Let ∼ be the equivalence closure of ↝; then, x∼x′ iff there is a zig-zag chain of ↝ relations such as: Notice that ∼ is a congruence with respect to arbitrary disjoint union, i.e. it satisfies:(10)∀j∈J,xj∼x′j⇒⊎Jxj∼⊎Jx′j since a zig-zag chain ...
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Uncertainty relations quantify the joint localisation in time respectively space domain and Fourier domain. For that reason they are an important tool in the design of wavelets. Uncertainty relations in higher dimension are most often realized as the tensor product of one dimensional uncertainty ...
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Traceable Sets Rupert H¨olzl and Wolfgang Merkle∗ Institut fu¨r Informatik, Ruprecht-Karls-Universit¨at, Heidelberg, Germany {hoelzl,merkle}@math.uni-heidelberg.de Abstract. We investigate systematically into the various possible no- tions of traceable sets and the relations they bear to each...
It proved to be an improvement for rule learning both in computing performance and in the usefulness of the rules derived from a case study on melanoma data [24]. Zhao et al. made an empirical experiment for letter recognition to demonstrate the usefulness of the discussed relations and reduct...
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开学季特惠,9月3日-11月30日,专业版用户每周AI豆3倍膨胀,快来领取吧! 摘要原文 Inherent in the operation of many decision support and continuous referral systems is the notion of the “influence” of a data point on the database. This notion arises in examples such as finding the set of cus...
A knowledge graph is a multi-rela- tional graph composed of entities (nodes) and relations (different types of edges), and the goal of knowledge graph embedding is to embed components of a knowl- edge graph including entities and relations into contin- uous vector spaces, so as to simplify...