One way to capture parametric and model uncertainties consists in the construction of a non-parametric probabilistic model, in which the reduced structural matrices are replaced by random matrices.
The method consists in the construction of a reduced basis approximation of the Galerkin solution and is independent of the stochastic discretization selected (polynomial chaos, stochastic multi-element or multi-wavelets).
The usual tool to derive an existence result consists in the construction of a modified problem that satisfies the two following properties.
The derivation of FUNC essentially consists in the construction of an observable (i.e. f(Q)) via an operator (i.e., f(Q)) from the probability distribution of a variable (i.e. f v(Q)) which number in turn is constructed from another variable, (i.e. v(Q)).
Their strategy consists in the construction of a multisummable formal solution written as a sum of formal series, each of them associated to a root of the symbol attached to the PDE using the so-called Puiseux expansion for the roots of polynomial with holomorphic coefficients.
The third step, which consists in the construction of a multiple alignment for each cluster, is particularly important, because the quality of a consensus sequence depends on the quality of the multiple sequence alignment (MSA) from which it is derived.
Another powerful approach utilizing transcriptomic resources consists in the construction of co-expression maps [ 11].
The main new contribution of the paper consists in realizing this construction using B-spline techniques.
Step 4 is one of the most important stages of our work and consists in the dynamic construction of a classier using Machine Learning techniques.
The most difficult part of the scheme discussed consists in the analytic construction of so many members of the parametrised iteration sequence (9.4) which is sufficient to establish the solvability of the periodic problem (see conditions (10.6), (10.7)) and achieve the required precision of approximation in (11.1).
