4,109 research outputs found
The energy-critical defocusing NLS on T^3
We prove global well-posedness in H^1(T^3) for the energy-critical defocusing
NLS.Comment: 24 page
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.
On the particle paths and the stagnation points in small-amplitude deep-water waves
In order to obtain quite precise information about the shape of the particle
paths below small-amplitude gravity waves travelling on irrotational deep
water, analytic solutions of the nonlinear differential equation system
describing the particle motion are provided. All these solutions are not closed
curves. Some particle trajectories are peakon-like, others can be expressed
with the aid of the Jacobi elliptic functions or with the aid of the
hyperelliptic functions. Remarks on the stagnation points of the
small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with
arXiv:1106.382
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
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