1,205 research outputs found
Level structures on the Weierstrass family of cubics
Let W -> A^2 be the universal Weierstrass family of cubic curves over C. For
each N >= 2, we construct surfaces parametrizing the three standard kinds of
level N structures on the smooth fibers of W. We then complete these surfaces
to finite covers of A^2. Since W -> A^2 is the versal deformation space of a
cusp singularity, these surfaces convey information about the level structure
on any family of curves of genus g degenerating to a cuspidal curve. Our goal
in this note is to determine for which values of N these surfaces are smooth
over (0,0). From a topological perspective, the results determine the
homeomorphism type of certain branched covers of S^3 with monodromy in
SL_2(Z/N).Comment: LaTeX, 12 pages; added section giving a topological interpretation of
the result
Fitting Voronoi Diagrams to Planar Tesselations
Given a tesselation of the plane, defined by a planar straight-line graph
, we want to find a minimal set of points in the plane, such that the
Voronoi diagram associated with "fits" \ . This is the Generalized
Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered
recently in \cite{Baner12}. Here we give an algorithm that solves this problem
with a number of points that is linear in the size of , assuming that the
smallest angle in is constant.Comment: 14 pages, 8 figures, 1 table. Presented at IWOCA 2013 (Int. Workshop
on Combinatorial Algorithms), Rouen, France, July 201
On kernel engineering via Paley–Wiener
A radial basis function approximation takes the form
where the coefficients a 1,…,a n are real numbers, the centres b 1,…,b n are distinct points in ℝ d , and the function φ:ℝ d →ℝ is radially symmetric. Such functions are highly useful in practice and enjoy many beautiful theoretical properties. In particular, much work has been devoted to the polyharmonic radial basis functions, for which φ is the fundamental solution of some iterate of the Laplacian. In this note, we consider the construction of a rotation-invariant signed (Borel) measure μ for which the convolution ψ=μ φ is a function of compact support, and when φ is polyharmonic. The novelty of this construction is its use of the Paley–Wiener theorem to identify compact support via analysis of the Fourier transform of the new kernel ψ, so providing a new form of kernel engineering
Full oxide heterostructure combining a high-Tc diluted ferromagnet with a high-mobility conductor
We report on the growth of heterostructures composed of layers of the
high-Curie temperature ferromagnet Co-doped (La,Sr)TiO3 (Co-LSTO) with
high-mobility SrTiO3 (STO) substrates processed at low oxygen pressure. While
perpendicular spin-dependent transport measurements in STO//Co-LSTO/LAO/Co
tunnel junctions demonstrate the existence of a large spin polarization in
Co-LSTO, planar magnetotransport experiments on STO//Co-LSTO samples evidence
electronic mobilities as high as 10000 cm2/Vs at T = 10 K. At high enough
applied fields and low enough temperatures (H < 60 kOe, T < 4 K) Shubnikov-de
Haas oscillations are also observed. We present an extensive analysis of these
quantum oscillations and relate them with the electronic properties of STO, for
which we find large scattering rates up to ~ 10 ps. Thus, this work opens up
the possibility to inject a spin-polarized current from a high-Curie
temperature diluted oxide into an isostructural system with high-mobility and a
large spin diffusion length.Comment: to appear in Phys. Rev.
Spectral properties of distance matrices
Distance matrices are matrices whose elements are the relative distances
between points located on a certain manifold. In all cases considered here all
their eigenvalues except one are non-positive. When the points are uncorrelated
and randomly distributed we investigate the average density of their
eigenvalues and the structure of their eigenfunctions. The spectrum exhibits
delocalized and strongly localized states which possess different power-law
average behaviour. The exponents depend only on the dimensionality of the
manifold.Comment: 31 pages, 9 figure
A Generalization of the Convex Kakeya Problem
Given a set of line segments in the plane, not necessarily finite, what is a
convex region of smallest area that contains a translate of each input segment?
This question can be seen as a generalization of Kakeya's problem of finding a
convex region of smallest area such that a needle can be rotated through 360
degrees within this region. We show that there is always an optimal region that
is a triangle, and we give an optimal \Theta(n log n)-time algorithm to compute
such a triangle for a given set of n segments. We also show that, if the goal
is to minimize the perimeter of the region instead of its area, then placing
the segments with their midpoint at the origin and taking their convex hull
results in an optimal solution. Finally, we show that for any compact convex
figure G, the smallest enclosing disk of G is a smallest-perimeter region
containing a translate of every rotated copy of G.Comment: 14 pages, 9 figure
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