Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

We develop a framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world networks) while still guaranteeing approximation ratios. The idea is to edit a given graph via vertex- or edge-deletions to put the graph into an algorithmically tractable class, apply known approximation algorithms for that class, and then lift the solution to apply to the original graph. We give a general characterization of when an optimization problem is amenable to this approach, and show that it includes many well-studied graph problems, such as Independent Set, Vertex Cover, Feedback Vertex Set, Minimum Maximal Matching, Chromatic Number, (l-)Dominating Set, Edge (l-)Dominating Set, and Connected Dominating Set. To enable this framework, we develop new editing algorithms that find the approximately-fewest edits required to bring a given graph into one of a few important graph classes (in some cases these are bicriteria algorithms which simultaneously approximate both the number of editing operations and the target parameter of the family). For bounded degeneracy, we obtain an O(r log{n})-approximation and a bicriteria (4,4)-approximation which also extends to a smoother bicriteria trade-off. For bounded treewidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w}))-approximation, and for bounded pathwidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w} * log n))-approximation. For treedepth 2 (related to bounded expansion), we obtain a 4-approximation. We also prove complementary hardness-of-approximation results assuming P != NP: in particular, these problems are all log-factor inapproximable, except the last which is not approximable below some constant factor 2 (assuming UGC)

Embolic strokes of undetermined source: prevalence and patient features in the ESUS Global Registry

Background: Recent evidence supports that most non-lacunar cryptogenic strokes are embolic. Accordingly, these strokes have been designated as embolic strokes of undetermined source (ESUS). Aims: We undertook an international survey to characterize the frequency and clinical features of ESUS patients across global regions. Methods: Consecutive patients hospitalized for ischemic stroke were retrospectively surveyed from 19 stroke research centers in 19 different countries to collect patients meeting criteria for ESUS. Results: Of 2144 patients with recent ischemic stroke, 351 (16%, 95% CI 15% to 18%) met ESUS criteria, similar across global regions (range 16% to 21%), and an additional 308 (14%) patients had incomplete evaluation required for ESUS diagnosis. The mean age of ESUS patients (62 years; SD = 15) was significantly lower than the 1793 non-ESUS ischemic stroke patients (68 years, p ≤ 0.001). Excluding patients with atrial fibrillation (n = 590, mean age = 75 years), the mean age of the remaining 1203 non-ESUS ischemic stroke patients was 64 years (p = 0.02 vs. ESUS patients). Among ESUS patients, hypertension, diabetes, and prior stroke were present in 64%, 25%, and 17%, respectively. Median NIHSS score was 4 (interquartile range 2–8). At discharge, 90% of ESUS patients received antiplatelet therapy and 7% received anticoagulation. Conclusions: This cross-sectional global sample of patients with recent ischemic stroke shows that one-sixth met criteria for ESUS, with additional ESUS patients likely among those with incomplete diagnostic investigation. ESUS patients were relatively young with mild strokes. Antiplatelet therapy was the standard antithrombotic therapy for secondary stroke prevention in all global regions

Levy Anomalous Diffusion and Fractional Fokker--Planck Equation

We demonstrate that the Fokker-Planck equation can be generalized into a 'Fractional Fokker-Planck' equation, i.e. an equation which includes fractional space differentiations, in order to encompass the wide class of anomalous diffusions due to a Levy stable stochastic forcing. A precise determination of this equation is obtained by substituting a Levy stable source to the classical gaussian one in the Langevin equation. This yields not only the anomalous diffusion coefficient, but a non trivial fractional operator which corresponds to the possible asymmetry of the Levy stable source. Both of them cannot be obtained by scaling arguments. The (mono-) scaling behaviors of the Fractional Fokker-Planck equation and of its solutions are analysed and a generalization of the Einstein relation for the anomalous diffusion coefficient is obtained. This generalization yields a straightforward physical interpretation of the parameters of Levy stable distributions. Furthermore, with the help of important examples, we show the applicability of the Fractional Fokker-Planck equation in physics.Comment: 22 pages; To Appear in Physica

Leg Injury - World Champion Super-Heavyweight Weightlifter

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A psycho-educational curriculum for sport career transition practitioners: Development and evaluation

Research question: This paper is an integration of three studies. Study 1 investigates sport career transition organisational intervention programmes for high performance athletes and training and development programmes for sport career transition practitioners in order to find a research gap with regard to sport career transition supporting services. A psycho-educational curriculum was developed for sport career transition practitioner in Study 2 to fill the research gap. In Study 3, the curriculum was examined to see if the curriculum contributed to enhancing practitioners’ confidence in key competences.  Research methods: A range of methods were applied to the studies including One Group Pre- and Post-test design, Case Study, Focus Group, Semi-Structured Interview, two-round Delphi-Method and Questionnaires. The data for Study 1 collected from 19 countries worldwide and total 16 participants based in seven different countries were invited to development and evaluation of the curriculum.  Results and Findings: A novel psycho-educational curriculum for sport career transition practitioner was developed and evaluated concerning four competences as a form of curriculum package. The findings revealed that the curriculum package increased the participants’ confidence in key competences concerning sport career transition.  Implications: The findings deepen the knowledge of sport career transition in the areas of organisational intervention programmes focusing on high performance athletes and sport career transition practitioners. These findings contribute to modifying the Conceptual Model of Adaptation to Career Transition (Lavallee, Park, & Taylor, 2014) by strengthening the organisational intervention perspective and applied work in respect of sporting organisation management strategie

Overlapping and Robust Edge-Colored Clustering in Hypergraphs

A recent trend in data mining has explored (hyper)graph clustering algorithms for data with categorical relationship types. Such algorithms have applications in the analysis of social, co-authorship, and protein interaction networks, to name a few. Many such applications naturally have some overlap between clusters, a nuance which is missing from current combinatorial models. Additionally, existing models lack a mechanism for handling noise in datasets. We address these concerns by generalizing Edge-Colored Clustering, a recent framework for categorical clustering of hypergraphs. Our generalizations allow for a budgeted number of either (a) overlapping cluster assignments or (b) node deletions. For each new model we present a greedy algorithm which approximately minimizes an edge mistake objective, as well as bicriteria approximations where the second approximation factor is on the budget. Additionally, we address the parameterized complexity of each problem, providing FPT algorithms and hardness results