Iterative Fitting Procedure Research Articles

Conditional Iterative Proportional Fitting for Gaussian Distributions

A Gaussian version of the iterative proportional fitting procedure (IFP-P) was applied by Speed and Kiiveri to solve the likelihood equations in graphical Gaussian models. The calculation of the maximum likelihood estimates can be seen as the problem to find a Gaussian distribution with prescribed Gaussian marginals. We extend the Gaussian version of the IPF-P so that additionally given conditionals of Gaussian type are taken into account. The convergence of both proposed procedures, called conditional iterative proportional fitting procedures (CIPF-P), is proved.

Heterogeneity of alpha 2-adrenoceptors in human and rat myometrium and differential expression during pregnancy.

1. The aim of this study was first, to characterize alpha 2-adrenoceptor subtypes in human and rat pregnant myometrium and second, to investigate the possibility of a differential expression of the putative subtypes according to the stage of pregnancy. 2. In both species, specific [3H]-rauwolscine binding was inhibited by five different compounds with an order of affinity characteristic of the one described for alpha 2-adrenoceptors (yohimbine > or = clonidine > noradrenaline > phenylephrine > propranolol). Binding affinities (pKi) for the compounds tested were, in human and rat, respectively: 7.63 and 8.93 for yohimbine, 6.91 and 8.71 for clonidine, 6.23 and 6.09 for noradrenaline, 5.37 and 5.73 for phenylephrine, 4.64 and 4.72 for propranolol. 3. By use of non-linear iterative curve fitting procedures and by fitting the data to a two-site model, analysis of [3H]-rauwolscine inhibition binding curves performed in the presence of oxymetazoline (alpha 2A-selective), ARC239, prazosin or chlorpromazine (alpha 2B- and alpha 2C-selective) indicated that pregnant human and rat myometrium contain at least two pharmacologically distinct alpha 2-adrenoceptor subtypes (alpha 2A, alpha 2B and/or alpha 2C). RNA blot analysis with probes specific for each cloned human and rat alpha 2-adrenoceptor subtype demonstrated that alpha 2A- and alpha 2B-subtypes were present in both species but alpha 2C seems to be expressed only in human tissues. 4. In the pregnant rat myometrium, subtype selective compounds competition curves revealed a predominant expression of alpha 2A-adrenoceptors at mid-pregnancy whereas, at term, alpha 2A- and alpha 2B-subtypes density reached approximately the same level (alpha 2A:alpha 2B ratio = 73:27 at mid-pregnancy and = 43:57 at term). In addition, quantification of alpha 2A- and alpha 2B-transcripts by densitometry, following data normalization with an oligo(dT)12-18 probe, showed a pattern of expression comparable to the one characterized by pharmacological studies. 5. In conclusion, these data demonstrate heterogeneity of alpha 2-adrenoceptors in pregnant human and rat myometria and an alteration of the alpha 2A-/alpha 2B-subtypes expression pattern during rat pregnancy. Such observations lead us to suggest a multiple role for alpha 2-adrenoceptors in regulating specific functions of myometrium throughout the time course of pregnancy.

EPR lineshapes and dynamics of TEMPOL solubilized in the aqueous microphase of lecithin/cyclohexane/water reverse micelles

EPR spectral lineshapes of the spin probe TEMPOL(4-hydroxy-2,2,6,6- tetramethyl-1-piperidinyl-1-oxyl), dissolved in the aqueous microphase of egg-yolk lecithin/cyclohexane/water reverse micelles, have been studied as a function of the water/lecithin molar ration, R. Although the spectral profiles reveal in general that the spin probe undergoes a ‘fast’ reorientational motion in the aqueous phase, the actual lineshapes are found to be non-Lorentzian. It is shown that, for an accurate lineshape analysis, the motion-dependent Lorentzian linewidths have to be convoluted with an appropriate motion-invariant Gaussian broadening factor representing unresolved isotropic superhyperfine interactions. Fast reorientational correlation times (τ), assessed from our iterative lineshape fitting procedure, span the range from 6.0 × 10 −10 to 3.0 × 10 −10 s as the R-value is increased.

Partitioned Flow Domains of Three Wisconsin Soils

AbstractPreferential flow mechanisms have been the subject of increasing research interest because these phenomena contribute to solute transport. Commonly, preferential flow paths are associated with macropores or highly structured soils. Sandy soils are typically weakly structured or structureless. However, they exhibit rapid drainage, which may mimic the hydrology and solute transport effects of macropores. We tested whether a flow domain partitioning scheme could be applied on two sandy soils, by collecting drainage data with time domain reflectometry across small time increments and implementing analytical models using a nonlinear iterative fitting procedure. The analysis was applied to both observed and Leaching Estimation and Chemistry Water Model (LEACHW) drainage of Sparta (mesic, uncoated, Typic Quartzipsamments) and Plainfield sand (mixed, mesic, Typic Udipsamment), as well as strongly structured Dubuque silt loam (fine‐silty, mixed, mesic, Typic Hapludalf), where water content was measured with a neutron meter. We found significant differences (P < 0.05) between soils and profile depths relating macropore and matrix flow domains of observed data. Maximum hydrologically effective macropore volumes ranged from 0.018 (1.8%) in Dubuque silt loam to 0.294 (29.4%) in Sparta sand. Mixed results were obtained with flow domain partitioning of drainage simulated with LEACHW. In 5 of 15 cases, macropore and micropore parameter estimates failed to converge. Best agreement of micropore and macropore parameter estimates between observed and modeled drainage was observed in Dubuque soil and poorest concordance in Sparta sand. This analytical scheme may be applied to a wide range of soils if appropriate data describing the hydrological character were available.

A Simple Justification of the Iterative Fitting Procedure for Generalized Linear Models

A Simple Justification of the Iterative Fitting Procedure for Generalized Linear Models

A Simple Justification of the Iterative Fitting Procedure for Generalized Linear Models

Abstract The extension of classical linear models to generalized linear models has had an important unifying impact on the exposition, teaching, and practice of statistical modeling. This article gives a new and simple justification of the commonly used iteratively reweighted least squares procedure for obtaining maximum likelihood parameter estimates.

A nearly free-electron model of the pair potential in molten copper

An effective interionic pair potential in liquid copper at 1393 K was extracted from the neutron-diffraction data using an iterative fitting procedure based on the modified hypernetted-chain approach. The procedure involved extensive molecular-dynamics simulation using a system of 16384 particles. The potential, constructed within the framework of the nearly-free-electron approximation, is based on the Dagens-Rasolt-Taylor model, and it is repulsive and positive around the first-neighbour distance. The proposed potential when used in molecular-dynamics calculations reproduces, within the limit of experimental accuracy, the structure factor measured by neutron diffraction, including the long-wavelength region of the structure factor and the isothermal compressibility limit, as well as the experimental value of the self-diffusion coefficient. The bridge function of liquid copper derived from the simulation data is compared with a hard-sphere fluid bridge function obtained in the context of the modified hypernetted-chain approximation.

Hydraulic borehole characterization through the application of moment methods to fluid conductivity logs

In any type of groundwater transport problem (contaminant solutes, heat, etc.), knowledge of the location and properties of pathways of increased hydraulic conductivity is essential. However, answering such questions in strongly heterogeneous media, such as fractured rock, can be very difficult and budget-intensive with standard geophysical or hydrogeological field investigations. We present a new testing concept and analysis procedure based on a time sequence of wellbore electric conductivity logs, which provides the exact location and the outflow parameters (transmissivity, formation fluid conductivity) of flowing features (fractures, faults, layers) intercepted by the borehole. Previously the quantitative analysis of this time sequence of electrical conductivity logs was based on a code, called BORE, used to simulate borehole fluid conductivity profiles given these parameters. The present report describes a new direct (not iterative) method for analyzing a short time series of electric conductivity logs which is based on moment quantities of the individual outflow peaks, and applies it to synthetic as well as to field data. The results of the method are promising and are discussed in terms of the method's advantages and limitations. In particular it is shown that the method is capable of reproducing hydraulic properties derived from packer tests well within a factor of three, which is below the range of what is recognized as the accuracy of packer tests themselves. Furthermore the new method is much quicker than the previously used iterative fitting procedure and is even capable of handling transient fracture outflow conditions.

Analyzing Doubly Censored Data with Covariates, with Application to AIDS

This paper proposes a method for incorporating covariate information in the analysis of survival data when both the time of the originating event and the failure event can be right- or interval-censored. This method generalizes the one-sample estimation results of De Gruttola and Lagakos (1989, Biometrics 45, 1-11) by allowing the distribution of time between the two events to be a function of covariates under a proportional hazards model. Estimates for the model coefficients, as well as the underlying distributions, are obtained by an iterative fitting procedure based on Turnbull's (1976, Journal of the Royal Statistical Society, Series B 38, 290-295) self-consistency algorithm in combination with the Newton-Raphson algorithm. The method is illustrated with data from a study of hemophiliacs infected with the human immunodeficiency virus.

Determination of concentrations by time domain fitting of proton NMR echo signals using prior knowledge.

A fast and flexible time domain iterative fitting procedure that can be used to fit free induction decays as well as echo-like signals is described. Damping constants of the first and second part of the echo do not have to be identical. Prior knowledge can be used to diminish the number of parameters to be fitted, which results in an improved accuracy. It is shown how prior knowledge is mathematically incorporated in the Gauss-Newton method. From proton NMR measurements of model solutions actual prior knowledge is extracted. With this knowledge relative concentrations are determined from a mixture of metabolites. The fitted results agree with the true values within the margins of the noise. After some minor changes the same prior knowledge was successfully used to analyze a series of in vivo rat brain measurements.

Semi-automated detection of aberrant chromosomes in bivariate flow karyotypes.

A method is described that is designed to compare, in a standardized procedure, bivariate flow karyotypes of Hoechst 33258 (HO)/Chromomycin A3 (CA) stained human chromosomes from cells with aberrations with a reference flow karyotype of normal chromosomes. In addition to uniform normalization of normal and abnormal flow karyotypes, the main purpose is detection of structurally abnormal chromosomes in often complex karyotypes of tumor cells. The method, which has been implemented in a computer program, consists of a comparison of individual chromosome peaks with the positions of peaks in the flow karyotype constituted by normal chromosomes and takes into account the natural variability in base composition of normal chromosomes among healthy individuals. Flow-karyotypes are normalized using an iterative fitting procedure, using corrections for (1) amplification of HO and CA fluorescence, (2) cross-talk between the fluorescence signals of HO and CA, and (3) offset of the HO and CA origin. Flow karyotypes of two cell lines, one with a simple deletion and the other with more complex karyotypic changes, were analyzed. The results of flow analysis were found to be in general agreement with the cytogenetic analysis of quinacrine banded karyotypes.

Automatic phase correction of Fourier-transform NMR data and estimation of peak area by fitting to a Lorentzian shape

The proposed method for automatically phasing NMR spectra (zero-order and first-order corrections) involves two (possibly three) stages. The first stage deals with the relation between real and imaginary amplitudes of the peak maximum, whose location is deduced from the power spectrum. Because of digitization, it is generally necessary to refine the phase angle by making use of the data points above peak half-eight in the magnitude spectrum (second stage). A further refinement (third stage) is carried out by an iterative fitting procedure applicable only to Lorentzian lines

A computer program for analyzing bivariate flow karyotypes

This article describes a computer program for analyzing bivariate flow karyotypes of human chromosomes stained with Hoechst 33258 (HO) and chromomycin A3 (CA). The karyotype first is divided into regions that contain chromosome peaks. The chromosomes that are associated with those areas are identified. The distributions in these areas then are fitted with mathematical functions of increasing complexity. The process starts by fitting a specified number of univariate Gauss functions to projections of the HO and CA distributions of each area. The final fit can include multiple bivariate Gauss functions, including a background function for debris subtraction. The results of one stage in the fitting process serve as seed values for the next, more complex step. Since the program autonomously estimates the starting values for the iterative fitting procedures, the fit results are insensitive to operator bias and the program will consistently converge to the same solutions. The resulting table of parameter values can be used to compare flow karyotypes to a reference data set.

Variations of the 1H spin-lattice relaxation in a fatty liver model as compared to normal liver

We report the results of an in vitro study on ethionine-injected rat liver (EI) and on normal rat liver (C) performed analyzing with iterative fitting procedures the 1H spin-lattice relaxation curves detected by IR pulse sequence at 20 MHz and at 37°C on fresh excised samples. Single-exponential functions did not adequately describe the experimental curves both in EI and in C group. The analysis of the curves by two-exponential hypothesis showed a small portion of the signal characterizable by a time constant of about 80 ms, common both to EI and to C samples. A slowing of about 30% in the relaxation characterized the remaining portion of the curve (90–95%) in EI as compared to C samples. The hypothesis that the 1H of the triglycerides vacuoles present in EI livers had a relaxation curve additional to the remaining signal was checked by three-exponential analysis. The results were not in contrast with the known value of the triglycerides percentage content and with the spin-lattice relaxation time of the CH 2 group 1H obtained in different experimental conditions in the same fatty liver model. The negative results of the three-exponential analysis on normal liver curves as well as the favorable controls performed to test the analysis procedure supported further this hypothesis. The remaining signal after subtraction of the triglycerides contribution showed still the small fast portion and the increase of the relaxation time of the major portion (from ∼300 ms up to ∼400 ms) as compared to C samples. Moreover this noticeable slowing of the 1H spin-lattice relaxation appeared independent from the water content and from the steatosis extent, as detected both macroscopically and at histological level.

Unambiguous curve fitting and error estimation for charpy impact test data of reactor pressure vessel steels, suitable for a small number of samples

On the basis of the requests of a reliability consideration a new concept for curve fitting is derived. Starting from an investigation of the distribution of the content of information about the free parameters of the analytical model (tanh), an iterative curve fitting procedure has been developed. This new approach may also be applied for any other functional description of a stochastic process. By means of the Monte Carlo method, error distributions for the parameters determined are calculated and demonstrate the unambiguity of the method developed. A series of calculations for a model curve with six measuring points with various distributions of temperatures and different initial errors is performed. A proposal for planing experiments with a small number of samples is derived.

Temporal resolution in sensorineural hearing-impaired listeners.

Temporal masking curves were obtained from 12 normal-hearing and 16 hearing-impaired listeners using 200-ms, 1000-Hz pure-tone maskers and 20-ms, 1000-Hz fixed-level probe tones. For the delay times used here (greater than 40 ms), temporal masking curves obtained from both groups can be well described by an exponential function with a single level-independent time constant for each listener. Normal-hearing listeners demonstrated time constants that ranged between 37 and 67 ms, with a mean of 50 ms. Most hearing-impaired listeners, with significant hearing loss at the probe frequency, demonstrated longer time constants (range 58-114 ms) than those obtained from normal-hearing listeners. Time constants were found to grow exponentially with hearing loss according to the function tau = 52e0.011(HL), when the slope of the growth of masking is unity. The longest individual time constant was larger than normal by a factor of 2.3 for a hearing loss of 52 dB. The steep slopes of the growth of masking functions typically observed at long delay times in hearing-impaired listeners' data appear to be a direct result of longer time constants. When iterative fitting procedures included a slope parameter, the slopes of the growth of masking from normal-hearing listeners varied around unity, while those from hearing-impaired listeners tended to be less (flatter) than normal. Predictions from the results of these fixed-probe-level experiments are consistent with the results of previous fixed-masker-level experiments, and they indicate that deficiencies in the ability to detect sequential stimuli should be considerable in hearing-impaired listeners, partially because of extended time constants, but mostly because forward masking involves a recovery process that depends upon the sensory response evoked by the masking stimulus. Large sensitivity losses reduce the sensory response to high SPL maskers so that the recovery process is slower, much like the recovery process for low-level stimuli in normal-hearing listeners.

CO in NGC 5055

The flocculent spiral galaxy NGC 5055 has been mapped along the major axis in the 12CO (J = 1-0) line using the Onsala 20-m telescope (HPBW = 33″). Figure 1, which gives the spatial velocity diagram of CO emission on the major axis with observed Hα velocities (Kruit and Bosma, 1978) superimposed, seems to imply higher velocities of the regions responsible for the optical emission. Taking into account the cruder spatial resolution of the CO observations, this effect is expected in a region where the rotation curve rises rapidly provided that the CO emission increases toward the centre. Figure 2 shows the rotation velocities for the eastern and western parts of the galaxy separately, as observed in Hα and CO. For CO we only give the portion of the rotation curve which is accurately determined, i.e. where it is relatively flat. The CO velocities in this region agree closely with those observed in HI (Bosma, 1978). These data suggest a difference of 10-20 km s−1 between the Hα and CO velocities at a distance of ∼ 60″ from the centre. The radial distribution of the CO emission, also indicated in Fig. 2, is defined by an iterative fitting procedure to the observed line profiles (see Scoville et al. 1983). This procedure requests an a priori knowledge of the velocity field, here assumed to be defined by the Hα data inside a radius of 60″. However, the shapes of the observed spectra and “best fit” model profiles differ significantly in some cases, again indicating that the Hα velocities do not apply to the molecular gas. The derived radial distribution of the CO emission is dependent on the assumed velocity field; however, the gross characteristics are retained for more feasible rotation curves (i.e. rotation curves giving better fits to the observed profiles).

Temporal masking curves and recovery from adaptation in hearing‐impaired listeners

Temporal masking curves, obtained from 12 normal‐hearing and 16 hearing‐impaired listeners using 200‐ms, 1000‐Hz pure‐tone maskers and 20‐ms, 1000‐Hz fixed‐level probe tones, were fit by an exponential function with a single level‐independent time constant. Normal‐hearing listeners' time constants ranged between 37–67 ms, with a mean of 50 ms. Hearing‐impaired listeners' time constants ranged between 58–114 ms and increased exponentially with hearing loss according to the function τ = 52e0.011(HL), when the slope (k) of the growth of masking was restricted to unity. When iterative fitting procedures included k as a free parameter, k values from normal‐hearing listeners varied around unity (mean = 1.03), while those from hearing‐impaired listeners were less (mean = 0.71). These data indicate that temporal resolution is poorer in hearing impaired listeners by factors as large as 2.3 for a hearing loss of 52 dB, but the major effect of hearing loss on the detectability of sequential signals is due to the sensitivity loss and to an exponential recovery process that is dependent upon sensory response not stimulus level. In impaired ears, sensitivity loss apparently reduces the sensory response to high‐level maskers so that the recovery process is slower, much like it is for low‐level maskers in normal‐hearing listeners. [Work supported by NINCDS.]

Kinetic and mechanistic studies on the reaction of dioxygen with hexa-aquamolybdenum(III)

The reaction of hexa-aquamolybdenum(III) with O2in p-toluenesulphonic acid (Hpts) solutions, I= 2.0 M [Li(pts)], gives the di-µ-oxo-molybdenum(V) ion [Mo2O4(H2O)6]2+ as product: 2Mo3++ O2+ 2H2O → Mo2O42+ 4H+. Use of isotopically labelled O2followed by i.r. spectroscopy on the isolated Mo2O42+ has demonstrated that at least some 18O is taken up in the µ-oxo-positions. With Mo3+ in large excess an intense yellow intermediate MoO2Mo6+(or a related form) with a peak at 395 nm (ε= 2 300 M–1 cm–1) is observed. At 25 °C stopped-flow studies on the decay of this intermediate give rate constants k3(obs.) which can be expressed as in equation (i). The various constants are as defined in equations (ii)–(iv), where values indicated are for 2.0 M Hpts. k3(obs.)=K1K2k3[Mo3+]2//1 +K1[Mo3+]+K1K2[Mo3+]2(i), Mo3++ O2⇌ MoO23+(K1 360 M–1)(ii), MoO23++ Mo3+⇌ MoO2Mo6+(K2 535 M–1)(iii), MoO2Mo6++ 2H2O → Mo2O42++ 4H+(k3 0.23 s–1)(iv) Estimates of rate constants for reactions (ii) and (iii) were obtained from studies on the formation of MoO2Mo6+. All parameters were further refined by an iterative fitting procedure using the program KINSIM for multi-step reactions. The values of k1(180 M–1 s–1) and k2(42 M–1 s–1) are in excess of previous substitution rate constants for Mo3+. With O2 in excess of Mo3+(0.72 × 10–4 M) there was no evidence for MoO2Mo6+, and an alternative route for conversion of MoO23+ to Mo2O42+, which is first order in MoO23+(k4= 0.037 s–1) was identified. In the refinement this step was included alongside (ii)–(iv). The reactions of MoO2Mo6+(k3) and MoO23+(k4) exhibit [H+]–1 dependences consistent with an increase in hydrolysis of the metal ion.

Evaluation of the chemical parameters of four systems of radioimmunological assay.

An iterative indirect model fitting (IIMF) procedure has been designed to evaluate antibody binding capacities and ligand affinities of fairly simple RIA systems. The information is provided by one or more series of standard equilibrium assays, the mass of tracer ligand, the residual fraction of free ligand which contaminates measured bound fractions, and the chemical purity of the tracer. The procedure uses theoretical models which describe systems with one or two antibodies with identical or different affinities towards the hot and the cold ligands. The tracer may be the purified radioactive ligand or a mixture of the hot and the cold ligands with the cold species as the major component. The theoretical models corresponding to two antibody systems are simplified and only strictly valid within limited ranges of ligand concentrations. The chemical parameters of both antibodies may in suitable cases be estimated by two runs of assays with different doses of antiserum and tracer. The IIMF procedure involves the computation of the regression line of a dose function for which the dependent variable is the model derived bound fraction over the measured bound fraction multiplied by the dose. Two tallies are combined of which the statistics of means of replicates being on the regression line has a higher priority than the minimal deviation of the slope of the regression line from 1. The procedure is applied to three RIA systems using carbon adsorption of the free ligand: prostaglandin E2 (PGE2), prostaglandin F2 alpha (PGF2 alpha) and angiotensin 1 (Ang. 1), and to one using antibody precipitation-arginine vasopressin (AVP). The consistency of the results was tested by repeated runs of standards or by varying the concentrations of the reactants and the temperature.