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A set <i>G</i> of points on a 1.5-dimensional terrain, also known as an <i>x</i>-monotone polygonal chain, is said to guard the terrain if every point on the terrain is seen by a point in <i>G</i>. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. The minimum terrain guarding problem(More)
Slowed myocardial conduction velocity (θ) is associated with an increased risk of re-entrant excitation, predisposing to cardiac arrhythmia. θ is determined by the ion channel and physical properties of cardiac myocytes and by their interconnections. Thus, θ is closely related to the maximum rate of action potential (AP) depolarization [(dV/dt)max], as(More)
AIMS Recent studies reported slowed conduction velocity (CV) in murine hearts homozygous for the gain-of-function RyR2-P2328S mutation (RyR2(S/S)) and associated this with an increased incidence of atrial and ventricular arrhythmias. The present experiments determined mechanisms contributing to the reduced atrial CV. METHODS AND RESULTS The determinants(More)
We provide an O(log log OPT)-approximation algorithm for the problem of guarding a simple polygon with guards on the perimeter. We first design a polynomial-time algorithm for building ε-nets of size O 1 ε log log 1 ε for the instances of Hitting Set associated with our guarding problem. We then apply the technique of Brönnimann and Goodrich to build an(More)
A guarding problem can naturally be modeled as a set system (U, S) in which the universe U of elements is the set of points we need to guard and our collection S of sets contains, for each potential guard g, the set of points from U seen by g. We prove bounds on the maximum VC-dimension of set systems associated with guarding both 1.5D terrains (monotone(More)
A hyperplane search tree is a binary tree used to store a set S of n d-dimensional data points. In a random hyperplane search tree for S, the root represents a hyperplane defined by d data points drawn uniformly at random from S. The remaining data points are split by the hyperplane, and the definition is used recursively on each subset. We assume that the(More)
Let P : R d → A be a query problem over R d for which there exists a data structure S that can compute P(q) in O(log n) time for any query point q ∈ R d. Let D be a probability measure over R d representing a distribution of queries. We describe a data structure T = T P,D , called the odds-on tree, of size O(n) that can be used as a filter that quickly(More)
Alterations in ECG QT intervals correlate with the risk of potentially fatal arrhythmias, for which transgenic murine hearts are becoming increasingly useful experimental models. However, QT intervals are poorly defined in murine ECGs. As a consequence, several different techniques have been used to measure murine QT intervals. The present work develops a(More)