Sparse data

Sparse data on the pyrazole isomers, pyrazolenines and isopyrazoles, are presented in Table 12. Besides the obvious upheld effect on the chemical shift due to the suppression of the ring current, these compounds behave normally. Data on pyrazolidinones and their salts show the behaviour of cyclic hydrazides (66T2461,67BSF3502). 

The second step concerns distance selection and metrization. Bound smoothing only reduces the possible intervals for interatomic distances from the original bounds. However, the embedding algorithm demands a specific distance for every atom pair in the molecule. These distances are chosen randomly within the interval, from either a uniform or an estimated distribution [48,49], to generate a trial distance matrix. Unifonn distance distributions seem to provide better sampling for very sparse data sets [48]. 

Note that although the bounds on the distances satisfy the triangle inequalities, particular choices of distances between these bounds will in general violate them. Therefore, if all distances are chosen within their bounds independently of each other (the method that is used in most applications of distance geometry for NMR strucmre determination), the final distance matrix will contain many violations of the triangle inequalities. The main consequence is a very limited sampling of the conformational space of the embedded structures for very sparse data sets [48,50,51] despite the intrinsic randomness of the tech-... 

This, more physical model that visualizes failure to result from random "shocks," was specialized from the more general model of Marshall and Olkin (1967) by Vesely (1977) for sparse data for the ATWS problem. It treats these shocks as binomially distributed with parameters m and p (equation 2.4-9). The BFR model like the MGL and BPM models distinguish the number of multiple unit failures in a system with more than two units, from the Beta Factor model,... 

Population pharmacokinetics is the application of pharmacokinetic and statistical methods to sparse data to derive a pharmacokinetic profile of central tendency. 

If the graph y vs. x suggests a certain functional relation, there are often several alternative mathematical formulations that might apply, e.g., y - /x, y = a - - exp(b (x + c))), and y = a-(l- l/(x + b)) choosing one over the others on sparse data may mean faulty interpretation of results later on. An interesting example is presented in Ref. 115 (cf. Section 2,3.1). An important aspect is whether a function lends itself to linearization (see Section 2.3.1), to direct least-squares estimation of the coefficients, or whether iterative techniques need to be used. 

Tellinghuisen, J. and Wilkerson, C. W. (1993). Bias and precision in the estimation of exponential decay parameters from sparse data. Anal. Chem. 65, 1240-6. 

Among the sparse data available on reactivity of the ring systems belonging to this chapter, a condensation reaction, a ring transformation, and a ring closure are discussed in this section. 

Biomedical spectra are often extremely complex. Hyphenated techniques such as MS-MS can generate databases that contain hundreds of thousands or millions of data points. Reduction of dimensionality is then a common step preceding data analysis because of the computational overheads associated with manipulating such large datasets.9 To classify the very large datasets provided by biomedical spectra, some form of feature selection10 is almost essential. In sparse data, many combinations of attributes may separate the samples, but not every combination is plausible. 

The Wilson plot is shown in Figure 4.At first sight all seems well except that the overall temperature factor is B=327 57a. This is clearly unlikely, but is a common feature when carrying out normalisation with such a sparse data set. To overcome the problem, a temperature factor of B=0.0A is imposed on the data. 

In the absence of replicate measurements, it is not possible to estimate interaction effects. These are bundled into the error term (see spreadsheets 2.9 and 2.10). Even with the sparse data of a single measurement for each combination of factors, the result is in agreement with the other calculations. The analysts are still significantly different ( columns P = 0.04452) but the batches are not ( rows P = 0.09274). 

The relatively sparse data on dense phase transport is described by Klinzing (1981) and Teo and Leung (1984). Here only the more important category of dilute phase transport will be treated. 

Since the frequencies of rare amino acid pairs can be relatively small, procedures to treat sparse data are employed [6]. 

Landau derivation of the diamagnetism no longer applies, and contributions from the orbital motion of the electrons may be expected. Here, as before, the free electron model only reproduces the broad trends of the data. Both model and the sparse data are essentially flat at concentrations above two mole % the free electron model should not be used at lower concentrations. The magnitudes agree as well as for the pure solid metal. 

The LD50 and TC50 for humans would be more directly applicable but, for obvious reasons, only very sparse data are available ... 

The FO method was the first algorithm available in NONMEM and has been evaluated by simulation and used for PK and PD analysis [9]. Overall, the FO method showed a good performance in sparse data situations. However, there are situations where the FO method does not yield adequate results, especially in data rich situations. For these situations improved approximation methods such as the first-order conditional estimation (FOCE) and the Laplacian method became available in NONMEM. The difference between both methods and the FO method lies in the way the linearization is done. 

This chapter summarizes the sparse data on 1,5-naphthyridines with substituents that are joined directly or indirectly to the nucleus through a sulfur atom. Included are any tautomeric or nontautomeric 1,5-naphthyridinethiones, extranuclear mercapto-1, 5-naphthyridines, alkylthio-1,5-naphthyridines, bis(l,5-naphthyridinyl) sulfides or disulfides, 1,5-naphthyridine sulfoxides or sulfones, and 1,5-naphthyridinesulfonic acids or their derivatives. However, several categories have no known representatives. 

Finally, in drug development or evaluation phase studies, logistical tradeoffs of pharmacokinetic-dynamic data may lead to reduced samples per patient (sparse data) and/or reduced patient group sizes, as well as noisy data (e.g., unknown variability in the dose strategy, noncompliance) (phase IV). 

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