Approximating Subadditive Hadamard Functions on Implicit Matrices

An important challenge in the streaming model is to maintain small-space approximations of entrywise functions performed on a matrix that is generated by the outer product of two vectors given as a stream. In other works, streams typically define matrices in a standard way via a sequence of updates, as in the work of Woodruff (2014) and others. We describe the matrix formed by the outer product, and other matrices that do not fall into this category, as implicit matrices. As such, we consider the general problem of computing over such implicit matrices with Hadamard functions, which are functions applied entrywise on a matrix. In this paper, we apply this generalization to provide new techniques for identifying independence between two vectors in the streaming model. The previous state of the art algorithm of Braverman and Ostrovsky (2010) gave a $(1 \pm \epsilon)$-approximation for the $L_1$ distance between the product and joint distributions, using space $O(\log^{1024}(nm) \epsilon^{-1024})$, where $m$ is the length of the stream and $n$ denotes the size of the universe from which stream elements are drawn. Our general techniques include the $L_1$ distance as a special case, and we give an improved space bound of $O(\log^{12}(n) \log^{2}({nm \over \epsilon})\epsilon^{-7})$

Corporal Punishment - Schools and School Districts - Constitutional Law

The United States District Court for the Western District of Pennsylvania has held that the infliction of corporal punishment on a child by school authorities against the expressed wishes of a parent is violative of a fundamental right of parental liberty. Glaser v. Marietta, 351 F. Supp. 555 (W.D. Pa. 1972)

Zero-One Laws for Sliding Windows and Universal Sketches

Given a stream of data, a typical approach in streaming algorithms is to design a sophisticated algorithm with small memory that computes a specific statistic over the streaming data. Usually, if one wants to compute a different statistic after the stream is gone, it is impossible. But what if we want to compute a different statistic after the fact? In this paper, we consider the following fascinating possibility: can we collect some small amount of specific data during the stream that is "universal," i.e., where we do not know anything about the statistics we will want to later compute, other than the guarantee that had we known the statistic ahead of time, it would have been possible to do so with small memory? This is indeed what we introduce (and show) in this paper with matching upper and lower bounds: we show that it is possible to collect universal statistics of polylogarithmic size, and prove that these universal statistics allow us after the fact to compute all other statistics that are computable with similar amounts of memory. We show that this is indeed possible, both for the standard unbounded streaming model and the sliding window streaming model

Spontaneous coronary artery dissection complicated by left ventricular free wall rupture in Turner syndrome

A 38-year-old with Turner syndrome presented with acute myocardial infarction due to multivessel spontaneous coronary artery dissection (SCAD) complicated by left ventricular free wall rupture. Conservative management for SCAD was pursued. She underwent sutureless repair for an oozing-type left ventricular free wall rupture. SCAD has not been previously reported in Turner syndrome.

Comparative risks of initial aortic events associated with genetic thoracic aortic disease

BACKGROUND: Pathogenic variants in 11 genes predispose individuals to heritable thoracic aortic disease (HTAD), but limited data are available to stratify the risk for aortic events associated with these genes. OBJECTIVES: This study sought to compare the risk of first aortic event, specifically thoracic aortic aneurysm surgery or an aortic dissection, among 7 HTAD genes and variant types within each gene. METHODS: A retrospective cohort of probands and relatives with rare variants in 7 genes for HTAD (n = 1,028) was assessed for the risk of first aortic events based on the gene altered, pathogenic variant type, sex, proband status, and location of recruitment. RESULTS: Significant differences in aortic event risk were identified among the smooth muscle contraction genes (ACTA2, MYLK, and PRKG1; P = 0.002) and among the genes for Loeys-Dietz syndrome, which encode proteins in the transforming growth factor (TGF)-β pathway (SMAD3, TGFB2, TGFBR1, and TGFBR2;P \u3c 0.0001). Cumulative incidence of type A aortic dissection was higher than elective aneurysm surgery in patients with variants in ACTA2, MYLK, PRKG1, and SMAD3; in contrast, patients with TGFBR2 variants had lower cumulative incidence of type A aortic dissection than elective aneurysm surgery. Cumulative incidence of type B aortic dissection was higher for ACTA2, PRKG1, and TGFBR2 than other genes. After adjusting for proband status, sex, and recruitment location, specific variants in ACTA2 and TGFBR2 were associated with substantially higher risk of aortic event with childhood onset. CONCLUSIONS: Gene- and variant-specific data on aortic events in individuals with HTAD support personalized aortic surveillance and clinical management

Letter by Harris et al regarding article, outcomes of patients with acute type a aortic intramural hematoma

Comment on Outcomes of patients with acute type a aortic intramural hematoma

Performance analysis of d-dimensional quantum cryptography under state-dependent diffraction

Standard protocols for quantum key distribution (QKD) require that the sender be able to transmit in two or more mutually unbiased bases. Here, we analyze the extent to which the performance of QKD is degraded by diffraction effects that become relevant for long propagation distances and limited sizes of apertures. In such a scenario, different states experience different amounts of diffraction, leading to state-dependent loss and phase acquisition, causing an increased error rate and security loophole at the receiver. To solve this problem, we propose a pre-compensation protocol based on pre-shaping the transverse structure of quantum states. We demonstrate, both theoretically and experimentally, that when performing QKD over a link with known, symbol-dependent loss and phase shift, the performance of QKD will be better if we intentionally increase the loss of certain symbols to make the loss and phase shift of all states same. Our results show that the pre-compensated protocol can significantly reduce the error rate induced by state-dependent diffraction and thereby improve the secure key rate of QKD systems without sacrificing the security.Comment: 10 pages, 6 figure

Decision Counseling in Prostate Cancer Screening

No abstract available