This article provides a comparison of the successive lumping (SL) methodology developed in [19] with the popular lattice path counting [24] in obtaining rate matrices for queueing models, satisfying the specific quasi birth and death structure as in [21], [22]. The two methodologies are compared both in terms of applicability requirements and numerical complexity by analyzing their performance ...

explosion has always been regarded as one of the most complicated engineering problems. as a result, many engineers have preferred rather simplified empirical approaches in comparison to extremely complex deterministic analyses. in this paper, however, a numerical simulation based on the combined finite/discrete element methodology is presented for analyzing the dynamic behavior of fracturing r...

In Response to: Giorelli M, Losignore NA, Bagnoli J, et al. The progression of posterior cortical atrophy to corticobasal syndrome: Lumping or splitting neurodegenerative diseases? Tremor Other Hyperkinet Mov. 2014; 4. doi: 10.7916/D81G0JCQ.

in this article, the discrete time state space model with first-order autoregressive dependent process noise is considered and the recursive method for filtering, prediction and smoothing of the hidden state from the noisy observation is designed. the explicit solution is obtained for the hidden state estimation problem. finally, in a simulation study, the performance of the designed method ...

We construct and analyze a new family of rectangular (two-dimensional) or cubic (three-dimensional) mixed finite elements for the approximation of the acoustic wave equations. The main advantage of this element is that it permits us to obtain through mass lumping an explicit scheme even in an anisotropic medium. Nonclassical error estimates are given for this new element.

The effect of linear lumping, linear transformation to reduce the number of state variables on controllability and observability of linear differential equations has been studied. Controllability of the original system implies the controllability of the lumped system. Examples taken from reaction kinetics illustrate our results.

We derive explicit formulae to quantify the Markov chain state-space compression, or lumping, that can be achieved in a broad range of dynamical processes on real-world networks, including models epidemics and voting behaviour, by exploiting redundancies due symmetries. These are applied large-scale study such symmetry-induced lumping from which we identify specific networks for enables exact a...