A modified Next Reaction Method for simulating chemical systems with time dependent propensities and delays

Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the Gillespie Algorithm or the Next Reaction Method. In this paper we make explicit use of the fact that the initiation times of the reactions can be represented as the firing times of independent, unit rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified Next Reaction Method and, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with time dependent propensities as well as to systems with delays.Comment: 25 pages, 1 figure. Some minor changes made to add clarit

Incorporating postleap checks in tau-leaping

By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes, we develop a new adaptive tau-leaping procedure. The procedure developed is novel in that accuracy is guaranteed by performing postleap checks. Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the postleap checks in such a way that the statistics of the sample paths generated will not be biased by the rejections of leaps. Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population valuesComment: Final version. Minor change

Measuring the U.S. Health Care System: A Cross-National Comparison

Compares U.S. healthcare data including hospital beds and physicians, hospital and physician visits, healthcare spending, and high-tech procedures per capita, as well as life expectancy with those of twenty-nine other industrialized countries

Intercalated Rare-Earth Metals under Graphene on SiC

Intercalation of rare earth metals ($RE$ = Eu, Dy, and Gd) is achieved by depositing the $RE$ metal on graphene that is grown on silicon-carbide (SiC) and by subsequent annealing at high temperatures to promote intercalation. STM images of the films reveal that the graphene layer is defect free and that each of the intercalated metals has a distinct nucleation pattern. Intercalated Eu forms nano-clusters that are situated on the vertices of a Moir{\`e} pattern, while Dy and Gd form randomly distributed nano-clusters. X-ray magnetic circular dichroism (XMCD) measurements of intercalated films reveal the magnetic properties of these $RE$'s nano-clusters. Furthermore, field dependence and temperature dependence of the magnetic moments extracted from the XMCD show paramagnetic-like behaviors with moments that are generally smaller than those predicted by the Brillouin function. XMCD measurements of $RE$-oxides compared with those of the intercalated $RE$'s under graphene after exposure to air for months indicate that the graphene membranes protect these intercalants against oxidation.Comment: 9 pages, 7 figure