37,957 research outputs found
Fast Mojette Transform for Discrete Tomography
A new algorithm for reconstructing a two dimensional object from a set of one
dimensional projected views is presented that is both computationally exact and
experimentally practical. The algorithm has a computational complexity of O(n
log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and
produces no artefacts in the reconstruction process, as is the case with
conventional tomographic methods. The reconstruction process is approximation
free because the object is assumed to be discrete and utilizes fully discrete
Radon transforms. Noise in the projection data can be suppressed further by
introducing redundancy in the reconstruction. The number of projections
required for exact reconstruction and the response to noise can be controlled
without comprising the digital nature of the algorithm. The digital projections
are those of the Mojette Transform, a form of discrete linogram. A simple
analytical mapping is developed that compacts these projections exactly into
symmetric periodic slices within the Discrete Fourier Transform. A new digital
angle set is constructed that allows the periodic slices to completely fill all
of the objects Discrete Fourier space. Techniques are proposed to acquire these
digital projections experimentally to enable fast and robust two dimensional
reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin
The determinant of the Dirichlet-to-Neumann map for surfaces with boundary
For any orientable compact surface with boundary, we compute the regularized
determinant of the Dirichlet-to-Neumann (DN) map in terms of particular values
of dynamical zeta functions by using natural uniformizations, one due to
Mazzeo-Taylor, the other to Osgood-Phillips-Sarnak. We also relate in any
dimension the DN map for the Yamabe operator to the scattering operator for a
conformally compact related problem by using uniformization.Comment: 16 page
On the asymptotics of Morse numbers of finite covers of manifolds
Let M be a closed connected manifold. Let m(M) be the Morse number of M, that
is, the minimal number of critical points of a Morse function on M. Let N be a
finite cover of M of degree d. M.Gromov posed the following question: what are
the asymptotic properties of m(N) as d goes to infinity? In this paper we study
the case of high dimensional manifolds M with free abelian fundamental group.
Let x be a non-zero element of H^1(M), let M(x) be the infinite cyclic cover
corresponding to x, and t be a generator of the structure group of this cover.
Set M(x,k)=M(x)/t^k. We prove that the sequence m(M(x,k))/k converges as k goes
to infinity. For x outside of a finite union of hyperplanes in H^1(M) we obtain
the asymptotics of m(M(x,k)) as k goes to infinity, in terms of homotopy
invariants of M related to Novikov homology of M.Comment: Amslatex file, 13 pages. To be published in "Topology
Thermal Dileptons at LHC
We predict dilepton invariant-mass spectra for central 5.5 ATeV Pb-Pb
collisions at LHC. Hadronic emission in the low-mass region is calculated using
in-medium spectral functions of light vector mesons within hadronic many-body
theory. In the intermediate-mass region thermal radiation from the Quark-Gluon
Plasma, evaluated perturbatively with hard-thermal loop corrections, takes
over. An important source over the entire mass range are decays of correlated
open-charm hadrons, rendering the nuclear modification of charm and bottom
spectra a critical ingredient.Comment: 2 pages, 2 figures, contributed to Workshop on Heavy Ion Collisions
at the LHC: Last Call for Predictions, Geneva, Switzerland, 14 May - 8 Jun
2007 v2: acknowledgment include
Localisable moving average stable and multistable processes
We study a particular class of moving average processes which possess a
property called localisability. This means that, at any given point, they admit
a ``tangent process'', in a suitable sense. We give general conditions on the
kernel g defining the moving average which ensures that the process is
localisable and we characterize the nature of the associated tangent processes.
Examples include the reverse Ornstein-Uhlenbeck process and the multistable
reverse Ornstein-Uhlenbeck process. In the latter case, the tangent process is,
at each time t, a L\'evy stable motion with stability index possibly varying
with t. We also consider the problem of path synthesis, for which we give both
theoretical results and numerical simulations
Quadratic functions on torsion groups
We investigate classification results for general quadratic functions on
torsion abelian groups. Unlike the previously studied situations, general
quadratic functions are allowed to be inhomogeneous or degenerate. We study the
discriminant construction which assigns, to an integral lattice with a
distinguished characteristic form, a quadratic function on a torsion group.
When the associated symmetric bilinear pairing is fixed, we construct an affine
embedding of a quotient of the set of characteristic forms into the set of all
quadratic functions and determine explicitly its cokernel. We determine a
suitable class of torsion groups so that quadratic functions defined on them
are classified by the stable class of their lift. This refines results due to
A.H. Durfee, V. Nikulin, C.T.C. Wall and E. Looijenga -- J. Wahl. Finally, we
show that on this class of torsion groups, two quadratic functions are
isomorphic if and only if they have equal associated Gauss sums and there is an
isomorphism between the associated symmetric bilinear pairings which preserves
the "homogeneity defects". This generalizes a classical result due to V.
Nikulin. Our results are elementary in nature and motivated by low-dimensional
topology.Comment: 15 pages; a few minor modifications (improved writing, lengthened
abstract
- âŠ