Unbiased Markov chain quasi-Monte Carlo for Gibbs samplers

In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased after a fixed number of iterations. Unbiased MCMC, an advancement achieved through coupling techniques, addresses this bias issue in MCMC. It allows us to run many short chains in parallel. Quasi-Monte Carlo (QMC), known for its high order of convergence, is an alternative of MC. By incorporating the idea of QMC into MCMC, Markov chain quasi-Monte Carlo (MCQMC) effectively reduces the variance of MCMC, especially in Gibbs samplers. This work presents a novel approach that integrates unbiased MCMC with MCQMC, called as an unbiased MCQMC method. This method renders unbiased estimators while improving the rate of convergence significantly. Numerical experiments demonstrate that unbiased MCQMC with a sample size of $N$ achieves convergence rates of approximately $O(N^{-1})$ in moderate dimensions for Gibbs sampling problems. In the setting of parallelization, unbiased MCQMC also performs better than unbiased MCMC, even running with short chains

Poly(2-oxazoline)s as new drug delivery systems

Taxane drugs, a class of important cancer chemotherapeutics, are often associated with excipient-related hypersensitivity, severe neurotoxicity, peripheral neuropathy, drug resistance and other limitations that influence the patients' quality of life and treatment prognosis. In order to overcome these limitations, this dissertation research focuses on the new poly(2-oxazoline)s (POx) polymers as versatile nano-scale drug delivery systems. The synthesis and characterization of several new monomers including 2-benzyl-2-oxazoline, 2-methyl-2-oxazine, and a cationic monomer is summarized. In addition, the exploration of newly synthesized POx polymers using above monomers and new functionality groups (e.g. clickable initiator) are also briefly discussed. The potential of a specific doubly amphiphilic POx triblock copolymer (previously termed P2) is further explored as a polymeric micelle system in delivering taxanes (paclitaxel, the 3rd generation of toxoids, and multiple-drug combinations). The P2/paclitaxel micelle formulation is characterized by a facile preparation, up to 50 % wt. drug loading, excellent shelf stability, controllable sub-100 nm size, a very high maximum tolerated dose in mice, and a significant enhancement in efficacy when treating three different breast cancer models. In addition to paclitaxel, a number of 3rd generation toxoids able to avoid common drug resistance mechanisms, are formulated in P2 micelles. An excellent solubilization of different 3rd generation taxoids is achieved irrespective of drug structures with up to 46 % wt. drug loading and less than 100 nm micelle size. Furthermore, a selected formulation with the new taxoid SB-T-1214 shows about one to two orders of magnitude more active in vitro than paclitaxel in LCC6-MDR, a multidrug resistant breast cancer cell line. It significantly inhibits the growth of LCC6-MDR orthotropic tumors, outperforming Taxol and Cremophor formulated SB-T-1214. Moreover, a number of chemotherapeutic drugs are simultaneously formulated in P2 micelles. The multi-drug loaded P2 micelles indicate a ratio-dependent synergistic activity against multiple cancer cells in vitro. This dissertation also involves the study of a new and first cationic oxazoline monomer and corresponding polymer containing side-chain secondary amine groups. The cationic polymer is able to condense plasmid DNA into a sub 100 nm polyplex which is stable upon dilution in saline and thermal challenge. These polyplexes exhibit minimum serum protein binding and very low cytotoxicity in vitro compared to the polyplexes of DNA and commonly used poly(ethylene glycol)105-b-poly(L-lysine)51 (PEG-PLL). The in vitro transfection efficiency of the polypelxes is also studied in B16 murine melanoma cells as well as RAW264.7 macrophage cells. The cationic polymer represents a comparably safe and promising platform for delivering genes to macrophages and cancer cells. In summary, POx polymers are versatile and promising platforms for taxane anticancer drugs delivery and gene delivery.Doctor of Philosoph