Adaptive and Natural Computing Algorithms: 10th by Ivan Bratko (auth.), Andrej Dobnikar, Uroš Lotrič, Branko à

By Ivan Bratko (auth.), Andrej Dobnikar, Uroš Lotrič, Branko à ter (eds.)

The two-volume set LNCS 6593 and 6594 constitutes the refereed complaints of the tenth foreign convention on Adaptive and typical Computing Algorithms, ICANNGA 2010, held in Ljubljana, Slovenia, in April 2010. The eighty three revised complete papers provided have been rigorously reviewed and chosen from a complete of one hundred forty four submissions. the 1st quantity comprises forty two papers and a plenary lecture and is geared up in topical sections on neural networks and evolutionary computation.

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Additional info for Adaptive and Natural Computing Algorithms: 10th International Conference, ICANNGA 2011, Ljubljana, Slovenia, April 14-16, 2011, Proceedings, Part I

Example text

K , which is defined on GK (X) as Kx , Ky K := K(x, y). For convolution kernels K(x, y) = k(x − y), where k has a positive Fourier transform, spaces HK (Rd ) can be characterized in terms of weighted Fourier transforms. The d-dimensional Fourier transform is the operator F defined on L2 ∩ L1 as 1 F (f )(s) = fˆ(s) = eix·s f (x) dx (2π)d/2 Rd and extended as an isometry to L2 [12]. The next theorem is from [13] (see also [14] for an earlier less rigorous formulation). Theorem 1. , K(x, y) = k(x − y) for all x, y ∈ Rd .

The work presented in this paper was supported by Polish national budget funds for science. References 1. : Model predictive control. Springer, London (1999) 2. : Neural networks – a comprehensive foundation. Prentice Hall, Englewood Cliffs (1999) 3. : Identification of nonlinear systems using neural networks and polynomial models: block oriented approach. Springer, London (2004) 4. : Computationally efficient nonlinear predictive control based on neural Wiener models. Neurocomputing 74, 401–417 (2010) 5.

Kainen Proposition 1. Let X ⊆ Rd , z = (u, v), where u = (u1 , . . , um ) ∈ X m and v = (v1 , . . , vm ) ∈ Rm . Then (i) Ez is continuous on (C(X), . sup ); (ii) for any symmetric positive semidefinite kernel K : X × X → Rd , Ez is continuous on (HK (X), . K ). Proof. (i) Let f, g ∈ C(X) be such that f − h sup < δ. ,m 2f (ui ). So Ez is continuous at f . (ii) Let Fu : HK (X) → Rd be an evaluation operator defined for every f ∈ HK (X) as Fu (f ) = (f (u1 ), . . , f (um )). Then Ez (f ) = Fu (f ) − v 22,m , where m 1 2 the norm .

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