Least-squares Curve-fitting Procedure Research Articles

New quantum assignments and analysis of high-resolution H212CO spectra in the range 3700–4450 cm-1

Four spectra of formaldehyde in natural isotopic abundance in the 3700–5200 cm-1 region were recorded at low temperature 160–166 K at Synchrotron SOLEIL for various pressures. Line positions and intensities were retrieved by non-linear least-squares curve-fitting procedures in the range 3700–4450 cm-1 and analyzed using ab initio based effective Hamiltonian and line intensities computed using new ab initio dipole moment surface. A new measured line list contains positions and intensities for 6177 features. Refined parameters of effective Hamiltonian were fitted to all assigned line positions with the RMS deviations of 0.001 cm-1. Updated line lists include intensity values based on ab initio variational calculations which were subsequently empirically optimized. Comparison of our theoretical simulation with previously available data as well as with high-resolution and low-resolution experimental spectra are reported.

Improved line list of 12CH4 in the 4100–4300 cm−1 region

Four spectra of methane in natural isotopic abundance in the 4100–4300 cm−1 region were recorded by using a Fourier transform spectrometer in Reims, France at long paths (202 m, 602 m, 1604 m and 1804 m) and different pressures. Additional spectra of 12CH4 covering the same region were obtained at 100–123 K for different pressures, 93 m path length at Synchrotron SOLEIL in Paris for different pressures and were used to measure low-J lines. Spectra of 12CH4 and 13CH4 obtained at 80 K at JPL in Pasadena were used for additional frequency calibrations. Line positions and intensities were retrieved by non-linear least-squares curve-fitting procedures and analyzed using effective Hamiltonian and effective dipole transition moment models. A new measured line list contains positions and intensities for 12,378 features. Quantum assignments were made for more than 11,520 new transitions, which represent ∼99% of the integrated line intensity observed in this region. Some of 4556 hot band transitions for (Dyad – Tetradecad) system were assigned. The resulting list of lines is significantly more accurate than previous empirical compilations. All assigned 6963 line positions were fitted to RMS standard deviations of 0.0015 cm−1. The sum of the observed intensities between 4100 and 4300 cm−1 falls within 5% of the predicted value from ab initio variational calculations reported in the TheoReTS database (http://theorets.univ-reims.fr; http://theorets.tsu.ru).

Line list of 12CH4 in the 4300–4600 cm−1 region

Four spectra of normal samples of CH4 in the 4300–4600 cm−1 region were recorded by using a Fourier transform spectrometer in Reims, France at long paths (202 m, 602 m, 1604 m, and 1804 m) and different pressures. Additional spectra of 12CH4 covering the same region were obtained at 80–123 K, and 93 m path length at SOLEIL Synchrotron in Paris for different pressures and were used to measure low-J lines. Line positions and intensities were retrieved by non-linear least-squares curve-fitting procedures and analyzed using effective Hamiltonian and effective dipole transition moment models. A new measured line list contains positions and intensities for 14,151 absorption features. Quantum assignments were made for more than 10,304 transitions of 12CH4, which represent ∼99% of the integrated line intensity observed in this region. Some 1699 hot band transitions for (Dyad – Tetradecad) system were assigned. The resulting list of lines is significantly more accurate than previous empirical compilations. Positions of 8605 cold band transitions for (GS – Octad) system were fitted with an RMS standard deviation of 0.0014 cm−1. The sum of observed intensities between 4300 and 4600 cm−1 fell within 8% of the predicted value from ab initio variational calculations reported in the TheoReTS database (http://theorets.univ-reims.fr; http://theorets.tsu.ru).

Studies in mice, hamsters, and rats demonstrate that repression of hepatic apoA-I expression by taurocholic acid in mice is not mediated by the farnesoid-X-receptor

It is claimed that apoA-I expression is repressed in mice by cholic acid (CA) and its taurine conjugate, taurocholic acid (TCA) via farnesoid X receptor (FXR) activation. We measured apoA-I expression in mice, hamsters, and rats treated with highly potent and selective synthetic FXR agonists or with TCA. All of the synthetic agonists bound to FXR with high affinity in a scintillation proximity assay. However, TCA did not compete with the radioligand up to the highest concentration used (100 μM). The C-site regulatory region of apoA-I, through which FXR has been reported to regulate its expression, is completely conserved across the species investigated. In both male and female human apoA-I-transgenic mice, we reproduced the previously reported strong inhibition of human apoA-I expression upon treatment with the typical supraphysiological dose of TCA used in such studies. However, in contrast to some previous reports, TCA did not repress murine apoA-I expression in the same mice. Also, more-potent and -selective FXR agonists did not affect human or murine apoA-I expression in this model. In LDL receptor-deficient mice and Golden Syrian hamsters, selective FXR agonists did not affect apoA-I expression, whereas in Wistar rats, some even increased apoA-I expression. In conclusion, selective FXR agonists do not repress apoA-I expression in rodents. Repression of human apoA-I expression by TCA in transgenic mice is probably mediated through FXR-independent mechanisms.

Complexation and thermodynamic studies of oxathiadibenzocrown ethers with Cu2+, Pb2+, Zn2+ and Cd2+ ions

A thermodynamic study of the complexation of Cu2+, Pb2+, Zn2+ and Cd2+ ions with 1 and 2 in acetonitrile has been carried out. The study was conducted in the temperature range 283–308 K using a conductometric technique. The observed molar conductivity, Λ, was found to decrease significantly for mole ratios [L]t/[M]t less than unity in all cases. A model involving 1:1 stoichiometry has been used to analyze the conductivity data. The stability constant, K, for each 1:1 complex was determined from the conductivity data by using a nonlinear least-squares curve fitting procedure. The results show that compound 1 has no peak selectivity for any of the metal cations, while compound 2 selectively associates with Cu2+ and Pb2+. Complexes of 1 have the following stability order Pb2+ > Cu2+ > Zn2+ > Cd2+ and Pb2+ > Cu2+ for the complexes of 2. The ∆H° and ∆S° values for the complexation process were obtained from the slope and intercept of the Van’t Hoff plots respectively. All ∆G° values were negative and were determined from the Gibbs–Helmholtz equation and the significance of these values is discussed.

A Procedure for Application of the Three-Omega Method to Measurement of Gas Thermal Conductivity

A non-linear least-squares curve-fitting procedure is proposed to analyze three-omega voltage data from a fine wire in a gas sample using the three-omega method. The method uses both three-omega components of the voltage arising from a sinusoidal heating current to determine the thermal conductivity of the surrounding medium. The proposed procedure is tested against simulated data and some experimental data for air at atmospheric pressure. Treating the technique as an absolute method and assuming a known sample heat capacity, the thermal conductivity of air has been measured at room temperature to within 11% of a reference value. Practical application of the method may require a calibrated effective wire length and wire diameter. An average wire temperature rise of around 10 K to ensure the three-omega components is enough for accurate measurement.

Border estimation of a disc observed with random errors solved in two steps

The problem of estimating the boundary of a uniform distribution on a disc is considered when data are measured with normally distributed additive random error. The problem is solved in two steps. In the first step the domain is subdivided into thin slices and the endpoints of slices are obtained within the framework of a corresponding one-dimensional problem. For the estimations implemented in that step the moment method and the maximum likelihood method are used. As there are numerical problems with calculating the variance of the estimator in the maximum likelihood approach, its good approximation is also given. In the second step the obtained endpoints are used to estimate the boundary using the total least-squares curve fitting procedure. A necessary and sufficient condition for the existence of the total least-squares solution is also given. Finally, simulation results are presented.

Border estimation of a two-dimensional uniform distribution if data are measured with additive error

The paper considers estimation of the boundary of an elliptical domain when the data without a measurement error are distributed uniformly on this domain but are superimposed by random errors. The problem is solved in two phases. In the first phase the domain is subdivided into thin slices and the endpoints of these slices are estimated within the framework of a corresponding one-dimensional problem. In the second phase the estimated endpoints are used to estimate the boundary using the total least-squares curve fitting procedure.

In Vitro Measurements of First and Second Tarsometatarsal Joint Stiffness

This study involved a biomechanical examination of the first and second tar-sometatarsal (TMT) joints. In the in vitro testing protocol, physiologic joint moments were applied to the first and second TMT joints of 10 cadaver specimens, which had been dissected to yield only the midfoot components comprising the tarsals, metatarsals, and associated ligaments. The isolated joints were placed in a 37 °C water bath and were independently cycled into and out of dorsiflexion, while angular displacement and resultant joint moments were collected. The specimens were sequentially cycled between zero and peak moment levels of 2.5, 5.0, 7.5, and 10 Nm, after which mean moment-angle curves were plotted for each TMT joint at each loading condition. Least-squares curve-fitting procedures, employing a root mean square error threshold of 0.005 Nm, were used to describe the average overall moment vs. angle relationship of each joint. Curves for the first and second TMT joints exhibited similar behavior. The joints displayed reasonably constant stiffness at low angles of dorsiflexion, followed by rapidly increasing stiffness at higher angles of dorsiflexion. These data provide new insight into the behavior of the TMT joints under load and are valuable for use in numerical models of the foot, as well as in the understanding and treatment of certain foot pathologies.

Comparison of the capability of peak functions in describing real chromatographic peaks

This paper describes the results of a comparison of four peak functions in describing real chromatographic peaks. They are the empirically transformed Gaussian, polynomial modified Gaussian, generalized exponentially modified Gaussian and hybrid function of Gaussian and truncated exponential functions. Real chromatographic peaks of different shapes (fronting, symmetric, and tailing) are obtained by various separation conditions of reversed-phase liquid chromatography. They are then fitted to the peak functions via the Marquardt–Levenberg algorithm, a nonlinear least-squares curve-fitting procedure, by Microsoft Solver. The qualities of the fits are evaluated by the sum of the squares of the residuals. It is concluded in the study that the empirically transformed Gaussian function offers the highest flexibility (best fits) to all shapes of chromatographic peaks, including extremely asymmetric tailing peaks with a peak asymmetry of up to 8. The flexibility of this function should improve our ability to process chromatographic peaks such as deconvolution of overlapped peaks and smoothing noisy peaks for the determination of statistical moments.

Use of intrinsic modes in biology: examples of indicial response of pulmonary blood pressure to +/- step hypoxia.

Recently, a new method to analyze biological nonstationary stochastic variables has been presented. The method is especially suitable to analyze the variation of one biological variable with respect to changes of another variable. Here, it is illustrated by the change of the pulmonary blood pressure in response to a step change of oxygen concentration in the gas that an animal breathes. The pressure signal is resolved into the sum of a set of oscillatory intrinsic mode functions, which have zero "local mean," and a final nonoscillatory mode. With this device, we obtain a set of "mean trends," each of which represents a "mean" in a definitive sense, and together they represent the mean trend systematically with different degrees of oscillatory content. Correspondingly, the oscillatory content of the signal about any mean trend can be represented by a set of partial sums of intrinsic mode functions. When the concept of "indicial response function" is used to describe the change of one variable in response to a step change of another variable, we now have a set of indicial response functions of the mean trends and another set of indicial response functions to describe the energy or intensity of oscillations about each mean trend. Each of these can be represented by an analytic function whose coefficients can be determined by a least-squares curve-fitting procedure. In this way, experimental results are stated sharply by analytic functions.

Thermodynamic study of the binding of dibenzo-18-crown-6 with Ag+, Pb2+and Cd2+in acetonitrile–water solvents

Thermodynamic data for the binding of Ag+, Pb2+ and Cd2+ nitrates with dibenzo-18-crown-6 in acetonitrile–water solvents have been obtained in the temperature range 288–308 K using a conductometric technique. The observed molar conductivities, Λ, were found to decrease significantly for mole ratios less than unity. The conductivity data have been analysed using a model involving 1 : 1 stoichiometry. The stability constant, K, and the limiting molar conductivity, Λc, for each 1 : 1 complex have been obtained from the measured conductivities by using a non-linear least-squares curve-fitting procedure. The complexation sequence, based on the value of log K at 298 K, was found to be Pb2+ > Cd2+ > Ag+. The significance of the reported values of ΔH0 and ΔS0 in the present work has been discussed.

Conductance study of the binding of methyl orange, o-methyl red and p-methyl red anions by α-cyclodextrin in water

A conductance study concerning the binding of methyl orange (MO, 4-[4-(dimethylamino)phenylaza]benzene-sulfonic acid), o-methyl red (o-MR, 2-[4-(dimethylamino)phenylaza]benzoic acid) and p-methyl red (p-MR) anions by α-cyclodextrin (α-CD) in water has been carried out at 25 °C. The observed molar conductances (Λs) were found to decrease significantly for mole ratios less than unity. A model involving 1 : 1 stoichiometry has been used to analyse the conductance data. The stability constant (K) and the molar conductance (Λc) for each 1 : 1 inclusion complex were determined from the conductance data by using a non-linear least-squares curve-fitting procedure. The binding sequence, based on the value of K at 25 °C, is found to be p-MR > MO > o-MR. The values of the ionic molar conductances of the complexed anions at infinite dilution are reported and the differences between such values and those of uncomplexed anions are in accord with the above binding sequence.

A circular dichroic study of helical structure in flagellar dynein

The circular dichroic spectra of outer arm dynein from sea urchin sperm flagella, of its separated alpha and beta heavy-chain complexes, and of the two major fragments produced by tryptic digestion of the beta heavy chain have been measured over the range 190-240 nm. Although the spectra show significant individuality, in all cases they qualitatively resemble those of typical globular proteins with mixed regions of alpha-helix and beta-sheet (alpha/beta-type structure) or with separate alpha-helix- and beta-sheet-rich regions (alpha+beta-type structure). Quantitative analyses of the spectra by both constrained and unconstrained least-squares curve-fitting procedures indicate that the intact dynein contains approximately 26% alpha-helix. The separated beta heavy-chain complex and its ATPase-containing amino-terminal domain (fragment A) both have spectra resembling that of intact dynein, and they appear to contain 32% and 23% alpha-helix, respectively. The carboxy-terminal domain of the beta heavy chain (fragment B) and the separated alpha heavy chain have significantly different spectra; however, they each appear to contain 26-36% alpha-helix. These data suggest that dynein does not contain an extensive alpha-helical domain, such as is found in the carboxy-terminal rod region of the other motor proteins myosin and kinesin.

Transient thermal strain measurements in electronic packages

Fractional fringe moire interferometry was successfully applied to monitor thermo/mechanical strain histories in a memory device as the temperature was changing from room temperature (25 degrees C) to an arbitrarily chosen final temperature of 80 degrees C. Full displacement fields were recorded at different temperatures and used to predict strains in a small region at the chip corner. Moreover, strains across the chip thickness along a line close to the chip corner were investigated. A dramatic change in the pattern of axial strain growth was observed for temperatures around 70 degrees C and above. It is suggested that the development of severe compressive stains due to bending of the package is responsible for such a change. A minor deficiency in the data collection procedure affected the accuracy of strains predicted for the selected region. This necessitated the use of a least-squares curve fitting procedure to represent deformations based on experimentally collected values. This yielded smooth strain distributions giving a clear qualitative picture of strain histories, but is introduced some errors in the strain magnitudes (10-15% of actual values). >

Electrical characteristics of ion bombarded Ni/n-Si Schottky contacts

The effect of 100 keV Si+ ion bombardment of Ni/n-Si Schottky contacts was studied by measuring the I-V characteristics over the substrate temperature range of 25–100°C, before and after implantation, as well as before and after annealing at 150, 180 and 220°C. From these characteristics the following parameters were obtained by means of a least-squares curve fitting procedure: the ideality constant n, the saturation current density Js, the series resistance R and the Schottky barrier height ΦB. Si+ implantation resulted in higher values for n and R (R with a negative temperature coefficient), but lower values for Js, compared to the unimplanted contacts. Both the values of R and Js depended on the implantation dose. Before annealing, the Schottky barrier height for both the implanted and unimplanted contacts had lower values than after annealing at 150°C. In the latter case, ΦB increased to 0.60±0.01, independent of implantation dose. ΦB remained unchanged after annealing at higher temperatures.

Secondary structural analysis of retrovirus integrase: Characterization by circular dichroism and empirical prediction methods

The retrovirus integrase (IN) protein is essential for integration of viral DNA into host DNA. The secondary structure of the purified IN protein from avian myeloblastosis virus was investigated by both circular dichroism (CD) spectroscopy and five empirical prediction methods. The secondary structures determined from the resolving of CD spectra through a least-squares curve fitting procedure were compared with those predicted from four statistical methods, e.g., the Chou-Fasman, Garnier-Osguthorpe-Robson, Nishikawa-Ooi, and a JOINT scheme which combined all three of these methods, plus a pure a priori one, the Ptitsyn-Finkelstein method. Among all of the methods used, the Nishikawa-Ooi prediction gave the closest match in the composition of secondary structure to the CD result, although the other methods each correctly predicted one or more secondary structural group. Most of the alpha-helix and beta-sheet states predicted by the Ptitsyn-Finkelstein method were in accord with the Nishikawa-Ooi method. Secondary structural predictions by the Nishikawa-Ooi method were extended further to include IN proteins from four phylogenetic distinct retroviruses. The structural relationships between the four most conserved amino acid blocks of these IN proteins were compared using sequence homology and secondary structure predictions.

Soluble fibrin-fibrinogen complexes as intermediates in fibrin gel formation.

Oligomer formation in fibrinogen solutions following addition of thrombin was studied by addition of thrombin inhibitor at various times subsequent to thrombin, followed by size-exclusion chromatography (SEC) on a high-performance SEC column capable of resolving species of molecular weights less than or equal to 10(6). Peaks corresponding to species with 1, 2, 3, and 4 or more times the molecular weight of fibrinogen were detected and quantified via nonlinear least-squares curve-fitting procedures. The evolution of each of these peaks with time is well accounted for by a kinetic model in which the predominant component of each oligomeric molecular weight species is a linear complex of fibrinogen and fibrin. The observed predominance of trimeric over dimeric oligomers even at short times suggests that the thrombin-catalyzed release of the two A fibrinopeptides from a single molecule of fibrinogen is highly cooperative.

Curve Fitting of Heterodyne Data

The least-squares curve fitting procedure of experimental data is described for heterodyne detection. Two independent methods, the Maximum Likelihood method of Fisher and SIMPLEX, have been tried. The relative merits and limitations are discussed in detail.

Kinetics of floc breakage and aggregation in agitated liquid suspensions

A complete population balance equation governing the floc size distribution interpreting both breakage and aggregation mechanisms was obtained in this work. The present work deals with floc formation and breakage in the presence of polymer coagulants. In order to obtain all the parameters involved in the proposed governing equation, a nonlinear least-squares curve fitting procedure was applied. The aggregation collision efficiency was found to be 0.33 for our clay-polymer flocculation system under optimum dosage. The floc splitting frequency was found to be proportional to the product of turbulent shear rate and parent floc volume. The rate of decrease of parent floc volume due to erosion was verified to be proportional to the product of turbulent shear rate and the mean particle volume of erosion fines. The “maximum stable floc size” in a given turbulence field was found to exist in our system.