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This paper has been withdrawn by the author, since one of the key results duplicates existing work, as pointed out by a reader. I am currently revising the manuscript.

This paper has been withdrawn by the author due to a crucial error in the definition of homomorphism.

There is a technical issue in the analysis that is not easily fixable. We, therefore, withdraw the submission. Sorry for the inconvenience.

The paper has been withdrawn by the authors.

With regard to the recently published article, ``Y.-Q. Wang, et al., Physical mechanism of equiprobable exclusion network with heterogeneous interactions in phase transitions: Analytical analyses of steady state evolving from initial state,…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

This paper has been withdrawn by the author(s), due a crucial error on the entanglement of $\Gamma$ registers.

This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.

This paper has been withdrawn by the author because it has been substantially modified.

Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic…

This paper has been withdrawn.

This paper has been withdrawn by the authors, due an error involving the weak* convergence argument in section 2

This paper has been withdrawn by the author due to a crucial error in the formulation.

The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…

This paper has been withdrawn by the author due to a crucial mistakes.

This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and…

Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…

The automation of text summarisation of biomedical publications is a pressing need due to the plethora of information available on-line. This paper explores the impact of several supervised machine learning approaches for extracting…

Pronouns are frequently omitted in pro-drop languages, such as Chinese, generally leading to significant challenges with respect to the production of complete translations. Recently, Wang et al. (2018) proposed a novel reconstruction-based…

This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.