We present a method for the automatic detection of vanishing points in urban scenes based on finding point alignments in a dual space, where converging lines in the image are mapped to aligned points. To compute this mapping the recently introduced PClines transformation is used. A robust point alignment detector is run to detect clusters of aligned points in the dual space. Finally, a post-pro...

It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction of standard basis vectors, provided the band width W raised to a power μ remains smaller than the matrix size N . For a Gaussian band ensemble, with mat...

We discuss algebraic properties for the symbols of geometric first order differential operators on almost Hermitian manifolds and Kähler manifolds. Through study on the universal enveloping algebra and higher Casimir elements, we know algebraic relations for the symbols like the Clifford algebra. From the relations, we have all the Bochner identities for the operators. As applications, we have ...

Given a one-dimensional formal group of height 2, let E be the Morava E theory spectrum associated to its universal deformation over the Lubin-Tate ring. By computing with moduli spaces of elliptic curves, we give an explicitation for an algebra of Hecke operators acting on E -cohomology. This leads to a vanishing result for Rezk’s logarithmic cohomology operation on the units of E . It identif...

In the present paper, we study robustness properties of a class of digital feedback control systems with time-varying sampling periods consisting of an interconnection of a continuous-time nonlinear plant (described by systems of rst-order ordinary diierential equations), a nonlinear digital controller (described by systems of rst-order ordinary diierence equations), and appropriate interface e...

The aim of this paper is to prove that if a planar set A has a difference set ∆(A) satisfying ∆(A) ⊂ Z + s for suitable s than A has at most 3 elements. This result is motivated by the conjecture that the disk has not more than 3 orthogonal exponentials. Further, we prove that if A is a set of exponentials mutually orthogonal with respect to any symmetric convex set K in the plane with a smooth...

We study the implications of scale invariance in four-dimensional quantum field theories. Imposing unitarity, we find that infinitely many matrix elements vanish in a suitable kinematical configuration. This vanishing is a nontrivial necessary condition for conformality. We provide an argument why this is expected to be a sufficient condition as well, thereby linking scale and conformal invaria...

Let A be a finite set of closed rational points in projective space, let I be the vanishing ideal of A , and let D(A ) be the set of exponents of those monomials which do not occur as leading monomials of elements of I . We show that the size of A equals the number of axes contained in D(A ). Furthermore, we present an algorithm for the construction of the Gröbner basis of I (A ), hence also of...

A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor l(l + 1) is replaced by (l + 1/2), are avoided. The semiclassical energy levels are shown to be exact to first order in h̄ with all higher order contribution...

Let A be a finite set of closed rational points in projective space, let I be the vanishing ideal of A , and let D(A ) be the set of exponents of those monomials which do not occur as leading monomials of elements of I . We show that the size of A equals the number of axes contained in D(A ). Furthermore, we present an algorithm for the construction of the Gröbner basis of I (A ), hence also of...