Nonlinear biological batch process monitoring and fault identification based on kernel fisher discriminant analysis

A novel nonlinear biological batch process monitoring and fault identification approach based on kernel Fisher discriminant analysis (kernel FDA) is proposed. This method has a powerful ability to deal with nonlinear data and does not need to predict the future observations of variables. So it is more sensitive to fault detection. In order to improve the monitoring performance, variable trajectories of the batch processes are separated into several blocks. Then data in the original space is mapped into high-dimensional feature space via nonlinear kernel function and the optimal kernel Fisher feature vector and discriminant vector are extracted to perform process monitoring and fault identification. The key to the proposed approach is to calculate the distance of block data which are projected to the optimal kernel Fisher discriminant vector between new batch and reference batch. Through comparing distance with the predefined threshold, it can be considered whether the batch is normal or abnormal. Similar degree between the present discriminant vector and the optimal discriminant vector of fault in historical data set is used to perform fault diagnosis. The proposed method is applied to the process of fed-batch penicillin fermentation simulator benchmark and shows that it can effectively capture nonlinear relationships among process variables and is more efficient than MPCA approach.     

The Treatment of Missing Values in Logistic Regression

The efficiencies of the estimators in the linear logistic regression model are examined using simulations under six missing value treatments. These treatments use either the maximum likelihood or the discriminant function approach in the estimation of the regression coefficients. Missing values are assumed to occur at random. The cases of multivariate normal and dichotomous independent variables are both considered. We found that in general, there is no uniformly best method. However, mean substitution and discriminant function estimation using existing pairs of values for correlations turn out to be favourable for the cases considered.     

Multivariate analysis of avian vocalizations

This paper examines several multivariate techniques that may be used in analyzing vocalizations. A general comparison of multiple linear regression, discriminant analysis, canonical correlation, cluster analysis, and principal components analysis is included with a discussion of when these tests may be appropriate for vocalization studies. Examples using vocalizations from Laysan and black-footed albatrosses are given to illustrate each technique.     

Fitting curves to data using nonlinear regression: a practical and nonmathematical review

Many types of data are best analyzed by fitting a curve using nonlinear regression, and computer programs that perform these calculations are readily available. Like every scientific technique, however, a nonlinear regression program can produce misleading results when used inappropriately. This article reviews the use of nonlinear regression in a practical and nonmathematical manner to answer the following questions: Why is nonlinear regression superior to linear regression of transformed data? How does nonlinear regression differ from polynomial regression and cubic spline? How do nonlinear regression programs work? What choices must an investigator make before performing nonlinear regression? What do the final results mean? How can two sets of data or two fits to one set of data be compared? What problems can cause the results to be wrong? This review is designed to demystify nonlinear regression so that both its power and its limitations will be appreciated.     

Use of nonlinear regression to analyze enzyme kinetic data: application to situations of substrate contamination and background subtraction

In a recent publication, A. Lundin, P. Arner, and J. Hellmér [Anal. Biochem. 177, 125-131 (1989)] describe a method whereby kinetic substrate assays can be performed when the assay mixture includes a significant contaminating levels of substrate. Their method requires various rearrangements of the data, and involves three separate linear regression calculations. We show how the same data may be analyzed directly, and far more simply, by nonlinear regression. Unlike the linear regression method, nonlinear regression allows direct calculation of the actual values for Km, Vmax, and the concentration of contaminating substrate (as well as estimates of their standard errors); the former method gives only apparent values. The nonlinear regression technique is also statistically a more valid means of analysis, as the rearrangements required to give linearized equations will considerably distort the error distribution and render simple unweighted linear regression inappropriate. The ease of incorporating extra parameters into standard equations when nonlinear regression is used is further illustrated by fitting enzyme reaction data which describe a first-order process when a significant nonspecific background is present. For this equation no simple rearranged linear plot is possible, but nonlinear regression is easily applied to determine the kinetic parameters.     

Markov entropy backbone electrostatic descriptors for predicting proteins biological activity

The spherical truncation of electrostatic interactions between aminoacids makes it possible to break down long-range spatial electrostatic interactions, resulting in short-range interactions. As a result, a Markov Chain model may be used to calculate the probabilities with which the effect of a given interaction reaches aminoacids at different distances within the backbone. The entropies of a Markov Chain model of this type may then be used to codify information about the spatial distribution of charges in the protein used in this study exploring the structure-activity relationship. In this paper, a linear discriminant analysis is reported, which correctly classified 92.3% of 26 under investigation in training and leave-one-out cross validation, purely for illustrative purposes. Classification was carried out for three possible activities: lysozymes, dihydrofolate reductases, and alcohol dehydrogenases. The discriminant analysis equations were contracted into two canonical roots. These simple canonical roots have high regression coefficients (R(c1)=0.903 and R(c2)=0.70). Root1 explains the biological activity of alcohol dehydrogenases while Root2 discriminates between lysozymes and dihydrofolate reductases. It was possible to profile the effect of core, middle, and surface aminoacids on biological activity. In contrast, a model considering classic physicochemical parameters such as: polarizability, refractivity, and partition coefficient classify correctly only the 80.8% of the proteins.     

Outlier Detection using Projection Quantile Regression for Mass Spectrometry Data with Low Replication

ABSTRACT: BACKGROUND: Mass spectrometry (MS) data are often generated from various biological or chemical experiments and there may exist outlying observations, which are extreme due to technical reasons. The determination of outlying observations is important in the analysis of replicated MS data because elaborate pre-processing is essential for successful analysis with reliable results and manual outlier detection as one of pre-processing steps is time-consuming. The heterogeneity of variability and low replication are often obstacles to successful analysis, including outlier detection. Existing approaches, which assume constant variability, can generate many false positives (outliers) and/or false negatives non-outliers). Thus, a more powerful and accurate approach is needed to account for the heterogeneity of variability and low replication. FINDINGS: We proposed an outlier detection algorithm using projection and quantile regression in MS data from multiple experiments. The performance of the algorithm and program was demonstrated by using both simulated and real-life data. The projection approach with linear, nonlinear, or nonparametric quantile regression was appropriate in heterogeneous high-throughput data with low replication. CONCLUSION: Various quantile regression approaches combined with projection were proposed for detecting outliers. The choice among linear, nonlinear, and nonparametric regressions is dependent on the degree of heterogeneity of the data. The proposed approach was illustrated with MS data with two or more replicates.     

Phenylketonuria heterozygote detection in families with affected children

Improved approaches to the problem of heterozygote detection for phenylketonuria (PKU) were developed in this study. The discrimination was based on 85 obligate heterozygotes and 45 controls who were neither pregnant nor on birth control medication. The best separation between hetrozygotes and normals was achieved with a linear discriminant function involving the logarithms of the serum concentrations of phenylalanine, tyrosine, and tryptophan. The theoretical overlap area between the distributions of heterozygotes and controls based on the above function, was 3.75%. In the 19 obligate hetrozygotes and 13 controls who were either pregnant or on birth control medication, the best separation was achieved with a linear discriminant function involving the logarithms of the serum concentrations of phenylalanine and tyrosine. The theoretical overlap area was 8.23%. The genetic accuracy of the discriminant function was confirmed by testing the results with parental-child exclusions, segregation analysis, and the frequency of heterozygosity in nonrelated collateral spouses. Finally, there was evidence suggesting that the antihypertensive agent, aldomet, alters serum tyrosine and tryptophan levels.     

A viscoelastic model of blood capillary extension and regression: derivation, analysis, and simulation

This work studies a fundamental problem in blood capillary growth: how the cell proliferation or death induces the stress response and the capillary extension or regression. We develop a one-dimensional viscoelastic model of blood capillary extension/regression under nonlinear friction with surroundings, analyze its solution properties, and simulate various growth patterns in angiogenesis. The mathematical model treats the cell density as the growth pressure eliciting a viscoelastic response from the cells, which again induces extension or regression of the capillary. Nonlinear analysis captures two cases when the biologically meaningful solution exists: (1) the cell density decreases from root to tip, which may occur in vessel regression; (2) the cell density is time-independent and is of small variation along the capillary, which may occur in capillary extension without proliferation. The linear analysis with perturbation in cell density due to proliferation or death predicts the global biological solution exists provided the change in cell density is sufficiently slow in time. Examples with blow-ups are captured by numerical approximations and the global solutions are recovered by slow growth processes, which validate the linear analysis theory. Numerical simulations demonstrate this model can reproduce angiogenesis experiments under several biological conditions including blood vessel extension without proliferation and blood vessel regression.     

Markers of cellular senescence in zero hour biopsies predict outcome in renal transplantation

Although chronological donor age is the most potent predictor of long-term outcome after renal transplantation, it does not incorporate individual differences of the aging-process itself. We therefore hypothesized that an estimate of biological organ age as derived from markers of cellular senescence in zero hour biopsies would be of higher predictive value. Telomere length and mRNA expression levels of the cell cycle inhibitors CDKN2A (p16INK4a) and CDKN1A (p21WAF1) were assessed in pre-implantation biopsies of 54 patients and the association of these and various other clinical parameters with serum creatinine after 1 year was determined. In a linear regression analysis, CDKN2A turned out to be the best single predictor followed by donor age and telomere length. A multiple linear regression analysis revealed that the combination of CDKN2A values and donor age yielded even higher predictive values for serum creatinine 1 year after transplantation. We conclude that the molecular aging marker CDKN2A in combination with chronological donor age predict renal allograft function after 1 year significantly better than chronological donor age alone.     

Evaluation of different models to describe egg and pupal development of Xyleborus fornicatus Eichh, （Coleoptera： Scolytidae）, the shot-hole borer of tea in Sri Lanka

Development data of eggs and pupae ofXyleborusfornicatus Eichh. （Coleoptera： Scolytidae）, the shot-hole borer of tea in Sri Lanka, at constant temperatures were used to evaluate a linear and seven nonlinear models for insect development. Model evaluation was based on fit to data （residual sum of squares and coefficient of determination or coefficient of nonlinear regression）, number of measurable parameters, the biological value of the fitted coefficients and accuracy in the estimation of thresholds. Of the nonlinear models, the Lactin model fitted experimental data well and along with the linear model, can be used to describe the temperature-dependent development of this species.     

Pattern analysis techniques to process fermentation curves: application to discrimination of enological alcoholic fermentations

In fermentation processes, kinetic curves are generally aimed at control purposes. However, these curves could also contain information about inherent features of the product (such as origin, quality, etc.). This article presents several pattern analysis techniques used to classify fermentation curves. An application to alcoholic fermentation is presented as an illustration: it aims at retrieving the origin of a must from its fermentation curve. The fermentation kinetics of five vineyard musts, harvested over 9 years on the same parcels, were recorded. From these curves two sets of variables were generated: The first (p(1)) gathers all the kinetic curve points. The second (p(2)) contains a restrained number of variables, generated by the expert knowledge of the enologist. The set p(2) was processed by two very different techniques: a linear one (factorial discriminant analysis) and a nonlinear one (artificial neural networks). The set p(1) was processed by a new chemometric technique, the discriminant partial least-squares regression. For all the sets and the techniques used the selection of variables was studied. The interest in the latter is largely demonstrated both by theoretical and practical discussions. The discrimination results (up to 94% of good predictions) enhance the interest of the on-line measurements and their use in such pattern analysis tools.