Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a metachain to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely. [Bayesian phylogenetic inference; heating parameter; Markov chain Monte Carlo; replicated chains.]

Practical considerations for the measurement of free light chains in serum

Background: A new immunoassay for free light chain measurements has been reported to be useful for the diagnosis and monitoring of monoclonal light chain diseases and nonsecretory myeloma. We describe experience with and some potential pitfalls of the assay. Methods: The assay was assessed for precision, sample type and stability, recovery, and harmonization of results between two analyzers on which the reagents are used. Free-light-chain concentrations were measured in healthy individuals (to determine biological variation), patients with monoclonal gammopathy of undetermined significance, myeloma patients after autologous stem cell transplants, and patients with renal disease. Results: Analytical imprecision (CV) was 6-11% for kappa and A free-light-chain measurement and 16% for the calculated kappa/lambda ratio. Biological variation was generally insignificant compared with analytical variation. Despite the same reagent source, values were not completely harmonized between assay systems and may produce discordant free-light-chain ratios. In some patients with clinically stable myeloma, or post transplantation, or with monoclonal gammopathy of undetermined significance, free-light-chain concentration and ratio were within the population reference interval despite the presence of monoclonal intact immunoglobulin in serum. In other patients with monoclonal gammopathy of undetermined significance, values were abnormal although there was no clinical evidence of progression to multiple myeloma. Conclusions: The use of free-light-chain measurements alone cannot differentiate some groups of patients with monoclonal gammopathy from healthy individuals. As with the introduction of any new test, it is essential that more scientific data about use of this assay in different subject groups are available so that results can be interpreted with clinical certainty. (C) 2003 American Association for Clinical Chemistry.

Encapsulation of lipopeptides within liposomes: Effect of number of lipid chains, chain length and method of liposome preparation

The purpose of this study was to systematically investigate the effect of lipid chain length and number of lipid chains present on lipopeptides on their ability to be incorporated within liposomes. The peptide KAVYNFATM was synthesized and conjugated to lipoamino acids having acyl chain lengths of C-8, C-12 and C-16. The C-12 construct was also prepared in the monomeric, dimeric and trimeric form. Liposomes were prepared by two techniques: hydration of dried lipid films (Bangham method) and hydration of freeze-dried monophase systems. Encapsulation of lipopeptide within liposomes prepared by hydration of dried lipid films was incomplete in all cases ranging from an entrapment efficiency of 70% for monomeric lipoamino acids at a 5% (w/w) loading to less than 20% for di- and trimeric forms at loadings of 20% (w/w). The incomplete entrapment of lipopeptides within liposomes appeared to be a result of the different solubilities of the lipopeptide and the phospholipids in the solvent used for the preparation of the lipid film. In contrast, encapsulation of lipopeptide within liposomes prepared by hydration of freeze-dried monophase systems was high, even up to a loading of 20% (w/w) and was much less affected by the acyl chain length and number than when liposomes were prepared by hydration of dried lipid films. Freeze drying of monophase systems is better at maintaining a molecular dispersion of the lipopeptide within the solid phospholipid matrix compared to preparation of lipid film by evaporation, particularly if the solubility of the lipopeptide in solvents is markedly different from that of the polar lipids used for liposome preparation. Consequently, upon hydration, the lipopeptide is more efficiently intercalated within the phospholipid bilayers. (C) 2005 Elsevier B.V. All rights reserved.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Measurement-based teleportation along quantum spin chains

We examine the teleportation of an unknown spin-1/2 quantum state along a quantum spin chain with an even number of sites. Our protocol, using a sequence of Bell measurements, may be viewed as an iterated version of the 2-qubit protocol of C. H. Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)]. A decomposition of the Hilbert space of the spin chain into 4 vector spaces, called Bell subspaces, is given. It is established that any state from a Bell subspace may be used as a channel to perform unit fidelity teleportation. The space of all spin-0 many-body states, which includes the ground states of many known antiferromagnetic systems, belongs to a common Bell subspace. A channel-dependent teleportation parameter O is introduced, and a bound on the teleportation fidelity is given in terms of O.

Replicated linkage for eye color on 15q using comparative ratings of sibling pairs

The aim of the study was to perform a genetic linkage analysis for eye color, for comparative data. Similarity in eye color of mono- and dizygotic twins was rated by the twins' mother, their father and/or the twins themselves. For 4748 twin pairs the similarity in eye color was available on a three point scale (not at all alike-somewhat alike-completely alike), absolute eye color on individuals was not assessed. The probability that twins were alike for eye color was calculated as a weighted average of the different responses of all respondents on several different time points. The mean probability of being alike for eye color was 0.98 for MZ twins (2167 pairs), whereas the mean probability for DZ twins was 0.46 (2537 pairs), suggesting very high heritability for eye color. For 294 DZ twin pairs genome-wide marker data were available. The probability of being alike for eye color was regressed on the average amount of IBD sharing. We found a peak LOD-score of 2.9 at chromosome 15q, overlapping with the region recently implicated for absolute ratings of eye color in Australian twins [Zhu, G., Evans, D. M., Duffy, D. L., Montgomery, G. W., Medland, S. E., Gillespie, N. A., Ewen, K. R., Jewell, M., Liew, Y. W., Hayward, N. K., Sturm, R. A., Trent, J. M., and Martin, N. G. (2004). Twin Res. 7:197-210] and containing the OCA2 gene, which is the major candidate gene for eye color [Sturm, R. A. Teasdale, R. D, and Box, N. F. (2001). Gene 277:49-62]. Our results demonstrate that comparative measures on relatives can be used in genetic linkage analysis.

Sensor scheduling in electronic support using Markov chains

In electronic support, receivers must maintain surveillance over the very wide portion of the electromagnetic spectrum in which threat emitters operate. A common approach is to use a receiver with a relatively narrow bandwidth that sweeps its centre frequency over the threat bandwidth to search for emitters. The sequence and timing of changes in the centre frequency constitute a search strategy. The search can be expedited, if there is intelligence about the operational parameters of the emitters that are likely to be found. However, it can happen that the intelligence is deficient, untrustworthy or absent. In this case, what is the best search strategy to use? A random search strategy based on a continuous-time Markov chain (CTMC) is proposed. When the search is conducted for emitters with a periodic scan, it is shown that there is an optimal configuration for the CTMC. It is optimal in the sense that the expected time to intercept an emitter approaches linearity most quickly with respect to the emitter's scan period. A fast and smooth approach to linearity is important, as other strategies can exhibit considerable and abrupt variations in the intercept time as a function of scan period. In theory and numerical examples, the optimum CTMC strategy is compared with other strategies to demonstrate its superior properties.