3,188 research outputs found
A view on extending morphisms from ample divisors
The philosophy that ``a projective manifold is more special than any of its
smooth hyperplane sections" was one of the classical principles of projective
geometry. Lefschetz type results and related vanishing theorems were among the
typically used techniques. We shall survey most of the problems, results and
conjectures in this area, using the modern setting of ample divisors, and (some
aspects of) Mori theory.Comment: To Appear in: Interactions of Classical and Numerical Algebraic
Geometry, ed. by A. Bates, G. Besana and S. Di Rocco, Contemporary
Mathematics, American Mathematical Societ
Nonlinear cross Gramians and gradient systems
We study the notion of cross Gramians for non-linear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that precisely correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
ContextVP: Fully Context-Aware Video Prediction
Video prediction models based on convolutional networks, recurrent networks,
and their combinations often result in blurry predictions. We identify an
important contributing factor for imprecise predictions that has not been
studied adequately in the literature: blind spots, i.e., lack of access to all
relevant past information for accurately predicting the future. To address this
issue, we introduce a fully context-aware architecture that captures the entire
available past context for each pixel using Parallel Multi-Dimensional LSTM
units and aggregates it using blending units. Our model outperforms a strong
baseline network of 20 recurrent convolutional layers and yields
state-of-the-art performance for next step prediction on three challenging
real-world video datasets: Human 3.6M, Caltech Pedestrian, and UCF-101.
Moreover, it does so with fewer parameters than several recently proposed
models, and does not rely on deep convolutional networks, multi-scale
architectures, separation of background and foreground modeling, motion flow
learning, or adversarial training. These results highlight that full awareness
of past context is of crucial importance for video prediction.Comment: 19 pages. ECCV 2018 oral presentation. Project webpage is at
https://wonmin-byeon.github.io/publication/2018-ecc
Weighted Low-Regularity Solutions of the KP-I Initial Value Problem
In this paper we establish local well-posedness of the KP-I problem, with
initial data small in the intersection of the natural energy space with the
space of functions which are square integrable when multiplied by the weight y.
The result is proved by the contraction mapping principle. A similar (but
slightly weaker) result was the main Theorem in the paper " Low regularity
solutions for the Kadomstev-Petviashvili I equation " by Colliander, Kenig and
Staffilani (GAFA 13 (2003),737-794 and math.AP/0204244). Ionescu found a
counterexample (included in the present paper) to the main estimate used in the
GAFA paper, which renders incorrect the proof there. The present paper thus
provides a correct proof of a strengthened version of the main result in the
GAFA paper
Helioseismic analysis of the solar flare-induced sunquake of 2005 January 15
We report the discovery of one of the most powerful sunquakes detected to
date, produced by an X1.2-class solar flare in active region 10720 on 2005
January 15. We used helioseismic holography to image the source of seismic
waves emitted into the solar interior from the site of the flare. Acoustic
egression power maps at 3 and 6 mHz with a 2 mHz bandpass reveal a compact
acoustic source strongly correlated with impulsive hard X-ray and
visible-continuum emission along the penumbral neutral line separating the two
major opposing umbrae in the -configuration sunspot that predominates
AR10720. The acoustic emission signatures were directly aligned with both hard
X-ray and visible continuum emission that emanated during the flare. The
visible continuum emission is estimated at J,
approximately 500 times the seismic emission of J. The
flare of 2005 January 15 exhibits the same close spatial alignment between the
sources of the seismic emission and impulsive visible continuum emission as
previous flares, reinforcing the hypothesis that the acoustic emission may be
driven by heating of the low photosphere. However, it is a major exception in
that there was no signature to indicate the inclusion of protons in the
particle beams thought to supply the energy radiated by the flare. The
continued strong coincidence between the sources of seismic emission and
impulsive visible continuum emission in the case of a proton-deficient
white-light flare lends substantial support to the ``back -- warming''
hypothesis, that the low photosphere is significantly heated by intense Balmer
and Paschen continuum-edge radiation from the overlying chromosphere in
white-light flares.Comment: 12 pages, 7 figures, published in MNRA
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