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For each realisation, we record β for 1000 TTIs where users are scheduled using the PF algorithm.
Monte Carlo simulations are run over 100 different network realisations, and for each realisation, 1000 TTIs are considered.
A least squares fitting routine is used to obtain a fit to each realisation, yielding a range of parameter values rather than a single set of absolute values.
Each realisation of these stochastic PDEs requires the solution of the linear first-order velocity pressure system comprising Darcy's law coupled with an incompressibility constraint.
For each realisation and set of parameter values we use Newton's method with 1000 randomly chosen initial values which satisfy (34).
Each realisation has an equal chance to be real and this provides an appropriate platform to analyse the risk-associated with the geological conditions (Goovaerts 1997; Vann et al. 2002; Dimitrakopoulos 2011; Topal and Ramazan 2012).
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This analysis consists of a sequence of operations for deriving probability distributions for a selected set of model parameters and repeating the simulation of each realisations of the parameter set (Swaney and Hong 2009b).
In brief, at each model realisation, we estimated the prevalence of anaemia in each of the risk groups based upon the posterior mean and SD of the Hb distribution within each school.
At each model realisation, malnutrition was categorised as either low, medium/high or severe for each school location, according to table 1.
An ensemble of fibre waviness profiles is generated from an assumed spectral density of waviness and the compressive strength for each such realisation is calculated directly by the finite element method.
We gathered the final, converged configurations in Additional files 1, 2, 3 and 4. Each initial realisation is run with the Hermite code, using standard double-precision, and with Brutus, using arbitrary-precision until a converged solution is obtained.
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