Latin transversals of rectangular arrays

Let m and n be integers, $2 \leq m \leq n$. An m by n array consists of mn cells, arranged in m rows and n columns, and each cell contains exactly one symbol. A transversal of an array consists of m cells, one from each row and no two from the same column. A latin transversal is a transversal in which no symbol appears more than once. We will establish a sufficient condition that a 3 by n array has a latin transversal.Comment: Theorem 4 has been added, which provides a lower bound on L(m,n

Gresham\u27s Law: Algorithm Drives Out Thought

Gresham\u27s law in economics states, Bad money drives good money out of circulation. An application of this law in mathematical pedagogy states that Algorithm drives out thought. While universities are ideally places where classes are meant to develop students\u27 independence and critical thinking skills, often mathematics courses reflect this altered version of Gresham\u27s law. This paper demonstrates the ways traditional mathematical pedagogy has held up Gresham\u27s law and presents several suggestions for ways to change this approach to mathematical education to focus more on critical thinking without sacrificing the necessity of algorithm

MR-Guided Focused Ultrasound Versus Radiofrequency Capsulotomy for Treatment-Refractory Obsessive-Compulsive Disorder: A Cost-Effectiveness Threshold Analysis

Meta-analytic techniques support neuroablation as a promising therapy for treatment-refractory obsessive-compulsive disorder (OCD). This technique appears to offer a more favorable complication rate and higher utility than deep brain stimulation. Moreover, these pooled findings suggest that bilateral radiofrequency (RF) capsulotomy has marginally greater efficacy than stereotactic radiosurgery or cingulotomy. MR-guided focused ultrasound (MRgFUS) capsulotomy is an emerging approach with a potentially more favorable profile than RF ablation and radiosurgery, with preliminary data suggesting safety and efficacy. As a clinical trial is being developed, our study examined the cost and clinical parameters necessary for MRgFUS capsulotomy to be a more cost-effective alternative to RF capsulotomy. A decision analytical model of MRgFUS with RF capsulotomy for OCD was performed using outcome parameters of percent surgical improvement in Yale-Brown Obsessive Compulsive Scale (Y-BOCS) score, complications, and side effects. The analysis compared measured societal costs, derived from Medicare reimbursement rates, and effectiveness, based on published RF data. Effectiveness was defined as the degree to which MRgFUS lowered Y-BOCS score. Given that MRgFUS is a new therapy for OCD with scant published data, theoretical risks of MRgFUS capsulotomy were derived from published essential tremor outcomes. Sensitivity analysis yielded cost, effectiveness, and complication rates as critical MRgFUS parameters defining the cost-effectiveness threshold. Literature search identified eight publications (162 subjects). The average reduction of preoperative Y-BOCS score was 56.6% after RF capsulotomy with a 22.6% improvement in utility, a measure of quality of life. Complications occurred in 16.2% of RF cases. In 1.42% of cases, complications were considered acute-perioperative and incurred additional hospitalization cost. The adverse events, including neurological and neurobehavioral changes, in the other 14.8% of cases did not incur further costs, although they impacted utility. Rollback analysis of RF capsulotomy yielded an expected effectiveness of 0.212 quality-adjusted life years/year at an average cost of $24,099. Compared to RF capsulotomy, MRgFUS was more cost-effective under a range of possible cost and complication rates. While further study will be required, MRgFUS lacks many of the inherent risks associated with more invasive modalities and has potential as a safe and cost-effective treatment for OCD

Spintronics: Fundamentals and applications

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.Comment: invited review, 36 figures, 900+ references; minor stylistic changes from the published versio