On the stability of stochastic jump kinetics

Motivated by the lack of a suitable constructive framework for analyzing popular stochastic models of Systems Biology, we devise conditions for existence and uniqueness of solutions to certain jump stochastic differential equations (SDEs). Working from simple examples we find reasonable and explicit assumptions on the driving coefficients for the SDE representation to make sense. By `reasonable' we mean that stronger assumptions generally do not hold for systems of practical interest. In particular, we argue against the traditional use of global Lipschitz conditions and certain common growth restrictions. By `explicit', finally, we like to highlight the fact that the various constants occurring among our assumptions all can be determined once the model is fixed. We show how basic long time estimates and some limit results for perturbations can be derived in this setting such that these can be contrasted with the corresponding estimates from deterministic dynamics. The main complication is that the natural path-wise representation is generated by a counting measure with an intensity that depends nonlinearly on the state

Not Even Cold in Her Grave: How Postbereavement Remarried Couples Perceive Family Acceptance

Following the interviews of 24 participants concerning the death of their spouse and subsequent remarriage, a pattern of unsolicited responses concerning perceived acceptance of family emerged. Through grounded theory qualitative analysis, a continuum of acceptance was developed ranging from welcoming acceptance to active disapproval. Themes that influenced the perceived level of acceptance were (a) the length of time between death and courtship; (b) the length of the courtship itself; and (c) the level of family involvement in the courtship. Findings support and enhance current literature on remarital adjustment, suggesting it is critical to not only include children, but also the extended family in which the family resides. Provisional hypotheses and clinical implications are provided to help clinicians navigate these complex family dynamics and potentially increase family support

Approximations for the Moments of Nonstationary and State Dependent Birth-Death Queues

In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier polynomials, we are able to estimate any moment of the Markov process even though the system of moment equations may not be closed. Using new weighted discrete Sobolev spaces, we derive explicit error bounds of the transition probabilities and new weak a priori estimates for approximating the moments of the Markov processs using a truncated form of the expansion. Using our error bounds and estimates, we are able to show that our approximations converge to the true stochastic process as we add more terms to the expansion and give explicit bounds on the truncation error. As a result, we are the first paper in the queueing literature to provide error bounds and estimates on the performance of a moment closure approximation. Lastly, we perform several numerical experiments for some important models in the queueing theory literature and show that our expansion techniques are accurate at estimating the moment dynamics of these Markov process with only a few terms of the expansion

Fast Matlab compatible sparse assembly on multicore computers

We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of interest to design a highly efficient implementation. We show how to do this, and moreover, we show how our implementation can be parallelized to utilize the power of modern multicore computers. Our freely available code, fully Matlab compatible, achieves about a factor of 5 times in speedup on a typical 6-core machine and 10 times on a dual-socket 16 core machine compared to the built-in serial implementation