Gaussian processes (GPs) are used widely in the analysis of astronomical time series. GPs with rational spectral densities have state-space representations which allow O(n) evaluation likelihood. We calculate analytic state space for damped simple harmonic oscillator and Mat\'ern 1/2, 3/2 5/2 processes.

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In many processes in real practice at the start-up stages the process parameters are not known a priori and there are no initial samples or data for executing Phase I monitoring and estimating the process parameters. In addition, the practitioners are interested in using one control chart instead of two or more for monitoring location and variability of processes. In this paper, we consider a s...

Metabolic networks consist of linked functional components, or modules. The mechanism underlying metabolic network modularity is of great interest not only to researchers of basic science but also to those in fields of engineering. Previous studies have suggested a theoretical model, which proposes that a change in the evolutionary goal (system-specific purpose) increases network modularity, an...

In this paper, we study shocks and related transitions in asymmetric simple exclusion processes of particles with nearest-neighbor interactions. We consider two kinds of interparticle interactions. In one case, the particle-hole symmetry is broken due to the interaction. In the other case, particles have an effective repulsion due to which the particle current density drops down near one-half f...