The Coxian Phase-type distribution with a Hidden Node

Healthcare providers are under increased pressure to ensure that the quality
of care delivered to patients are off the highest standard. Modelling quality of
care is difficult due to the many ways of defining it. This paper introduces a potential
model which could be used to take quality of care into account when modelling
length of stay. The Coxian phase-type distribution is used to model length of stay
and quality of care incorporated into this using a Hidden Markov model. This model
is then applied to

Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates
is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth’s magnetotail region.

Enteric methane emissions and nitrogen utilisation efficiency for two genotype of hill hoggets offered fresh, ensiled and pelleted ryegrass

Thirty-six 12-month-old hill hoggets were used in a 2 genotype (18 Scottish Blackface vs. 18 Swaledale×Scottish Blackface)×3 diet (fresh vs. ensiled vs. pelleted ryegrass) factorial design experiment to evaluate the effects of hogget genotype and forage type on enteric methane (CH4) emissions and nitrogen (N) utilisation. The hoggets were offered 3 diets ad libitum with no concentrate supplementation in a single period study with 6 hoggets for each of the 6 genotype×diet combinations (n=6). Fresh ryegrass was harvested daily in the morning. Pelleted ryegrass was sourced from a commercial supplier (Aylescott Driers & Feeds, Burrington, UK) and the ryegrass silage was ensiled with Ecosyl (Lactobacillus plantarum, Volac International Limited, Hertfordshire, UK) as an additive. The hoggets were housed in individual pens for at least 14 d before being transferred to individual respiration chambers for a further 4 d with feed intake, faeces and urine outputs and CH4 emissions measured. There was no significant interaction between genotype and forage type on any parameter evaluated. Sheep offered pelleted grass had greater feed intake (e.g. DM, energy and N) but less energy and nutrient apparent digestibility (e.g. DM, N and neutral detergent fibre (NDF)) than those given fresh grass or grass silage (P<0.001). Feeding pelleted grass, rather than fresh grass or grass silage, reduced enteric CH4 emissions as a proportion of DM intake and gross energy (GE) intake (P<0.01). Sheep offered fresh grass had a significantly lower acid detergent fibre (ADF) apparent digestibility, and CH4 energy output (CH4-E) as a proportion of GE intake than those offered grass silage (P<0.001). There was no significant difference, in CH4 emission rate or N utilisation efficiency when compared between Scottish Blackface and Swaledale × Scottish Blackface. Linear and multiple regression techniques were used to develop relationships between CH4 emissions or N excretion and dietary and animal variables using data from sheep offered fresh ryegrass and grass silage. The equation relating CH4-E (MJ/d) to GE intake (GEI, MJ/d), energy apparent digestibility (DE/GE) and metabolisability (ME/GE) resulted in a high r2 (CH4-E=0.074 GEI+9.2 DE/GE−10.2 ME/GE−0.37, r2=0.93). N intake (NI) was the best predictor for manure N excretion (Manure N=0.66 NI+0.96, r2=0.85). The use of these relationships can potentially improve the precision and decrease the uncertainty in predicting CH4 emissions and N excretion for sheep production systems managed under the current feeding conditions.