Fractals from genomes: exact solutions of a biology-inspired problem

This is a review of a set of recent papers with some new data added. After a brief biological introduction a visualization scheme of the string composition of long DNA sequences, in particular, of bacterial complete genomes, will be described. This scheme leads to a class of self-similar and self-overlapping fractals in the limit of infinitely long constotuent strings. The calculation of their exact dimensions and the counting of true and redundant avoided strings at different string lengths turn out to be one and the same problem. We give exact solution of the problem using two independent methods: the Goulden-Jackson cluster method in combinatorics and the method of formal language theory.Comment: 24 pages, LaTeX, 5 PostScript figures (two in color), psfi

Study of Intermediate Oxidation Products in Chemical and Enzymatic Degradation of Carbon Nanomaterials

With increasing applications of carbon nanomaterials, toxicity of the material itself and the degradation products in biological systems and environment becomes a valid concern. At present, most of the toxicity studies only focus on the bulk property of carbon nanomaterials and the relevant conclusions are ambiguous. To better understand the degradation mechanism and the potential source of toxicity, we separated the oxidation products and studied the “small molecules” and “large particles” respectively in detail. In the first oxidation method, graphene oxide was degraded by Fenton reagent (Fe2+/Fe3+/H2O2) under UV irradiation. Through techniques including mass spectrometry, nuclear magnetic resonance and liquid chromatography, we successfully proposed plausible product structures and discovered several structure patterns of the products. By using atomic force microscopy and fluorimeter, we monitored the morphology transformation of graphene oxide flakes (~ 600 nm × 1 nm) to graphene quantum dots (~ 25 nm × 5 nm), in both aqueous solution and immobilized system. Given the similarity of Fenton reagent chemical oxidation and horseradish peroxidase enzymatic degradation of carbon nanomaterials, our results will help to understand the enzymatic degradation mechanism in biosystem and in the environment and to assess the toxicity at different stages during the degradation process. In the second part, we studied the degradation of SWNTs in both MPO and NaClO systems and further optimization is required to eliminate the ion suppression resulting from the high concentration of salt in these systems

Investigation of momentum exchange term closures for the Eulerian-Eulerian model applied to bubbly flows

The objective of the study presented in this thesis is to improve the accuracy of the two-fluid model for simulating the flow behavior in bubble columns. To achieve this investigation, CFD simulations were conducted by using the open source software OpenFOAMî. Results were compared to the experimental measurements of Harteveld (2005). The CFD simulations were performed using the two-fluid solver in OpenFOAM, which describes the phases as interpenetrating continua, identified by the corresponding phase volume fractions. Several models for drag, lift, virtual mass and wall-lubrication were validated in the present work. The following objectives were accomplished in order to achieve the final goal. Firstly, different drag, lift, wall lubrication, and virtual mass models were applied to the two-fluid model to test model accuracy for 2D rectangular bubble column. Then, OpenFOAM simulations of a 3D rectangular bubble column were performed us-ing the pre-tested sub-models, and the flow behavior was compared to previous 2D simulation and experimental results. In the end, a stability test was studied on the 2D rectangular bubble column. With fully studying of rectangular bubble column simulations, 3D cylinder bubble column was simulated. Mesh independence study was performed, and simulation results were compared to experimental data. Finally, stability analysis of the 3D cylinder bubble column was performed by varying inject velocities

Mixed Response Model in Credit Risk Modelling

Statistical methods are motivated by the desire of learning from data to solve problems in the real world. The credit risk management area of the banking book in the financial industry is a field extensively applying statistical knowledge to solve the problems and continually innovating new statistical methods. In credit risk area, a fundamental assumption of the probability of default (PD) rates for a portfolio is that the PD rates are monotonic increasing as the borrower's creditworthiness worsen. However, since the banks' internal data are not big enough, the empirical realized PD rates often violate this assumption. For the same reason, the violation of the assumption for the PD transition matrix also happens often. These violations will cause a severe problem if we directly calibrate the risk models based this non-smoothed empirical observed PD rates. We propose a smoothing algorithm for the observed PD rates and PD transition matrix by using Constrained Maximum a Posteriori (CMAP) method to solve these problems. The results from the proposed smoothing method are validated by simulation and real default data showing that CMAP method can provide the smoothed and consistent PD rates. We also propose a new approach in this dissertation to estimate the correlated mixed response variable which is often found in credit risk area. The proposed approach simultaneously estimates the mixed response regression and estimates the correlation among the response variables. Moreover, we extend this methodology to the high dimensional mixed response regression models by using the pairwise composite likelihood method. The simulation results show that the proposed method can provide accurate coefficients and correlation for mixed response variables model