Abstract. We consider the 2-dimensional Toda lattice tau functions τn(t, s; η, θ) deforming the probabilities τn(η, θ) that a randomly chosen matrix from the unitary group U(n), for the Haar measure, has no eigenvalues within an arc (η, θ) of the unit circle. We show that these tau functions satisfy a centerless Virasoro algebra of constraints, with a boundary part in the sense of Adler, Shiota...

Abstrac t . The Kreiss Matrix Theorem asserts the uniform equivalence over all N x N matrices of power boundedness and a certain resolvent estimate. We show that the ratio of the constants in these two conditions grows linearly with N, and we obtain the optimal proportionality factor up to a factor of 2. Analogous results are also given for the related problem involving matrix exponentials e At...

In this paper different filtering techniques for nonlinear state estimation are explored and compared. We distinguish between approaches that approximate the nonlinear function (extended Kalman filter) and other approaches approximating the distribution of measurements and state (unscented Kalman filter and sequential Monte Carlo filter). The paper is showing both, the algorithms and simulated ...

Recently, there has been considerable interest in skinning circles and spheres. In this paper we present a simple algorithm for skinning circles in the plane. Our novel approach allows the skin to touch a particular circle not only at a point, but also along a whole circular arc. This results in naturally looking skins. Due to the simplicity of our algorithm, it can be generalised to branched s...

Although general methods led me to a complete solution, I soon saw that the result is obtained faster when the general procedure is left, and when one follows the path suggested by the particular problem at hand. S. Bernstein first lines of [6] Abstract. One establishes inequalities for the coefficients of orthogonal polynomials Φn(z) = z n + ξnz n−1 + · · · + Φn(0), n = 0, 1, . . . which are o...

Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most one, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P , we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n) time algorithm to co...

We present a new method for automatically detecting circular objects in images: we detect an osculating circle to an elliptic arc using a Hough transform, iteratively deforming it into an ellipse, removing outlier pixels, and searching for a separate edge. The voting space is restricted to one and two dimensions for efficiency, and special weighting schemes are introduced to enhance the accurac...

A feature detection system has been developed for real-time identification of lines, circles and legs from laser data. A new method suitable for arc/circle detection is proposed: the Internal Angle Variance (IAV). Lines are detected using a recursive line fitting method. The people leg detection is based on geometrical constrains. The system was implemented as a fiducial driver in Player, a mob...

Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation, trapezoid, chordal, disk, circle graphs are more important. In this article, a brief introduction of each of these intersection graphs is given. Some basic ...

We prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Velázquez [13]) associated with matrix-valued Verblunsky coefficients. More precisely, we find an explicit formula for the Verblunsky coefficients of a reflectionless CMV matrix whose spectrum consists of a connected arc on the unit circle. This extends a recent result [39...