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The discrete-state continuous-time processes occurring in binding and release of analytes in affinity-based biosensors are formulated using stochastic differential equations (SDEs). The Fokker Planck (FP) equation is used to solve for the governing probability density function (pdf) of the number of captured analytes. A derivation method from the Markovian Master equation to the Fokker Planck equation...
Systems and synthetic biology are two emerging disciplines that hold promise to revolutionize our understanding of biological systems and to herald a new era of programmable hardware, respectively. Mathematical abstraction and today's abundance of quantitative biological data enables the up-scaling of analysis and design methodologies. In this tutorial paper we provide an engineering-centered introduction...
Some results are given for a continuous time long run growth optimal portfolio that has proportional costs consisting of the sum of a fixed proportional cost and a cost that is proportional to the volume of each transaction. An obligatory portfolio diversification is given that requires at least a small portion of the wealth be invested in each asset. It is assumed that the price of each asset is...
We analyze the average-case behaviour of the Next-Fit algorithm for bin-packing, and obtain closed-form expressions for distributions of interest. Our analysis is based on a novel technique of partitioning the interval (0, 1) suitably and then formulating the problem as a matrix-differential equation. We compare our analytic results with previously known simulation results and show that there is an...
Two complementary but equivalent semantic interpretations of a high level probabilistic programming language are given. One of these interprets programs as partial measurable functions on a measurable space. The other interprets programs as continuous linear operators on a Banach space of measures. It is shown how the ordered domains of Scott and others are embedded naturally into these spaces. Two...
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