Reduction and solution of the chemical master equation using time scale separation and finite state projection

The dynamics of chemical reaction networks often takes place on widely differing time scales--from the order of nanoseconds to the order of several days. This is particularly true for gene regulatory networks, which are modeled by chemical kinetics. Multiple time scales in mathematical models often lead to serious computational difficulties, such as numerical stiffness in the case of differential equations or excessively redundant Monte Carlo simulations in the case of stochastic processes. We present a model reduction method for study of stochastic chemical kinetic systems that takes advantage of multiple time scales. The method applies to finite projections of the chemical master equation and allows for effective time scale separation of the system dynamics. We implement this method in a novel numerical algorithm that exploits the time scale separation to achieve model order reductions while enabling error checking and control. We illustrate the efficiency of our method in several examples motivated by recent developments in gene regulatory networks.     

Comparative Study of the CDW Systems

The physics of conducting trichalcogenides (NbSe 3) and organic metals (TTF-TCNQ) is considered from the point of view of 1d many body theories. It is argued that the former belong to the Peierls and the latter to the strongly correlated CDW limit.     

ICP-MS Determination of Antimicrobial Metals in Microcapsules

Silver (Ag) and zinc (Zn) are very powerful antimicrobial metals. Therefore, in this research, a high-throughput, sensitive, and rapid method was developed for the determination of Ag and Zn in microcapsules using inductively coupled plasma mass spectrometry (ICP-MS). The sample preparation procedure employed simple microwave digestion of the microcapsules with 55.55% v/v HNO₃ and 44.45% v/v H₂O₂. The method was applied to determine Ag and Zn in microcapsule samples of different sizes (120 and 450 μm) after their preparation with and without chitosan. Prepared microcapsules, after characterization, were bonded to a polymer carrier by sol-gel procedure and the materials were characterized by FTIR spectroscopy and high-resolution optical microscopy. Significant differences were found in Ag and Zn levels between microcapsules samples prepared with and without chitosan. The results have shown that samples with chitosan had up to 20% higher levels of Zn than Ag: 120 μm microcapsules contained 351.50 μg/g of Ag and 85.51 μg/g of Zn, respectively. In contrast, samples prepared without chitosan showed larger overall variability: In microcapsules with a diameter of 120 μm, the amounts of antimicrobial metals were 98.32 μg/g of Ag and 106.75 μg of Zn, respectively. Moreover, 450 μm microcapsules contained 190.98 μg/g of Ag and 121.35 μg/g of Zn. Those quantities are high enough for efficient antimicrobial activity of newly prepared microcapsules, enabling the application of microcapsules in different antimicrobial coatings.