We give several criteria that are equivalent to the basic singular value majorization inequality (1.1) that is common to both the usual and Hadamard products. We then use these criteria to give a uniied proof of the basic majorization inequality for both products. Finally, we introduce natural generalizations of the usual and Hadamard products and show that although these generalizations do not...

Cell fate assignment in the nervous system of vertebrates and invertebrates often hinges on the unequal distribution of molecules during progenitor cell division. We address asymmetric fate determinant localization in the developing Drosophila nervous system, specifically the control of the polarized distribution of the cell fate adapter protein Miranda. We reveal a step-wise polarization of Mi...

Asymmetric division of Drosophila neuroblasts, sensory organ precursor cells, and cells in the procephalic neurogenic region involves the segregation of Numb and Prospero proteins into one of the two daughter cells. We have isolated a novel gene, miranda, based on the ability of its gene product to interact with the Prospero asymmetric localization domain. miranda expression coincides spatially...

Miranda warnings enshrine the constitutional rights of custodial suspects against self-incrimination. However, the wording and sentence complexity of Miranda warnings and waivers vary dramatically from jurisdiction to jurisdiction. This study is the first extensive investigation of Miranda warning variations examining 560 Miranda warnings from across the United States. With Flesch-Kincaid readi...

Moderated greedy search is based on the idea that it is helpful for greedy search algorithms to make non-optimal choices “once in a while.” This notion can be made precise by using the majorizationtheoretic approach to greedy algorithms. Majorization is the study of pre-orderings induced by doubly stochastic matrices. A majorization operator when applied to a distribution makes it “less unequal...

let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...

The appearance of Marshall and Olkin’s 1979 book on inequalities with special emphasis on majorization generated a surge of interest in potential applications of majorization and Schur convexity in a broad spectrum of fields. After 25 years this continues to be the case. The present article presents a sampling of the diverse areas in which majorization has been found to be useful in the past 25...

Given an approximate invariant subspace we discuss the effectiveness of majorization bounds for assessing the accuracy of the resulting Rayleigh-Ritz approximations to eigenvalues of Hermitian matrices. We derive a slightly stronger result than previously for the approximation of k extreme eigenvalues, and examine some advantages of these majorization bounds compared with classical bounds. From...

The adaptor protein Miranda plays a pivotal role in the asymmetric cell division of neuroblasts by asymmetrically segregating key differentiation factors. Miranda localization requires Myosin VI and Myosin II. The apical-then-basal localization pattern of Miranda detected in fixed tissue, and the localization defects in embryos lacking Myosin VI, suggest that Miranda is transported to the basal...