Purification of nucleic acids from a low quantity of bacterial cells in minute volume is important in many clinical and biological applications. We developed a novel microfluidic liquid phase nucleic acid purification chip to selectively isolate DNA or RNA from bacterial cells in the range of 5000 down to a single cell in the sample volume of 1 μl or 125 nl, which can be directly put through on-chip quantitative PCR assay. The aqueous phase bacterial lysate was isolated in an array of microwells, after which an immiscible organic (phenol-chloroform) phase was introduced in a headspace channel connecting the microwell array. Continuous flow of the organic phase increases the interfacial contact with the aqueous phase to achieve purification of target nucleic acid through phase partitioning. Significantly enhanced nucleic acid recovery yield, up to 10 fold higher, was achieved using the chip-based liquid phase nucleic acid purification technique compared to that obtained by the conventional column-based solid phase nucleic acid extraction method. One step vacuum-driven microfluidics allowed an on-chip quantitative PCR assay to be carried out in the same microwells within which bacterial nucleic acids were isolated, avoiding sample loss during liquid transfer. Using this nucleic acid purification device set in a two-dimensional (2D) array format of 900 microwells, it was demonstrated for the first time that high-throughput extraction of RNA couple with direct on-chip PCR analysis from single bacterial cells could be achieved. Our microfluidic platform offered a simple and effective solution for nucleic acid preparation, which can be integrated for automated bacterial pathogen detection and high throughput transcriptional profiling.

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We study a stochastic differential game between two insurance companies who employ reinsurance to reduce the risk of exposure. Under the assumption that the companies have large insurance portfolios compared to any individual claim size, their surplus processes can be approximated by stochastic differential equations. We formulate competition between the two companies as a game with a single payoff function which depends on the surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize this expected payoff, while the other company simultaneously chooses a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of this stochastic differential game and solve it explicitly for the case of maximizing/minimizing the exit probability.

No abstract

We study a stochastic differential game between two insurance companies who employ reinsurance to reduce the risk of exposure. Under the assumption that the companies have large insurance portfolios compared to any individual claim size, their surplus processes can be approximated by stochastic differential equations. We formulate competition between the two companies as a game with a single payoff function which depends on the surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize this expected payoff, while the other company simultaneously chooses a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of this stochastic differential game and solve it explicitly for the case of maximizing/minimizing the exit probability.