We examine several types of visibility graphs: bar and semi-bar k-visibility graphs, rectangle k-visibility graphs, arc and circle k-visibility graphs, and compact visibility graphs. We improve the upper bound on the thickness of bar k-visibility graphs from 2k(9k − 1) to 6k, and prove that the upper bound must be at least k + 1. We also show that the upper bound on the thickness of semi-bar k-...

Fitting lines and circles to a sequence of pixels, where the t is determined by minimizing the distance between the pixel coordinates and the tted line or circle, is a commonly used procedure in image analysis and computer vision. In this paper we derive analytic expressions for the variance of the estimated parameters as a function of image noise. We verify the analytic expresssions by compari...

The rolling circle DNA replication structures generated by the in vitro phage T4 replication system were analyzed using two-dimensional agarose gels. Replication structures were generated in the presence or absence of T4 primase (gp61), permitting the analysis of replication forks with either duplex or single-stranded tails. A characteristic arc shape was visualized when forks with single-stran...

The eigenvalues of Wilson loop matrices in SU(N) gauge theories in dimensions 2,3,4 at infinite N are supported on a small arc on the unit circle centered at z = 1 for small loops, but expand to the entire unit circle for large loops. These two regimes are separated by a large N phase transition whose universal properties are the same in d = 2, 3 and 4. Hopefully, this large N universality coul...

Joel E. Cohen (1981) conjectured that any stochastic matrix P = fpi;jg could be represented by some circle rotation f in the following sense: For some partition fSig of the circle into sets consisting of …nite unions of arcs, we have (*) pi;j = (f (Si) \ Sj) = (Si), where denotes arc length. In this paper we show how cycle decomposition techniques originally used (Alpern, 1983) to establish Coh...

Trajectories are given that describe the evolution of the ellipse of polarization in the complex plane for light propagating in a homogeneous anisotropic medium and along the helical axis of a cholesteric liquid crystal. For the general homogeneous anisotropic medium that exhibits combined birefringence and dichroism the trajectory is a spiral that converges to the low-absorption eigenpolarizat...

We find equilibrium configurations of open and closed lines of charge on a sphere, and track them with respect to varying sphere radius. Closed lines transition from a circle to a spiral-like shape through two low-wave-number bifurcations-"baseball seam" and "twist"-which minimize Coulomb energy. The spiral shape is the unique stable equilibrium of the closed line. Other unstable equilibria ari...

We present a polynomial-time algorithm for nding an almost optimal solution to the following combinatorial problem, which is motivated by the problem of balancing communication in networks having the structure of rings. Input: a circle and a multiset of c chords, having n distinct endpoints, representing desired point-to-point communications; c 0 of the chords are distinct. The task: to map eac...

While automatic detection of point sources in astronomical images has experienced a great degree of success, less effort has been directed towards the detection of extended and low-surface brightness features. At present, existing telescopes still rely on human expertise to reduce the raw data to usable images and then to analyse the images for non-pointlike objects. However, the next generatio...

Abstract Let γ be a smooth closed curve of length 2π in R3, and let κ(s) be its curvature, regarded as a function of arc length. We associate with this curve the one-dimensional Schrödinger operator Hγ = − d 2 ds + κ 2(s) acting on the space of square integrable 2π-periodic functions. A natural conjecture is that the lowest spectral value e0(γ) of Hγ is bounded below by 1 for any γ (this value ...