Ergodic theory of amenable semigroup actions

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.     

High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Let _l be the critical exponent associated with the probability thatl independentN-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ₂=0.6240±0.0005±0.0011 and ₃=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ₂=5/8 and ₃=35/24.     

Schrödinger invariance and strongly anisotropic critical systems

The extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated. For the special case of an anisotropy or dynamical exponent =z=2, the group of local scale transformation considered is the Schrödinger group, which can be obtained as the nonrelativistic limit of the conformal group. The requirement of Schrödinger invariance determines the two-point function in the bulk and reduces the three-point function to a scaling form of a single variable. Scaling forms are also derived for the two-point function close to a free surface which can be either spacelike or timelike. These results are reproduced in several exactly solvable statistical systems, namely the kinetic Ising model with Glauber dynamics, lattice diffusion, Lifshitz points in the spherical model, and critical dynamics of the spherical model with a nonconserved order parameter. For generic values of , evidence from higher-order Lifshitz points in the spherical model and from directed percolation suggests a simple scaling form of the two-point function.     

On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.     

Adaptive adversarial prototyping network for few-shot prototypical translation

Translating multiple real-world source images to a single prototypical image is a challenging problem. Notably, these source images belong to unseen categories that did not exist during model training. We address this problem by proposing an adaptive adversarial prototype network (AAPN) and enhancing existing one-shot classification techniques. To overcome the limitations that traditional works cannot extract samples from novel categories, our method tends to solve the image translation task of unseen categories through a meta-learner. We train the model in an adversarial learning manner and introduce a style encoder to guide the model with an initial target style. The encoded style latent code enhances the performance of the network with conditional target style images. The AAPN outperforms the state-of-the-art methods in one-shot classification of brand logo dataset and achieves the competitive accuracy in the traffic sign dataset. Additionally, our model improves the visual quality of the reconstructed prototypes in unseen categories. Based on the qualitative and quantitative analysis, the effectiveness of our model for few-shot classification and generation is demonstrated.     

一种3D眼镜虚拟试戴系统的实现

针对人脸图像试戴3D眼镜过程中存在的镜腿遮挡人脸问题,文中提出一种基于人脸图像的3D眼镜虚拟试戴技术。利用构建的人脸形状的三维模型,使其在虚拟试戴中对镜腿起到消隐作用,解决镜腿的遮挡问题。文中对输入的人脸图像进行关键点检测,结合Graham扫描法求得人脸形状的凸多边形,利用平移扫描构建人脸形状的三维模型。此外,文中根据定位人脸图像上的关键点以及姿态估计后对三维眼镜模型的变换,将眼镜模型佩戴到人脸图像上。实验结果表明,该方法对于多视角的人脸图像实现了虚拟试戴效果,解决了多种视角下人脸图像试戴过程中镜腿的遮挡问题,虚拟试戴中镜腿遮挡平均准确率为94.5%,遮挡精度较高。     

航空机载软件全数字仿真测试系统的设计与实现

针对航空机载软件测试环境与开发环境冲突、测试环境可控性和通用性差、非干预性测试困难的问题,分析了全物理实装测试环境、半实物仿真测试环境的优缺点,研究了全数字仿真测试技术,设计并实现了一种航空机载软件全数字仿真测试系统。该系统由仿真核心平台、仿真工具组件、协同仿真组件和人机交互组件构成,提供了航空机载处理器、内存、外设等多种可重用库。提出了基于底层虚拟机的动态二进制翻译技术、协同仿真时间同步和数据通信机制等关键技术,实现了航空机载软件全数字高速闭环仿真运行。工程实践证明,该系统能达到降低硬件设备的依耐性、简化测试环境搭建的复杂度、提高测试效率约42%的目的。     

Three-body interactions,rotational invariance and the elastic consistency of lattice dynamical models for face-centred tetragonal indium

The origin of the elastic inconsistency ofdaf, mas andgtf models for non-cubic solids and the failure of their force constants to comply with all the rotational invariance conditions are analysed by resolving the atomic displacements of face-centred tetragonal indium along three mutually perpendicular directions. It is shown that a lattice dynamical model suffers from these deficiencies as a consequence of its neglect of three-body interactions as well as the mixed neighbour interactions associated with the angular forces, while thecgw model which incorporates both these interactions is elastically consistent and its potential energy rotationally invariant. The degree of equivalence that exists among the force constants ofdaf, mas, gtf andcgw models, the distortions introduced by the elastic inconsistency into the phonon dispersion curves of fct indium as well as the consequences of imposing the rotational invariance conditions on the force constants of a lattice dynamical model are discussed.