Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $\epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/\epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-\epsilon)(m-k)$ demands

Attachment styles and personal growth following romantic breakups: The mediating roles of distress, rumination, and tendency to rebound

© 2013 Marshall et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.This article has been made available through the Brunel Open Access Publishing Fund.The purpose of this research was to examine the associations of attachment anxiety and avoidance with personal growth following relationship dissolution, and to test breakup distress, rumination, and tendency to rebound with new partners as mediators of these associations. Study 1 (N = 411) and Study 2 (N = 465) measured attachment style, breakup distress, and personal growth; Study 2 additionally measured ruminative reflection, brooding, and proclivity to rebound with new partners. Structural equation modelling revealed in both studies that anxiety was indirectly associated with greater personal growth through heightened breakup distress, whereas avoidance was indirectly associated with lower personal growth through inhibited breakup distress. Study 2 further showed that the positive association of breakup distress with personal growth was accounted for by enhanced reflection and brooding, and that anxious individuals’ greater personal growth was also explained by their proclivity to rebound. These findings suggest that anxious individuals’ hyperactivated breakup distress may act as a catalyst for personal growth by promoting the cognitive processing of breakup-related thoughts and emotions, whereas avoidant individuals’ deactivated distress may inhibit personal growth by suppressing this cognitive work

Photonic quantum technologies

The first quantum technology, which harnesses uniquely quantum mechanical effects for its core operation, has arrived in the form of commercially available quantum key distribution systems that achieve enhanced security by encoding information in photons such that information gained by an eavesdropper can be detected. Anticipated future quantum technologies include large-scale secure networks, enhanced measurement and lithography, and quantum information processors, promising exponentially greater computation power for particular tasks. Photonics is destined for a central role in such technologies owing to the need for high-speed transmission and the outstanding low-noise properties of photons. These technologies may use single photons or quantum states of bright laser beams, or both, and will undoubtably apply and drive state-of-the-art developments in photonics

Waist circumference, abdominal obesity, and depression among overweight and obese U.S. adults: national health and nutrition examination survey 2005-2006

<p>Abstract</p> <p>Background</p> <p>Obesity is associated with an increased risk of mental illness; however, evidence linking body mass index (BMI)-a measure of overall obesity, to mental illness is inconsistent. The objective of this study was to examine the association of depressive symptoms with waist circumference or abdominal obesity among overweight and obese U.S. adults.</p> <p>Methods</p> <p>A cross-sectional, nationally representative sample from the 2005-2006 National Health and Nutrition Examination Survey was used. We analyzed the data from 2,439 U.S. adults (1,325 men and 1,114 nonpregnant women) aged ≥ 20 years who were either overweight or obese with BMI of ≥ 25.0 kg/m². Abdominal obesity was defined as waist circumference of > 102 cm for men and > 88 cm for women. Depressive symptoms (defined as having major depressive symptoms or moderate-to-severe depressive symptoms) were assessed by the Patient Health Questionnaire-9 diagnostic algorithm. The prevalence and the odds ratios (ORs) with 95% confidence intervals (CIs) for having major depressive symptoms and moderate-to-severe depressive symptoms were estimated using logistic regression analysis.</p> <p>Results</p> <p>After multivariate adjustment for demographics and lifestyle factors, waist circumference was significantly associated with both major depressive symptoms (OR: 1.03, 95% CI: 1.01-1.05) and moderate-to-severe depressive symptoms (OR: 1.02, 95% CI: 1.01-1.04), and adults with abdominal obesity were significantly more likely to have major depressive symptoms (OR: 2.18, 95% CI: 1.35-3.59) or have moderate-to-severe depressive symptoms (OR: 2.56, 95% CI: 1.34-4.90) than those without. These relationships persisted after further adjusting for coexistence of multiple chronic conditions and persisted in participants who were overweight (BMI: 25.0-< 30.0 kg/m²) when stratified analyses were conducted by BMI status.</p> <p>Conclusion</p> <p>Among overweight and obese U.S. adults, waist circumference or abdominal obesity was significantly associated with increased likelihoods of having major depressive symptoms or moderate-to-severe depressive symptoms. Thus, mental health status should be monitored and evaluated in adults with abdominal obesity, particularly in those who are overweight.</p

Analysis of protein-coding genetic variation in 60,706 humans

Large-scale reference data sets of human genetic variation are critical for the medical and functional interpretation of DNA sequence changes. Here we describe the aggregation and analysis of high-quality exome (protein-coding region) DNA sequence data for 60,706 individuals of diverse ancestries generated as part of the Exome Aggregation Consortium (ExAC). This catalogue of human genetic diversity contains an average of one variant every eight bases of the exome, and provides direct evidence for the presence of widespread mutational recurrence. We have used this catalogue to calculate objective metrics of pathogenicity for sequence variants, and to identify genes subject to strong selection against various classes of mutation; identifying 3,230 genes with near-complete depletion of predicted protein-truncating variants, with 72% of these genes having no currently established human disease phenotype. Finally, we demonstrate that these data can be used for the efficient filtering of candidate disease-causing variants, and for the discovery of human 'knockout' variants in protein-coding genes