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Language & Common Sense: Integrating across psychology, linguistics, and computer science
A simple remark on a flat projective morphism with a Calabi-Yau fiber
If a K3 surface is a fiber of a flat projective morphisms over a connected
noetherian scheme over the complex number field, then any smooth connected
fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the
same is true for higher dimensional Calabi-Yau fibers. We shall give an
explicit negative answer to his question as well as a proof of his initial
observation.Comment: 8 pages, main theorem is generalized, one more remark is added,
mis-calculation and typos are corrected etc
On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces
We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces
X and vector fields v which are K-stable in the sense of Berman-Nystrom and
therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide
some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor
correction
Remarks on hard Lefschetz conjectures on Chow groups
We propose two conjectures of Hard Lefschetz type on Chow groups and prove
them for some special cases. For abelian varieties, we shall show they are
equivalent to well-known conjectures of Beauville and Murre.Comment: to appear in Sciences in China, Ser. A Mathematic
Varieties of vacua in classical supersymmetric gauge theories
We give a simple description of the classical moduli space of vacua for
supersymmetric gauge theories with or without a superpotential. The key
ingredient in our analysis is the observation that the lagrangian is invariant
under the action of the complexified gauge group \Gc. From this point of view
the usual -flatness conditions are an artifact of Wess--Zumino gauge. By
using a gauge that preserves \Gc invariance we show that every constant
matter field configuration that extremizes the superpotential is \Gc
gauge-equivalent (in a sense that we make precise) to a unique classical
vacuum. This result is used to prove that in the absence of a superpotential
the classical moduli space is the algebraic variety described by the set of all
holomorphic gauge-invariant polynomials. When a superpotential is present, we
show that the classical moduli space is a variety defined by imposing
additional relations on the holomorphic polynomials. Many of these points are
already contained in the existing literature. The main contribution of the
present work is that we give a careful and self-contained treatment of limit
points and singularities.Comment: 14 pages, LaTeX (uses revtex.sty
The Moduli of Reducible Vector Bundles
A procedure for computing the dimensions of the moduli spaces of reducible,
holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds X is
presented. This procedure is applied to poly-stable rank n+m bundles of the
form V + pi* M, where V is a stable vector bundle with structure group SU(n) on
X and M is a stable vector bundle with structure group SU(m) on the base
surface B of X. Such bundles arise from small instanton transitions involving
five-branes wrapped on fibers of the elliptic fibration. The structure and
physical meaning of these transitions are discussed.Comment: 33+1 page
Affine T-varieties of complexity one and locally nilpotent derivations
Let X=spec A be a normal affine variety over an algebraically closed field k
of characteristic 0 endowed with an effective action of a torus T of dimension
n. Let also D be a homogeneous locally nilpotent derivation on the normal
affine Z^n-graded domain A, so that D generates a k_+-action on X that is
normalized by the T-action. We provide a complete classification of pairs (X,D)
in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1.
This generalizes previously known results for surfaces due to Flenner and
Zaidenberg. As an application we compute the homogeneous Makar-Limanov
invariant of such varieties. In particular we exhibit a family of non-rational
varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo
On localization in holomorphic equivariant cohomology
We prove a localization formula for a "holomorphic equivariant cohomology"
attached to the Atiyah algebroid of an equivariant holomorphic vector bundle.
This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's
localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the
exposition. v4: final version to appear in Centr. Eur. J. Mat
Five-year study assessing the clinical utility of anti-Müllerian hormone measurements in reproductive-age women with cancer
An important discussion point before chemotherapy is ovarian toxicity, a side-effect that profoundly affects young women with cancer. Their quality of life after successful treatment, including the ability to conceive, is a major concern. We asked whether serum anti-Müllerian hormone (AMH) measurements before chemotherapy for two most common malignancies are predictive of long-term changes in ovarian reserve? A prospective cohort study measured serum AMH in 66 young women with lymphoma and breast cancer, before and at 1 year and 5 years after chemotherapy, compared with 124 healthy volunteers of the same age range (18-43 years). Contemporaneously, patients reported their menses and live births during 5-year follow-up. After adjustment for age, serum AMH was 1.4 times higher (95% CI 1.1 to 1.9; P < 0.02) in healthy volunteers than in cancer patients before chemotherapy. A strong correlation was observed between baseline and 5-year AMH in the breast cancer group (P < 0.001, regression coefficient = 0.58, 95% CI 0.29 to 0.89). No significant association was found between presence of menses at 5 years and serum AMH at baseline (likelihood ratio test from logistics regression analysis). Reproductive-age women with malignancy have lower serum AMH than healthy controls even before starting chemotherapy. Pre-chemotherapy AMH was significantly associated with long-term ovarian function in women with breast cancer. At key time points, AMH measurements could be used as a reproductive health advisory tool for young women with cancer. Our results highlight the unsuitability of return of menstruation as a clinical indicator of ovarian reserve after chemotherapy. [Abstract copyright: Crown Copyright © 2019. Published by Elsevier Ltd. All rights reserved.
Generating multimedia presentations: from plain text to screenplay
In many Natural Language Generation (NLG) applications, the output is limited to plain text – i.e., a string of words with punctuation and paragraph breaks, but no indications for layout, or pictures, or dialogue. In several projects, we have begun to explore NLG applications in which these extra media are brought into play. This paper gives an informal account of what we have learned. For coherence, we focus on the domain of patient information leaflets, and follow an example in which the same content is expressed first in plain text, then in formatted text, then in text with pictures, and finally in a dialogue script that can be performed by two animated agents. We show how the same meaning can be mapped to realisation patterns in different media, and how the expanded options for expressing meaning are related to the perceived style and tone of the presentation. Throughout, we stress that the extra media are not simple added to plain text, but integrated with it: thus the use of formatting, or pictures, or dialogue, may require radical rewording of the text itself
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