Fitting a linear relationship with confidence intervals by correlation

The study of the empirical linear relationship between two measured variables should use correlation analysis which treats the variables symmetrically, rather than linear regression which inappropriately assumes a dependent and an independent variable. An APL computer program calculates the best fitting bivariate Gaussian distribution and plots the data with the superimposed straight line relationship and the confidence interval.     

An approach to incorporate linkage disequilibrium structure into genomic association analysis

In this study, we propose to use the principal component analysis (PCA) and regression model to incorporate linkage disequilibrium (LD) in genomic association data analysis. To accommodate LD in genomic data and reduce multiple testing, we suggest performing PCA and extracting the PCA score to capture the variation of genomic data, after which regression analysis is used to assess the association of the disease with the principal component score. An empirical analysis result shows that both genotype-basod correlation matrix and haplotype-based LD matrix can produce similar results for PCA. Principal component score seems to be more powerful in detecting genetic association because the principal component score is quantitatively measured and may be able to capture the effect of multiple loci.     

Remarks upon Empirical Regression Belt

In the presented paper the method of the empirical regression belt is demonstrated. An empirical regression curve r(x), which is determined by the realizations (measured points) (x₁, y₁), i = 1,…., n of a continuous two-dimensional random variable (X, Y), is enclosed by a belt, the local width of which varies dependent on local frequency and variance of the measured points. This empirical regression belt yields certain information for evaluating the empirical regression curve, providing a useful basis for the biomathematical forming of a model. By giving three examples derived from morphometrics the authors discuss important qualities of the empirical regression belt.     

INAKT - an interactive non-linear regression program for enzyme inactivation and affinity labelling studies

An interactive program for analysing enzyme activity-time data using non-linear regression analysis is described. Protection studies can also be dealt with. The program computes inactivation rates, dissociation constants and promotion or inhibition parameters with their standard errors. It can also be used to distinguish different inactivation models. The program is written in SIMULA and is menu-oriented for refining or correcting data at the different levels of computing.     

Imaging system for morphometric assessment of absorption or fluorescence in stained cells

An image acquisition and processing system has been developed for quantitative microscopy of absorption or fluorescence in stained cells. Three different light transducers are used in the system to exploit the best characteristics of these sensors for different biological measurements. A digital scanner, in the form of a linear array charge-coupled device (CCD), acquires data with high spatial and photometric resolution. A color (RGB) camera is employed when spectral information is required for the segmentation of cellular subcomponents. An image-intensified charged-injection device (CID) camera provides for very low light intensity measurements, primarily for fluorescence-labeled cells. Properties of these transducers, such as contrast transfer function, linearity, and photo-response nonuniformity, have been measured. Two dedicated image processing units were incorporated into the system. The front-end processor, based on a digital signal processor, provides functions such as object detection, raw image calibration, compression, artifact removal, and filtering. The second image processor is associated with the frame memory and includes a histogram processor, a dedicated arithmetic logic unit for image processing functions, and a graphics module for one-bit overlay functions. An interactive program was developed to acquire cell images and to experiment with a range of segmentation algorithms, feature extractions, and other image processing functions. The results of any image operation are displayed on the video monitor. Once a desired processing sequence is determined, the sequence may be stored to become part of a command library and can be executed thereafter as a single instruction.     

Surface Renewal: An Advanced Micrometeorological Method for Measuring and Processing Field-Scale Energy Flux Density Data

Advanced micrometeorological methods have become increasingly important in soil, crop, and environmental sciences. For many scientists without formal training in atmospheric science, these techniques are relatively inaccessible. Surface renewal and other flux measurement methods require an understanding of boundary layer meteorology and extensive training in instrumentation and multiple data management programs. To improve accessibility of these techniques, we describe the underlying theory of surface renewal measurements, demonstrate how to set up a field station for surface renewal with eddy covariance calibration, and utilize our open-source turnkey data logger program to perform flux data acquisition and processing. The new turnkey program returns to the user a simple data table with the corrected fluxes and quality control parameters, and eliminates the need for researchers to shuttle between multiple processing programs to obtain the final flux data. An example of data generated from these measurements demonstrates how crop water use is measured with this technique. The output information is useful to growers for making irrigation decisions in a variety of agricultural ecosystems. These stations are currently deployed in numerous field experiments by researchers in our group and the California Department of Water Resources in the following crops: rice, wine and raisin grape vineyards, alfalfa, almond, walnut, peach, lemon, avocado, and corn.     

System for flow sorting chromosomes on the basis of pulse shape

Sorting on the basis of the complex features resolved by chromosome slit-scan analysis requires rapid and flexible pulse shape acquisition and processing for determining sort decisions before droplet breakoff. Fluorescence scans of chromosome morphology contain centromeric index and banding information suitable for chromosome classification, but these scans are often characterized by variability in length and height and require sophisticated data processing procedures for identification. Setting sort criteria on such complex morphological data requires digitization and subsequent computation by an algorithm tolerant of variations in overall pulse shape. We demonstrate here the capability to sort individual chromosomes based on their morphological features measured by slit-scan flow cytometry. To do this we have constructed a sort controller capable of acquiring an 128 byte chromosome waveform and executing a series of numerical computations resulting in an area-based centromeric index sort decision in less than 2 ms. The system is configured in a NOVIX microprocessor, programmed in FORTH, and interfaced to a slit-scan flow cytometer data acquisition system. An advantage of this configuration is direct control over the machine state during program execution for minimal processing time. Examples of flow sorted chromosomes are shown with their corresponding fluorescence pulse shapes.     

Application Fields of the Empirical Regression - A Case Study

Empirical regression is defined as conditional expected value based on an estimation of a twodimensional density. It is a modelfree mathematical means for a first evaluation of measured data of an unknown stochastical relation between two quantities. The numerical procedures may be applied for calculation of the mean course of an unknown relation hidden in the measured data. Disregarding the statistical background an other aspect of application is the analyzing of time series, especially smoothing of time series and modelfree recording of the trend component in non-stationary time series. The calculated regression curve provides an objective basis for comparing of different measured courses as well as for a further evaluation, e. g. in respect of a suitable choice of an analytical expression. The possibility of interpolation and the smoothing properties of empirical regression give essential advantages for internal regression as one step in the process of model construction.     

Using empirical likelihood to combine data: application to food risk assessment

Summary .  This article introduces an original methodology based on empirical likelihood, which aims at combining different food contamination and consumption surveys to provide risk managers with a risk measure, taking into account all the available information. This risk index is defined as the probability that exposure to a contaminant exceeds a safe dose. It is naturally expressed as a nonlinear functional of the different consumption and contamination distributions, more precisely as a generalized U-statistic. This nonlinearity and the huge size of the data sets make direct computation of the problem unfeasible. Using linearization techniques and incomplete versions of the U-statistic, a tractable "approximated" empirical likelihood program is solved yielding asymptotic confidence intervals for the risk index. An alternative "Euclidean likelihood program" is also considered, replacing the Kullback–Leibler distance involved in the empirical likelihood by the Euclidean distance. Both methodologies are tested on simulated data and applied to assess the risk due to the presence of methyl mercury in fish and other seafood.     

Sediment porewater salinity, inundation frequency and mangrove vegetation height in Bragança, North Brazil: an ecohydrology-based empirical model

An empirical model based on an ecohydrological approach was developed, which allows the integration of hydrographical, topographical and physicochemical information with vegetation characteristics of mangroves and marshes of the Bragança Peninsula, North Brazil. A synoptic distribution of sediment porewater salinity was produced with isolines derived from predicted porewater salinity values from a GIS-based, multiple regression model. It includes a non-linear function of calculated inundation frequencies, the measured salinity distribution in the adjacent estuaries and sediment porewater salinities determined in the dry season. An excellent fit between measured and predicted porewater salinities was obtained. Highly significant correlations were found between vegetation height, inundation frequency and predicted porewater salinities. The relationship between vegetation height and predicted porewater salinities indicated the existence of at least three data ‘clusters’, which probably respond to different height to diameter-in-breast-height proportions according to age and environmental stress conditions. The porewater salinities produced by the model proved to be a solid proxy for the average stress situation of mangrove vegetation. The model offers good potential as a tool for analysing wetland dynamics, particularly at a synoptic, basin level.     

Analysis of ligand-receptor binding by the difference method

A new method has been proposed for analysis of experimental data on ligand-receptor binding at equilibrium. This method makes it possible to detect heterogeneity of a receptor system in cases where the contribution of the high-affinity site to total binding is rather small and the problem of graphic discrimination of a model cannot be solved unambiguously by other methods. The difference method permits us to exclude experiments on measuring nonspecific binding. A computer program for analysis of ligand-receptor binding has been worked out in which the difference method and traditional methods of binding isotherm analysis are realized. Numerical modeling has shown that the best strategy in experimental data processing is the treatment of total binding isotherms by both the difference method and regression analysis, including the nonspecific binding constant as one of the regression parameters.     

Predicting Quantitative Traits With Regression Models for Dense Molecular Markers and Pedigree

The availability of genomewide dense markers brings opportunities and challenges to breeding programs. An important question concerns the ways in which dense markers and pedigrees, together with phenotypic records, should be used to arrive at predictions of genetic values for complex traits. If a large number of markers are included in a regression model, marker-specific shrinkage of regression coefficients may be needed. For this reason, the Bayesian least absolute shrinkage and selection operator (LASSO) (BL) appears to be an interesting approach for fitting marker effects in a regression model. This article adapts the BL to arrive at a regression model where markers, pedigrees, and covariates other than markers are considered jointly. Connections between BL and other marker-based regression models are discussed, and the sensitivity of BL with respect to the choice of prior distributions assigned to key parameters is evaluated using simulation. The proposed model was fitted to two data sets from wheat and mouse populations, and evaluated using cross-validation methods. Results indicate that inclusion of markers in the regression further improved the predictive ability of models. An R program that implements the proposed model is freely available.     

Eddy-correlation system for long-term monitoring of fluxes of heat, water vapour and CO2

An eddy-correlation system is presented that was designed with special focus on long-term measurements of turbulent fluxes in the atmospheric boundary layer. It consists of a SOLENT sonic anemometer, a fast temperature sensor, and a LI-COR LI 6262 closed-path infrared gas analyser. The use of a fast temperature sensor turned out to be necessary because of errors in the sound virtual temperature measured by the sonic anemometer at high wind speeds. The components are combined with special attention paid to protection against lightning and other environmental stresses. The data acquisition program SOLCOM runs on standalone systems or in a network environment and performs ‘quasi on-line’ data processing, on-line graphical display of single data and fluxes, and on-line correction of the raw data. Raw data can be stored continuously on DAT tapes. All data handling can be done by remote access, thus only a minimum amount of m situ maintenance is required. Power spectra of vertical and longitudinal wind speed, air temperature, air humidity and carbon dioxide concentration showed to follow the -2/3 law quite well. There was some noise in the high frequency range of the carbon dioxide spectrum. However, the corresponding cross spectra with the vertical wind component showed less deviation from a straight line in the high frequency range. The sum of convective heat fluxes and soil heat flux showed good agreement with the measured net radiation for several months and it was concluded that the system described here constitute a good platform for long-term flux measurements over forest.     

Plant Growth Analysis: a Program for the Fitting of Lengthy Series of Data by the Method of B-splines*

A method is presented for fitting curves to lengthy and/or complicatedseries of data on plant growth. A computer program which derivesthe usual plant growth analytical quantities, and their errors,from these fitted curves is also described and offered for circulation.The fitted curves are splined cubic polynomial exponentials.Examples of their application are given, employing both realand artificial data. In any set of data the number of splines,and the position of the knots joining them, may be determinedeither by objective statistical tests or by the experimenterhimself, who thus retains a considerable degree of control overthe process but can call on the assistance of the program ifrequired. The value of this method is considered in relationto other curve-fitting approaches to plant growth analysis andit is concluded that, provided sufficient primary data are available,the method is free from many of the problems which beset earlierwork in this field, and also provides new possibilities of itsown. growth curves, approximating functions, empirical models, regression analysis, growth analysis     

An off-line data processing system for biochemistry profiling based on a 2K programmable calculator.

An off-line data processing system based on a Hewlett Packard 2K programmable calculator to be used with a biochemistry profiling system is described. The program is in two sections. A Data Acquisition phase calculates results from Auto Analyser II peak heights after corrections for drift and stores them on magnetic tape cassettes. Quality control statistics are produced. A Reporting phase types the profile results on self-adhesive pre-printed labels to be attached to the test-request form and also prepares a laboratory record sheet. The system is routinely used to process up to 2000 peak heights per day. Non-profile heights may also be read using this program.     

OutlierD: an R package for outlier detection using quantile regression on mass spectrometry data

It is important to preprocess high-throughput data generated from mass spectrometry experiments in order to obtain a successful proteomics analysis. Outlier detection is an important preprocessing step. A naive outlier detection approach may miss many true outliers and instead select many non-outliers because of the heterogeneity of the variability observed commonly in high-throughput data. Because of this issue, we developed a outlier detection software program accounting for the heterogeneous variability by utilizing linear, non-linear and non-parametric quantile regression techniques. Our program was developed using the R computer language. As a consequence, it can be used interactively and conveniently in the R environment. AVAILABILITY: An R package, OutlierD, is available at the Bioconductor project at http://www.bioconductor.org     

Computer-assisted sequencing,interval graphs,and molecular evolution

In 1945, Fox developed the strategy for sequencing long proteins by using overlapping fragments. We show how the formal mathematical technique for the construction of interval graphs (Gilmore and Hoffman, 1964) is useful both pedagogically for understanding the underlying logic of sequencing linear molecules and is more amenable to automation because of its algorithmic nature. We also present a computer program, that employs the interval graph algorithm, which can be used to sequence proteins when given digest data. An example is given to illustrate all the steps involved in the algorithmic processing of the data. The need for such developments with respect to molecular evolution is discussed.     

A nonlinear regression program for small computers

A BASIC computer program for performing weighted nonlinear regression is described and a listing of the program is given. The program, which is small and simple to use, has been designed to be run by users with little knowledge of mathematics or computers. Robust methods of analysis are described which may be applied to data in which experimental errors are not normally distributed, and the program incorporates one such method. It is shown that the program is useful for the analysis of data conforming to the Michaelis-Menten equation, a single exponential, and to binding equations, and other applications are discussed.