Expression of the Irp gene is regulated in part by the nutrients available to the cell, and is decreased in rich medium, in glucose minimal media enriched with amino acids, and in minimal medium with alternative carbon sources, such as acetate and succinate. When Lrp production is increased in a given medium, expression of its target genes is also increased. However, when the medium is changed from glucose to acetate, the response of the target genes is governed by many factors.
Recently, a fast deterministic block Kaczmarz (FDBK) method which uses a greedy criterion of the row selections and contains pseudoinverse-free computation is presented. In this work, we introduce a maximum residual rule into FDBK and develop a new block Kaczmarz method which is also considered as a fast deterministic pseudoinverse-free block extension of Motzkin (FBEM) method. In addition, we prove that FBEM converges linearly to the unique least-norm solution of the linear systems. Furthermore, by incorporating the Polyak momentum technique into the FBEM iteration method, we establish an accelerated variant of FBEM (mFBEM) and show its global linear convergence. Numerical examples using artificial and real datasets demonstrate the effectiveness of FBEM as well as mFBEM.
Abstract| The authors describe a new windowing technique for frames partitioned region-wise or using variable-size blocks, where the virtual repartitioning operation for a given region is carried out adaptively and performed locally. Compared to the existing methods, this technique utilizes more pixels that are in the close neighborhood of the boundaries of the regions in the windowing operation, resulting in a substantial reduction in the prediction error as well as in the blocking effect.
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