An algebraic integer (AI) based time-multiplexed row-parallel architecture and two final-reconstruction step (FRS) algorithms are proposed for the implementation of bivariate AI-encoded 2-D discrete cosine transform (DCT). The architecture directly realizes an error-free 2-D DCT without using FRSs between row-column transforms, leading to an 8×8 2-D DCT which is entirely free of quantization er...

An area efficient row-parallel architecture is proposed for the real-time implementation of bivariate algebraic integer (AI) encoded 2-D discrete cosine transform (DCT) for image and video processing. The proposed architecture computes 8×8 2-D DCT transform based on the Arai DCT algorithm. An improved fast algorithm for AI based 1-D DCT computation is proposed along with a single channel 2-D DC...

In this paper, one-dimensional (1-D) fast 8 8 inverse integer transform algorithm for Windows Media Video 9 (WMV-9/VC-1) is proposed. Based on the symmetric property of the integer transform matrix and the matrix operations, which denote the row/column permutations and the matrix decompositions, the efficient fast 1-D 8 8 inverse integer transform is developed. Therefore, the computational comp...

The use of large N approximations to treat strongly interacting quantum systems been very extensive in the last decade. The approach originated in elementary particles theory, but has found many applications in condensed matter physics. Initially, the large N expansion was developed for the Kondo and Anderson models of magnetic impurities in metals. Soon thereafter it was extended to the Kondo ...

We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erd˝ os-Rényi random graphs [5, 6], vertex random graphs are generalizations of geometric random graphs [16], and vertex-edge random graphs generalize both. The names of these three types of random graphs describe where the randomness in the models lies: in...

Let LD8(1, 0) and LE8(1, 0) be the simple vertex operator algebras associated to untwisted affine Lie algebra ĝD8 and ĝE8 with level 1 respectively. In the 1980s by I. Frenkel, Lepowsky and Meurman as one of the many important preliminary steps toward their construction of the moonshine module vertex operator algebra, they use roots lattice showing that LD8(1, 0) can embed into LE8(1, 0) as a v...