The square root rank of a nonnegative matrix A is the minimum rank of a matrix B such that A = B ◦B, where ◦ denotes entrywise product. We show that the square root rank of the slack matrix of the correlation polytope is exponential. Our main technique is a way to lower bound the rank of certain matrices under arbitrary sign changes of the entries using properties of the roots of polynomials in...

Four thyroid function indices were determined in the sera of 181 patients: total thyroxine (T-4), the triiodothyronine resin uptake (T-3 B.C.-index), the free thyroxine (T-4) index, and the effective thyroxine ratio (E.T.R.).A statistically significant correlation between the free T-4 index and E.T.R. could be established though this correlation seemed to be worse than could be expected from th...

BACKGROUND The rank correlation test introduced by Begg and Mazumdar is extensively used in meta-analysis to test for publication bias in clinical and epidemiological studies. It is based on correlating the standardized treatment effect with the variance of the treatment effect using Kendall's tau as the measure of association. To our knowledge, the operational characteristics regarding the sig...

The receptor activator of nuclear factor κB ligand (RANKL)/RANK pathway plays an important role in the prognosis of several solid tumor types, but its role in gastric cancer prognosis has been poorly characterized. A total of 116 gastric cancer patients who underwent surgical resection were enrolled in this study. Expressions of RANKL and RANK in gastric cancer tissues were detected using immun...

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (i) definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (ii) generation of samples from uncertain analysis inputs, (iii) propagation of sampled inputs through an analysis, (iv) presentation of uncertainty analysis results, and (v) deter...

We consider the following problem: given two matrices A and B, find a rank-r approximation of their product ATB. This type of linear algebra problem has many applications in the machine learning and statistics domain. For example, if A = B, then this general problem reduces to the well-known problem of finding principal components of a given data matrix. Another example is the low-rank approxim...

Classification algorithm selection is an important issue in many disciplines. Since it normally involves more than one criterion, the task of algorithm selection can be modeled as multiple criteria decision making (MCDM) problems. Different MCDM methods evaluate classifiers from different aspects and thus they may produce divergent rankings of classifiers. The goal of this paper is to propose a...