Intrinsic warp

The term used in the stochastic literature for these models is intrinsic random fields (IRFs) they appear under that name in textbooks of geostatistics (e.g. Cressie, 1991 Chiles and Delfiner, 1999). This chapter also introduces the intrinsic warps (IWs) intended to replace my principal and partial warps of 1989 for data analysis of landmark-like configurations under symmetries of scale. These IWs could well implement the movable potentially homologous characters that may someday underlie computer-assisted algorithms for stable ordinations or ecophenotypy surveillance much better than existing techniques could likely do. 

So we have a noise model. What kinds of scientific descriptions can we pursue with its aid By analogy with the bending energy of the thin-plate spline, which led to useful formalisms such as time partial warps, the gauge metric of these self-similar processes likewise has an eigenstructure, which 1 have tentatively named the intrinsic warps (IWs) of the mean point configuration. Keep in mind that these exist only in the non-uniform subspace of the overall shape space, though they apply at all scales. 

FIGURE 5.6 All 10 intrinsic warps (IWs) for the mean form driving the simulations in Figure 5.1. Each is drawn in the horizontal direction except for the first and second, which are drawn both horizontally and vertically. 

FIGURE 5.7 The first relative intrinsic warp (RIW) for the real data of DeQuardo et al. (1996) for two groups of brain images compared to the actual group mean difference between schizophrenics and their psychiatric ward staff as found there. The RIW emphasizes the last few IWs from Figure 5.6. 

So here is my working hypothesis if there is landmark-like covariance structure in your warped image data-set, these new relative intrinsic warps (relative now with respect to the IWs instead of the old PWs), may have a fair chance of finding it. In other words, ordinary biometric principal components with respect to the new featureless covariance structure - relative intrinsic warps might be the nearest thing yet that morphometries can offer as a formalism based in image deformation that nevertheless refers to the sorts of features systematists have typically found useful in thinking about their taxonomic task. 

Continuous mixture theory found application in industry and was, as I understand it, incorporated into some of the models the chemical and oil companies were developing. Some of the work on polymerization and coal devolatization also used the notions of continuous mixtures, but there was little development on the formal side until the work of Astarita and Ocone in the latter eighties. Their paper (AIChE J. 34 1299, 1988) introduced the idea of uniform kinetics. This allowed the time scale to be warped and results to be obtained when the underlying reactions were not of the first order. Indeed, it was shown that intrinsic kinetics (i.e. rate laws for A(x)dx) could be found that would mimic any kinetic law for the lump as a whole (AIChE J. 35 529,1989 [248, 249, 259]). 

It is obvious that (apart from processing conditions) the degree of warping, the reversion and the impact strength are also determined by intrinsic properties of the polymer. Goppel and Van der Vegt (1966) showed that the first two effects increase with molecular mass and with broader molecular mass distribution. On the other hand, the impact strength increases with molecular mass and with narrower molecular mass distribution. 

An important point about Eq. (128) is that it shows that, in the warped time scale T, the behavior is entirely independent of the form of the functional F[ ] the latter influences only the relationship between the warped time r and the actual time t. The case of first-order intrinsic kinetics (Aris and Gavalas, 1966) is recovered by simply setting t = r. 

RF transmission and reception of the NMR signal. For the stimulated pulse sequence, three hard pulses were used with the spin-warp sequence as discussed in Section 3.1. It is also necessary to obtain images corresponding to the porosity distribution as described in Section 2, in addition to the velocity images. This is because the images obtained in the velocity experiment are measures of the intrinsic velocity, the actual velocity of the fluid within the pore space. Darcy s law, however, is written in terms of the superficial velocity. The two velocities are simply related by the porosity ... 

Corrstrained yams in the fabric or other textile stractures reveal mechanical responses, which are different in compare with the free yams. Therefore, their intrinsic behavior would not be displayed perfectly. This is actually the reason of representation of Equations (13) and (15). Table 3 reveals fabric modulus along the warp direction the modiCbd warp yams modulns the spring stiffness constarrt, and the equivalent spring stiffness constant for the weft yam of each fabric. 

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