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PubMed1985

Multifit: a flexible non-linear least squares regression program in BASIC.

MULTIFIT, a program in BASIC for implementation on microcomputers, has been developed for non-linear least squares regression fitting of enzyme kinetic, pharmacokinetic and other data to specific models. The program contains a simple procedure for insertion of model equations with up to five parameters (to be fitted) up to 3 independent variables and 1 dependent variable, and can be used to generate a family of programs with pre-set model functions.

Computers↗

PubMed2002

Using fuzzy logic to confirm the integrity of a pattern recognition algorithm for long genomic sequences: the W-curve.

The W-curve is a numerical mapping algorithm that provides tertiary information content of long and short genomic sequences. The most popular genomic pattern recognition algorithms depend on string matching of the primary information content of short genomic sequences. Herein, we describe a way to define the fuzzy properties of the W-curve. This approach improves a distance (dissimilarity) between two or more homologous long genomic sequences. Fourier analysis of W-curves delivers a smoother function for gap-stripped regions. Calculation of respective Fourier energies may improve the accuracy of the distance metric used to generate a phylogenetic tree of analyzed genomic sequences. This is especially the case for long genomic sequences that have been gap-stripped and aligned with the aid of previously published heuristic methods. These previous methods involved W-curve alignments used in concert with such programs as Clustal that use linear dynamic programming to align multiple gap-stripped W-curves.

Algorithms↗

PubMed2003

[Study on relations of variables: attributions of somatic symptoms, fatigue, chronic pain and depression in the elderly].

PURPOSE: The purpose of this study was to investigate the relationships among variables of somatic attribution, chronic pain, depression and chronic fatigue in the elderly. METHODS: Empirical data for testing hypothetical models was collected from 311 people over 65 years old in a community settings in Seoul, Korea in June and July, 2000. Data were analyzed by descriptive statistics and correlational analysis using pc-SAS program. The Linear Structural Modeling(LISREL) 8.0 program was used to find the best fit model which explained causal relationship of variables. RESULT: According to Accepted model, the relation of variables is that the somatic attribution is the influencing variable to chronic pain and depression and chronic pain and depression is the influencing variable to chronic fatigue. CONCLUSION: The findings of this study give useful information to construct intervention program relating chronic pain, depression and chronic fatigue for the elderly.

English Abstract↗

PubMed1978

Program to estimate parameters of linear systems without numerical differentiation.

This paper describes a computer program for estimating the parameters of a linear differential equation systen with constant coefficients by use of a nonlinear least-squares method. For minimization the sum of squares of an existing standard program, the Gauss-Newton gradient procedure, is employed. The differential equation system is solved by the Taylor expansion method. The advantage of this approach is that the derivatives with respect to the parameters are available without numerical differentiation. Therefore the inaccuracy inherent in numerical differentiation and the problem of choosing the modification of the parameters are eliminated. The given procedure is applicable for all the first order gradient methods. The presented method was tested with generated data from a four-compartmental model.

Computers↗

PubMed1991

Comparison of power and exponential field programming in field-flow fractionation.

Field programming in field-flow fractionation has the purpose of expanding the molecular weight or particle diameter range subject to a single analytical run. The two most widely used field programs are those in which the field strength decays with time according to an exponential function and a power function, respectively. The performances of these two programming functions are compared by obtaining limiting equations showing how retention time tr, standard deviation in retention sigma t, and fractionating power Fd vary with particle diameter d. It is shown that uniform fractionating power (Fd independent of d) can be obtained with power programming but that in exponential programming Fd is always non-uniform, varying as d-1/2. In exponential programming a linear relationship arises between tr and log d. This particular relationship is impossible to realize in power programming but an alternative linear relationship can be obtained by plotting tr versus dt/3. These results are made more concrete by plotting and comparing field strength, relative field strength, Fd and tr for specific programming cases.

Chemical Fractionation↗

PubMed1987

LILLY--a linear least squares curve fitting program for one independent variable.

A program was written to perform a linear least squares curve fitting on data. It includes facilities to report the usual statistics and digital plotter output. Seven types of curves are available for fitting the data. Other features of LILLY include provision of facilities for the selection of subsets in different symbols and separate curve fitting for these subsets. The program also provides a confidence region about the fitted line and the prediction interval for data points. Examples of the use of the program are described.

Mathematical Computing↗

PubMed1989

The use of a non-linear regression approach for the analysis of the ouabain-K+ interaction with (Na+ + K+)-ATPase from guinea pig and rat hearts.

1. The interaction between ouabain and K+ and their effects on (Na+ + K+)-ATPase activity were studied using microsomes from guinea pig and rat heart. 2. Microsomes were incubated in the presence of various concentrations of K+ and ouabain and ATPase activity was estimated by measuring the inorganic phosphate liberated. The experimental data were analyzed statistically by micro-computer, using a non-linear regression program based on the steepest descent technique. 3. The experimental data were best fitted by a model which assumes that ouabain acts like a mixed inhibitor with respect to the apparently cooperative K+ activation of (Na+ + K+)-ATPase. This quantitative approach provided estimates (with approximate standard deviations) of all the parameters involved in the model. 4. The inhibition constant for the uncompetitive term of the effect was 7- to 9-fold higher than the inhibition constant for the competitive term for both the guinea pig and rat heart preparations. 5. The present results indicate that graphical analyses are helpful for illustrative purposes but suggest that a computerized, non-linear regression program simultaneously analyzing all the non-linearized data should be used to quantify the complex kinetic parameters and to discriminate objectively among possible models.

Animals↗

PubMed1980

An algorithm and computer program for deconvolution in linear pharmacokinetics.

The procedure of deconvolution to evaluate the rate and the extent of input from absorption data and data from intravenous administration is the most fundamental and least assumptive method of accurately evaluating drug absorption in linear pharmacokinetics. It is shown for linear systems that if the absorption response and the response from an intravenous infusion or bolus administration are both well approximated by a polyexponential function, then the rate of absorption can be expressed as a sum of exponentials. An algorithm and computer program are presented whereby the absorption function is uniquely defined from the model-independent parameters of the polyexponential expressions fitted to the absorption data and data from intravenous administration. Fitting a sum of exponentials to data has become a routine procedure in pharmacokinetics. The method presented therefore makes the previously complex task of deconvolution a simple procedure. The deconvolution approach is discussed in relation to conventional methods of evaluating drug absorption and appears to have some distinct advantages over these methods. The method is tested using simulated data and demonstrated using pentobarbital and cimetidine data from human subjects.

Absorption↗

PubMed2004

Synthesis of linear and tripoidal oligo(phenylene ethynylene)-based building blocks for application in modular DNA-programmed assembly.

Rigid linear and tripoidal organic modules based on the oligo(phenylene ethynylene) backbone having salicylaldehyde-derived termini are synthesized. A highly functionalized 5-iodosalicyl aldehyde was prepared and coupled to each ethynyl group of 1,4-diethynylbenzene or 1,3,5-triethynylbenzene in Sonogashira couplings. The two or three termini of the compounds are functionalized for incorporation in linear and branched oligonucleotide strands. For the linear module (LM), the two termini are equipped with amide spacers, and one of these was functionalized with a DMTr (dimethoxytrityl)-protected hydroxy group and the other with a phosphoramidite. One of the tripoidal modules is prepared with DMTr groups in two of its three termini. A tripoidal module is also synthesized with three different groups on its hydroxy termini: a phosphoramidite, a DMTr group, and an Fmoc group. Extended studies have shown that these rigid linear and tripoidal organic modules can be incorporated into short oligonucleotides. Several of these modules can be applied for DNA-directed assembly and covalent coupling into structures of predetermined connectivity. Such structures have potential application for molecular electronics and nanotechnology.

Alkynes↗

PubMed2006

[Studies on quality control methods of nuxvomica].

Two quality control methods of nuxvomica were established for mutual. By selecting the appropriate measuring wavelength or wavelength range, the contents of strychnine and brucine in nuxvomica were determined without any preliminary separation by a new rapid spectrophotometry and a multi-wavelength linear regression spectrophotometry and with a computer program. The linear range of strychnine measured was 8.0-30.0 microg x mL(-1) (r = 0.999 9); The linear range of brucine measured was 7.0-31.2 microg x mL(-1) (r = 0.999 4). The average recoveries and relative standard deviations of strychnine and brucine were 98.18%-99.82%, 0.56%-1.54% and 100.5%-100.6%, 0.57%-0.62%, respectively. The methods are simple, rapid and reproducible, the interference of two components with each other may be eliminated and the methods are appropriate for quality control of nuxvomica.

Drugs, Chinese Herbal↗

PubMed1998

Assembling genes from predicted exons in linear time with dynamic programming.

In a number of programs for gene structure prediction in higher eukaryotic genomic sequences, exon prediction is decoupled from gene assembly: a large pool of candidate exons is predicted and scored from features located in the query DNA sequence, and candidate genes are assembled from such a pool as sequences of nonoverlapping frame-compatible exons. Genes are scored as a function of the scores of the assembled exons, and the highest scoring candidate gene is assumed to be the most likely gene encoded by the query DNA sequence. Considering additive gene scoring functions, currently available algorithms to determine such a highest scoring candidate gene run in time proportional to the square of the number of predicted exons. Here, we present an algorithm whose running time grows only linearly with the size of the set of predicted exons. Polynomial algorithms rely on the fact that, while scanning the set of predicted exons, the highest scoring gene ending in a given exon can be obtained by appending the exon to the highest scoring among the highest scoring genes ending at each compatible preceding exon. The algorithm here relies on the simple fact that such highest scoring gene can be stored and updated. This requires scanning the set of predicted exons simultaneously by increasing acceptor and donor position. On the other hand, the algorithm described here does not assume an underlying gene structure model. Indeed, the definition of valid gene structures is externally defined in the so-called Gene Model. The Gene Model specifies simply which gene features are allowed immediately upstream which other gene features in valid gene structures. This allows for great flexibility in formulating the gene identification problem. In particular it allows for multiple-gene two-strand predictions and for considering gene features other than coding exons (such as promoter elements) in valid gene structures.

Algorithms↗

PubMed2000

Peak capacity, peak-capacity production rate, and boiling point resolution for temperature-programmed GC with very high programming rates

Recent advances in column heating technology have made possible very fast linear temperature programming for high-speed gas chromatography. A fused-silica capillary column is contained in a tubular metal jacket, which is resistively heated by a precision power supply. With very rapid column heating, the rate of peak-capacity production is significantly enhanced, but the total peak capacity and the boiling-point resolution (minimum boiling-point difference required for the separation of two nonpolar compounds on a nonpolar column) are reduced relative to more conventional heating rates used with convection-oven instruments. As temperature-programming rates increase, elution temperatures also increase with the result that retention may become insignificant prior to elution. This results in inefficient utilization of the down-stream end of the column and causes a loss in the rate of peak-capacity production. The rate of peak-capacity production is increased by the use of shorter columns and higher carrier gas velocities. With high programming rates (100-600 degrees C/min), column lengths of 6-12 m and average linear carrier gas velocities in the 100-150 cm/s range are satisfactory. In this study, the rate of peak-capacity production, the total peak capacity, and the boiling point resolution are determined for C10-C28 n-alkanes using 6-18 m long columns, 50-200 cm/s average carrier gas velocities, and 60-600 degrees C/min programming rates. It was found that with a 6-meter-long, 0.25-mm i.d. column programmed at a rate of 600 degrees C/min, a maximum peak-capacity production rate of 6.1 peaks/s was obtained. A total peak capacity of about 75 peaks was produced in a 37-s long separation spanning a boiling-point range from n-C10 (174 degrees C) to n-C28 (432 degrees C).

Journal Article↗

PubMed1990

The influence of dose constraint point placement on optimized radiation therapy treatment planning.

To efficiently use linear and quadratic programming for treatment planning optimization on a routine basis, automated methods are needed for placing dose constraint points. We have investigated, for linear programming optimization, the minimum number of constraint points needed to achieve an acceptable approximation to the desired (ideal) solution. Seven different constraint point placement algorithms were evaluated for a given objective function. One of these algorithms was chosen for routine clinical use at our institution. This algorithm places constraint points on the perimeter of the target volume and on the perimeter and in the interior of each normal structure. Additional points are placed on the perimeter of a constant thickness buffer region surrounding the target volume. Excellent optimization results are obtained with 40-70 constraint points per treatment planning slice.

Computer Simulation↗

PubMed1971