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Improving the quantification of highly overlapping chromatographic peaks by using product unit neural networks modeled by an evolutionary algorithm.

This work investigates the ability of multiplicative (on the basis of product units) and sigmoidal neural models built by an evolutionary algorithm to quantify highly overlapping chromatographic peaks. To test this approach, two N-methylcarbamate pesticides, carbofuran and propoxur, were quantified using a classic peroxyoxalate chemiluminescence reaction as a detection system for chromatographic analysis. The four-parameter Weibull curve associated with the profile of the chromatographic peak estimated by the Levenberg-Marquardt method was used as input data for both models. Straightforward network topologies (one output) allowed the analytes to be quantified with great accuracy and precision. Product unit neural networks provided better information ability, smaller network architectures, and more robust models (smaller standard deviation). The reduced dimensions of the selected models enabled the derivation of simple quantification equations to transform the input variables into the output variable. These equations can be more easily interpreted from a chemical point of view than those provided by sigmoidal neural networks, and the effect of both analytes on the characteristics of chromatographic bands, namely profile, dispersion, peak height, and residence time, can be readily established.

Journal Article↗
PubMed2006

Fit of four curve-linear models to decay profiles for pest control substances in soil.

Experiments that investigate the pattern of degradation of pest control substances in soil are often undertaken to estimate the persistence of compounds in the environment. Mathematical models are typically fit to decay data to facilitate the interpretation of the results and make predictions concerning the environmental fate of xenobiotics in soil. Four mathematical models were fit to 61 data sets to compare their performance in conforming to empirical patterns of degradation of pest control substances in soil. The use of composite residual plots allowed comparisons of the performance of the different models over many data sets. While an exponential model, estimated using nonlinear regression, fit many data sets very well, a shift-log, biexponential, and Monod equation appears superior in many cases, and systematic deviations from data sets are often less evident with the latter models. A knowledge of the patterns of bias typically exhibited by each model across many data sets may be useful for selecting models with reduced bias when fitting individual data sets.

Linear Models↗
PubMed2006

Conformational stability of a model macrocycle tetraamide: an ab initio study.

Ab initio calculations are carried out to investigate the conformational stability of a model macrocyle tetraamide. The four amide groups in the selected model are present in the sequence: -(O=CNH)-Ph-(NHC=O)-CH=CH-(O=CNH)-Ph-(NHC=O)-CH=CH-. In this sequence, two phenyl rings and two ethene groups act as bridges between the amide units. Each amide motif bonds to a phenyl ring through its amide nitrogen and to an ethene group through its amide carbon. Four clearly distinct minimum-energy conformations are found upon full geometry optimization using the B3LYP/6-31+G(d) method. Frequency calculations using the same method confirm that the four conformations are indeed minima in the macrocycle potential energy surface. Relative to the most stable conformer, the other conformations are higher in energy by 0.86, 2.09, and 9.17 kcal/mol, respectively, at the MP2/6-31+G(d,p) level. The stability of the macrocycle conformations is correlated primarily to the existence and strength of intramolecular N-H...O=C hydrogen bonds. Additional stability to the conformations is found to come from weak Ph-H...O=C hydrogen bonding between a carbonyl oxygen and a hydrogen atom of a phenyl group. Solvent effects play an important role in the relative energies of the various conformations, as indicated by the simple SCRF = dipole model calculations for the case of aqueous solution.

Journal Article↗
PubMed2005

Structural equation modeling of paired-comparison and ranking data.

L. L. Thurstone's (1927) model provides a powerful framework for modeling individual differences in choice behavior. An overview of Thurstonian models for comparative data is provided, including the classical Case V and Case III models as well as more general choice models with unrestricted and factor-analytic covariance structures. A flow chart summarizes the model selection process. The authors show how to embed these models within a more familiar structural equation modeling (SEM) framework. The different special cases of Thurstone's model can be estimated with a popular SEM statistical package, including factor analysis models for paired comparisons and rankings. Only minor modifications are needed to accommodate both types of data. As a result, complex models for comparative judgments can be both estimated and tested efficiently.

Choice Behavior↗
PubMed1980

Analysis of progress curves. Rate law of pyruvate kinase type I from Escherichia coli.

Progress curves of the reaction catalysed by pyruvate kinase from Escherichia coli K12, designed to cover the four-dimensional concentration space of phosphoenolpyruvate, ADP, Mg2+ and ATP in the regulatory region, were recorded with the pH-stat method (pH 7.0 and 25 degrees C). Additional initial-rate measurement were performed to assess specific points. Two methods for the evaluation of progress curves were used: fitting the rate law to the rates obtained from the tangents of the progress curves and fitting the integrated rate law directly to the curves. Two models, both extensions of the concerted model given by Monod, Wyman & Changeux [(1965) J. Mol. Biol. 12, 88--118] with four protomers, could be fitted to the data within the experimental error. Model discrimination in favour of one of these models was possible by proper experimental design. In the selected model one conformational state of the enzyme forms the active complex. The active site of a second conformational state forms abortive complexes with Mg2+, causing strong inhibition at high Mg2+ concentrations. In the absence of ligands, most of the enzyme is in a third state that binds ATP at an allosteric site.

Adenosine Diphosphate↗
PubMed2000

Local Competition, Inbreeding, and the Evolution of Sex-Biased Dispersal.

Using game theory, we developed a kin-selection model to investigate the consequences of local competition and inbreeding depression on the evolution of natal dispersal. Mating systems have the potential to favor strong sex biases in dispersal because sex differences in potential reproductive success affect the balance between local resource competition and local mate competition. No bias is expected when local competition equally affects males and females, as happens in monogamous systems and also in polygynous or promiscuous ones as long as female fitness is limited by extrinsic factors (breeding resources). In contrast, a male-biased dispersal is predicted when local mate competition exceeds local resource competition, as happens under polygyny/promiscuity when female fitness is limited by intrinsic factors (maximal rate of processing resources rather than resources themselves). This bias is reinforced by among-sex interactions: female philopatry enhances breeding opportunities for related males, while male dispersal decreases the chances that related females will inbreed. These results meet empirical patterns in mammals: polygynous/promiscuous species usually display a male-biased dispersal, while both sexes disperse in monogamous species. A parallel is drawn with sex-ratio theory, which also predicts biases toward the sex that suffers less from local competition. Optimal sex ratios and optimal sex-specific dispersal show mutual dependence, which argues for the development of coevolution models.

kin selection↗
PubMed2002

Strategies to fit pattern-mixture models.

Whereas most models for incomplete longitudinal data are formulated within the selection model framework, pattern-mixture models have gained considerable interest in recent years (Little, 1993, 1994). In this paper, we outline several strategies to fit pattern-mixture models, including the so-called identifying restrictions strategy. Multiple imputation is used to apply this strategy to realistic settings, such as quality-of-life data from a longitudinal study on metastatic breast cancer patients.

Journal Article↗
PubMed1999

DNA sequence variation and the recombinational landscape in Drosophila pseudoobscura: a study of the second chromosome.

The relationship between rates of recombination and DNA sequence polymorphism was analyzed for the second chromosome of Drosophila pseudoobscura. We constructed integrated genetic and physical maps of this chromosome using molecular markers at 10 loci spanning most of its physical length. The total length of the map was 128.2 cM, almost twice that of the homologous chromosome arm (3R) in D. melanogaster. There appears to be very little centromeric suppression of recombination, and rates of recombination are quite uniform across most of the chromosome. Levels of sequence variation (theta(W), based on the number of segregating sites) at seven loci (tropomyosin 1, Rhodopsin 3, Rhodopsin 1, bicoid, Xanthine dehydrogenase, Myosin light chain 1, and ribosomal protein 49) varied from 0.0036 to 0.0167. Generally consistent with earlier studies, the average estimate of theta(W) at total sites is 1.5-fold higher than that in D. melanogaster, while average theta(W) at silent sites is almost 3-fold higher. These estimates of variation were analyzed in the context of a background selection model under the same parameters of mutation rate and selection as have been proposed for D. melanogaster. It is likely that a significant fraction of the higher level of sequence variation in D. pseudoobscura can be explained by differences in regional rates of recombination rather than a larger species-level effective population size. However, the distribution of variation among synonymous, nonsynonymous, and noncoding sites appears to be quite different between the species, making direct comparisons of neutral variation, and hence inferences about effective population size, difficult. Tajima's D statistics for 6 out of the 7 loci surveyed are negative, suggesting that D. pseudoobscura may have experienced a rapid population expansion in the recent past or, alternatively, that slightly deleterious mutations constitute an important component of standing variation in this species.

Animals↗
PubMed2005

Bayesian calibration of process-based forest models: bridging the gap between models and data.

Process-based forest models generally have many parameters, multiple outputs of interest and a small underlying empirical database. These characteristics hamper parameterization. Bayesian calibration offers a solution to the calibration problem because it applies to models of any type or size. It provides parameter estimates, with measures of uncertainty and correlation among the parameters. The procedure begins by quantifying the uncertainty about parameter values in the form of a prior probability distribution. Then data on the output variables are used to update the parameter distribution by means of Bayes' Theorem. This yields a posterior calibrated distribution for the parameters, which can be summarized in the form of a mean vector and variance matrix. The predictive uncertainty of the model can be quantified by running it with different parameter settings, sampled from the posterior distribution. In a further step, one may evaluate the posterior probability of the model itself (rather than that of the parameters) and compare that against the probability of other models, to aid in model selection or improvement. Bayesian calibration of process-based models cannot be performed analytically, so the posterior parameter distribution must be approximated in the form of a representative sample of parameter values. This can be achieved by means of Markov Chain Monte Carlo simulation, which is suitable for process-based models because of its simplicity and because it does not require advance knowledge of the shape of the posterior distribution. Despite the suitability of Bayesian calibration, the technique has rarely been used in forestry research. We introduce the method, using the example of a typical forest model. Further, we show that reductions in parameter uncertainty, and thus in output uncertainty, can be effected by increasing the variety of data, increasing the accuracy of measurements and increasing the length of time series.

Algorithms↗
PubMed2004

Population pharmacokinetics of APOMINE: a meta-analysis in cancer patients and healthy males.

AIMS: 1) To characterize the population pharmacokinetics of apomine in healthy males and in male and female patients with solid tumours and 2) to understand more fully the influence of induction and between- and within-subject variability on exposure to drug using Monte Carlo simulation. METHODS: Apomine was administered once- or twice-daily with or without food in single and multiple oral doses of 30-2100 mg to healthy males (n = 19) and patients with solid tumours (n = 19). The data were divided into model development and validation sets. Models were developed using standard population methods. These were the identification of an appropriate base model, calculation of the empirical Bayes estimates of the primary pharmacokinetic parameters, covariate screening, forward stepwise addition of covariates using the likelihood ratio test as a model selection criteria, and backwards elimination to obtain the final model. To study the influence of data from individual subjects, the model development dataset was subjected to the delete-1 jack-knife and the final model was fitted to each jack-knifed dataset. Principal components analysis of the jack-knifed matrix of model parameters identified two influential subjects who were removed from the dataset, and the final model contained data from the remaining subjects. Model validation was examined using goodness of fit statistics and relative error measures using independent datasets from cancer patients. The model provided a reasonable approximation to the pharmacokinetic measurements in the validation datasets. Computer simulations were undertaken to understand further the pharmacokinetics of apomine in otherwise healthy females, a population not yet studied. RESULTS: Apomine pharmacokinetics were complex and consistent with a two-compartment model with a lag-time. Apparent oral clearance at baseline and apparent volume of distribution at steady-state were larger in healthy males than in cancer patients (41 ml h(-1) and 14.1 l vs 10 ml h(-1) and 8.9 l, respectively, for a 75 kg person). Clearance was time-variant showing a maximal increase with full induction of 320 ml h(-1), independent of patient type. The time to reach 50% maximal induction was about 2 days. The fraction of drug absorbed was relatively constant at doses less than 100-200 mg once daily but decreased at higher doses. Food also decreased relative bioavailability by 36%. Patient characteristics had no effect on apomine pharmacokinetics except for weight, which was proportional to the volume of the central compartment. Between-subject variability (68% for clearance, 30% for central volume, and 141% for peripheral volume) was moderate to large and independent of patient type. Inter-occasion variability was small (18% for both clearance and central volume). Residual variability was modelled with an additive and proportional error model. Cancer patients had slightly higher plasma concentrations than healthy males but this difference was probably not clinically significant. Steady-state was reached in about 3-4 days after once-daily drug administration. The half-life of apomine after three weeks of once-daily dosing was 41 h in cancer patients and 32 h in healthy males. CONCLUSIONS: A population model for apomine has been developed has been developed that characterizes its pharmacokinetics in cancer patients and healthy subjects under a variety of conditions.

Adolescent↗
PubMed1998

Antidepressant selection and use and healthcare expenditures. An empirical approach.

The purpose of this study was to evaluate whether 1-year total healthcare expenditures differed between patients who initiated therapy on a tricyclic antidepressant (TCA) or a selective serotonin reuptake inhibitor (SSRI) after controlling for initial antidepressant selection and antidepressant use pattern. A retrospective claims database covering a privately insured population in the US was used. Patients who initiated therapy in the outpatient setting (primary care or psychiatrist) were considered. Two-stage sample selection models were estimated that included controls for initial antidepressant selection and use pattern. The analyses indicated that: (i) self-selection due to initial antidepressant selection was a statistically significant determinant of expenditures for patients who initiated therapy on a TCA but not an SSRI; (ii) after controlling for initial antidepressant selection, antidepressant use pattern was a statistically significant and positive determinant of expenditures for both TCA and SSRI patients; and (iii) after controlling for initial antidepressant selection and use pattern, 1-year total direct healthcare expenditures were significantly lower for patients who initiated therapy on an SSRI than for patients who initiated therapy on a TCA.

Antidepressive Agents↗
PubMed2001

Accuracy and precision of computer models to predict passage of crude protein and amino acids to the duodenum of lactating cows.

To evaluate the ability of several models to accurately and precisely predict the passage of crude protein (CP) and amino acids to the duodenum of lactating cows, we simulated data from six published studies using the 1989 National Research Council equations, the Mepron Dairy Ration Evaluator (version 1.1), the University of Pennsylvania release of the Net Carbohydrate and Protein System (version 2.12p), the Cornell Net Carbohydrate and Protein System (version 3), and CPM Dairy (version 1.0). Models overestimated the passage of CP from microbes by an average of 323 g/d, and underestimated the passage of CP from feed by an average of 874 g/d. These two errors were partially canceled when CP from microbes and feed were summed to estimate passage of total CP to the duodenum. Many dietary composition variables appeared to bias the predictions; however, the influence of any one variable was small. The efficiency of modeling was high for most predictions but was variable for predicting passage of specific individual amino acids to the small intestine depending on the model selected. These simulations indicated no obvious advantage for any model over the others tested. The models responded to changes in diets by altering the amount of protein from microbes and feed that reached the duodenum, resulting in improved accuracy of predictions of duodenal CP passage compared with simply assuming a constant value for passage of CP to the duodenum.

Amino Acids↗
PubMed1991

C. R. Henderson: the unfinished legacy.

Ideas and methods developed by Henderson have been applied widely to BLUP of additive genetic merit of animals and estimation of components of variance. However, a number of other contributions of Henderson to theory and application of animal breeding and statistics have not been as fully examined and exploited. Some of these contributions are complete in their own right and others lay the groundwork to help resolve remaining problems. Henderson had insight and made contributions to the areas of analysis of line and breed cross data, hypothesis testing under mixed linear models, prediction of breeding values with unknown variances, and selection models. The general flexibility of Henderson's mixed model methods to quantify a large variety of biological effects is also illustrated and discussed in light of new technologies in genetics and biology.

Animals↗
PubMed1999

Clinical prediction of deep vein thrombosis in patients with leg symptoms.

Symptoms and clinical signs individually are inaccurate for the diagnosis of DVT. However, when assessing patients with leg symptoms, clinicians have access to additional information, such as whether or not DVT risk factors are present that could improve the accuracy of clinical judgment. The purpose of this study was to identify which clinical variables best predict DVT, and to use these variables to create a clinical prediction index for DVT. We studied 271 university hospital patients with a first episode of symptomatic, clinically suspected DVT. The prevalence of DVT was 27%, of which 71% were proximal. At baseline, information was collected on demographic features, comorbidity, and symptoms and signs. A Bayesian model selection strategy was used to estimate the logistic regression model that best predicted DVT. Male sex [OR = 2.8 (1.5, 5.1)], orthopedic surgery [OR = 5.4 (2.2, 13.6)], warmth [OR = 2.1 (1.2, 3.9)] and superficial venous dilation on exam [OR = 2.9 (1.4, 5.7)] were independent predictors of DVT. Using the model, a clinical prediction index that categorized patients into different levels of DVT risk was created, and was useful in a theoretical strategy aimed to limit the need for contrast venography in patients with suspected DVT, such that 96% of study patients could have avoided contrast venography. This index should be evaluated prospectively in other patient populations.

Adult↗
PubMed1994

Computer simulation of glenohumeral and patellofemoral subluxation. Estimating pathological articular contact.

Analytic stereophotogrammetry and an interactive computer graphics program were used to obtain first order assessments of joint contact patterns in patellofemoral and glenohumeral joints, simulating normal and abnormal articulations. Precise (90 microns accuracy) computer graphic representations of the humeral head, glenoid, patella, and femoral articular surfaces were obtained from cadaver knees and shoulders. These surface representations were then manipulated into an articulated position, and joint contact areas computed by a proximity criterion. Pathologic states were then simulated, and contact recomputed. Simulated glenohumeral subluxations dramatically reduced contact area, and focused it eccentrically on the glenoid rim. Simulated size mismatch of humeral heads to glenoids reduced contact area, producing a pattern of peripheral contact on the glenoid if the humeral head had a larger radius of curvature, and central contact on the glenoid if the humeral head had a smaller radius of curvature. At 30 degrees knee flexion, the patellofemoral joint demonstrated a broad distribution of contact along the distal aspect of the patella and proximal aspect of the trochlea. Simulated lateral tilt (5 degrees) and translation (5 mm) of the patella resulted in shift of the predominant contact area laterally, along with a drastic decrease in the contact area. These results have implications for prosthetic sizing and biomechanical modeling of the glenohumeral and patellofemoral joints, and in selecting models for more rigorous empiric studies of joint contact. Furthermore, this technique allows a first order assessment of the effects of specific surgical reconstructions on articular mechanics.

Computer Graphics↗
PubMed2005

Life history traits in selfing versus outcrossing annuals: exploring the 'time-limitation' hypothesis for the fitness benefit of self-pollination.

BACKGROUND: Most self-pollinating plants are annuals. According to the 'time-limitation' hypothesis, this association between selfing and the annual life cycle has evolved as a consequence of strong r-selection, involving severe time-limitation for completing the life cycle. Under this model, selection from frequent density-independent mortality in ephemeral habitats minimizes time to flower maturation, with selfing as a trade-off, and/or selection minimizes the time between flower maturation and ovule fertilization, in which case selfing has a direct fitness benefit. Predictions arising from this hypothesis were evaluated using phylogenetically-independent contrasts of several life history traits in predominantly selfing versus outcrossing annuals from a data base of 118 species distributed across 14 families. Data for life history traits specifically related to maturation and pollination times were obtained by monitoring the start and completion of different stages of reproductive development in a greenhouse study of selfing and outcrossing annuals from an unbiased sample of 25 species involving five pair-wise family comparisons and four pair-wise genus comparisons. RESULTS: Selfing annuals in general had significantly shorter plant heights, smaller flowers, shorter bud development times, shorter flower longevity and smaller seed sizes compared with their outcrossing annual relatives. Age at first flower did not differ significantly between selfing and outcrossing annuals. CONCLUSIONS: This is the first multi-species study to report these general life-history differences between selfers and outcrossers among annuals exclusively. The results are all explained more parsimoniously by selection associated with time-limitation than by selection associated with pollinator/mate limitation. The shorter bud development time reported here for selfing annuals is predicted explicitly by the time-limitation hypothesis for the fitness benefit of selfing (and not by the alternative 'reproductive assurance' hypothesis associated with pollinator/mate limitation). Support for the time-limitation hypothesis is also evident from published surveys: whereas selfers and outcrossers are about equally represented among annual species as a whole, selfers occur in much higher frequencies among the annual species found in two of the most severely time-limited habitats where flowering plants grow--deserts and cultivated habitats.

Asteraceae↗
PubMed2003

Further properties of Gavrilets' one-locus two-allele model of maternal selection.

I derive several properties of the model proposed by Gavrilets for maternal selection at a single diallelic locus. Most notably, (i) stable oscillations of genotype frequencies (i.e., cycling) can occur and (ii) in the special case in which maternal effects and standard viability selection act multiplicatively, maternal selection effectively acts on maternally derived alleles only.

Alleles↗
PubMed2004

The molecular population genetics of HIV-1 group O.

HIV-1 group O originated through cross-species transmission of SIV from chimpanzees to humans and has established a relatively low prevalence in Central Africa. Here, we infer the population genetics and epidemic history of HIV-1 group O from viral gene sequence data and evaluate the effect of variable evolutionary rates and recombination on our estimates. First, model selection tools were used to specify suitable evolutionary and coalescent models for HIV group O. Second, divergence times and population genetic parameters were estimated in a Bayesian framework using Markov chain Monte Carlo sampling, under both strict and relaxed molecular clock methods. Our results date the origin of the group O radiation to around 1920 (1890-1940), a time frame similar to that estimated for HIV-1 group M. However, group O infections, which remain almost wholly restricted to Cameroon, show a slower rate of exponential growth during the twentieth century, explaining their lower current prevalence. To explore the effect of recombination, the Bayesian framework is extended to incorporate multiple unlinked loci. Although recombination can bias estimates of the time to the most recent common ancestor, this effect does not appear to be important for HIV-1 group O. In addition, we show that evolutionary rate estimates for different HIV genes accurately reflect differential selective constraints along the HIV genome.

Bayes Theorem↗