1,299 research outputs found
Regularity of quotients of Drinfeld modular schemes
Let be the coordinate ring of a projective smooth curve over a finite
field minus a closed point. For a nontrivial ideal , Drinfeld
defined the notion of structure of level on a Drinfeld module.
We extend this to that of level , where is a finitely generated
torsion -module. The case where , where is the rank of
the Drinfeld module,coincides with the structure of level . The moduli
functor is representable by a regular affine scheme.
The automorphism group acts on the moduli space. Our
theorem gives a class of subgroups for which the quotient of the moduli scheme
is regular. Examples include generalizations of and of .
We also show that parabolic subgroups appearing in the definition of Hecke
correspondences are such subgroups
Unsupervised Domain Adaptation for MRI Volume Segmentation and Classification Using Image-to-Image Translation
Unsupervised domain adaptation is a type of domain adaptation and exploits
labeled data from the source domain and unlabeled data from the target one. In
the Cross-Modality Domain Adaptation for Medical Image Segmenta-tion challenge
(crossMoDA2022), contrast enhanced T1 MRI volumes for brain are provided as the
source domain data, and high-resolution T2 MRI volumes are provided as the
target domain data. The crossMoDA2022 challenge contains two tasks,
segmentation of vestibular schwannoma (VS) and cochlea, and clas-sification of
VS with Koos grade. In this report, we presented our solution for the
crossMoDA2022 challenge. We employ an image-to-image translation method for
unsupervised domain adaptation and residual U-Net the segmenta-tion task. We
use SVM for the classification task. The experimental results show that the
mean DSC and ASSD are 0.614 and 2.936 for the segmentation task and MA-MAE is
0.84 for the classification task
String-theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
It is known that the L-function of an elliptic curve defined over Q is given
by the Mellin transform of a modular form of weight 2. Does that modular form
have anything to do with string theory? In this article, we address a question
along this line for elliptic curves that have complex multiplication defined
over number fields. So long as we use diagonal rational N=(2,2) superconformal
field theories for the string-theory realizations of the elliptic curves, the
weight-2 modular form turns out to be the Boltzmann-weighted
(q^{L_0-c/24}-weighted) sum of U(1) charges with F e^{ \pi i F} insertion
computed in the Ramond sector.Comment: 48 pages; minor corrections and improvements in v
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