Hotelling's T2 vs. the Rank Transform With Real Likert Data

Hotelling ' s T 2 VS . The Rank Transform With Real Likert Data

The Reduced Rank Transform Square Root Filter for Data Assimilation

During the last decade, several suboptimal filtering schemes for data assimilation have been proposed. One of these algorithms, which has succesfully been used in several applications, is the Reduced Rank Square Root filter. In this paper, a numerically more efficient variation, the Reduced Rank Transform Square Root filter, is introduced. A theoretical comparison of both filters is given and t...

Nonnegative Rank vs. Binary Rank

Motivated by (and using tools from) communication complexity, we investigate the relationship between the following two ranks of a 0-1 matrix: its nonnegative rank and its binary rank (the log of the latter being the unambiguous nondeterministic communication complexity). We prove that for partial 0-1 matrices, there can be an exponential separation. For total 0-1 matrices, we show that if the ...

Combined Reduced-Rank Transform

We propose and justify a new approach to constructing optimal nonlinear transforms of random vectors. We show that the proposed transform improves such characteristics of rank-reduced transforms as compression ratio, accuracy of decompression and reduces required computational work. The proposed transform Tp is presented in the form of a sum with p terms where each term is interpreted as a part...

MR Spin Behavior During RF Pulses: T2 vs. T2' Relaxation

Introduction: We investigate the behavior of the MR magnetization vector during RF pulses in the presence of rapid transverse relaxation. The transverse relaxation is divided into two separate mechanisms: Homogeneously broadened lines which resulting in irreversible T2 amplitude decay, and inhomogeneously broadened lines resulting in dephasing and in principle refocusable T2’. While the two dif...