A note on maximally repeated sub-patterns of a point set

We answer a question raised by P. Brass on the number of maximally repeated sub-patterns in a set of $n$ points in \mathbbR^d. We show that this number, which was conjectured to be polynomial, is in fact $\Theta(2^n/2)$ in the worst case, regardless of the dimension $d$

A note on maximally repeated sub-patterns of a point set

International audienceWe answer a question raised by P. Brass on the number of maximally repeated sub-patterns in a set of $n$ points in $\mathbb{R}^d$. We show that this number, which was conjectured to be polynomial, is in fact $\Theta(2^{n/2})$ in the worst case, regardless of the dimension $d$

Farthest-Polygon Voronoi Diagrams

Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log^3 n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k-1 connected components, but if one component is bounded, then it is equal to the entire region

Geometric Permutations of Disjoint Unit Spheres

http://www.elsevier.com/locate/comgeoWe show that a set of $n$ disjoint unit spheres in $R^d$ admits at most two distinct geometric permutations if $n \geq 9$, and at most three if $3 \leq n \leq 8$. This result improves a Helly-type theorem on line transversals for disjoint unit spheres in $R^3$: if any subset of size $18$ of a family of such spheres admits a line transversal, then there is a line transversal for the entire family

Disjoint Unit Spheres Admit At Most Two Line Transversals

http://www.springerlink.comInternational audienceWe show that a set of $n$~disjoint unit spheres in \Rd admits at most \emph{two} distinct geometric permutations, or line transversals, if $n$ is large enough. This bound is optimal

Anti-CV2/CRMP5 Paraneoplastic Chorea Effectively Managed with Intravenous Amantadine

Background: Paraneoplastic chorea is typically a subacute progressive hyperkinetic movement disorder. The mainstay of treatment is managing the underlying neoplasm. However, the clinical course may be variable, and effective symptomatic management can precede the start of cancer treatment. Case report: A 63-year-old man presented with insidious onset, slowly progressive generalized chorea for 1 year, later diagnosed as anti-CV2/CRMP5 autoantibody positive paraneoplastic chorea. His chorea was markedly improved with intravenous amantadine. Discussion: In patients with anti-CV2/CRMP5 autoantibody-related chorea, sequential follow-up of brain magnetic resonance imaging reveals progression from active inflammation to atrophy. Our report highlights the efficacy of intravenous amantadine in paraneoplastic chorea

On the Number of Maximal Free Line Segments Tangent to Arbitrary Three-dimensional Convex Polyhedra

We prove that the lines tangent to four possibly intersecting convex polyhedra in $^3$ with $n$ edges in total form $\Theta(n^2)$ connected components in the worst case. In the generic case, each connected component is a single line, but our result still holds for arbitrary degenerate scenes. More generally, we show that a set of $k$ possibly intersecting convex polyhedra with a total of $n$ edges admits, in the worst case, $\Theta(n^2k^2)$ connected components of maximal free line segments tangent to any four of the polytopes. This bound also holds for the number of connected components of possibly occluded lines tangent to any four of the polytopes

Spontaneous Rupture of the Extensor Pollicis Longus Tendon in a Tailor

A spontaneous rupture of the extensor pollicis longus (EPL) tendon is associated with rheumatoid arthritis, fractures of the wrist, systemic or local steroids and repetitive, and excessive abnormal motion of the wrist joint. The authors encountered a case of a spontaneous rupture of the EPL tendon. The patient had no predisposing factors including trauma or steroid injection. Although the patient had a positive rheumatoid factor, he did not demonstrate other clinical or radiological findings of rheumatoid arthritis. During surgery, the EPL tendon was found to be ruptured at the extensor retinaculum (third compartment). Reconstruction of the extensor tendon using the palmaris longus tendon was performed. At the 18-month follow-up, the patient showed satisfactory extension of the thumb and 40° extension and flexion at the wrist