Benchmark curve

We anticipate that continued development of minimalist models, in conjunction with more efficient multi-reference approaches and a wider array of benchmark curves, will result in a better understanding of the theoretical challenges of bond breaking processes and increased ability of electronic structure theory to model them. 

Traditional yield spread analysis for a nongovernment bond involves calculating the difference between the risky bond s yield and the yield on a comparable maturity benchmark government security. As an illustration, let s use a 5.25% coupon BMW Finance bond described in Exhibit 3.10 that matures on 1 September 2006. Bloomberg s Yield Spread Analysis screen is presented in Exhibit 3.14. The yield spreads against various benchmarks appear in a box at the bottom left-hand corner of the screen. Using a settlement date of 9 July 2003, the yield spread is 31 basis points versus the interpolated 3.1-year rate on the Euro Benchmark Curve. This yield spread measure is referred to as the nominal spread. 

Interest Rate Swaps as the Benchmark Curve ter Eure Bevies... 

To illustrate the performance of SCS-MP2 and SCSN-MP2, Figure 4 presents errors in the potential energy curves for several Ti-interaction complexes when compared to estimated CCSD(T)/CBS benchmark curves. The MP2/CBS curves are significantly overbound and are not included in Figure 4. In all cases, the errors vs. the benchmark values are only a few tenths of 1 kcal mol . The largest errors are observed for SCS-MP2 at shorter intermonomer separations, and SCS-MP2 tends to have positive errors (underbinds) while SCSN-MP2 tends to have negative errors (overbinds) in the CBS limit. 

Benchmark Dose (BMD)—Usually defined as the lower confidence limit on the dose that produces a specified magnitude of changes in a specified adverse response. For example, a BMDio would be the dose at the 95% lower confidence limit on a 10% response, and the benchmark response (BMR) would be 10%. The BMD is determined by modeling the dose response curve in the region of the dose response relationship where biologically observable data are feasible. 

Figure 12.3. Benchmark of peer-reviewed academic reports of organic semiconductor device field-effect mobility versus time of report. All data points are for spin-coated organic semiconducting transistors. Solid points are derived from the benchmark study completed in 2002 by Brazis and Dyrc at Motorola (unpublished). The curve is a calculated estimation, based on these data, of what the expected mobility values will be in the future. The open points are data derived in 2005 from the public journals for verification of the 2002 prediction.6 38... 

For all toxic effects other than carcinogenicity, a threshold in the dose-response curve is assumed. The lowest NOAEL from all available studies is assumed to be the approximate threshold for the groups of subjects (humans or animals) in which toxicity data were collected. Alternatively, a benchmark dose (BMD) may be estimated from the observed dose-response curve, and used as the point-of-departure for risk assessment (see below and Box). 

Figure 8.1 Dose-response curves for carcinogens and illustration of low-dose extrapolation using linear, no-threshold model. Benchmark dose (BMD) is also illustrated.

The recent versions of the slow motion approach were applied to direct fitting of experimental data for a series of Ni(II) complexes of varying symmetry (97). An example of an experimental data set and a fitted curve is shown in Fig. 9. Another application of the slow-motion approach is to provide benchmark calculations against which more approximate theoretical tools can be tested. As an example of work of this kind, we wish to mention the paper by Kowalewski et al. (98), studying the electron spin relaxation effects in the vicinity and beyond the Redfield limit. 

Mathematical modelling of the dose-response relationship is an alternative approach to quantify the estimated response within the experimental range. This approach can be used to determine the BMD or benchmark concentration (BMC) for inhalation exposure, which can be used in place of the LOAEL or NOAEL (Crump, 1984). The BMD (used here for either BMD or BMC) is defined as the lower confidence limit on a dose that produces a particular level of response (e.g., 1%, 5%, 10%) and has several advantages over the LOAEL or NOAEL (Kimmel Gaylor, 1988 Kimmel, 1990 USEPA, 1995 IPCS, 1999). For example, (1) the BMD approach uses all of the data in fitting a model instead of only data indicating the LOAEL or NOAEL (2) by fitting all of the data, the BMD approach takes into account the slope of the dose-response curve (3) the BMD takes into account variability in the data and (4) the BMD is not limited to one experimental dose. Calculation and use of the BMD approach are described in a US EPA... 

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