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A classification of low dimensional multiplicative Hom-Lie superalgebras

100%
Wang C., Zhang Q., Wei Z.
Open Mathematics
|
2016
|
tom 14
|
nr 1
613-628
EN
We study a twisted generalization of Lie superalgebras, called Hom-Lie superalgebras. It is obtained by twisting the graded Jacobi identity by an even linear map. We give a complete classification of the complex multiplicative Hom-Lie superalgebras of low dimensions.
2
Content available remote

Classification of invariant AHS-structures on semisimple locally symmetric spaces

88%
Gregorovič J.
Open Mathematics
|
2013
|
tom 11
|
nr 12
2062-2075
EN
We discuss which semisimple locally symmetric spaces admit an AHS-structure invariant under local symmetries. We classify them for all types of AHS-structures and determine possible equivalence classes of such AHS-structures.
3
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Bias-variance decomposition in Genetic Programming

63%
Kowaliw T., Doursat R.
Open Mathematics
|
2016
|
tom 14
|
nr 1
62-80
EN
We study properties of Linear Genetic Programming (LGP) through several regression and classification benchmarks. In each problem, we decompose the results into bias and variance components, and explore the effect of varying certain key parameters on the overall error and its decomposed contributions. These parameters are the maximum program size, the initial population, and the function set used. We confirm and quantify several insights into the practical usage of GP, most notably that (a) the variance between runs is primarily due to initialization rather than the selection of training samples, (b) parameters can be reasonably optimized to obtain gains in efficacy, and (c) functions detrimental to evolvability are easily eliminated, while functions well-suited to the problem can greatly improve performance-therefore, larger and more diverse function sets are always preferable.
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