Optimal quantum trajectories for discrete measurements

Using the method of quantum trajectories we show that a known pure state can be optimally monitored through time when subject to a sequence of discrete measurements. By modifying the way that we extract information from the measurement apparatus we can minimize the average algorithmic information of the measurement record, without changing the unconditional evolution of the measured system. We define an optimal measurement scheme as one which has the lowest average algorithmic information allowed. We also show how it is possible to extract information about system operator averages from the measurement records and their probabilities. The optimal measurement scheme, in the limit of weak coupling, determines the statistics of the variance of the measured variable directly. We discuss the relevance of such measurements for recent experiments in quantum optics.

Genetic association and cellular function of MC1R variant alleles in human pigmentation

We have examined MC1R variant allele frequencies in the general population of South East Queensland and in a collection of adolescent dizygotic and monozygotic twins and family members to define statistical associations with hair and skin color, freckling, and mole count. Results of these studies are consistent with a linear recessive allelic model with multiplicative penetrance in the inheritance of red hair. Four alleles, D84E, R151C, R160W, and D294H, are strongly associated with red hair and fair skin with multinomial regression analysis showing odds ratios of 63, 118, 50, and 94, respectively. An additional three low-penetrance alleles V60L, V92M, and R163Q have odds ratios 6, 5, and 2 relative to the wild-type allele. To address the cellular effects of MC1R variant alleles in signal transduction, we expressed these receptors in permanently transfected HEK293 cells. Measurement of receptor activity via induction of a cAMP-responsive luciferase reporter gene found that the R151C and R160W receptors were active in the presence of NDP-MSH ligand, but at much reduced levels compared with that seen with the wild-type receptor. The ability to stimulate phosphorylation of the cAMP response element binding protein (CREB) transcription factor was also apparent in all stimulated MC1R variant allele-expressing HEK293 cell extracts as assessed by immunoblotting. In contrast, human melanoma cell lines showed wide variation in the their ability to undergo cAMP-mediated CREB phosphorylation. Culture of human melanocytes of known MC1R genotype may provide the best experimental approach to examine the functional consequences for each MC1R variant allele. With this objective, we have established more than 300 melanocyte cell strains of defined MC1R genotype.