By De-Shuang Huang, Kyungsook Han

ISBN-10: 3319220527

ISBN-13: 9783319220529

ISBN-10: 3319220535

ISBN-13: 9783319220536

This e-book - at the side of the double quantity LNCS 9225-9226 - constitutes the refereed lawsuits of the eleventh overseas convention on clever Computing, ICIC 2015, held in Fuzhou, China, in August 2015.

The eighty four papers of this quantity have been conscientiously reviewed and chosen from 671 submissions. unique contributions concerning this subject matter have been particularly solicited, together with theories, methodologies, and functions in technology and know-how. This 12 months, the convention targeted as a rule on computing device studying thought and techniques, smooth computing, snapshot processing and machine imaginative and prescient, wisdom discovery and information mining, average language processing and computational linguistics, clever keep an eye on and automation, clever verbal exchange networks and net purposes, bioinformatics idea and techniques, healthcare and scientific equipment, and knowledge security.

**Read or Download Advanced Intelligent Computing Theories and Applications: 11th International Conference, ICIC 2015, Fuzhou, China, August 20-23, 2015. Proceedings, Part III PDF**

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**Additional resources for Advanced Intelligent Computing Theories and Applications: 11th International Conference, ICIC 2015, Fuzhou, China, August 20-23, 2015. Proceedings, Part III**

**Example text**

A . 1 2 h½n; Xm ; Yn i .. 1 ½ n; X h m ; Y1 i Á Á Á 2 Measurable function on G is qðnÞ ¼ jxðnÞj4 þ16jyðnÞj2 14 ; n 2 G; Koranyi unit ball on G is n BG ðe; 1Þ ¼ n 2 GnÀ1 eG o 1 ; e ¼ ð0; . ; 0Þ: The above contents can be seen in [4–6]. Now we introduce the concept of polar coordinates on G (see [7, 8]). 0 Let q ¼ qðn; eÞ ¼ knkG , h 2 @BG ð0; 1Þ, then ðq; hÞ 2 Rþ Â X are polar coordi0 nates on G, here X is a subset in the Koranyi unit sphere S1G ¼ @BG ðe; 1Þ, let q ¼ knkG and u : @BG ðe; 1Þ !

Almost, the sparse GP models can be mathematically deﬁned by the following equations [32]: V $ N½0; KðU; UÞ; ð5Þ pðF; F Ã jVÞ ¼ qðFjVÞqðF Ã jVÞ; ð6Þ yt jft $ Nðft ; r2 Þ i:i:d:; ð7Þ yÃt jftÃ $ NðftÃ ; r2 Þ i:i:d:; ð8Þ where Eq. (5) means the latent pseudo outputs V fulﬁll a GP, as in Eqs. , the latent responses for training dataset and test dataset are conditionally independent given V. In Eq. (6), q(F|V) and q(F*|V) can be approximations of the following GP predictive distributions h i pðF Ã jVÞ $ N KðX Ã ; UÞT KðU; UÞÀ1 V; KðX Ã ; X Ã Þ À KðX Ã ; UÞKðU; UÞÀ1 KðU; X Ã Þ h i pðFjVÞ $ N KðX; UÞT KðU; UÞÀ1 V; KðX; XÞ À KðX; UÞKðU; UÞÀ1 KðU; XÞ ; ð9Þ respectively, and the forms of q(F|V) and q(F*|V) determine the kind of SGP models, including SoR, DTC, FITC and PITC models [32].

Wang and X. Yang then uðnÞ 0 in N. Now we will further generalize the maximum principle to Heisenberg type group G as following: Theorem 1. Let X be an open connected subset of G such that the following conditions hold: there exists n0 2 G such that n0 X lies on one side of an hyperplane parallel to y1 axis, suppose that there exists uðnÞ 2 CðXÞ bounded above, solution of & then uðnÞ LuðnÞ þ cuðnÞ ! 0; n 2 X; c uðnÞ 0; n 2 @X; 0; ð1Þ 0 in X. The following deﬁnitions are introduced in [4] by Kaplan.

### Advanced Intelligent Computing Theories and Applications: 11th International Conference, ICIC 2015, Fuzhou, China, August 20-23, 2015. Proceedings, Part III by De-Shuang Huang, Kyungsook Han

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