Strict solutions to stochastic parabolic evolution equations in M-type 2 Banach spaces

We study a stochastic linear evolution equation $dX+A(t)Xdt=F(t)dt+ G(t)dw_t$ in a Banach space of M-type 2. We construct unique strict solutions to the equation on the basis of the theory of deterministic linear evolution equations. The abstract results are applied to stochastic diffusion equations.Comment: 27 pages, to appear in Funkcialaj Ekvacio

Hierarchical Video Generation from Orthogonal Information: Optical Flow and Texture

Learning to represent and generate videos from unlabeled data is a very challenging problem. To generate realistic videos, it is important not only to ensure that the appearance of each frame is real, but also to ensure the plausibility of a video motion and consistency of a video appearance in the time direction. The process of video generation should be divided according to these intrinsic difficulties. In this study, we focus on the motion and appearance information as two important orthogonal components of a video, and propose Flow-and-Texture-Generative Adversarial Networks (FTGAN) consisting of FlowGAN and TextureGAN. In order to avoid a huge annotation cost, we have to explore a way to learn from unlabeled data. Thus, we employ optical flow as motion information to generate videos. FlowGAN generates optical flow, which contains only the edge and motion of the videos to be begerated. On the other hand, TextureGAN specializes in giving a texture to optical flow generated by FlowGAN. This hierarchical approach brings more realistic videos with plausible motion and appearance consistency. Our experiments show that our model generates more plausible motion videos and also achieves significantly improved performance for unsupervised action classification in comparison to previous GAN works. In addition, because our model generates videos from two independent information, our model can generate new combinations of motion and attribute that are not seen in training data, such as a video in which a person is doing sit-up in a baseball ground.Comment: Our supplemental material is available on http://www.mi.t.u-tokyo.ac.jp/assets/publication/hierarchical_video_generation_sup/ Accepted to AAAI201

Critical Behavior in Doping-Driven Metal−-Insulator Transition on Single-Crystalline Organic Mott-FET

We present the carrier transport properties in the vicinity of a doping-driven Mott transition observed at a field-effect transistor (FET) channel using a single crystal of the typical two-dimensional organic Mott insulator $\kappa$-(BEDT-TTF)$_2$CuN(CN)$_2$Cl ($\kappa$-Cl).The FET shows a continuous metal$-$insulator transition (MIT) as electrostatic doping proceeds. The phase transition appears to involve two-step crossovers, one in Hall measurement and the other in conductivity measurement. The crossover in conductivity occurs around the conductance quantum $e^2/h$ , and hence is not associated with "bad metal" behavior, which is in stark contrast to the MIT in half-filled organic Mott insulators or that in doped inorganic Mott insulators. Through in-depth scaling analysis of the conductivity, it is found that the above carrier transport properties in the vicinity of the MIT can be described by a high-temperature Mott quantum critical crossover, which is theoretically argued to be a ubiquitous feature of various types of Mott transitions. [This document is the unedited Authors' version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright \copyright American Chemical Society after peer review. To access the final edited and published work see http://dx.doi.org/10.1021/acs.nanolett.6b03817]Comment: 40 pages, 16 figures in Nano Letters, ASAP (2017

EXPONENTIAL ATTRACTORS FOR NON-AUTONOMOUS DISSIPATIVE SYSTEM

In this paper we will introduce a version of exponential attractor for non-autonomous equations as a time dependent set with uniformly bounded finite fractal dimension which is positively invariant and attracts every bounded set at an exponential rate. This is a natural generalization of the existent notion for autonomous equations. A generation theorem will be proved under the assumption that the evolution operator is a compact perturbation of a contraction. In the second half of the paper, these results will be applied to some non-autonomous chemotaxis system