The floodlight problem

Given three angles summing to 2, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specied angles not exceeding can be placed at n xed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2. We give O(n log n) algorithms for both these problems

Locked and Unlocked Polygonal Chains in 3D

In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a simple orthogonal projection onto some plane, it can be straightened. For closed chains, we show that there are unknotted but locked closed chains, and we provide an algorithm for convexifying a planar simple polygon in 3D with a polynomial number of moves

Testing for Network and Spatial Autocorrelation

Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in continuous variables. In this paper we propose two contributions to the literature on tests for autocorrelation. First, we propose a new test for autocorrelation in categorical variables. While some methods currently exist for assessing spatial autocorrelation in categorical variables, the most popular method is unwieldy, somewhat ad hoc, and fails to provide grounds for a single omnibus test. Second, we discuss the importance of testing for autocorrelation in data sampled from the nodes of a network, motivated by social network applications. We demonstrate that our proposed statistic for categorical variables can both be used in the spatial and network setting

A cluster of blood-based protein biomarkers associated with decreased cerebral blood flow relates to future cardiovascular events in patients with cardiovascular disease

Biological processes underlying decreased cerebral blood flow (CBF) in patients with cardiovascular disease (CVD) are largely unknown. We hypothesized that identification of protein clusters associated with lower CBF in patients with CVD may explain underlying processes. In 428 participants (74% cardiovascular diseases; 26% reference participants) from the Heart-Brain Connection Study, we assessed the relationship between 92 plasma proteins from the Olink® cardiovascular III panel and normal-appearing grey matter CBF, using affinity propagation and hierarchical clustering algorithms, and generated a Biomarker Compound Score (BCS). The BCS was related to cardiovascular risk and observed cardiovascular events within 2-year follow-up using Spearman correlation and logistic regression. Thirteen proteins were associated with CBF (ρSpearman range: −0.10 to −0.19, pFDR-corrected &lt;0.05), and formed one cluster. The cluster primarily reflected extracellular matrix organization processes. The BCS was higher in patients with CVD compared to reference participants (pFDR-corrected &lt;0.05) and was associated with cardiovascular risk (ρSpearman 0.42, p &lt; 0.001) and cardiovascular events (OR 2.05, p &lt; 0.01). In conclusion, we identified a cluster of plasma proteins related to CBF, reflecting extracellular matrix organization processes, that is also related to future cardiovascular events in patients with CVD, representing potential targets to preserve CBF and mitigate cardiovascular risk in patients with CVD.</p