Goodness Of Fit Parameters Research Articles

Mathematical Model for the Characterization and Objective Comparison of Antioxidant Activities

The available data about the interference of antioxidants in the kinetics of lipid oxidation are abundant, but often they allow only semiquantitative conclusions, not always with sufficient basis. One of the causes of this problem is the absence of formal models able to guide the experimental design and to calculate characterizing parameters. In this regard, the model which we propose allows us to obtain the simultaneous solution of a series of oxidation kinetics in the presence of any number of antioxidant concentrations. It describes satisfactorily simulations in which substrate and antioxidant compete for oxygen in a second order kinetic scheme, as well as experimental results from other authors, in different systems and under different conditions. Its application is simple, it provides parametric estimates which characterize both the oxidative process and the antioxidant activity, and it facilitates rigorous comparisons among the effects of different compounds and experimental approaches. In all experimental data tested, the calculated parameters were always statistically significant (Student's t test, alpha = 0.05), the equations were consistent (Fisher's F-test), and the goodness of fit parameters (adj r(2), adjusted coefficients of multiple determination) were up to 0.97.

Subzero water transport characteristics and optimal rates of freezing rhesus monkey (Macaca mulatta) ovarian tissue

The purpose of the present study was to examine the effect of two different suprazero (room temperature +25 degrees C to +4 degrees C) cooling conditions on the measured water transport response of primate (Macaca mulatta) ovarian tissue in the presence and absence of cryoprotective agents (CPAs). Freshly collected Macaca mulatta (rhesus monkey) ovarian tissue sections were cooled at either 0.5 degrees C/min or 40 degrees C/min from 25 to 4 degrees C. A shape independent differential scanning calorimeter (DSC) technique was then used to measure the volumetric shrinkage during freezing of ovarian tissue sections at a freezing rate of 5 degrees C/min in the presence and absence of three different CPAs (0.85 M glycerol, 0.85 M dimethylsulfoxide, and 0.85 M ethylene glycol). Thus, water transport during freezing of primate ovarian tissue was obtained at eight different conditions (i.e., at four different freezing media with two different suprazero cooling conditions). The water transport response of ovarian tissue cooled rapidly from 25 to 4 degrees C was significantly different (P < 0.01) than that of slow cooled tissue, in the freezing media without CPAs and with dimethylsulfoxide. However, the differences in the measured water transport response due to the imposed suprazero cooling conditions were reduced with the addition of glycerol and ethylene glycol (statistically different with P < 0.05). By fitting a model of water transport to the experimentally obtained volumetric shrinkage data the best-fit membrane permeability parameters (L(pg) and E(Lp)) were determined. The best-fit parameters of water transport in primate ovarian tissue sections ranged from: L(pg) = 0.7 to 0.15 microm/min-atm and E(Lp) = 22.1 to 32.1 kcal/mol (the goodness of fit parameter, R(2) > 0.96). These parameters suggest that the "optimal rates of cryopreservation" for ovarian tissue are significantly dependent upon suprazero cooling conditions and the choice of CPA.

Field study of pesticide leaching in a Himatangi sand (Manawatu) and a Kiripaka bouldery clay loam (Northland). 2. Simulation using LEACHM, HYDRUS-1D, GLEAMS, and SPASMO models

Abstract We applied 5 pesticides, along with bromide as a conservative tracer, at 2 field sites (Northland and Manawatu, North Island of New Zealand), and their distributions in the soil profile were monitored through soil core and suction cup sampling for 18 months. Field-measured values were simulated using LEACHM, HYDRUS-1D, GLEAMS, and SPASMO models and compared against the measured datasets at both these sites. All 4 models predicted the measured dataset for each of the compounds with reasonable degree of accuracy; however, some discrepancies were observed. Prediction by GLEAMS was by far the best, as indicated by the goodness of fit parameters. Pesticide leaching parameters, organic carbon partition coefficient (Koc), and degradation half-life (T1/2) were optimised using the PEST optimisation package. For diazinon and terbuthylazine the parameters obtained for each of the models were generally close to the literature range. However, Koc and T1/2 values for atrazine, hexazinone, and procymidone were found to be slightly lower than the available literature range data.

U(VI) adsorption on natural iron-coated sands: comparison of approaches for modeling adsorption on heterogeneous environmental materials

Adsorption of U(VI) on 6 samples of natural Fe-rich sands from Oyster, VA was studied over a range of U(VI) concentrations (0.1–100 μM), pH values (3–7.6), and dithionite–citrate–bicarbonate (DCB) extractable amounts of Fe (3.1–12.3 μmol/g). Four modeling approaches were applied to represent the U(VI) adsorption data. Model I was a two-site, diffuse double layer, surface complexation model based on data for synthetic ferrihydrite [Geochim. Cosmochim. Acta 58 (1994) 5465–5478]. Considering the magnitude of approximations necessary for application of the laboratory-based model to natural sands, Model I was surprisingly accurate, as determined by the goodness of fit parameter, χ 2/ N of 53.1–22.2. Model II was based on the reactions and diffuse double layer treatment of Model I, but was calibrated to a portion of U(VI) adsorption data for each sand, and then used to predict adsorption data for the same sand under different experimental conditions. Model II did not increase the accuracy of the predictions made with Model I, χ 2/ N of 42.4–27.6. Models III and IV were four-site affinity spectrum models, without an explicit electric double layer model or explicit surface hydrolysis reactions. Model III was based on a discrete log K spectrum approach, and Model IV was obtained from adjusting all surface stability constants and site concentrations for all surface sites. Models III and IV represented the U(VI) adsorption data with the greatest accuracy, χ 2/ N ranged from 13.8 to 4.4. Model I provides evidence supporting the practice of using pure phase thermodynamic reaction constants for describing the adsorption characteristics of environmentally important sorbents in certain simple cases. Yet, affinity spectrum approaches (Models III and IV) become increasingly important as more accurate interpolation of adsorption data is necessary, the sorbent becomes increasingly complex, or the range of experimental conditions expands.

Parameter Estimation for the Constant Capacitance Surface Complexation Model: Analysis of Parameter Interdependencies

Results of extensive application of the 2-pK constant capacitance surface complexation model (CCM) to surface charge data of a range of minerals in 0.1Melectrolytes are summarized where the program FITEQL has simultaneously been used to study the interdependence of the involved optimized parameters.To illustrate representative results, surface complexation and goodness of fit parameters are given as a function of the capacitance value (C). For all (ca. 150) tested data sets, one of three patterns is observed, two of which do not allow a unique parameter set to be obtained.The results indicate that the optimized site density parameter is relatively insensitive to a wide variation ofC; optimized site density is rather low in this range of (higher)Cand tends toward maximum proton uptake in the respective data set which in turn will be close to sometimes experimentally observed saturation levels. At low and with further decreasingCa steep increase of site density may occur; in this case, ΔpKastrongly increases after a ΔpKaminimum. Alternatively at lowC, ΔpKamay continue to decrease and site density decreases simultaneously after a site density maximum. The observed patterns can be explained by the constraint ofCon the electrostatic correction factor.Linear correlation coefficients (which are very useful parameters but do not receive much attention) show that in the region of lowC, the optimized parameters become fully correlated, which finally causes nonconvergence in parameter optimization. In the region where the optimized site density is not significantly affected by a decrease inCthe optimized parameters are more weakly correlated. When site concentration is co-optimized high correlation between adjustable parameters suggests that it is preferable to have an estimate for this parameter.Overall, it can be stated that substantial difficulties were observed in the effort to obtain unique (and thus meaningful) parameters for the CCM in about 60% of the data sets treated.

Comparison of 1-pK and 2-pK Versions of Surface Complexation Theory by the Goodness of Fit in Describing Surface Charge Data of (Hydr)oxides

1-pK and 2-pK formulations exist in surface complexation theory with respect to the description of basic charging behavior of (hydr)oxide electrolyte interfaces. The 2-pK approach has been commonly used with at least four different electrostatic models, whereas the 1-pK model has been primarily used with only one of those electrostatic models. In this paper the 1-pK approach is combined with three more electrostatic models. The eight resulting possible combinations have been tested on several sets of data. Applying the 2-pK basic Stern model (BSM) and the triple-layer model (TLM) was not satisfactory: due to the high number of adjustable parameters involved in these model variations the optimization procedure of the applied computer codes did not converge. This was taken as an a priori justification to exclude even more complicated (four-layer) models. For the remaining six models which could be successfully applied in the present paper, the goodness of fit parameter given by a computer code was used to compare the quality of the description of the chosen experimental data by the respective models. A purely diffuse layer model (DLM) generally gave the poorest fit to experimental data when combined with the 1-pK approach and was only sligthly better when combined with the 2-pK formalism. Either the 1-pK BSM or the 2-pK constant capacitance model (CCM) gave the best fit to the data in all the examples. However, it was found in two cases that some arbitrary constraint was necessary to define a unique (and thus meaningful) parameter set for the 2-pK CCM. The 1-pK TLM version allowed in more than half of the examples to determine a unique parameter set, which is impossible with the 2-pK TLM. It is concluded that the 1-pK BSM should be considered as the first choice model with respect to the goodness of fit and the uniqueness of the estimated parameters. The 2-pK CCM is still a good choice for a constant ionic strength case when the experimental data allow a determination of unique parameters and if only goodness of fit is used as a criterion.

Age and character of basaltic rocks of the Yucca Mountain region, southern Nevada

Volcanism in the Yucca Mountain region of southern Nevada in the last 5 m.y. is restricted to moderate‐to‐small volumes of subalkaline basaltic magmas, produced during at least 6 intervals, and spanning an age range from 4.6 Ma to about 125 ka. Where paleomagnetic evidence is available, the period of volcanism at individual eruptive centers apparently was geologically short‐lived, even where multiple eruptions involved different magma types. K‐Ar studies are consistent with most other geochronologic information, such as the minimum ages of exposure‐dating techniques, and show no evidence of renewed volcanism after a significant quiescence at any of the centers in the Yucca Mountain region. A volcanic recurrence interval of 860 ± 350 kyr is computed from a large K‐Ar data set and an evaluation of their uncertainties. Monte Carlo error propagations demonstrate the validity of uncertainties obtained for weighted‐mean ages when modified using the goodness of fit parameter, MSWD. Elevated 87Sr/86Sr initial ratios (Sri) in the basalts, nearly constant at 0.707, combined with low SiO2 and Rb/Sr ratios indicate a subcontinental, lithospheric mantle source, previously enriched in radiogenic Sr and depleted in Rb. Beginning with eruptions of the most voluminous eruptive center, the newly dated Pliocene Thirsty Mountain volcano, basaltic magmas have decreased in eruptive volume, plagioclase‐phenocryst content, various trace element ratios, and TiO2, while increasing in light rare earth elements, U, Th, P2O5, and light REE/heavy REE ratios. These time‐correlated changes are consistent with either increasing depths of melting or a decreasing thermal gradient in the Yucca Mountain region during the last 5 m.y.

Surface X-ray diffraction on the potassium-induced reconstruction of the Ag(001) surface

Surface X-ray diffraction experiments have been performed on the K-induced super structures on Ag(001). Both, the (2 × 1) and the (3 × 1) superstructure which are formed at K-coverages of about 0.15 and 0.30 ML, are found to consist of missing row type reconstructions, where one and two Ag-rows are missing along [110¯], respectively. In both cases the K-atoms reside within the large grooves of the missing row structures. For the (2 × 1) structure we find the K-atoms adsorbed on bridge sites relative to second-layer Ag-atoms, thereby coordinated by six Ag-atoms (four first-layer Ag-atoms and two second-layer Ag-atoms) at a distance of 3.44 (5) Å. The consideration of anharmonic displacement factors for the top layer Ag atoms is necessary for the proper description of the structure, leading to a significant better agreement with the data as compared to pure harmonic refinement as expressed by the goodness of fit parameter (GOF = 0.93 versus GOF = 1.67). Allowing for anharmonic displacement parameters we determine a Ag interlayer spacing d 12 which is contracted relative to the bulk spacing by only 3.2% instead of 12.7% if anharmonic contributions are neglected. In the (3 × 1) superstructure the K-atoms form staggered double rows along [11¯0], in this way forming a distorted quasihexagonal overlayer. The K-atoms are located close to bridge sites to second layer Ag-atoms at a minimum distance of 3.55 (5) Å. Additional defects are found in the first Ag-layer. For this more open reconstruction the Ag-interlayer spacing, d 12, is contracted by about 10% confirming recent investigations on FCC (110) surfaces regarding the polarization-induced compression of the interlayer distances.

An objective computer‐oriented method for the calculation of formation constants from the formation function. A weighted least‐squares curve fitting

AbstractA computer program has been developed that calculates, using the weighted least‐squares technique, the overall formation constants, Bi, of mononuclear complexes, the standard deviations of Bi, SDVi, and an estimate of goodness of fit, Goodness‐of‐Fit Parameter (GOFP), given a set of average ligand numbers, VNj, the corresponding free ligand concentrations, VAj, and an error parameter P. The formation function used is ∑(VNj – i) · (Bi) · (VAj)i = 0 where i ranges from O to n with a maximum of 10 and j ranges from O to l with a maximum of 40. The Bi and (Bi – SDVi) must be positive and GOFP must be either unity or as close to unity as possible. An option is available that allows the computation of P, if it is not provided, so that GOFP is equal or very close to unity. The method has been applied to the formation of the complexes Cadmium‐Imidazole, Cobalt(II)‐Bis(2‐Quinaldylphenyl Ketone), Copper‐Ammonia, Silver‐4‐Aminobutan‐1‐ol Nitrate, and Copper(II)‐Bis(2‐Quinaldylphenyl Ketone). The results are quite satisfactory and reliable as compared with other computational techniques. Input data and results for the five complexes mentioned are shown.

Calculating palaeomagnetic poles for oceanic plates

b The information available for determining palaeopoles for oceanic plates includes data of four types: (1) palaeomagnetic measurements of inclinations but not declinations from core samples; (2) palaeopoles determined from magnetic anomalies over seamounts; (3) phase shifts of linear magnetic anomalies; and (4) palaeoequators determined from geological analysis of sediment cores. A method is presented which combines these different kinds of data and their respective confidence limits to yield a best fit pole, a confidence ellipse, estimates of the data importances and goodness of fit parameters. Using this method we calculate the Campanian pole position for the Pacific plate which is shown by a chi-squared test to be a reasonable fit to the data. We conclude that the method should be a useful tool for calculating pole paths for oceanic plates such as the Pacific and Indian plates.