2,006 research outputs found
On the intermittency front of stochastic heat equation driven by colored noises
We study the propagation of high peaks (intermittency front) of the solution
to a stochastic heat equation driven by multiplicative centered Gaussian noise
in . The noise is assumed to have a general homogeneous
covariance in both time and space, and the solution is interpreted in the
senses of the Wick product. We give some estimates for the upper and lower
bounds of the propagation speed, based on a moment formula of the solution.
When the space covariance is given by a Riesz kernel, we give more precise
bounds for the propagation speed
Stochastic heat equation with rough dependence in space
This paper studies the nonlinear one-dimensional stochastic heat equation
driven by a Gaussian noise which is white in time and which has the covariance
of a fractional Brownian motion with Hurst parameter
1/4\textless{}H\textless{}1/2 in the space variable. The existence and
uniqueness of the solution u are proved assuming the nonlinear coefficient is
differentiable with a Lipschitz derivative and vanishes at 0. In the case of a
multiplicative noise, that is the linear equation, we derive the Wiener chaos
expansion of the solution and a Feynman-Kac formula for the moments of the
solution. These results allow us to establish sharp lower and upper asymptotic
bounds for the moments of the solution
On the intermittency front of stochastic heat equation driven by colored noises
We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in RdRd. The noise is assumed to have a general homogeneous covariance in both time and space, and the solution is interpreted in the senses of the Wick product. We give some estimates for the upper and lower bounds of the propagation speed, based on a moment formula of the solution. When the space covariance is given by a Riesz kernel, we give more precise bounds for the propagation speed
New bounding techniques for channel codes over quasi-static fading channels
This thesis is intended to provide several new bounding techniques for channel codes over quasi-static fading channels (QSFC). This type of channel has drawn more and more attention recently with the demanding need for higher capacity and more reliable wireless communication systems. Although there have been some published results on analyzing the performance of channel codes over QSFCs, most of them produced quite loose performance upper bounds. In this thesis, the general Gallager bounding approach which provides convergent upper bounds of coded systems over QSFCs is addressed first. It is shown that previous Gallager bounds employing trivial low SNR bounds tended to be quite loose. Then improved low instantaneous SNR bounds are derived for two classes of convolutional codes including turbo codes. Consequently, they are combined with the classical Union-Chernoff bound to produce new performance upper bounds for simple convolutional and turbo codes over single-input single-output (SISO) QSFCs. The new bound provides a much improved alternative to characterizing the performance of channel codes over QSFCs over the existing ones. Next the new bounding approach is extended to cases of serially concatenated space-time block codes, which show equivalence with SISO QSFCs. Tighter performance bounds are derived for this coding scheme for two specific cases: first a convolutional code, and later a turbo code. Finally, the more challenging cases of multiple-input multiple-output (MIMO) QSFCs are investigated. Several performance upper bounds are derived for the bit error probability of different cases of space-time trellis codes (STTC) over QSFCs using a new and tight low SNR bound. Also included in this work is an algorithm for computing the unusual information eigenvalue spectrum of STTCs
The link between X-efficiencies and the share prices of banks before and after M&A--Evidence from China
This research focuses on the impact of mergers and acquisitions on the cost efficiency and stock price of China’s listed banks from 2008 to 2018,and further explores the relationship between cost efficiency and stock price. The results show that after the M&A , the cost efficiency has improved. However, M&A do not improve short-term performance to banks. Finally, the regression result shows that there is a significant negative correlation between bank cost efficiency and stock price in a period of time before and after M&A
SlotDiffusion: Object-Centric Generative Modeling with Diffusion Models
Object-centric learning aims to represent visual data with a set of object
entities (a.k.a. slots), providing structured representations that enable
systematic generalization. Leveraging advanced architectures like Transformers,
recent approaches have made significant progress in unsupervised object
discovery. In addition, slot-based representations hold great potential for
generative modeling, such as controllable image generation and object
manipulation in image editing. However, current slot-based methods often
produce blurry images and distorted objects, exhibiting poor generative
modeling capabilities. In this paper, we focus on improving slot-to-image
decoding, a crucial aspect for high-quality visual generation. We introduce
SlotDiffusion -- an object-centric Latent Diffusion Model (LDM) designed for
both image and video data. Thanks to the powerful modeling capacity of LDMs,
SlotDiffusion surpasses previous slot models in unsupervised object
segmentation and visual generation across six datasets. Furthermore, our
learned object features can be utilized by existing object-centric dynamics
models, improving video prediction quality and downstream temporal reasoning
tasks. Finally, we demonstrate the scalability of SlotDiffusion to
unconstrained real-world datasets such as PASCAL VOC and COCO, when integrated
with self-supervised pre-trained image encoders.Comment: Project page: https://slotdiffusion.github.io/ . An earlier version
of this work appeared at the ICLR 2023 Workshop on Neurosymbolic Generative
Models: https://nesygems.github.io/assets/pdf/papers/SlotDiffusion.pd
Neural Wavelet-domain Diffusion for 3D Shape Generation
This paper presents a new approach for 3D shape generation, enabling direct
generative modeling on a continuous implicit representation in wavelet domain.
Specifically, we propose a compact wavelet representation with a pair of coarse
and detail coefficient volumes to implicitly represent 3D shapes via truncated
signed distance functions and multi-scale biorthogonal wavelets, and formulate
a pair of neural networks: a generator based on the diffusion model to produce
diverse shapes in the form of coarse coefficient volumes; and a detail
predictor to further produce compatible detail coefficient volumes for
enriching the generated shapes with fine structures and details. Both
quantitative and qualitative experimental results manifest the superiority of
our approach in generating diverse and high-quality shapes with complex
topology and structures, clean surfaces, and fine details, exceeding the 3D
generation capabilities of the state-of-the-art models
- …