Scalable Active Subspace Low-Rank Graph Representation for Continuous System Online Security Evaluation with Input Corruption

We address the scalability issues in low-rank matrix learning problems. Usually these problems resort to solving nuclear norm regularized optimization problems (NNROPs), which often suffer from high computational complexities if based on existing solvers, especially in large-scale settings. Based on the fact that the optimal solution matrix to an NNROP is often low rank, we revisit the classic mechanism of low-rank matrix factorization, based on which we present an active subspace algorithm for efficiently solving NNROPs by transforming large-scale NNROPs into small-scale problems. The transformation is achieved by factorizing the large solution matrix into the product of a small orthonormal matrix (active subspace) and another small matrix. Although such a transformation generally leads to nonconvex problems, we show that a suboptimal solution can be found by the augmented Lagrange alternating direction method. For the robust PCA (RPCA) (Candès, Li, Ma, & Wright, 2009 ) problem, a typical example of NNROPs, theoretical results verify the suboptimality of the solution produced by our algorithm. For the general NNROPs, we empirically show that our algorithm significantly reduces the computational complexity without loss of optimality.

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Mosul University WLAN Security: Evaluation, Analysis and Improvement

Iraqi Journal for Electrical And Electronic Engineering ◽

10.33762/eeej.2011.50306 ◽

2011 ◽

Vol 7 (2) ◽

pp. 138-143

Author(s):

Omar Ahmed Hachum

Keyword(s):

Security Evaluation

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MILP-Aided Security Evaluation of Differential Attacks on KCipher-2

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.2020cip0018 ◽

2021 ◽

Vol E104.A (1) ◽

pp. 203-212

Author(s):

Jin HOKI ◽

Kosei SAKAMOTO ◽

Fukang LIU ◽

Kazuhiko MINEMATSU ◽

Takanori ISOBE

Keyword(s):

Security Evaluation ◽

Differential Attacks

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Tensor Recovery via Nonconvex Low-Rank Approximation

2020 28th European Signal Processing Conference (EUSIPCO) ◽

10.23919/eusipco47968.2020.9287404 ◽

2021 ◽

Author(s):

Lin Chen ◽

Xue Jiang ◽

Xingzhao Liu ◽

Zhixin Zhou

Keyword(s):

Low Rank ◽

Low Rank Approximation ◽

Tensor Recovery ◽

Rank Approximation

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The Influences of the Rank of Coal on Methane Sorption Capacity in Coals/Wpływ Rzędu Węgla Na Pojemność Sorpcyjną Metanu W Węglach

Archives of Mining Sciences ◽

10.2478/amsc-2014-0037 ◽

2014 ◽

Vol 59 (2) ◽

pp. 509-516

Author(s):

Andrzej Olajossy

Keyword(s):

Sorption Capacity ◽

Coalbed Methane ◽

Vitrinite Reflectance ◽

Sorption Isotherms ◽

Volatile Matter ◽

Low Rank ◽

Hard Coal ◽

Petrographic Composition ◽

Methane Sorption ◽

Indian Coals

Abstract Methane sorption capacity is of significance in the issues of coalbed methane (CBM) and depends on various parameters, including mainly, on rank of coal and the maceral content in coals. However, in some of the World coals basins the influences of those parameters on methane sorption capacity is various and sometimes complicated. Usually the rank of coal is expressed by its vitrinite reflectance Ro. Moreover, in coals for which there is a high correlation between vitrinite reflectance and volatile matter Vdaf the rank of coal may also be represented by Vdaf. The influence of the rank of coal on methane sorption capacity for Polish coals is not well understood, hence the examination in the presented paper was undertaken. For the purpose of analysis there were chosen fourteen samples of hard coal originating from the Upper Silesian Basin and Lower Silesian Basin. The scope of the sorption capacity is: 15-42 cm3/g and the scope of vitrinite reflectance: 0,6-2,2%. Majority of those coals were of low rank, high volatile matter (HV), some were of middle rank, middle volatile matter (MV) and among them there was a small number of high rank, low volatile matter (LV) coals. The analysis was conducted on the basis of available from the literature results of research of petrographic composition and methane sorption isotherms. Some of those samples were in the form (shape) of grains and others - as cut out plates of coal. The high pressure isotherms previously obtained in the cited studies were analyzed here for the purpose of establishing their sorption capacity on the basis of Langmuire equation. As a result of this paper, it turned out that for low rank, HV coals the Langmuire volume VL slightly decreases with the increase of rank, reaching its minimum for the middle rank (MV) coal and then increases with the rise of the rank (LV). From the graphic illustrations presented with respect to this relation follows the similarity to the Indian coals and partially to the Australian coals.

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