of upto 10 Tb/in 2 . It uniquely differs from other proposed next-generation architectures because of its reliance on sophisticated two-dimensional signal processing algorithms. Recently, a number of contributions have been made in the development of read-channel models and detectors for TDMR systems. In this paper, we provide a detailed review on all important readchannel models under consideration. Our discussion focuses on the purpose of each of these models, placing a special emphasis on the suitability of the Voronoi model for the purpose of designing detectors. We also propose several detection schemes for TDMR based on the Voronoi model and present some numerical results.
We introduce a family of planar regions, called Aztec diamonds, and study tilings of these regions by dominoes. Our main result is that the Aztec diamond of order n has exactly 2n(n+1)/2 domino tilings. In this, the first half of a two-part paper, we give two proofs of this formula. The first proof exploits a connection between domino tilings and the alternating-sign matrices of Mills, Robbins, and Rumsey. In particular, a domino tiling of an Aztec diamond corresponds to a compatible pair of alternating-sign matrices. The second proof of our formula uses monotone triangles, which constitute another form taken by alternating-sign matricess by assigning each monotone triangle a suitable weight, we can count domino tilings of an Aztec diamond.
MLL1 regulates circadian promoters by depositing H3K4 trimethyl marks, whose levels are also modulated by the NAD+-dependent deacetylase SIRT1. SIRT1 is now shown to promote circadian deacetylation of MLL1, thus affecting MLL1's methyltransferase activity.