40,289 research outputs found

### Learning to Generate Time-Lapse Videos Using Multi-Stage Dynamic Generative Adversarial Networks

Taking a photo outside, can we predict the immediate future, e.g., how would
the cloud move in the sky? We address this problem by presenting a generative
adversarial network (GAN) based two-stage approach to generating realistic
time-lapse videos of high resolution. Given the first frame, our model learns
to generate long-term future frames. The first stage generates videos of
realistic contents for each frame. The second stage refines the generated video
from the first stage by enforcing it to be closer to real videos with regard to
motion dynamics. To further encourage vivid motion in the final generated
video, Gram matrix is employed to model the motion more precisely. We build a
large scale time-lapse dataset, and test our approach on this new dataset.
Using our model, we are able to generate realistic videos of up to $128\times
128$ resolution for 32 frames. Quantitative and qualitative experiment results
have demonstrated the superiority of our model over the state-of-the-art
models.Comment: To appear in Proceedings of CVPR 201

### On minima of sum of theta functions and Mueller-Ho Conjecture

Let $z=x+iy \in \mathbb{H}:=\{z= x+ i y\in\mathbb{C}: y>0\}$ and $\theta
(s;z)=\sum_{(m,n)\in\mathbb{Z}^2 } e^{-s \frac{\pi }{y }|mz+n|^2}$ be the theta
function associated with the lattice $\Lambda ={\mathbb Z}\oplus z{\mathbb Z}$.
In this paper we consider the following pair of minimization problems $\min_{
\mathbb{H} } \theta (2;\frac{z+1}{2})+\rho\theta (1;z),\;\;\rho\in[0,\infty),$
$\min_{ \mathbb{H} } \theta (1; \frac{z+1}{2})+\rho\theta (2;
z),\;\;\rho\in[0,\infty),$
where the parameter $\rho\in[0,\infty)$ represents the competition of two
intertwining lattices. We find that as $\rho$ varies the optimal lattices admit
a novel pattern: they move from rectangular (the ratio of long and short side
changes from $\sqrt3$ to 1), square, rhombus (the angle changes from $\pi/2$ to
$\pi/3$) to hexagonal; furthermore, there exists a closed interval of $\rho$
such that the optimal lattices is always square lattice. This is in sharp
contrast to optimal lattice shapes for single theta function ($\rho=\infty$
case), for which the hexagonal lattice prevails. As a consequence, we give a
partial answer to optimal lattice arrangements of vortices in competing systems
of Bose-Einstein condensates as conjectured (and numerically and experimentally
verified) by Mueller-Ho \cite{Mue2002}.Comment: 42 pages; comments welcom

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