In this paper we introduce the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process components. We use the physical interpretation of a Rational Arrival Process (RAP), developed by Asmussen and Bladt, to consider such a Markov process. We exploit this interpretation to develop an analytic method for such a process, that parallels the analysis of a traditional QBD. We d...

Monosodium urate (MSU) crystals, which are highly precipitated in the joint cartilage, increase the production of cartilage-degrading enzymes and pro-inflammatory mediators in cartilage, thereby leading to gouty inflammation and joint damage. In this study, we investigated the effect of MSU crystals on the viability of human articular chondrocytes and the mechanism of MSU crystal-induced chondr...

Continued fractions (CFs) play a fundamental role in many investigations due to its applications to diverse fields like number theory, special functions, approximations, moment problems, digital networks, statistics, and signal processing. Their importance has grown further with the advent of fast computing facilities. The problem of converting a continued fraction into a power series is import...

When modeling longitudinal data using a set of hidden processes such as state-space models, a common assumption is that the number of hidden processes is fixed, and all hidden processes have the same life span (i.e., all start at the onset of the data stream and terminate at the end of the data stream). In this report I outline a framework of modeling complex longitudinal data using a birth-dea...

We present an efficient, reliable, and easy-to-implement algorithm to compute steady-state probabilities for birth-death processes whose upper-tail probabilities decay geometrically or faster. The algorithm can provide any required accuracy and it avoids overand underflow. In addition to steady-state probabilities, the algorithm can compute any performance measure that can be expressed as the e...

We consider a birth-death process with the birth rates iλ and death rates iμ+i(i−1)θ, where i is the current state of the process. A positive competition rate θ is assumed to be small. In the supercritical case when λ > μ this process can be viewed as a demographic model for a population with a high carrying capacity around λ−μ θ . The article reports in a self-contained manner on the asymptoti...

Programmed cell death involves the removal of cell corpses by other cells in a process termed engulfment. Genetic studies of the nematode Caenorhabditis elegans have led to a framework not only for the killing step of programmed cell death but also for the process of cell-corpse engulfment. This work has defined two signal transduction pathways that act redundantly to control engulfment. Signal...

In this paper, we study a birth/immigration-death processes under mild (binomial) catastrophes. We obtain explicit expressions for both the time-dependent (transient) and the limiting (equilibrium) factorial moments, which are then used to construct the transient and equilibrium distribution of the population size. We demonstrate that our approach is also applicable to multidimensional systems ...

First, we revisit a classic two-type branching process which describes cell proliferation and mutation; widespread application has been seen in cancer and microbial modelling. As the mutation rate tends to zero and the population size to infinity, the mutation times converge to a Poisson process. This yields the number of mutants and clone sizes. Other limits and exact results are also explored...