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The purpose of this paper is to provide an explicit time-dependent solution for the / /1 k M E queueing system when initially there are "a" customers in the system. The solution is expressed in terms of a generalised modified Bessel function of the second type. Computation results are provided as well as an application of this model to a 24-hour traffic flow profile on the Severn Bridge.

Schizophrenia is a common complex disorder with polygenic inheritance. Here we show that by using an approach that compares the individual loads of rare variants in 1,042 schizophrenia cases and 961 controls, schizophrenia cases carry an increased burden of deleterious mutations. At a genome-wide level, our results implicate non-synonymous, splice site as well as stop-altering single-nucleotide variations occurring at minor allele frequency of ≥0.01% in the population. In an independent replication sample of 5,585 schizophrenia cases and 8,103 controls of European ancestry we confirm an enrichment in cases of the alleles identified in our study. In addition, the genes implicated by the increased burden of rare coding variants highlight the involvement of neurodevelopment in the aetiology of schizophrenia., Schizophrenia is a complex disorder with high heritability but poorly understood genetics. Here Olde Loohuis et al. compare schizophrenia patients to unaffected individuals and identify an increased individual burden of rare deleterious mutations in patients.

The single-channel queueing equations considered in this paper are characterised by Poisson-distributed arrivals and Erlang service times. The transient phase probabilities are obtained in terms of a new generalisation of the modified Bessel function, and the mean waiting time in the queue is evaluated.

We study the exponential type inequalities for the distribution of the supremum of a random field that arises as the solution of the heat equation with a random initial condition that is a strictly sub-Gaussian random field.

Inversion of radiative transfer models using a lookup-table (LUT) approach against hyperspectral data streams leads to retrievals of biophysical parameters such as chlorophyll content (Chl), but necessary optimization strategies are not consolidated yet. Here, various regularization options have been evaluated to the benefit of improved Chl retrieval from hyperspectral CHRIS data, being: i) the role of added noise, ii) the role of multiple best solutions, and iii) the role of applied cost functions in LUT-based inversion. By using data from the ESA-led field campaign SPARC (Barrax, Spain), it was found that introducing noise and opting for multiple best solutions in the inversion considerably improved retrievals. However, the widely used RMSE was not the best performing cost function. Three families of alternative cost functions were applied here: information measures, minimum contrast and M-estimates. We found that so-called ‘Power divergence measure’, ‘Trigonometric’ and spectral measure with ‘Contrast function K(x)=−log(x)+x’ outperformed RMSE. The whole inversion approach, including more than 60 different cost functions, has been implemented in the ARTMO (Automated Radiative Transfer Models Operator) GUI toolbox and can easily be applied to other kinds of multispectral or hyperspectral images.

This paper focuses on Pearson diffusions and the spectral high-order approximation of their related Fokker–Planck equations. The Pearson diffusions is a class of diffusions defined by linear drift and quadratic squared diffusion coefficient. They are widely used in the physical and chemical sciences, engineering, rheology, environmental sciences and financial mathematics. In recent years diffusion models have been studied analytically and numerically primarily through the solution of stochastic differential equations. Analytical solutions have been derived for some of the Pearson diffusions, including the Ornstein–Uhlenbeck, Cox–Ingersoll–Ross and Jacobi processes. However, analytical investigations and computations for diffusions with so-called heavy-tailed ergodic distributions are more difficult to perform. The novelty of this research is the development of an accurate and efficient numerical method to solve the Fokker–Planck equations associated with Pearson diffusions with different boundary conditions. Comparisons between the numerical predictions and available time-dependent and equilibrium analytical solutions are made. The solution of the Fokker–Planck equation is approximated using a reduced basis spectral method. The advantage of this approach is that many models for pricing options in financial mathematics cannot be expressed in terms of a stochastic partial differential equation and therefore one has to resort to solving Fokker–Planck type equations.