Let x n = (x1, n,..., x P, n ) be the n-th example where n ∈ {1,..., N}, and the i-th feature value, i ∈ {1,..., P}, of the n-th example is denoted by x i, n.
Class labels of the N examples will be denoted by y = (y1,..., y N ).
Example 3.2 In this example, we denote by X = C ( [ 0, 1 ] ) the set of real continuous functions on [ 0, 1 ].
Backward reactions can also be written explicitly, e.g. E + S <- C ; b = 6 Sources, for example gene expression, and sinks, for example protein degradation, are denoted by null: null -> A ; s = 10 A -> null ; d = 0.1 implying that protein A is produced at a rate of 10 s-1 and degrades at a rate of 0.1 s-1.
For each class, a syllable has been chosen and is displayed in Fig. 10 along with its spectrogram (where the syllable denoted by example 1 was taken from class 1, example 2 from class 2 and so forth).
For example, denote by R n the n-dimensional Euclidean space and by R + the set of all nonnegative real scalars, i.e., R + = { t ∈ R ∣ t ≥ 0 }.
Figure 5 shows a representative example of extracted TMP information (denoted by gray dots).
For example, we denote by (GL_{n}(R)) the n-dimensional general linear group over (R^{1}) and consider the system x' = f t, x), qquad'=frac{mathrm{d}}{mathrm{d}t}, (1) where (f: R^{1}times R^{n} to R^{n}) is continuous, and for some (Qin GL_{n}(R)), the following affine symmetry holds: f(t+T, x) = Qf bigl t, Q^{-1}x bigr).
We have already seen, for example, that a knowledge domain denoted by Δ and composed of KUs can be represented as: Delta = left{delta_{1}, delta_{2}, delta_{3}, ldots, delta_{n}right} (2).
where d is a distance between distributions (for example the Kolmogorov-Smirnov distance, denoted by dKS in the following), dpercept is a perceptual distance between audio signals and dth is the audibility threshold for this distance.
