Numericalmethods for Volterra integral equations with discontinuous kernel need to be tuned to their peculiar form. Here we propose a version of the trapezoidal direct quadrature method adapted to such a type of equations. In order to delineate its stability properties, we first investigate about the behavior of the solution of a suitable (basic) test equation and then we find out under which hypotheses the trapezoidal direct quadrature method provides numerical solutions which inherit the properties of the continuous problem.
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.
Conclusion:
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 webcite
user friendly software
time course microarray
Bayes Factor
We are concerned with the discretization of optimal control problems when a Runge-Kutta scheme is selected for the related Hamiltonian system. It is known that Lagrangian's first order conditions on the discrete model, require a symplectic partitioned Runge-Kutta scheme for state-costate equations. In the present paper this result is extended to growth models, widely used in Economics studies, where the system is described by a current Hamiltonian.
Si affronta il problema della ottimizzazione delle risorse in interventi di rimozione di inquinanti dal sottosuolo mediante bioventing
The report deals with the problem of resource optimization in the removal of pollutants from the subsoil by bioventing
La Calcolatrice Bootstrap e' programmata in Java. Essa comprende sei voci indipendenti: la Media, la Media pesata, la Mediana, la Varianza, la Correlazione e la Regressione. Per ciascuna voci ci sono quattro sottovoci: File, Metodi, Lingua e Aiuto che ne permettono l'uso adeguato. In particolare la Regressione e' distinta tra multipla e polinomiale con la rispettiva variabile dipendente e le covariate. L'esecuzione in Java viene mostrata per esteso. I valori possono essere di diverso tipo: ambientali, fisici, chimici, metrologici, ecc.
