The GSReg package allows to analyze pathways based on the variability of the expression of sets of genes that are targets of those pathways. Basing this set statistic on variability enables inference of dysregulated pathways in diseases, including notably cancers. The first set statistic for gene variability was in the work of Eddy and his colleagues (see [1]) which used a ranked based methodol...

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

We derive a consistency result, in the L 1 -sense, for incomplete U-statistics non-standard case where kernel at hand has infinite second-order moments. Assuming that finite moments of order p ( ≥ ) , we obtain bound on distance between U-statistic and its Dirac weak limit, which allows us to obtain, any fixed an upper rate. Our results hold most classical sampling schemes are used U-statistics.

we assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the dirac matrices. then by making use of a suitable ansatz, the dirac equation has a very simple solution which is exact. we then have calculated the static properties of the nucleon in the ground...

Due to the lack of experimental values concerning some material properties at the nanoscale, it is interesting to evaluate this theoretically. Through a "top-down" approach, a universal equation is developed here which is particularly helpful when experiments are difficult to lead on a specific material property. It only requires the knowledge of the surface area to volume ratio of the nanomate...

The problem of primordial nucleosynthesis of helium in brane cosmology is studied using a semi-analytical method, where the Fermi-Dirac statistic is ignored. This semi-analytical method agrees with a more complete numerical calculation with a precision of order of 10% or better. The quadratic term for the matter density is the only source considered in the modified Einstein equations predicted ...

We assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the Dirac matrices. Then by making use of a suitable ansatz, the Dirac equation has a very simple solution which is exact. We then have calculated the static properties of the nucleon in the ...