Sheaf cohomology for fragment-sequencing in hierarchical block rectangular matrices with spectral gaps in the presence of random effects and white noise: the chain

New analytical techniques for fragment sequencing are developped. The fragment sequencing is obtained after the topological Markov chain of the adjacency matrix of the corresponding undirected graph; the presence of white noise and that of random effects are comprehended. The paradigm consists in defining the hierarchical block rectangular matrices, from which the Topological Hidden Markov Models are issued (as clusters), with the aspects of Hidden Markov Models of 'multivariate Gaussian data' with vanishing mean; the generalized covariance matrix is studied. The model is compared with the stochastic properties of the corresponding decomposition of approximation of experimental data. The analysed problem belongs to the NP hard class of complexity.