Strong Correlations

If the parameters were to become increasingly correlated, the confidence ellipses would approach a 45 line and it would become impossible to determine a unique set of parameters. As discussed by Fabrics and Renon (1975), strong correlation is common for nearly ideal solutions whenever the two adjustable parameters represent energy differences. 

In Figure 4 the measured attenuation values (TT) and the corresponding estimates are plotted against each other. Ideally (with error free estimates) all sample points should lie on the straight line through the origin with unit slope. Clearly there is a strong correlation between the estimates and the true values. 

Anisimov V I, Aryasetiawan F and Liechtenstein A I 1997 First-principles calculations of the electronic structure and spectra of strongly correlated systems The LDA+U method J. Phys. Condens Matters 767... 

The second application of the CFTI approach described here involves calculations of the free energy differences between conformers of the linear form of the opioid pentapeptide DPDPE in aqueous solution [9, 10]. DPDPE (Tyr-D-Pen-Gly-Phe-D-Pen, where D-Pen is the D isomer of /3,/3-dimethylcysteine) and other opioids are an interesting class of biologically active peptides which exhibit a strong correlation between conformation and affinity and selectivity for different receptors. The cyclic form of DPDPE contains a disulfide bond constraint, and is a highly specific S opioid [llj. Our simulations provide information on the cost of pre-organizing the linear peptide from its stable solution structure to a cyclic-like precursor for disulfide bond formation. Such... 

An application of correlation analysis is the detection of related chemical de.scriptors when analyzing chemical data, correlation analysis should be used as a first step to identify those descriptors which are interrelated. 1 f two descriptors are strongly correlated, i.e, the correlation coefficient of two descriptors exceeds a certain value, e.g., r > 0.90, one of the descriptors can be excluded from the data set. 

The copolymer fiber shows a high degree of drawabiUty. The spun fibers of the copolymer were highly drawn over a wide range of conditions to produce fibers with tensile properties comparable to PPT fibers spun from Hquid crystalline dopes. There is a strong correlation between draw ratio and tenacity. Typical tenacity and tensile modulus values of 2.2 N/tex (25 gf/den) and 50 N/tex (570 gf/den), respectively, have been reported for Technora fiber (8). 

Semiconductor devices ate affected by three kinds of noise. Thermal or Johnson noise is a consequence of the equihbtium between a resistance and its surrounding radiation field. It results in a mean-square noise voltage which is proportional to resistance and temperature. Shot noise, which is the principal noise component in most semiconductor devices, is caused by the random passage of individual electrons through a semiconductor junction. Thermal and shot noise ate both called white noise since their noise power is frequency-independent at low and intermediate frequencies. This is unlike flicker or ///noise which is most troublesome at lower frequencies because its noise power is approximately proportional to /// In MOSFETs there is a strong correlation between ///noise and the charging and discharging of surface states or traps. Nevertheless, the universal nature of ///noise in various materials and at phase transitions is not well understood. 

This is illustrated in Eig. 2.30 [2.167]. The surface was that of a fractured compact of SiC to which horon and carhon had been added to aid the sintering process. The aim of the analysis was to establish the uniformity of distribution of the additives and the presence or absence of impurities. The Auger maps show not only very non-uniform distribution of boron (Eig. 2.30a) but also strong correlation of boron with sodium (Eig. 2.30c), and weaker correlation of boron with potassium (Eig. 2.30b). Point analyses for points A and B marked on the images reveal the presence of sulfur and cal-... 

The relative leaving-group abilities of R 0 and are strongly correlated with the... 

Simple alkyl radicals such as methyl are considered to be nonnucleophilic. Methyl radicals are somewhat more reactive toward alkenes bearing electron-withdrawing substituents than towards those with electron-releasing substituents. However, much of this effect can be attributed to the stabilizing effect that these substiments have on the product radical. There is a strong correlation of reaction rate with the overall exothermicity of the reaction. Hydroxymethyl and 2-hydroxy-2-propyl radicals show nucleophilic character. The hydroxymethyl radical shows a slightly enhanced reactivity toward acrylonitrile and acrolein, but a sharply decreased reactivity toward ethyl vinyl ether. Table 12.9 gives some of the reactivity data. 

Fig. 7.12. The monoclinic to tetragonal conversion of shock-modified zirconia was studied with DTA by Hammetter and co-workers. The conversion temperature was found to be strongly changed and dependent on shock-modification conditions. The higher-pressure behavior was found to be strongly correlated with reduction in crystallite size [84H01],...

Ionic liquid conductivity appears to be most strongly correlated with viscosity (q). Figure 3.6-3 shows a plot of conductivity versus viscosity for the data in Tables 3.6-3-3.6-5. This figure clearly demonstrates an inverse relationship between conductivity and viscosity. 

Olfactory and stereochemical similarities to benzaldehyde have been examined for a large number of homologs of benzaldehyde and nitrobenzene each with the Me, Et, i-Pr, or t-Bu group at the ortho, meta, or para position. There exists a strong correlation between the two the more closely a compound resembles benzaldehyde in molecular shape, the more similar it is to benzaldehyde in almond odour 46). 

I here is a strong correlation between a driver s blood alcohol I concentration (BAC) and the likelihood that he or she will be involved in an accident (Figure A). At a BAC of 0.08% his or her chance of colliding with another car is four times greater than that of a sober driver. 

Coleman et al. have performed a preliminary structure/activity study for a series of analogues of 77 [149]. They found that removal of the naphthoate moiety (88 Scheme 11.11) dramatically reduced the yield of DNA alkylation, while replacement of the NH2 group with O-benzyl (89 and 90) abolished DNA alkylation completely. Compound 91 alkylated DNA with reduced efficiency, so this effect is not simply due to a requirement for a hydrogen bond donor at this position. Perhaps the amide is required at this position to increase the ability of the C=0 to act as a hydrogen bond acceptor. Importantly, they found a strong correlation between the extent of in vitro DNA alkylation and cell culture cytotoxicity. 

Another way of looking at high ionic conductivities of solid electrolytes is to consider the activation enthalpy as illustrated in Fig. 8. Generally, the activation enthalpy is strongly correlated with the room-temperature ionic conductivity the higher the room-temperature ionic conductivity, the lower the activation enthalpy. The straight lines in the Arrhenius... 

In principle, only the expressions for the correct desorption order should give a straight line at higher temperatures. In practice, however, the experimental scatter, possible inaccuracy in corrections of the output data, inherent departures from the simple model considered (mainly the dependence of Ea on 0), together with a rather strong correlation which can be shown to exist between the functions In [(1 /nB) — (l/nB0) ] and ln[ln(na0) — ln(n ) ], can seriously impair the plot and make the estimate of the desorption order rather dubious. Statistical methods should be helpful in this case, but to our knowledge they have not been employed so far. 

Here we will not discuss these problems and the intriguing observation that am and resonance parameters denoted by F and R respectively (after an original proposal of Swain and Lupton, 1968), which can be considered as independent of each other. The secondary parameters R + and R reflect the potential for an additional mesomeric donor-acceptor interaction (as in 7.7, and the opposite type with a donor instead of NQ2 and the reaction site as acceptor). 

For electron diffraction, the nonbonded distances of the tetrahedral sulfur bond configurations in sulfonyl molecules are closely spaced and cause strong correlation among the relevant parameters. Assuming one of them (O O) to be known can greatly facilitate the determination of the rest of the parameters (see more details in Reference 5). 

The main lesson from the analysis given above is that the activation free energy of the reaction is strongly correlated with the stabilization of the ionic resonance structure by the protein-active site. The generality of this concept will be considered in the following chapters. 

It has long been recognized that local environmental characteristics influence the rates of material corrosion. After two years of measurements at 39 sites in Europe and North America, significant relationships have been shown between corrosion rates of building materials and atmospheric pollutants( 5). While direction of exposure relative to weather and other factors such as frequency and duration of wetting significantly influence corrosion, Kucera (46) has shown that sulphur oxides are strongly correlated with deterioration of structural materials. 

In evaluating the influence of individual climate controls, we have three major concerns the time frame over which the control operates, the potential magnitude of the control s influence on climate, and whether a strong correlation between some forcing phenomenon and climatic response actually indicates a cause-effect relationship. 

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