A single master equation is given describing spin s=2 test fields that are gaugeand
tetrad-invariant perturbations of the spinning C metric space-time representing
a source with mass M, uniformly rotating with angular momentum per unit mass a,
and uniformly accelerated with acceleration A. This equation can be separated into
its radial and angular parts. The behavior of the radial functions near the black hole
outer horizon is studied to examine the influence of A on the phenomenon of
super-radiance, while the angular equation leads to modified spin-weighted spheroidal
harmonic solutions generalizing those of the Kerr space-time. Finally the
coupling between the spin of the perturbing field and the acceleration parameter A
is discussed.
Background
Gene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular treatment or a biological process of interest. From methodological and computational point of view, analyzing high-dimensional time course microarray data requires very specific set of tools which are usually not included in standard software packages. Recently, the authors of this paper developed a fully Bayesian approach which allows one to identify differentially expressed genes in a `one-sample' time-course microarray experiment, to rank them and to estimate their expression profiles. The method is based on explicit expressions for calculations and, hence, very computationally efficient.
Results
The software package BATS (Bayesian Analysis of Time Series) presented here implements the methodology described above. It allows an user to automatically identify and rank differentially expressed genes and to estimate their expression profiles when at least 5-6 time points are available. The package has a user-friendly interface. BATS successfully manages various technical difficulties which arise in time-course microarray experiments, such as a small number of observations, non-uniform sampling intervals and replicated or missing data.
Conclusions
BATS is a free user-friendly software for the analysis of both simulated and real microarray time course experiments. The software, the user manual and a brief illustrative example are freely available online at the BATS website: http://www.na.iac.cnr.it/bats
Bayesian approaches
Time course microarray
Software
We introduce some numerical approximations to a quasilinear problem proposed by G. I. Barenblatt to describe non-equilibrium two-phase fluid flows in permeable porous media, which apply to secondary oil recovery from natural reservoirs. Taking into account the theoretical results of global existence and uniqueness, we approximate the solutions by three numerical schemes, namely, the Diagonal First Order schemes (DFO and DFO2) and the Diagonal Second Order scheme (DSO). For DFO schemes convergence is proved. The schemes' behaviour is analysed and discussed through some numerical experiments.
