arXiv subjects
Publications and source records attributed to Yutao Liu.
We develop a new method in the computation of equivariant homotopy, which is based on the splitting of cofiber sequences associated to universal spaces in the category of equivariant spectra. In particular, we use this method to compute the homotopy of $H\underline{\mathbb{Z}}$ for $G=D_{2p}$ and $A_5$.
Let $G$ be a finite group. We re-analyze the splitting of rational $G$-spectra, which is discussed in Barne's thesis and traces back to Greenlees and May. We will study how the splitting behaves under a localization which is weaker than rationalization and discuss its application in computing equivariant cohomology of $G$-spectra. In particular, we will explicitly compute $π_\bigstar(H\underline{\mathbb{Z}})$ and $π_\bigstar(HA_G)$ for the dihedral group $G=D_{2p}$. The additive structures and partial multiplicative structures are already computed by Kriz, Lu, and Zou. Our new method will provide a systematic way to compute them as $RO(D_{2p})$-graded rings.
We consider inference from non-random samples in data-rich settings where high-dimensional auxiliary information is available both in the sample and the target population, with survey inference being a special case. We propose a regularized prediction approach that predicts the outcomes in the population using a large number of auxiliary variables such that the ignorability assumption is reasonable while the Bayesian framework is straightforward for quantification of uncertainty. Besides the auxiliary variables, inspired by Little & An (2004), we also extend the approach by estimating the propensity score for a unit to be included in the sample and also including it as a predictor in the machine learning models. We show through simulation studies that the regularized predictions using soft Bayesian additive regression trees yield valid inference for the population means and coverage rates close to the nominal levels. We demonstrate the application of the proposed methods using two different real data applications, one in a survey and one in an epidemiology study.
The depth images denoising are increasingly becoming the hot research topic nowadays because they reflect the three-dimensional (3D) scene and can be applied in various fields of computer vision. But the depth images obtained from depth camera usually contain stains such as noise, which greatly impairs the performance of depth related applications. In this paper, considering that group-based image restoration methods are more effective in gathering the similarity among patches, a group based nuclear norm and learning graph (GNNLG) model was proposed. For each patch, we find and group the most similar patches within a searching window. The intrinsic low-rank property of the grouped patches is exploited in our model. In addition, we studied the manifold learning method and devised an effective optimized learning strategy to obtain the graph Laplacian matrix, which reflects the topological structure of image, to further impose the smoothing priors to the denoised depth image. To achieve fast speed and high convergence, the alternating direction method of multipliers (ADMM) is proposed to solve our GNNLG. The experimental results show that the proposed method is superior to other current state-of-the-art denoising methods in both subjective and objective criterion.
This is an expository paper about a $\mathcal{C}_2$-equivariant analog of the bar construction. We will explain its construction and prove how it acts as a $σ$-fold delooping machine on twisted monoids, where $σ$ denotes the sign representation.