Toward the Universal Rigidity of General Frameworks

Let (G,P) be a bar framework of n vertices in general position in R^d, d <= n-1, where G is a (d+1)-lateration graph. In this paper, we present a constructive proof that (G,P) admits a positive semi-definite stress matrix with rank n-d-1. We also prove a similar result for a sensor network where the graph consists of m(>= d+1) anchors.Comment: v2, a revised version of an earlier submission (v1

On Sensor Network Localization Using SDP Relaxation

A Semidefinite Programming (SDP) relaxation is an effective computational method to solve a Sensor Network Localization problem, which attempts to determine the locations of a group of sensors given the distances between some of them [11]. In this paper, we analyze and determine new sufficient conditions and formulations that guarantee that the SDP relaxation is exact, i.e., gives the correct solution. These conditions can be useful for designing sensor networks and managing connectivities in practice. Our main contribution is twofold: We present the first non-asymptotic bound on the connectivity or radio range requirement of the sensors in order to ensure the network is uniquely localizable. Determining this range is a key component in the design of sensor networks, and we provide a result that leads to a correct localization of each sensor, for any number of sensors. Second, we introduce a new class of graphs that can always be correctly localized by an SDP relaxation. Specifically, we show that adding a simple objective function to the SDP relaxation model will ensure that the solution is correct when applied to a triangulation graph. Since triangulation graphs are very sparse, this is informationally efficient, requiring an almost minimal amount of distance information. We also analyze a number objective functions for the SDP relaxation to solve the localization problem for a general graph.Comment: 20 pages, 4 figures, submitted to the Fields Institute Communications Series on Discrete Geometry and Optimizatio

Developing Effective Questionnaire-Based Prediction Models for Type 2 Diabetes for Several Ethnicities

Background: Type 2 diabetes disproportionately affects individuals of non-white ethnicity through a complex interaction of multiple factors. Early disease prediction and detection is therefore essential and requires tools that can be deployed at large scale. We aimed to tackle this problem by developing questionnaire-based prediction models for type 2 diabetes for multiple ethnicities.Methods: Logistic regression models, using questionnaire-only features, were trained on the White population of the UK Biobank, and validated in five other ethnicities and externally in Lifelines. In total, 631,748 individuals were included for prevalence prediction and 67,083 individuals for the eight-year incidence prediction. Predictive accuracy was assessed and a detailed sensitivity analysis was conducted to assess potential clinical utility. Furthermore, we compared the questionnaire algorithms to clinical non-laboratory type 2 diabetes risk tools.Findings: Our algorithms accurately predicted type 2 diabetes prevalence (AUC=0·901) and eight-year incidence (AUC=0·873) in the White UK Biobank population. Both models replicate well in Lifelines, with AUCs of 0·917 and 0·817 for prevalence and incidence. Both models performed consistently well across ethnicities, with AUCs of 0·855 to 0·894 for prevalence and from 0·819 to 0·883 for incidence. These models generally outperformed two clinically validated non-laboratory tools and correctly reclassified &gt;3,000 type 2 diabetes cases. Model performance improved with the addition of blood biomarkers, but not with the addition of physical measurements.Interpretation: Easy-to-implement, questionnaire-based models can predict prevalent and incident type 2 diabetes with high accuracy across all ethnicities, providing a highly-scalable solution for population-wide risk stratification

der Georg-August-Universität zu Göttingen

landmark protein Bud8p links yeast cell polarity to translation. Submitted for publication