Peter Williams , University of Tennessee - Knoxville. Computer modeling and analysis methods are developed for two modes of operation of an instrument for sensitive fluorescence detection of individual dye-labeled molecules in solution. First, Monte Carlo simulations of experiments for single-molecule imaging SMI are extended to include effects of sample flow, sticking of molecules to surfaces, and the finite depth-of-focus of the optics. The results have a bearing on a patented method for high-speed single-molecule DNA sequencing. They indicate that the imaging of freely moving fluorescent labels within a microfluidic flowcell will be considerably more involved than that of immobilized molecules at a surface, which is the usual situation in SMI experiments. Second, the detection of single molecules as they pass through a tightly focused laser beam is discussed, with an emphasis on fluorescence correlation spectroscopy and the analysis of the autocorrelation function of the photon counts.
PHD THESIS: ANALYSIS OF FLUCTUATIONS AND CORRELATIONS IN KINETIC MONTE CARLO METHODS
Master Thesis: Efficient Markov Chain Monte Carlo Techniques for
In the context of nuclear reactor safety, the development of predictive, reliable and fast calculation tools for multiphysics simulation of the nuclear reactor cores coupling the neutron flux with thermal-hydraulics feedbacks, under stationary and transient conditions is the subject of a very extensive research program. Until very recently, time-dependent neutron transport calculations were based almost exclusively on deterministic methods, generally very fast for stationary problems. Since the approximations inherent to deterministic codes are specific to each reactor type, the validity of the results obtained and the quantification of the uncertainties associated with the physical quantities of interest depend on the configuration under analysis. In order to overcome these constraints and to be able to validate non-stationary deterministic codes, it is essential to have a reference calculation method, especially so due to the very limited available experimental data for accidental transient regimes.
Markov chain Monte Carlo
Sign in. A Monte Carlo Markov Chain MCMC is a model describing a sequence of possible events where the probability of each event depends only on the state attained in the previous event. MCMC have a wide array of applications, the most common of which is the approximation of probability distributions.
By constructing a Markov chain that has the desired distribution as its equilibrium distribution , one can obtain a sample of the desired distribution by recording states from the chain. The more steps are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis—Hastings algorithm. MCMC methods are primarily used for calculating numerical approximations of multi-dimensional integrals , for example in Bayesian statistics , computational physics ,  computational biology  and computational linguistics. In Bayesian statistics, the recent development of MCMC methods has made it possible to compute large hierarchical models that require integrations over hundreds to thousands of unknown parameters.