Search results for "Probability measure"
showing 2 items of 22 documents
Peptide classification using optimal and information theoretic syntactic modeling
2010
Accepted version of an article published in the journal: Pattern Recognition. Published version available on Sciverse: http://dx.doi.org/10.1016/j.patcog.2010.05.022 We consider the problem of classifying peptides using the information residing in their syntactic representations. This problem, which has been studied for more than a decade, has typically been investigated using distance-based metrics that involve the edit operations required in the peptide comparisons. In this paper, we shall demonstrate that the Optimal and Information Theoretic (OIT) model of Oommen and Kashyap [22] applicable for syntactic pattern recognition can be used to tackle peptide classification problem. We advoca…
$$\mathscr {K}$$-Convergence of Finite Volume Solutions of the Euler Equations
2020
We review our recent results on the convergence of invariant domain-preserving finite volume solutions to the Euler equations of gas dynamics. If the classical solution exists we obtain strong convergence of numerical solutions to the classical one applying the weak-strong uniqueness principle. On the other hand, if the classical solution does not exist we adapt the well-known Prokhorov compactness theorem to space-time probability measures that are generated by the sequences of finite volume solutions and show how to obtain the strong convergence in space and time of observable quantities. This can be achieved even in the case of ill-posed Euler equations having possibly many oscillatory s…