The constraints we impose on the reconstruction process are threefold: The initial chemical graphs represent all sets of at most m metabolites among those involved in the set R of reactions, for some fixed, but arbitrary, m (in examples and applications in this paper we shall always take m = 2).
We note that for the graph Γ ( S M 6 ) in Example 1, MWB ( Γ ( S M 6 ) ) = 5.
The reference rectangle ABCD now is as shown in Fig. 10 a with a priory known the information: (A D //(B C),(A B //(C D) and the width of the lane (3 m in this example).
Since b is no longer constant, we use b w, a weighted average of the risk differences b i in the groups with weights depending on the within-group exposure variances (b w is also obtained by regressing the individual-level data while adjusting for group; see appendix 3): (b e - b w ) = (b c - b w ) M In the example, b w is approximately 0.296 (appendix 6).
We show the figure of M-NSC in Example 1 in Figure 1.
Combining Propositions 1 and 2, we can get the first main theorem which shows us the equivalence relationship between (l_{2,0} -minimization and (l_{2,0} -minimization. Figure 1 M-NSC in Exandl_{2,p} -minimization
In this study, weight distances of 2,000, 500, and 100 m were adopted in Example 1 (sampling interval of 5 min and actual average spatial interval of 2,170 m), Example 2 (1 min and 298 m), and Example 3 (20 s and 82 m), respectively.
Example 14 Consider ( X = R, M e ) as in Example 7.
Consider the sequence ((E_{k})) of subsets of M as defined in Example 2.6.
For a = 1, consider the non-Archimedean fuzzy normed space ( Y, N 1, T M ) defined as in Example 2.6, Theorem 3.3 yields Theorem 2 in [7].
