Error bars

Figure B2.5.19. The collisional deactivation rate constant /c, (O3) (equation B2.5.42 ) as a fimction of the vibrational level v". Adapted from [ ]. Experimental data are represented by full circles with error bars. The broken curve is to serve as a guide to the eye.

Figure B3.2.11. Total energy versus lattice constant of gallium arsenide from a VMC calculation including 256 valence electrons [118] the curve is a quadratic fit. The error bars reflect the uncertainties of individual values. The experimental lattice constant is 10.68 au, the QMC result is 10.69 (+ 0.1) an (Figure by Professor W Schattke).

Fig. 11. Dose—response curves for (A,A) inhibition of cyclic AMP formation and stimulation of IP formation by carbachol (A,D) before and (A,H) after reduction of receptor number by irreversible alkylation (carbachol) is in M. Error bars ( ) are shown for some studies.

Fig. 3. Release rate of pilocarpine from Ocusert Pilo-20. Data points shown with standard deviation error bars (94).

Figure 7 The production and emission of NO during denitrification in agricultural soil treated with NO3 fertilizer (KNO3) and the nitrification inhibitor Dyciandiamide (10%) under aerobic (air) and anerobic conditions (N,). Fluxes are means from three soil columns, error bars represent standard deviations from the mean. V = vertical flow through the column H = Horizontal flow over the soil surface.

Figure 12 Widths of the broad Lorentzian components fit to structure factors for lipid H atoms obtained from an MD simulation of a fully hydrated DPPC bilayer and quasielastic neutron scattering experiments on DPPC bilayers containing 23% water for (a) motion in the plane of the bilayer and (b) motion in the direction of the bilayer normal. The error bars on the experimental points are approximately 150 xeV.

Because LEED theory was initially developed for close packed clean metal surfaces, these are the most reliably determined surface structures, often leading to 7 p factors below 0.1, which is of the order of the agreement between two experimental sets of 7-V curves. In these circumstances the error bars for the atomic coordinates are as small as 0.01 A, when the total energy range of 7-V curves is large enough (>1500 eV). A good overview of state-of-the-art LEED determinations of the structures of clean metal surfaces, and further references, can be found in two recent articles by Heinz et al. [2.272, 2.273]. 

Fig. 25. Relationship between the measured interfacial strength and the (negative) Gibbs free energy of mixing, (-AG )o5, for glass beads treated with various silane coupling agents embedded in a PVB matrix. Error bars correspond to 95% mean confidence intervals. Redrawn from ref. [165].

FIG. 5 Relative difference x of the lattice constants of Ne and Ne as a function of temperature. Lines are experimental values [346], symbols are PIMC results, the error bars of the lO x( ) fata values are about 0.03. (Reprinted with permission from Ref. 288, Fig. 8. 1995, American Physical Society.)... 

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

FIG. 16 Phase diagram of fluid vesicles as a function of pressure increment p and bending rigidity A. Solid lines denote first-order transitions, dotted lines compressibility maxima. The transition between the prolate vesicles and the stomatocytes shows strong hysteresis efifects, as indicated by the error bars. Dashed line (squares) indicates a transition from metastable prolate to metastable disk-shaped vesicles. (From Gompper and KroU 1995 [243]. Copyright 1995 APS.)... 

This same data is plotted in the chart on the following page. The mean absolute deviation and standard deviation are plotted as points with error bars, and the shaded blocks plot the largest positive and negative-magnitude errors. 

Figure 12 AES spectra of the W-SiC composite sample, (a) Schematic diagram of the sample (the shaded regions represent the reaction zone), (b) C and O line-scan profiles. The maximum PE noise is indicated by an error bar. (From Ref. 74.)...

Figure 6-14. Average domain size vs. inverse deposition temperature Tor different film thicknesses. Error bars represent the mean absolute error and straight lines the best lit for each film thickness. Doited line is the locus of the transition from grains to lamellae. Data for 50-nm films are estimated from the correlation length of the topography fluctuations. Adapted from Ref. [501.

Fatty Acid Transporters. Figure 2 Quencher-based real-time fatty acid uptake assay with a fluorescently labeled FFA analogue (C1-Bodipy-C12). Predominantly protein-mediated fatty acid uptake by 3T3-L1 adipocytes (diamonds) was compared with diffusion-driven uptake by fibroblasts (squares) using the QBT Fatty Acid Uptake reagent (Molecular Devices Corp., CA, USA), which contains C1-Bodipy-C12 as substrate in conjunction with a cell impermeable quencher. Uptake kinetics was recorded using a Gemini fluorescence plate reader. Error bars indicate the standard deviations from 12 independent wells. RFU relative fluorescence units. 

Fig. 3.13. Density-dependence of the Qo, branch line width y of methane (the dashed line is for pure vibrational dephasing, supposed to be Unear in density), (o) experimental data (with error bars) [162] Top part rotational contribution yR and its theoretical estimation in motional narrowing limit [162] (solid line) the points were obtained by subtraction of dephasing contribution y

Fig. 5.20. Full width of nitrogen Q-branch CARS spectra measured at 295 K versus densities (squares) and calculated width using the MEG law (circles) [14]. Shown also are the error bar and the width measured in liquid nitrogen (triangle), (a) Density range up to 700 amagat. (b) Density range up to 100 amagat showing part of Fig. 5.20(a) in more detail...

Fig. 10-15 Organic carbon fluxes with depth in the water column normalized to mean annual primary production rates at the sites of sediment trap deployment. The undulating line indicates the base of the euphotic zone the horizontal error bars reflect variations in mean annual productivity as well as replicate flux measurements during the same season or over several seasons vertical error bars are depth ranges of several sediment trap deployments and uncertainities in the exact depth location. (Reproduced with permission from E. Suess (1980). Particulate organic carbon flux in the oceans - surface productivity and oxygen utilization, Nature 288 260-263, Macmillan Magazines.)...

Fig. 7. vs gp) mean values for bone collagens of herbivores and omnivores including humans from Great Britain, Hungary, Peru and Canada dating from the Neolithic to the mid-15th century AD (adapted from Reynard Hedges 2008). Error bars indicate one standard error of the mean of 10 to 15 samples per species. 

Figure 2.9. The confidence interval for an individual result CI( 3 ) and that of the regression line s CLj A are compared (schematic, left). The information can be combined as per Eq. (2.25), which yields curves B (and S, not shown). In the right panel curves A and B are depicted relative to the linear regression line. If e > 0 or d > 0, the probability of the point belonging to the population of the calibration measurements is smaller than alpha cf. Section 1.5.5. The distance e is the difference between a measurement y (error bars indicate 95% CL) and the appropriate tolerance limit B this is easy to calculate because the error is calculated using the calibration data set. The distance d is used for the same purpose, but the calculation is more difficult because both a CL(regression line) A and an estimate for the CL( y) have to be provided.

Error bars defined by the confidence limits CL(y,) will shrink or expand, most likely in an asymmetric manner. Since we here presuppose near absence of error from the abscissa values, this point applies only to y-transformations. A numerical example is 17 1 ( 5.9%, symmetric CL), upon logarithmic transformation becomes 1.23045 -0.02633. .. 1.23045 + 0.02482. 

Figure 4.47. Drug assay using HPLC respectively UV Spectroscopy. Correlation of HPLC and UV results obtained on four batches of a cream. The vertical error bars each give the mean + standard deviation of 6 HPLC determinations because the Student s t-factor for five d.f. is nearly equal to /6 (see Section 1.3.2), the bars can also be interpreted as 95% confidence limits. The circles connected by a line indicate the corresponding duplicate UV determinations. The proportionality line passes through the origin and the center of mass for the four coordinates. The drug is slightly overdosed (= 103-104% the traditional UV assay apparently is not as selective as it should be an interference adds about 4% to the result.

Rotational Barrier in Ethylene. It is well known that the rotational barrier of the ethylene molecule cannot be adequately described by a single reference Hartree-Fock calculation SCF calculations on this level resulted in values of 126 kcal/mole (30) and 129 kcal/mole (31) whereas the experimental value is 65 kcal/mole (32). Open-shell ab initio calculations of double zeta+polarization quality give the more acceptable value of 48 kcal/mole (33). Inclusion of correlation such as in CEPA calculations yield theoretical results within the experimental error bar (34), albeit at a considerable computational cost. 

It is remarkable that LDF theory also describes the bond length and vibrational frequency of the fluorine molecule with the same error bar as the other systems discussed here. This finding is significant as it shows that the error made in the LDF approach appears to be consistent in a wide class of different systems. In fact, recent calculations on ferrocene (52) show that also this type of metallo-organic compound does not present an exception - the Fe/ring distance agrees within 0.002 A with experiment. 

Fig. 11. Capillary data showing an increase in the release of intracellular calcium content (340/380 ratio) as s increases. Data refer to experiments in which the cell suspension was circulated through a fine bore capillary for 15 min. Error bars represent the 8.0% standard deviation [87]...

Fig. 14. Calcium response of Sf-9 insect cells subjected to different values of e in a stirred bioreactor equipped with a 5.1 cm diameter 6-bladed Rushton impeller (closed circles) or in the capillary flow system (open squares). Error bars for stirred bioreactor are standard deviation for each experiment but for the capillary, data are hard to discern [99]...

Fig. 25. Total and viable cell concentrations of TB/C3 hybridomas versus duration of shear in a cone and plate viscometer (shear stress 208 Nm ). The error bars indicate the 95% confidence intervals [62]...

Whole cell OPH activity was measured by following the increase in absorbancy of p-nitrophenol from the hydrolysis of substrate (0.1 mM Paraoxon) at 400 nm (sm = 17,000 M cm ). Samples of culture (1 ml) were centrifuged at 10,000 g and 4 C for 5 min. The cells were washed, resuspended with distilled water, and 100 pi was added to an assay mixture containing 400 pi 250 mM CHES [2-(N-cyclohexylamino)ethane-sulfonic acid] buffer, pH 9.0, 100 pi 1 mM Paraoxon, and 400 pi distilled water. One unit of OPH activity was defined as pmoles Paraoxon hydrolyzed per min. Each value and error bar represents the mean of two independent experiments and its standard deviation. 

Fig. 2. Whole cell biocatalytic reactions for four types of recombinant whole cell systems. Bioconversion reactions were performed in resting cell condition. All data were based on unit cell concentration (1 mg-dry cell weight ml ). Each value and error bar represents the mean of two independent experiments and its standard deviation.

Figure 15. Circular dichroism of the C=0 C li peak (BE = 292.7 eV) in fenchone at three different photon energies, indicated, (a) Photoelectron spectrum of the carbonyl peak of the (1S,4R) enantiomer, recorded with right (solid line) and left (broken line) circularly polarized radiation at the magic angle, 54.7° to the beam direction, (b) The circular dichroism signal for fenchone for (1R,4A)-fenchone (x) and the (lS,41 )-fenchone (+) plotted as the raw difference / p — /rep of the 54.7° spectra, for example, as in the row above, (c) The asymmetry factor, F, obtained by normalizing the raw difference. In the lower rows, error bars are included, but are often comparable to size of plotting symbol (l/ ,4S)-fenchone (x), (lS,4R)-fenchone (+). Data are taken from Ref. [38],...

The partial cross-sections on the n = 3 levels are displayed in Table 4 and Fig. 6 and show a fairly good overall agreement with the experimental results of Cotte et al. [4,7] and Dijkkamp et al. [9j. From a numerical point of view, the error bar has been estimated experimentally to 30% by Cotte et al. [4,7] and to 5% by Dijkkamp et al. [9]. Theoretically, the error bar could be evaluated to about 20%., the main difficulty arising in the determination of the sharp radial couplings. 

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