME per cow per day in experiment 2. The two supplements given in both years were rolled maize grain (MG) and a mixture of foods formulated to nutritionally balance the diet (BR). In experiment 2, another treatment, of a generous pasture allowance (60 to 75 kg DM per cow per day) (AP), was imposed on an additional group of early lactation cows during each season. Direct milk solids (MS) (milk fat plus milk protein) responses in experiment 1 to MG were 169, 279, 195 and 251 g MS per cow per day in spring, summer, autumn and winter, respectively, while those to BR were 107, 250, 192, 289 g MS per cow per day. In experiment 2, however, milk solids responses to both supplements during spring were slightly below the control treatment, with values similar to those in experiment 1 in summer and autumn for cows on the BR but not the MG supplement. Milk solids responses to supplementary foods were largest during seasons of the year when the quantity and quality of pasture on offer resulted in the lowest milk solids yield from unsupplemented cows. When carry-over effects of feeding MG and BR on milk solids production were detected, they were only about half the magnitude of the direct effects. Serum urea concentrations were higher in control cows than those offered MG with a similar effect for BR in all but summer in experiment 1, while serum glucose concentrations were highest in winter and lowest in summer. The most important factor influencing milk solids responses was the relative food deficit (RFD) represented by the decline in milk solids yield of the respective control groups after,changing from a generous pasture allowance to restricted allowance when the feeding treatments were imposed. Total milk solids responses (direct and carry-over) to supplements were greatest when severe food restrictions, relative to the cows' current food demand, resulted in large reductions in milk solids yield of the control groups. The RFD was the best predictor of milk solids response to supplementary foods. Therefore, it is likely that cows are most responsive to supplementary foods during or immediately after the imposition of a severe food restriction

Responses to supplementation by dairy cows given low pasture allowances in different seasons 1. Pasture intake and substitution

Two factorial experiments were designed to determine the effects of stage of lactation, and season of the year, on cow responses to supplementary feeding. These experiments were conducted over consecutive years with 128 high genetic merit multiparous Holstein-Friesian cows in early, mid and late lactation in spring, summer, autumn and winter. At each stage of lactation, and in each season of the year, cows were offered a restricted pasture allowance (25 to 35 kg dry matter (DM) per cow per day), either unsupplemented (control) or supplemented with 50 MJ metabolizable energy (ME) per cow per day in experiment 1 and 80 MJ ME per cow per day in experiment 2. Two different supplements were offered, namely, rolled maize grain (MG) and a mixture of foods (BR) formulated to nutritionally balance the diet. In experiment 2, a fourth treatment consisting solely of a generous pasture allowance (60 to 75 kg DM per cow per day, AP) was introduced. Offering MG and BR increased DM intake (DMI). At the restricted pasture allowance, increasing total ME allowance (MEA) by offering supplementary foods increased ME intake (MEI) by 0.68 (s.e. 0.047) MJ per extra MJ ME offered. This highly significant (P < 0.001) linear relationship was consistent across seasons, and did not diminish at higher MEA. In experiment 2, cows in early lactation had lower substitution rates than mid and late lactation cows irrespective of season. Substitution rate was higher when higher pasture allowance or quality of pasture on offer enabled the unsupplemented cows to achieve higher DMI from pasture than at other times of the year. These results suggest that one of the key factors determining the intake response to supplementary foods is pasture allowance. Within spring calving dairying systems, the largest increases in total DMI per kg of supplement offered is likely when offering supplements to early lactation cows grazing restricted allowances of high quality pasture

The effect of COVID-19 restrictions on rehabilitation and functional outcome following total hip and knee arthroplasty during the first wave of the pandemic

Aims: The primary aim was to assess the patient-perceived effect of restrictions imposed due to COVID-19 on rehabilitation following total hip arthroplasty (THA) and total knee arthroplasty (TKA). Secondary aims were to assess perceived restrictions, influence on mental health, and functional outcome compared to patients undergoing surgery without restriction. Methods: During February and March 2020, 105 patients underwent THA (n = 48) or TKA (n = 57) and completed preoperative and six-month postoperative assessments. A cohort of 415 patients undergoing surgery in 2019 were used as the control. Patient demographic data, BMI, comorbidities, Oxford Hip Score (OHS) or Knee Score (OKS), and EuroQoL five-domain (EQ-5D) score were collected preoperatively and at six months postoperatively. At six months postoperatively, the 2020 patients were also asked to complete a questionnaire relating to the effect of the social restrictions on their outcome and their mental health. Results: Nearly half of the patients (47.6%, n = 50/105) felt that the restrictions imposed by COVID-19 had limited their rehabilitation and were associated with a significantly worse postoperative OKS (p < 0.001), EQ-5D score (p < 0.001), and lower satisfaction rate (p = 0.019). The reasons for the perceived limited rehabilitation were: being unable to exercise (n = 32, 64%), limited access to physiotherapy (n = 30, 60%), and no face-to-face follow-up (n = 30, 60%). A quarter (n = 26) felt that their mental health had deteriorated postoperatively; 17.1% (n = 18) felt depressed and 26.7% (n = 28) felt anxious. Joint-specific scores and satisfaction for the 2020 group were no different to the 2019 group, however patients undergoing THA in 2020 had a significantly worse postoperative EQ-5D compared to the 2019 cohort (difference 0.106; p = 0.001) which was not observed in patients undergoing TKA. Conclusion: Half of the 2020 cohort felt that their rehabilitation had been limited and was associated with worse postoperative Oxford and EQ-5D scores, and lower rates of patient satisfaction, but relative to the 2019 cohort their overall outcomes were no different, with the exception of THA patients who had a worse general health score. Level of evidence: Prospective study, Level 2

Realistic Earth escape strategies for solar sailing

With growing interest in solar sailing comes the requirement to provide a basis for future detailed planetary escape mission analysis by drawing together prior work, clarifying and explaining previously anomalies. Previously unexplained seasonal variations in sail escape times from Earth orbit are explained analytically and corroborated within a numerical trajectory model. Blended-sail control algorithms, explicitly independent of time, which providenear-optimal escape trajectories and maintain a safe minimum altitude and which are suitable as a potential autonomous onboard controller, are then presented. These algorithms are investigated from a range of initial conditions and are shown to maintain the optimality previously demonstrated by the use of a single-energy gain control law but without the risk of planetary collision. Finally, it is shown that the minimum sail characteristic acceleration required for escape from a polar orbit without traversing the Earth shadow cone increases exponentially as initial altitude is decreased