Analysis of Agglomerative Clustering

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarchy of approximate solutions to this problem (for all values of $k$) is the agglomerative clustering algorithm with the complete linkage strategy. For decades, this algorithm has been widely used by practitioners. However, it is not well studied theoretically. In this paper, we analyze the agglomerative complete linkage clustering algorithm. Assuming that the dimension $d$ is a constant, we show that for any $k$ the solution computed by this algorithm is an $O(\log k)$-approximation to the diameter $k$-clustering problem. Our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm. Furthermore, we analyze the closely related $k$-center and discrete $k$-center problem. For the corresponding agglomerative algorithms, we deduce an approximation factor of $O(\log k)$ as well.Comment: A preliminary version of this article appeared in Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS '11), March 2011, pp. 308-319. This article also appeared in Algorithmica. The final publication is available at http://link.springer.com/article/10.1007/s00453-012-9717-

The differential effects of concurrent planning practice elements on reunification and adoption

Objective: The child welfare practice of concurrent planning attempts to shorten children\u27s stays in foster care. There is very little quantitative research on concurrent planning\u27s effects. This study examines the influence of concurrent planning practice elements (reunification prognosis, concurrent plan, full disclosure, and discussion of voluntary relinquishment) on reunification and adoption. Method: Using a sample of 885 children, an observational design, and statistical controls, children who received concurrent planning elements were compared to those who did not. Results: Findings show discussion of voluntary relinquishment to be positively associated with adoption and full disclosure to be negatively associated with reunification. Conclusions: Concurrent planning\u27s benefits may require more intensive services to be fully realized. Care should be taken to ensure activities achieve their intended effects

Meta-analysis in more than 17,900 cases of ischemic stroke reveals a novel association at 12q24.12

Results: In an overall analysis of 17,970 cases of ischemic stroke and 70,764 controls, we identified a novel association on chromosome 12q24 (rs10744777, odds ratio [OR] 1.10 [1.07-1.13], p 5 7.12 3 10-11) with ischemic stroke. The association was with all ischemic stroke rather than an individual stroke subtype, with similar effect sizes seen in different stroke subtypes. There was no association with intracerebral hemorrhage (OR 1.03 [0.90-1.17], p 5 0.695).Conclusion: Our results show, for the first time, a genetic risk locus associated with ischemic stroke as a whole, rather than in a subtype-specific manner. This finding was not associated with intracerebral hemorrhage.Methods: Using the Immunochip, we genotyped 3,420 ischemic stroke cases and 6,821 controls. After imputation we meta-analyzed the results with imputed GWAS data from 3,548 case

Predicting Long Term Outcome in Patients Treated With Continuous Flow Left Ventricular Assist Device: The Penn—Columbia Risk Score

Background: Predicting which patients are unlikely to benefit from continuous flow left ventricular assist device (LVAD) treatment is crucial for the identification of appropriate patients. Previously developed scoring systems are limited to past eras of device or restricted to specific devices. Our objective was to create a risk model for patients treated with continuous flow LVAD based on the preimplant variables. Methods and Results: We performed a retrospective analysis of all patients implanted with a continuous flow LVAD between 2006 and 2014 at the University of Pennsylvania and included a total of 210 patients (male 78%; mean age, 56±15; mean follow‐up, 465±486 days). From all plausible preoperative covariates, we performed univariate Cox regression analysis for covariates affecting the odds of 1‐year survival following implantation (P<0.2). These variables were included in a multivariable model and dropped if significance rose above P=0.2. From this base model, we performed step‐wise forward and backward selection for other covariates that improved power by minimizing Akaike Information Criteria while maximizing the Harrell Concordance Index. We then used Kaplan–Meier curves, the log‐rank test, and Cox proportional hazard models to assess internal validity of the scoring system and its ability to stratify survival. A final optimized model was identified based on clinical and echocardiographic parameters preceding LVAD implantation. One‐year mortality was significantly higher in patients with higher risk scores (hazard ratio, 1.38; P=0.004). This hazard ratio represents the multiplied risk of death for every increase of 1 point in the risk score. The risk score was validated in a separate patient cohort of 260 patients at Columbia University, which confirmed the prognostic utility of this risk score (P=0.0237). Conclusion: We present a novel risk score and its validation for prediction of long‐term survival in patients with current types of continuous flow LVAD support

“God is Hidden in the Earthly Kingdom:” The Lutheran Two-Kingdoms Theory as Foundation of Scandavanian Secularity

Martin Luther’s signature “two kingdoms” teaching of the sixteenth century was an early and innovative theory of secularization that lies at the heart of historical Scandinavian culture. Defying the organic medieval models of Western Christendom, Luther separated the heavenly and earthly kingdoms, the saint and the sinner, faith and reason, church and the state, Gospel and the Law, as well as the spiritual and secular uses of law, government and authority. Though God is separated from day-to-day life, Luther wrote, God is still hidden in the earthly kingdom” and can be seen through various “masks,” “mists,” and “mimes.” Though the visible church is separated from the state and other institutions, religion remains pervasive in the common callings of every person to be God’s prophet, priest and king in every vocation and location of life. Luther’s two kingdoms theory is a complicated and controversial part of this thinking, but it is worth re-exploring today as pluralistic Scandinavia faces strong new pressures of both sacralization and secularization and seeks to discern anew “the hidden sacraliity of the secular.

ARIA 2016: Care pathways implementing emerging technologies for predictive medicine in rhinitis and asthma across the life cycle

The Allergic Rhinitis and its Impact on Asthma (ARIA) initiative commenced during a World Health Organization workshop in 1999. The initial goals were (1) to propose a new allergic rhinitis classification, (2) to promote the concept of multi-morbidity in asthma a