Cross-correlation Subject

McLeman<7, ) used a method which was really a pre-cursor of the cross-correlation technique. He injected a pulse of air into the conveying line as a result of which there was a very short period during which the walls at any particular point were not subject to... 

As stated in the previous section, the major reactant feed was chosen as the manipulated variable. In the trial this feed was subjected to a pseudo-random binary sequence (PRBS) signal in an open loop operation of the process. The results of the trial, plotted in Fig. 2, show a strong -- but delayed -- cross-correlation between the manipulated feed rate and the reactor temperature. Using techniques described by Box and Jenkins (2), a transfer function relating the manipulated variable to the control variable of interest can be developed. The general form of this transfer function is... 

When r s, one has interconversion between operators Br and Bs, and Rrs is a cross-relaxation rate. Note that the cross-relaxation may or may not contain interference effects depending on the indices l and /, which keep track of interactions Cyj and C,. Cross-correlation rates and cross-relaxation rates have not been fully utilized in LC. However, there is a recent report41 on this subject using both the 13C chemical shielding anisotropy and C-H dipolar coupling relaxation mechanisms to study a nematic, and this may be a fruitful arena in gaining dynamic information for LC. We summarize below some well known (auto-)relaxation rates for various spin interactions commonly encountered in LC studies. 

It should be mentioned that rotational anisotropy of the molecule will result in an increase in the R2 values for NH vectors having particular orientation with respect to the diffusion tensor frame [46]. This increase could be misinterpreted as conformational exchange contributions, and, vice versa, small values of Rex, usually of the order or 1 s 1 or less, could be mistaken for the manifestation of the rotational anisotropy. Therefore, identification of residues subjected to conformational exchange is critical for accurate analysis of relaxation data. Additional approaches are necessary to distinguish between the two effects. As suggested earlier [27] (see also Ref. [26]), a comparison between R2 and the cross-correlation rate r]xy could serve this purpose, as tjxy contains practically the same combination of spec-... 

Authors efforts in this part of the work have been concentrated on developing turbulence closures for the statistical description of two-phase turbulent flows. The primary emphasis is on development of models which are more rigorous, but can be more easily employed. The main subjects of the modeling are the Reynolds stresses (in both phases), the cross-correlation between the velocities of the two phases, and the turbulent fluxes of the void fraction. Transport of an incompressible fluid (the carrier gas) laden with monosize particles (the dispersed phase) is considered. The Stokes drag relation is used for phase interactions and there is no mass transfer between the two phases. The particle-particle interactions are neglected the dispersed phase viscosity and pressure do not appear in the particle momentum equation. 

Cross-correlation and spectral analysis have proven invaluable tools for quantifying the frequency dependent characteristics of the human subject. The cross-spectral density function, or cross-spectrum Sxyif), can be obtained from the random target x t) and random response y t) by taking the Fourier transform of the cross-correlation function Vxyir), that is, Sxyif) = Ffr yfr), or in the frequency domain via Sxy if) = X(/) y(/), or by a nonparametric system identification approach (e.g., spa.m in Matlab ). The cross-spectrum provides estimates of the relative amphtude (i.e., gain) and phase-lag at each frequency. Gain, phase, and remnant frequency response curves provide objective measures of pursuit... 

Cross-correlations between the general activity, different stress indicators and motor activity (n = 43 subjects 80 hr standard-tasks 141 hr project-tasks time lag -9 = - 3 min, +9 = +3 min). The values are generated by a multiplication of the mean cross-correlation value (mean of 20 subjects) by the number of correlations found on the respective significance level. 

The reactions of SO2 with [Cr(NN)3] (NN = bpy, phen, and derivatives) when subjected to visible light (laser pulse) are threefold. " Quenching yields [Cr(NN)3] which undergoes back electron transfer. The predominant reaction is electron transfer between SO2 and [Cr(NN)3] yielding the transient SO2. The rate constants obtained may be utilized in a Marcus cross-correlation relation to calculate a self-exchange rate of between 1 x 10" M s and 18 x 10" s for... 

Cross-correlation and spectral analysis have proven invaluable tools for quantifying the frequency-dependent characteristics of the human subject. The cross-spectral density function, or cross-spectrum can be obtained from the random target x t) and random response y(t) by taking the... 

Accordingly, Kohl et al. reported an in vitro protease assay for two-photon cross-correlation analysis based solely on the fluorescent proteins rsGFP and DsRed [88]. A GFP-peptide-DsRed construct named STEV-ST was purified and subjected to proteolysis separating the fluorophores. With regard to future... 

For more detailed structural analyses it will be important to make use of new techniques that have emerged in protein NMR spectroscopy. The main breakthroughs are probably the introduction of TROSY spectroscopy [74], extending the size limit of biological macromolecules that can be subjected to NMR analyses, the creation of so called cross correlation experiments [75] that allow the direct measurement of dihedral angles, and the measurement of residual dipolar couplings [76] that complement data from NOESY spectroscopy. Unfortunately, all of these techniques require, or at least benefit from isotope enrichment which remains a difficult and expensive task for carbohydrates. Consequently, only few examples utilizing e.g. C-labelled carbohydrates have been published so far [23, 40-42]. It is... 

Olfactory receptors have been a subject of great interest (9). Much that has been postulated was done by analogy to the sense of sight in which there are a limited number of receptor types and, as a consequence, only three primary colors. Thus attempts have been made to recognize primary odors that can combine to produce all of the odors that can be perceived. Evidence for this includes rough correlations of odors with chemical stmctural types and the existence in some individuals having specific anosmias. Cross-adaptation studies, in which exposure to one odorant temporarily reduces the perception of a chemically related one, also fit into this hypothetical framework. Implicit in this theory is the idea that there is a small number of well-defined odor receptors, so that eventually the shape and charge distribution of a specific receptor can be learned and the kinds of molecular stmctures for a specified odor can be deduced. 

Miller first used Eq. (7-41) to correlate multiple variations, and this approach has more recently been subjected to considerable development. Many cross-interaction constants have been evaluated multiple regression analysis is one technique, but Miller and Dubois et ah discuss other methods. Lee et al. consider Pxy to be a measure of the distance between groups x and y in the transition state... 

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