Anycast is widely used in critical Internet infrastructures, including root DNS servers, to improve their scalability, resilience, and geographic proximity to clients. In practice, anycast depends on interdomain routing to direct clients to their “closest” sites. As a result, anycast’s performance is largely a result of available BGP routes. We provide what we believe to be the first longitudin...

Lemma 2.2. It suffices to find disjoint L,R ∈ V such that they are (1) Large in Ω(n), or more formally stated, |L||R| ≥ α(n). (2) ∆-separated for ∆ = Ω( 1 logn) Let us define what ∆-separated means so that we can formalize this notion of “farness”. Recall that a distance from a vertex i to a set S is defined as d(i, S) = minj∈S d(i, j) (distance to the closest point in the set) and a distance f...

Finding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(n logn) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum)...

Inoculation of mice on the cornea with herpes simplex virus, type I, results in demyelination of central nervous system (CNS) axons at the trigeminal root entry zone. This study examined the process of remyelination in this area. Between eight and 15 days after corneal infection, increasing numbers of Schwann cells appeared on the CNS side of the trigeminal root entry zone, where they encircled...

The minimal folding pathway or trajectory for a biopolymer can be defined as the transformation that minimizes the total distance traveled between a folded and an unfolded structure. This involves generalizing the usual Euclidean distance from points to one-dimensional objects such as a polymer. We apply this distance here to find minimal folding pathways for several candidate protein fragments...

It has been reported that coronary atherosclerosis risk assessment using coronary artery calcium and thoracic aorta calcium quantification may improve risk stratification as it can lead to the reclassification of persons at increased risk. The aortic root has been characterized by its close anatomical proximity to the ostial origins of the right and left coronary arteries, and it can be evaluat...

Premature ventricular contractions (PVCs) or ventricular tachycardia (VT), with QRS morphologies of left bundle branch block (LBBB) and inferior axis can be ablated successfully from the right ventricular outflow tract (RVOT). However, it is not uncommon that PVCs or VT assumed to originate from the RVOT actually arise from the aortic root because of the proximity of the RVOT to the aortic root...

Root and Variaya proved the existence of codes that can communicate reliably over any linear Gaussian channel for which the mutual information exceeds the information rate of the code. In this paper we demonstrate that properly designed Low-Density Parity-Check (LDPC) codes are such codes and that their performance lies in close proximity to the Root and Variaya capacity for the linear Gaussian...