First Hitting Time Analysis of the Independence Metropolis Sampler

In this paper, we study a special case of the Metropolis algorithm, the Independence Metropolis Sampler (IMS), in the finite state space case. The IMS is often used in designing components of more complex Markov Chain Monte Carlo algorithms. We present new results related to the first hitting time of individual states for the IMS. These results are expressed mostly in terms of the eigenvalues of the transition kernel. We derive a simple form formula for the mean first hitting time and we show tight lower and upper bounds on the mean first hitting time with the upper bound being the product of two factors: a “local” factor corresponding to the target state and a “global” factor, common to all the states, which is expressed in terms of the total variation distance between the target and the proposal probabilities. We also briefly discuss properties of the distribution of the first hitting time for the IMS and analyze its variance. We conclude by showing how some non-independence Metropolis–Hastings algorithms can perform better than the IMS and deriving general lower and upper bounds for the mean first hitting times of a Metropolis–Hastings algorithm.     

Rare-Earth Metal Complexes of the Antibacterial Drug Oxolinic Acid: Synthesis,Characterization, DNA/Protein Binding and Cytotoxicity Studies

“Drug repositioning” is a current trend which proved useful in the search for new applications for existing, failed, no longer in use or abandoned drugs, particularly when addressing issues such as bacterial or cancer cells resistance to current therapeutic approaches. In this context, six new complexes of the first-generation quinolone oxolinic acid with rare-earth metal cations (Y³⁺, La³⁺, Sm³⁺, Eu³⁺, Gd³⁺, Tb³⁺) have been synthesized and characterized. The experimental data suggest that the quinolone acts as a bidentate ligand, binding to the metal ion via the keto and carboxylate oxygen atoms; these findings are supported by DFT (density functional theory) calculations for the Sm³⁺ complex. The cytotoxic activity of the complexes, as well as the ligand, has been studied on MDA-MB 231 (human breast adenocarcinoma), LoVo (human colon adenocarcinoma) and HUVEC (normal human umbilical vein endothelial cells) cell lines. UV-Vis spectroscopy and competitive binding studies show that the complexes display binding affinities (K_b) towards double stranded DNA in the range of 9.33 × 10⁴ − 10.72 × 10⁵. Major and minor groove-binding most likely play a significant role in the interactions of the complexes with DNA. Moreover, the complexes bind human serum albumin more avidly than apo-transferrin.