Properties of Bayes Sequential Tests

Consider the problem of sequentially testing composite, contiguous hypotheses where the risk function is a linear combination of the probability of error in the terminal decision and the expected sample size. Assume that the common boundary of the closures of the null and the alternative hypothesis is compact. Observations are independent and identically distributed. We study properties of Bayes tests. One property is the exponential boundedness of the stopping time. Another property is continuity of the risk functions. The continuity property is used to establish complete class theorems as opposed to the essentially complete class theorems in Brown, Cohen and Strawderman

Bounded Stopping Times for a Class of Sequential Bayes Tests

Consider the problem of sequentially testing a null hypothesis vs an alternative hypothesis when the risk function is a linear combination of probability of error in the terminal decision and expected sample size (i.e., constant cost per observation.) Assume that the parameter space is the union of null and alternative, the parameter space is convex, the intersection of null and alternative is empty, and the common boundary of the closures of null and alternative is nonempty and compact. Assume further that observations are drawn from a p-dimensional exponential family with an open p-dimensional parameter space. Sufficient conditions for Bayes tests to have bounded stopping times are given

Anxiety and Depression During Childhood and Adolescence: Testing Theoretical Models of Continuity and Discontinuity

The present study sought to clarify the trajectory (i.e., continuous vs. discontinuous) and expression (i.e., homotypic vs. heterotypic) of anxiety and depressive symptoms across childhood and adolescence. We utilized a state-of-the-science analytic approach to simultaneously test theoretical models that describe the development of internalizing symptoms in youth. In a sample of 636 children (53% female; M age = 7.04; SD age = 0.35) self-report measures of anxiety and depression were completed annually by youth through their freshman year of high school. For both anxiety and depression, a piecewise growth curve model provided the best fit for the data, with symptoms decreasing until age 12 (the “developmental knot”) and then increasing into early adolescence. The trajectory of anxiety symptoms was best described by a discontinuous homotypic pattern in which childhood anxiety predicted adolescent anxiety. For depression, two distinct pathways were discovered: A discontinuous homotypic pathway in which childhood depression predicted adolescent depression and a discontinuous heterotypic pathway in which childhood anxiety predicted adolescent depression. Analytical, methodological, and clinical implications of these findings are discussed

Constant Approximation for kk-Median and kk-Means with Outliers via Iterative Rounding

In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon the large implicit constant approximation ratio of Chen [Chen, SODA 2018]. For $k$-means with outliers, we give an $(\alpha_2+\epsilon \leq 53.002 + \epsilon)$-approximation, which is the first $O(1)$-approximation for this problem. The iterative algorithm framework is very versatile; we show how it can be used to give $\alpha_1$- and $(\alpha_1 + \epsilon)$-approximation algorithms for matroid and knapsack median problems respectively, improving upon the previous best approximations ratios of $8$ [Swamy, ACM Trans. Algorithms] and $17.46$ [Byrka et al, ESA 2015]. The natural LP relaxation for the $k$-median/$k$-means with outliers problem has an unbounded integrality gap. In spite of this negative result, our iterative rounding framework shows that we can round an LP solution to an almost-integral solution of small cost, in which we have at most two fractionally open facilities. Thus, the LP integrality gap arises due to the gap between almost-integral and fully-integral solutions. Then, using a pre-processing procedure, we show how to convert an almost-integral solution to a fully-integral solution losing only a constant-factor in the approximation ratio. By further using a sparsification technique, the additive factor loss incurred by the conversion can be reduced to any $\epsilon > 0$

Exploration and exploitation in the presence of network externalities

This paper examines the conditions under which exploration of a new, incompatible technologyis conducive to firm growth in the presence of network externalities. In particular, this studyis motivated bythe divergent evolutions of the PC and the workstation markets in response to a new technology: reduced instruction set computing (RISC). In the PC market, Intel has developed new microprocessors bymaintaining compatibilitywith the established architecture, whereas it was radicallyr eplaced byRISC in the workstation market. History indicates that unlike the PC market, the workstation market consisted of a large number of power users, who are less sensitive to compatibilitythan ordinaryusers. Our numerical analysis indicates that the exploration of a new, incompatible technologyis more likelyto increase the chance of firm growth when there are a substantial number of power users or when a new technologyis introduced before an established technologytakes off. (; ; ;

Turning points: the personal and professional circumstances that lead academics to become middle managers

In the current higher education climate, there is a growing perception that the pressures associated with being an academic middle manager outweigh the perceived rewards of the position. This article investigates the personal and professional circumstances that lead academics to become middle managers by drawing on data from life history interviews undertaken with 17 male and female department heads from a range of disciplines, in a post-1992 UK university. The data suggests that experiencing conflict between personal and professional identities, manifested through different socialization experiences over time, can lead to a ‘turning point’ and a decision that affects a person’s career trajectory. Although the results of this study cannot be generalized, the findings may help other individuals and institutions move towards a firmer understanding of the academic who becomes head of department—in relation to theory, practice and research

NRG Oncology-Radiation Therapy Oncology Group Study 1014: 1-Year Toxicity Report From a Phase 2 Study of Repeat Breast-Preserving Surgery and 3-Dimensional Conformal Partial-Breast Reirradiation for In-Breast Recurrence.

PURPOSE: To determine the associated toxicity, tolerance, and safety of partial-breast reirradiation. METHODS AND MATERIALS: Eligibility criteria included in-breast recurrence occurring \u3e1 year after whole-breast irradiation, \u3c3 \u3ecm, unifocal, and resected with negative margins. Partial-breast reirradiation was targeted to the surgical cavity plus 1.5 cm; a prescription dose of 45 Gy in 1.5 Gy twice daily for 30 treatments was used. The primary objective was to evaluate the rate of grade ≥3 treatment-related skin, fibrosis, and/or breast pain adverse events (AEs), occurring ≤1 year from re-treatment completion. A rate of ≥13% for these AEs in a cohort of 55 patients was determined to be unacceptable (86% power, 1-sided α = 0.07). RESULTS: Between 2010 and 2013, 65 patients were accrued, and the first 55 eligible and with 1 year follow-up were analyzed. Median age was 68 years. Twenty-two patients had ductal carcinoma in situ, and 33 had invasive disease: 19 ≤1 cm, 13 \u3e1 to ≤2 cm, and 1 \u3e2 cm. All patients were clinically node negative. Systemic therapy was delivered in 51%. All treatment plans underwent quality review for contouring accuracy and dosimetric compliance. All treatment plans scored acceptable for tumor volume contouring and tumor volume dose-volume analysis. Only 4 (7%) scored unacceptable for organs at risk contouring and organs at risk dose-volume analysis. Treatment-related skin, fibrosis, and/or breast pain AEs were recorded as grade 1 in 64% and grade 2 in 7%, with only 1 ( CONCLUSION: Partial-breast reirradiation with 3-dimensional conformal radiation therapy after second lumpectomy for patients experiencing in-breast failures after whole-breast irradiation is safe and feasible, with acceptable treatment quality achieved. Skin, fibrosis, and breast pain toxicity was acceptable, and grade 3 toxicity was rare

Distinct signals and immune cells drive liver pathology and glomerulonephritis in ABIN1[D485N] mice

We report that TLR7, IL-6, and the adaptive immune system are essential for autoimmunity and glomerulonephritis but not for liver pathology in mice expressing the ubiquitin-binding-defective ABIN1[D485N] mutant. The blood and organs of ABIN1[D485N] mice have exceptionally high numbers of patrolling monocytes (pMo), which develop independently of IL-6 and the adaptive immune system. They are detectable in the blood months before autoimmunity and organ pathology are seen and may have diagnostic potential. The splenic pMo, inflammatory monocytes (iMo), and neutrophils of ABIN1[D485N] mice expressed high levels of mRNAs encoding proteins released during NETosis, which together with the high numbers of monocyte-derived dendritic cells (MoDCs) may drive the liver pathology in ABIN1[D485N] mice, and contribute to the pathology of other organs. The splenic iMo of ABIN1[D485N] mice displayed high expression of mRNAs encoding proteins controlling cell division and were actively dividing; this may underlie the increased pMo and MoDC numbers, which are derived from iMo. An orally active IRAK4 inhibitor suppressed all facets of the disease phenotype and prevented the increase in pMo numbers

Common evolutionary origin of acoustic communication in choanate vertebrates

Acoustic communication, broadly distributed along the vertebrate phylogeny, plays a fundamental role in parental care, mate attraction and various other behaviours. Despite its importance, comparatively less is known about the evolutionary roots of acoustic communication. Phylogenetic comparative analyses can provide insights into the deep time evolutionary origin of acoustic communication, but they are often plagued by missing data from key species. Here we present evidence for 53 species of four major clades (turtles, tuatara, caecilian and lungfish) in the form of vocal recordings and contextual behavioural information accompanying sound production. This and a broad literature-based dataset evidence acoustic abilities in several groups previously considered non-vocal. Critically, phylogenetic analyses encompassing 1800 species of choanate vertebrates reconstructs acoustic communication as a homologous trait, and suggests that it is at least as old as the last common ancestor of all choanate vertebrates, that lived approx. 407 million years before present