A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Comparison of fusion phage libraries displaying VH or single-chain Fv antibody fragments derived from the antibody repertoire of a vaccinated melanoma patient as a source of melanoma-specific targeting molecules

A single-chain Fv (scFv) fusion phage library derived from random combinations of VH and VL (variable heavy and light chains) domains in the antibody repertoire of a vaccinated melanoma patient was previously used to isolate clones that bind specifically to melanoma cells. An unexpected finding was that one of the clones encoded a truncated scFv molecule with most of the VL domain deleted, indicating that a VH domain alone can exhibit tumor-specific binding. In this report a VH fusion phage library containing VH domains unassociated with VL domains was compared with a scFv fusion phage library as a source of melanoma-specific clones; both libraries contained the same VH domains from the vaccinated melanoma patient. The results demonstrate that the clones can be isolated from both libraries, and that both libraries should be used to optimize the chance of isolating clones binding to different epitopes. Although this strategy has been tested only for melanoma, it is also applicable to other cancers. Because of their small size, human origin and specificity for cell surface tumor antigens, the VH and scFv molecules have significant advantages as tumor-targeting molecules for diagnostic and therapeutic procedures and can also serve as probes for identifying the cognate tumor antigens.

DNA sequencing and genotyping by transcriptional synthesis of chain-terminated RNA ladders and MALDI-TOF mass spectrometry

Sets of RNA ladders can be synthesized by transcription of a bacteriophage-encoded RNA polymerase using 3′-deoxynucleotides as chain terminators. These ladders can be used for sequencing of DNA. Using a nicked form of phage SP6 RNA polymerase in this study substantially enhanced yields of transcriptional sequencing ladders. Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) of chain-terminated RNA ladders allowed DNA sequence determination of up to 56 nt. It is also demonstrated that A→G and C→T variations in heterozygous and homozygous samples can be unambiguously identified by the mass spectrometric analysis. As a step towards single-tube sequencing reactions, α-thiotriphosphate nucleotide analogs were used to overcome problems caused by chain terminator-independent, premature termination and by the small mass difference between natural pyrimidine nucleotides.

Random circular permutation of genes and expressed polypeptide chains: application of the method to the catalytic chains of aspartate transcarbamoylase.

Recent studies on proteins whose N and C termini are in close proximity have demonstrated that folding of polypeptide chains and assembly of oligomers can be accomplished with circularly permuted chains. As yet no methodical study has been conducted to determine how extensively new termini can be introduced and where such termini cannot be tolerated. We have devised a procedure to generate random circular permutations of the catalytic chains of Escherichia coli aspartate transcarbamoylase (ATCase; EC 2.1.3.2) and to select clones that produce active or stable holoenzyme containing permuted chains. A tandem gene construct was made, based on the desired linkage between amino acid residues in the C- and N-terminal regions of the polypeptide chain, and this DNA was treated with a suitable restriction enzyme to yield a fragment containing the rearranged coding sequence for the chain. Circularization achieved with DNA ligase, followed by linearization at random with DNase I, and incorporation of the linearized, repaired, blunt-ended, rearranged genes into a suitable plasmid permitted the expression of randomly permuted polypeptide chains. The plasmid with appropriate stop codons also contained pyrI, the gene encoding the regulatory chain of ATCase. Colonies expressing detectable amounts of ATCase-like molecules containing permuted catalytic chains were identified by an immunoblot technique or by their ability to grow in the absence of pyrimidines in the growth medium. Sequencing of positive clones revealed a variety of novel circular permutations. Some had N and C termini within helices of the wild-type enzyme as well as deletions and insertions. Permutations were concentrated in the C-terminal domain and only few were detected in the N-terminal domain. The technique, which is adaptable generally to proteins whose N and C termini are near each other, can be of value in relating in vivo folding of nascent, growing polypeptide chains to in vitro renaturation of complete chains and determining the role of protein sequence in folding kinetics.

Basis for selection of improved carbohydrate-binding single-chain antibodies from synthetic gene libraries.

A technique is described for the simultaneous and controlled random mutation of all three heavy or light chain complementarity-determining regions (CDRs) in a single-chain Fv specific for the O polysaccharide of Salmonella serogroup B. Sense oligonucleotides were synthesized such that the central bases encoding a CDR were randomized by equimolar spiking with A, G, C, and T at a level of 10% while the antisense strands contained inosine in the spiked regions. Phage display of libraries assembled from the spiked oligonucleotides by a synthetic ligase chain reaction demonstrated a bias for selection of mutants that formed dimers and higher oligomers. Kinetic analyses showed that oligomerization increased association rates in addition to slowing dissociation rates. In combination with some contribution from reduced steric clashes with residues in heavy-chain CDR2, oligomerization resulted in functional affinities that were much higher than that of the monomeric form of the wild-type single-chain Fv.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

Poster presented in the 24th European Symposium on Computer Aided Process Engineering (ESCAPE 24), Budapest, Hungary, June 15-18, 2014.

Handling of Uncertainty in Life Cycle Inventory by Correlated Multivariate Lognormal Distributions: Application to the Design of Supply Chain Networks

In this work, we analyze the effect of incorporating life cycle inventory (LCI) uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear programming (MILP) coupled with a two-step transformation scenario generation algorithm with the unique feature of providing scenarios where the LCI random variables are correlated and each one of them has the desired lognormal marginal distribution. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study of a petrochemical supply chain. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact, and moreover the correlation among environmental burdens provides more realistic scenarios for the decision making process.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Modeling the molecular weight distribution of block copolymer formation in a reversible addition-fragmentation chain transfer mediated living radical polymerization

Block copolymers have become an integral part of the preparation of complex architectures through self-assembly. The use of reversible addition-fragmentation chain transfer (RAFT) allows blocks ranging from functional to nonfunctional polymers to be made with predictable molecular weight distributions. This article models block formation by varying many of the kinetic parameters. The simulations provide insight into the overall polydispersities (PDIs) that will be obtained when the chain-transfer constants in the main equilibrium steps are varied from 100 to 0.5. When the first dormant block [polymer-S-C(Z)=S] has a PDI of 1 and the second propagating radical has a low reactivity to the RAFT moiety, the overall PDI will be greater than 1 and dependent on the weight fraction of each block. When the first block has a PDI of 2 and the second propagating radical has a low reactivity to the RAFT moiety, the PDI will decrease to around 1.5 because of random coupling of two broad distributions. It is also shown how we can in principle use only one RAFT agent to obtain block copolymers with any desired molecular weight distribution. We can accomplish this by maintaining the monomer concentration at a constant level in the reactor over the course of the reaction. (c) 2005 Wiley Periodicals, Inc.

An identification tool for the Australian weedy Sporobolus species based on random amplified polymorphic DNA (RAPD) profiles

Based on morphological features alone, there is considerable difficulty in identifying the 5 most economically damaging weed species of Sporobolus [ viz. S. pyramidalis P. Beauv., S. natalensis ( Steud.) Dur and Schinz, S. fertilis ( Steud.) Clayton, S. africanus (Poir.) Robyns and Tourney, and S. jacquemontii Kunth.] found in Australia. A polymerase chain reaction (PCR)-based random amplified polymorphic DNA ( RAPD) technique was used to create a series of genetic markers that could positively identify the 5 major weeds from the other less damaging weedy and native Sporobolus species. In the initial RAPD pro. ling experiment, using arbitrarily selected primers and involving 12 species of Sporobolus, 12 genetic markers were found that, when used in combination, could consistently identify the 5 weedy species from all others. Of these 12 markers, the most diagnostic were UBC51(490) for S. pyramidalis and S. natalensis; UBC43(310,2000,2100) for S. fertilis and S. africanus; and OPA20(850) and UBC43(470) for S. jacquemontii. Species-specific markers could be found only for S. jacquemontii. In an effort to understand why there was difficulty in obtaining species-specific markers for some of the weedy species, a RAPD data matrix was created using 40 RAPD products. These 40 products amplified by 6 random primers from 45 individuals belonging to 12 species, were then subjected to numerical taxonomy and multivariate system (NTSYS pc version 1.70) analysis. The RAPD similarity matrix generated from the analysis indicated that S. pyramidalis was genetically more similar to S. natalensis than to other species of the 'S. indicus complex'. Similarly, S. jacquemontii was more similar to S. pyramidalis, and S. fertilis was more similar to S. africanus than to other species of the complex. Sporobolus pyramidalis, S. jacquemontii, S. africanus, and S. creber exhibited a low within-species genetic diversity, whereas high genetic diversity was observed within S. natalensis, S. fertilis, S. sessilis, S. elongates, and S. laxus. Cluster analysis placed all of the introduced species ( major and minor weedy species) into one major cluster, with S. pyramidalis and S. natalensis in one distinct subcluster and S. fertilis and S. africanus in another. The native species formed separate clusters in the phenograms. The close genetic similarity of S. pyramidalis to S. natalensis, and S. fertilis to S. africanus may explain the difficulty in obtaining RAPD species-specific markers. The importance of these results will be within the Australian dairy and beef industries and will aid in the development of integrated management strategy for these weeds.

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.]

The impact of supply chain performance measurement systems on dynamic behaviour in supply chains

The amplification of demand variation up a supply chain widely termed ‘the Bullwhip Effect’ is disruptive, costly and something that supply chain management generally seeks to minimise. Originally attributed to poor system design; deficiencies in policies, organisation structure and delays in material and information flow all lead to sub-optimal reorder point calculation. It has since been attributed to exogenous random factors such as: uncertainties in demand, supply and distribution lead time but these causes are not exclusive as academic and operational studies since have shown that orders and/or inventories can exhibit significant variability even if customer demand and lead time are deterministic. This increase in the range of possible causes of dynamic behaviour indicates that our understanding of the phenomenon is far from complete. One possible, yet previously unexplored, factor that may influence dynamic behaviour in supply chains is the application and operation of supply chain performance measures. Organisations monitoring and responding to their adopted key performance metrics will make operational changes and this action may influence the level of dynamics within the supply chain, possibly degrading the performance of the very system they were intended to measure. In order to explore this a plausible abstraction of the operational responses to the Supply Chain Council’s SCOR® (Supply Chain Operations Reference) model was incorporated into a classic Beer Game distribution representation, using the dynamic discrete event simulation software Simul8. During the simulation the five SCOR Supply Chain Performance Attributes: Reliability, Responsiveness, Flexibility, Cost and Utilisation were continuously monitored and compared to established targets. Operational adjustments to the; reorder point, transportation modes and production capacity (where appropriate) for three independent supply chain roles were made and the degree of dynamic behaviour in the Supply Chain measured, using the ratio of the standard deviation of upstream demand relative to the standard deviation of the downstream demand. Factors employed to build the detailed model include: variable retail demand, order transmission, transportation delays, production delays, capacity constraints demand multipliers and demand averaging periods. Five dimensions of supply chain performance were monitored independently in three autonomous supply chain roles and operational settings adjusted accordingly. Uniqueness of this research stems from the application of the five SCOR performance attributes with modelled operational responses in a dynamic discrete event simulation model. This project makes its primary contribution to knowledge by measuring the impact, on supply chain dynamics, of applying a representative performance measurement system.

Variational Markov Chain Monte Carlo for Bayesian smoothing of non-linear niffusions

In this paper we develop set of novel Markov chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. Flexible blocking strategies are introduced to further improve mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample, applications the algorithm is accurate except in the presence of large observation errors and low observation densities, which lead to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient.

Dynamics of linear polymers in random media

We study phenomenological scaling theories of the polymer dynamics in random media, employing the existing scaling theories of polymer chains and the percolation statistics. We investigate both the Rouse and the Zimm model for Brownian dynamics and estimate the diffusion constant of the center-of-mass of the chain in such disordered media. For internal dynamics of the chain, we estimate the dynamic exponents. We propose similar scaling theory for the reptation dynamics of the chain in the framework of Flory theory for the disordered medium. The modifications in the case of correlated disorders are also discussed. .

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.