Topological uncertainty

Conflict between optimizations, especially under accelerated versus delayed transformation, as well as sensitivity to topological uncertainty, result in more than one equally plausible scenario for the early evolution of pleurocarpy. Rather than adopt a universal preference for, say ACCTRAN over DELTRAN a priori, it is useful to examine conflicting scenarios individually in the light of the nature of the morphological transformations they require. 

Though topologically correct, the scales have been deliberately distorted to encompass both cases, and especially near the origin to dramatize the effect of some designs on the uncertainty of the intercept and the ratio xp/xQ.)... 

The present experiments may be subject to some uncertainty in terms of molecular weight estimates and diffusion effects that could affect the exactness of these interpretations. The conclusion is reached that the experiments strongly suggest evidence for discontinuous topological quantification. In other words, the order and rate of fragment release is consistent with expectations based on fragment topology. 

In mathematics, earlier, algebra and topology were fighting for the soul of mathematics. Ultimately both are co-existing and are enriching each other. Similarly today there is a struggle between probability theory and fuzzy set theory to capture the soul of uncertainty. I am sure ultimately both will co-exist and enrich each other. Already the debate has led to a deeper understanding of what we mean... 

Correlations based on fundamental molecular (or atomic) properties (LSERs, predictions based on molecular mechanics) and molecular topology (MC indices) show much promise. In spite of their empiricism, MC indices are attractive because of their high correlations with many physical, chemical, and biological variables. Their deterministic nature is an advantage relative to variables such as /C w, which can have large measurement uncertainties. 

According to the proposed prediction calculation procedure, it is clear that the actual distance between the two elements 5 and t, which satisfies the prediction conditions for any unknown element u, is crucial, and the larger the distance the larger the potential uncertainty in the prediction. Thus, a first topological measure of the prediction precision is provided by the connectivity operator C(s,t) previously defined the precision decreases for increased C(s,t). 

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