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We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis(More)
MOTIVATION Cellular signal transduction involves spatial-temporal dynamics and often stochastic effects due to the low particle abundance of some molecular species. Others can, however, be of high abundances. Such a system can be simulated either with the spatial Gillespie/Stochastic Simulation Algorithm (SSA) or Brownian/Smoluchowski dynamics if space and(More)
In this paper, we discuss a method for decomposition, abstraction and reconstruction of the stochastic semantics of rule-based systems with conserved number of agents. Abstraction is induced by counting fragments instead of the species, which are the standard entities of information in molecular signaling. The rule-set can be decomposed to smaller(More)
The study is aimed at quantifying the relative contribution of key heat transfer modes in lyophilization. Measurements of vial heat transfer rates in a laboratory-scale freeze-dryer were performed using pure water, which was partially sublimed under various conditions. The separation distance between the shelf and the vial was systematically varied, and(More)
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach fail to account for or to exploit this multi-scale nature, respectively. In this paper, we propose a jump-diffusion approximation for(More)
We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that(More)
Freeze-drying is al ow-pressure,l ow-temperature condensation pumping processw idelyu sedi n the manufacture of pharmaceuticals forr emovalo fs olventsb ys ublimation. Keyp erformance characteristicso fafreeze-dryerc ondenser arel argely dependent on thev apor andi ce dynamics in thel ow-pressuree nvironment.T he main objectiveo fthisw ork is to develop am(More)
Product temperature during the primary drying step of freeze-drying is controlled by a set point chamber pressure and shelf temperature. However, recent computational modeling suggests a possible variation in local chamber pressure. The current work presents an experimental verification of the local chamber pressure gradients in a lab-scale freeze-dryer.(More)
The flow physics in the product chamber of a freeze dryer involves coupled heat and mass transfer at different length and time scales. The low-pressure environment and the relatively small flow velocities make it difficult to quantify the flow structure experimentally. The current work presents the three-dimensional computational fluid dynamics (CFD)(More)
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal process given the full set of observations. This, in particular, leads to systematic approximations of the smoothing(More)