This paper is devoted to construct approximations of the probability density function of the non-autonomous first-order homogeneous linear random differential equation, where the initial condition ...and the diffusion coefficient are assumed to be a random variable and a stochastic process, respectively. We combine Random Variable Transformation technique and Karhunen–Loève expansion to construct reliable approximations under general conditions. Several numerical examples illustrate our theoretical findings.
The random variable transformation technique is a powerful method to determine the probabilistic solution for random differential equations represented by the first probability density function of ...the solution stochastic process. In this paper, that technique is applied to construct a closed form expression of the solution for the Bernoulli random differential equation. In order to account for the general scenario, all the input parameters (coefficients and initial condition) are assumed to be absolutely continuous random variables with an arbitrary joint probability density function. The analysis is split into two cases for which an illustrative example is provided. Finally, a fish weight growth model is considered to illustrate the usefulness of the theoretical results previously established using real data.
In the present paper, a homogeneous equilibrium model with a barotropic equation of state has been used for modeling cavitation in a real multi-hole microsac nozzle. The turbulence effects have been ...taking into account by Large Eddy Simulation (LES), using the Smagorinsky model as the sub-grid scale turbulent model and the Van Driest model for the wall damping.
Firstly, the code has been validated at real operating diesel engine conditions with experimental data in terms of mass flow, momentum flux and effective velocity, showing that the model is able to predict with a high level of confidence the behavior of the internal flow at cavitating conditions. Once validated, the code has allowed to study in depth the turbulence developed in the discharge orifices and its interaction with cavitation phenomenon.
Classical Markov models are defined through a stochastic transition matrix, i.e., a matrix whose columns (or rows) are deterministic values representing transition probabilities. However, in practice ...these quantities could often not be known in a deterministic manner, therefore, it is more realistic to consider them as random variables. Following this approach, this paper is aimed to give a technical generalization of classical Markov methodology in order to improve modelling of stroke disease when dealing with real data. With this goal, we randomize the entries of the transition matrix of a Markov chain with three states (susceptible, reliant and deceased) that has been previously proposed to model the stroke disease. This randomization of the classical Markov model permits the computation of the first probability density function of the solution stochastic process taking advantage of the so-called Random Variable Transformation technique. Afterwards, punctual and probabilistic predictions are computed from the first probability density function. In addition, the probability density functions of the time instants until a certain proportion of the total population remains susceptible, reliant and deceased are also computed. The study is completed showing the usefulness of our computational approach to determine, from a probabilistic point of view, key quantities in medical decision making, such as the cost-effectiveness ratio.
•A randomization of a Markov model for study the stroke is proposed.•Random Variable Transformation method gives a probabilistic solution of the model.•First probability density of the solution to randomized Markov model is determined.•Time until a certain proportion of susceptibles remains in the population is given.•Key quantities in medical decision making are determined.
In this paper, the validity of a code implemented for OpenFOAM
® for modeling cavitation phenomena has been checked by comparing data acquired by numerical simulations against data obtained for a ...simple contraction nozzle and for a real diesel injector nozzle. The comparison of numerical and experimental data has been performed, for the simple nozzle, in terms of mass flow rate, velocity at the exit and pressure and cavitation distributions. The numerical results for the real diesel nozzle geometry have been validated with experimental measurements of mass flow rate, momentum flux and effective injection velocity. The results obtained in both cases and their comparison with available experimental data showed that the model is able to predict with a high level of confidence the behavior of the fluid in such conditions.
In this paper, a random finite difference scheme to solve numerically the random Cauchy one-dimensional advection–diffusion partial differential equation is proposed and studied. Throughout our ...analysis both the advection and diffusion coefficients are assumed to be random variables while the deterministic initial condition is assumed to possess a discrete Fourier transform. For the sake of generality in our study, we consider that the advection and diffusion coefficients are statistical dependent random variables. Under mild conditions on the data, it is demonstrated that the proposed random numerical scheme is mean square consistent and stable. Finally, the theoretical results are illustrated by means of two numerical examples.
In this paper a complete probabilistic description for the solution of random homogeneous linear second-order differential equations via the computation of its two first probability density functions ...is given. As a consequence, all unidimensional and two-dimensional statistical moments can be straightforwardly determined, in particular, mean, variance and covariance functions, as well as the first-order conditional law. With the aim of providing more generality, in a first step, all involved input parameters are assumed to be statistically dependent random variables having an arbitrary joint probability density function. Second, the particular case that just initial conditions are random variables is also analysed. Both problems have common and distinctive feature which are highlighted in our analysis. The study is based on random variable transformation method. As a consequence of our study, the well-known deterministic results are nicely generalized. Several illustrative examples are included.
Objective Fetal cerebroplacental ratio is emerging as a better proxy than birthweight for placental insufficiency and as a marker of fetal compromise at term. The extent to which these fetal Doppler ...changes are related to neonatal outcomes has not been systematically assessed. The main aim of this study was to evaluate the association between estimated fetal weight percentile, cerebroplacental ratio recorded at 34+0 –35+6 weeks’ gestation, and neonatal unit admission at term. Study Design This was a retrospective cohort study in a tertiary referral center over an 11 year period from 2002 to 2012. The umbilical artery pulsatility index (PI), middle cerebral artery PI, and cerebroplacental ratio were recorded at 34+0 –35+6 weeks. Weight values were converted into percentiles and Doppler parameters into multiples of the median (MoM), adjusting for gestational age. Logistic regression analysis was performed to identify, and adjust for, potential confounders. Results We identified 2518 pregnancies in which a scan was performed at 34+0 –35+6 weeks and delivery occurred at or beyond 37 weeks. In the 2485 pregnancies included in the analysis, the umbilical artery PI MoM was significantly higher, and the middle cerebral artery PI and cerebroplacental ratio MoM significantly lower in the babies requiring neonatal unit admission ( P < .05). However, the estimated fetal weight percentile was not significantly different between those who required neonatal unit admission and those who did not ( P = .087). According to multivariate logistic regression, cerebroplacental ratio MoM (odds ratio, 0.39; 95% confidence interval, 0.19–0.79; P = .008) and gestational age at delivery (odds ratio, 0.70; 95% confidence interval, 0.61–0.80; P < .001) were significantly associated with the risk of neonatal unit admission, whereas maternal age and birthweight percentile were not ( P = .183 and P = .460, respectively). Irrespective of birthweight or estimated fetal weight percentile, the fetal cerebroplacental ratio appears to be a better predictor of the need for neonatal unit admission ( P < .001). Conclusion Lower cerebroplacental ratio and gestational age at delivery, but not fetal size, were independently associated with the need for admission to the neonatal unit at term in a high-risk patient group. The extent to which fetal hemodynamic assessment could be used to predict perinatal morbidity and optimize the timing of delivery merits further investigation.
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