By Adrian Horzyk (auth.), Mikko Kolehmainen, Pekka Toivanen, Bartlomiej Beliczynski (eds.)

ISBN-10: 3642049206

ISBN-13: 9783642049200

This publication constitutes the completely refereed post-proceedings of the ninth foreign convention on Adaptive and traditional Computing Algorithms, ICANNGA 2009, held in Kuopio, Finland, in April 2009.

The sixty three revised complete papers provided have been conscientiously reviewed and chosen from a complete of 112 submissions. The papers are equipped in topical sections on impartial networks, evolutionary computation, studying, tender computing, bioinformatics in addition to applications.

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Additional resources for Adaptive and Natural Computing Algorithms: 9th International Conference, ICANNGA 2009, Kuopio, Finland, April 23-25, 2009, Revised Selected Papers

Sample text

Thus Hd -variation is sometimes called variation with respect to half-spaces. The next corollary estimates worst-case . ∞ -errors in approximation of balls in Hd -variation. Corollary 2. Let d be a positive integer and rd > 0, then for every positive integer n √ 1/2 −1/2 δ(Brd ( . Hd ), spann Hd )M(Rd ) ≤ 6 3 d1/2 rd (log n) n . Proof. The statement follows by Theorem 1 (iii) and the fact that the co-VC dimension of the set Hd of closed half-space indicator functions on Rd is equal to d [17, p.

So the statement follows again by the definition of deviation. (iii) This follows by [17, Theorem 3]. In the upper bounds in Theorem 1 (i)-(iii), the functions ξ(d) are of the forms ξ(d) = sd rd , ξ(d) = h∗d sd rd , and ξ(d) = d1/2 sd rd , resp. , grow polynomially with d increasing. Note that sd and h∗d,Θ are determined by the choice of Gd , but rd can be chosen in such a way that ξ(d) is a polynomial. 4 Tractability for Gaussian Radial-Basis-Function Networks In this section, we investigate tractability of approximation by Gaussian radialbasis function (RBF) networks.

Dimension-independent rates of approximation by neural networks. , K´ arn´ y, M. ) Computer-Intensive Methods in Control and Signal Processing. The Curse of Dimensionality, pp. 261–270. Birkh¨ auser, Basel (1997) 19. : Introductory Real Analysis. Dover Publications Inc. (1970) On Tractability of Neural-Network Approximation 21 20. : Error estimates for approximate optimization by the extended Ritz method. SIAM J. on Optimization 15, 461–487 (2005) 21. : Singular Integrals and Differentiability Properties of Functions.

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Adaptive and Natural Computing Algorithms: 9th International Conference, ICANNGA 2009, Kuopio, Finland, April 23-25, 2009, Revised Selected Papers by Adrian Horzyk (auth.), Mikko Kolehmainen, Pekka Toivanen, Bartlomiej Beliczynski (eds.)

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