Some Results on Majorization of Matrices

For two n×m real matrices X and Y, X is said to be majorized by Y, written as X≺Y if X=SY for some doubly stochastic matrix of order n. Matrix majorization has several applications in statistics, wireless communications and other fields of science and engineering. Hwang and Park obtained the necessary and sufficient conditions for X,Y to satisfy X≺Y for the cases where the rank of Y=n−1 and the rank of Y=n. In this paper, we obtain some necessary and sufficient conditions for X,Y to satisfy X≺Y for the cases where the rank of Y=n−2 and in general for rank of Y=n−k, where 1≤k≤n−1. We obtain some necessary and sufficient conditions for X to be majorized by Y with some conditions on X and Y. The matrix X is said to be doubly stochastic majorized by Y if there is S∈Ωm such that X=YS. In this paper, we obtain some necessary and sufficient conditions for X to be doubly stochastic majorized by Y. We introduced a new concept of column stochastic majorization in this paper. A matrix X is said to be column stochastic majorized by Y, denoted as X⪯cY, if there exists a column stochastic matrix S such that X=SY. We give characterizations of column stochastic majorization and doubly stochastic majorization for (0,1) matrices

Augmented reality assistance for aging people:a systematic literature review

Abstract The development of Augmented Reality is becoming robust and matured by the combination of real-time performance with virtual information. With the proliferating geriatric population, the benefits of AR systems can be suitably harnessed for supporting the elderly in home activities, mobility and entertainment, among others. Hence, the development of AR to assist aging population is now feasible, but an overview of the existing research is not yet attempted. The objective of this systematic literature review is to provide the detail technical progress on the current situation of AR application and reviews the different domains using AR for supporting the ageing population. Search was conducted on five databases including Scopus, IEEE Xplore, Science Direct, ACM Digital Library and Springer Link.350 papers were initially searched and after detail study 71 were selected for the review. To conclude, the review proposed six components to be noted when developing new AR applications for the elderly

A Tablet-Based Tool for Accurate Measurement of Hand Proprioception After Stroke

Background and Purpose: Proprioceptive deficits in the hand are common following stroke, but current clinical measurement techniques are too imprecise to detect subtle impairments or small changes. We developed a tablet-based tool to measure static hand proprioception using an adaptive staircase procedure. Methods: In 16 individuals with chronic stroke and age-matched controls, we quantified proprioception at the metacarpophalangeal joint of the index finger using 3 methods: the tablet task, a custom passive movement direction discrimination test (PMDD), and a manual assessment similar to the Fugl-Meyer (F-M) proprioception subsection. Results: The tablet-based measure and the PMDD both identified impaired proprioception in the affected hand relative to the unaffected hand (P = 0.024 and 0.028), and relative to the control group (P = 0.040 and 0.032), while manual assessment did not. The PMDD had a ceiling effect as movement excursions greater than 15^ were not biomechanically feasible. The tablet-based measure and the PMDD detected impaired proprioception in 56% to 75%, and the F-M in only 29%, of patients. PMDD and tablet-based measures were both correlated with primary tactile sensation, but not manual dexterity. Discussion and Conclusions: Both the tablet-based tool and the custom PMDD performed better than manual assessment. The PMDD may be useful when the deficit is mild or assessment of dynamic proprioception is desired. As the tablet-based measure does not have the ceiling effect that is associated with the PMDD, it may be useful with any level of proprioceptive impairment, and may be preferable if testing or clinician training time needs to be minimized, or pain or spasticity is present