7,713 research outputs found
Persistence Modules on Commutative Ladders of Finite Type
We study persistence modules defined on commutative ladders. This class of
persistence modules frequently appears in topological data analysis, and the
theory and algorithm proposed in this paper can be applied to these practical
problems. A new algebraic framework deals with persistence modules as
representations on associative algebras and the Auslander-Reiten theory is
applied to develop the theoretical and algorithmic foundations. In particular,
we prove that the commutative ladders of length less than 5 are
representation-finite and explicitly show their Auslander-Reiten quivers.
Furthermore, a generalization of persistence diagrams is introduced by using
Auslander-Reiten quivers. We provide an algorithm for computing persistence
diagrams for the commutative ladders of length 3 by using the structure of
Auslander-Reiten quivers.Comment: 48 page
The On The Fly Imaging Technique
The On-The-Fly (OTF) imaging technique enables single-dish radio telescopes
to construct images of small areas of the sky with greater efficiency and
accuracy. This paper describes the practical application of the OTF imaging
technique. By way of example the implementation of the OTF imaging technique at
the NRAO 12 Meter Telescope is described. Specific requirements for data
sampling, image formation, and Doppler correction are discussed.Comment: 10 pages, 13 figures, accepted A&
The 125 GeV boson: A composite scalar?
Assuming that the 125 GeV particle observed at the LHC is a composite scalar
and responsible for the electroweak gauge symmetry breaking, we consider the
possibility that the bound state is generated by a non-Abelian gauge theory
with dynamically generated gauge boson masses and a specific chiral symmetry
breaking dynamics motivated by confinement. The scalar mass is computed with
the use of the Bethe-Salpeter equation and its normalization condition as a
function of the SU(N) group and the respective fermionic representation. If the
fermions that form the composite state are in the fundamental representation of
the SU(N) group, we can generate such light boson only for one specific number
of fermions for each group. In the case of small groups, like SU(2) to SU(5),
and two fermions in the adjoint representation we find that is quite improbable
to generate such light composite scalar.Comment: 24 pages, 5 figures, discussion extended, references added; version
to appear in Phys. Rev.
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