Asymmetry Helps: Eigenvalue and Eigenvector Analyses of Asymmetrically Perturbed Low-Rank Matrices

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly perturbed version $\mathbf{M}$ is observed. The noise matrix $\mathbf{M}-\mathbf{M}^{\star}$ is composed of zero-mean independent (but not necessarily homoscedastic) entries and is, therefore, not symmetric in general. This might arise, for example, when we have two independent samples for each entry of $\mathbf{M}^{\star}$ and arrange them into an {\em asymmetric} data matrix $\mathbf{M}$. The aim is to estimate the leading eigenvalue and eigenvector of $\mathbf{M}^{\star}$. We demonstrate that the leading eigenvalue of the data matrix $\mathbf{M}$ can be $O(\sqrt{n})$ times more accurate --- up to some log factor --- than its (unadjusted) leading singular value in eigenvalue estimation. Further, the perturbation of any linear form of the leading eigenvector of $\mathbf{M}$ --- say, entrywise eigenvector perturbation --- is provably well-controlled. This eigen-decomposition approach is fully adaptive to heteroscedasticity of noise without the need of careful bias correction or any prior knowledge about the noise variance. We also provide partial theory for the more general rank-$r$ case. The takeaway message is this: arranging the data samples in an asymmetric manner and performing eigen-decomposition could sometimes be beneficial.Comment: accepted to Annals of Statistics, 2020. 37 page

Construction of Human Neuromuscular Disease-Related Gene Site-Specific Mutant Cell Line by Cas9 Mutation System

Objective: to construct human neuromuscular disease-related gene site-specific mutant cell line by Cas9 mutation system. Methods: according to the principle of CRISPR/Cas9 target design, the exon region of CXCR4 gene sequence was found in the National Center for Biotechnology Information (NCBI) of the United States. Two sgRNAs were designed. Lenticrisprv2 was used as the vector to construct the lenticrisprv2-sgrna recombinant plasmid, which was transformed into the sensitive stbl3 strain. The monoclonal sequencing was selected to verify and expand the culture of the plasmid, then it was transferred to 293T cells for packaging to a slow virus. The virus was collected and infected with 4T1 cells. The monoclonal cells were isolated and cultured by puromycin screening and limited dilution method. The genomic DNA of the selected monoclonal cells was extracted and the DNA fragment near the knockout site was amplified by PCR and sequenced. Results: one cell line had 6 deletion mutations, including DYSF mutation site of neuromuscular disease gene and HEK293T cell model knocked out by DYSF mutation site of neuromuscular disease gene. Conclusion: the recombinant plasmid targeting CXCR4 gene was obtained by CRISPR/Cas9 system, and the human neuromuscular disease-related gene site-specific mutant cell line was successfully constructed

Educational pedagogical and adaptational work with international students and preparatory department attendees of Pavlo Tychyna Uman State Pedagogical University

To address the sustainability, scalability, and reliability problems that data centers are currently facing, we propose three passive optical interconnect (POI) architectures on top of the rack. The evaluation results show that all three architectures offer high reliability performance (connection availability for intra-rack interconnections higher than 99.999%) in a cost-efficient way.QC 20160525</p

Bernstein Theorems for Space-like Graphs with Parallel Mean Curvature and Controlled Growth

In this paper, we obtain an Ecker-Huisken type result for entire graphs with parallel mean curvature.Comment: 12 page

Seasonal variation of thermal sensations in residential buildings in the hot summer and cold winter zone of China

The seasonal differences of neutral or acceptable temperatures between summer and winter were revealed by previous researchers, but the studies on the difference of human thermal adaption in transitional seasons are insufficient. To clarify this, this paper analyzes the data from a nationwide field study database, including a year-long survey which was carried out in 505 residential buildings in six cities located in the Hot Summer and Cold Winter (HSCW) zone of China involving 11,524 subjects. Results show a significant difference of adaptive responses in different seasons. Air temperature is found to be the most significant driver for behavioral responses, and a lag of behavioral responses behind climate change in transitional seasons is observed. Occupants not only adjust clothing insulation according to air temperature in different seasons, but also actively control indoor air movement, including closing/opening windows and using fans. The seasonal, monthly and daily neutral temperatures are studied, implying that occupants’ thermal experience history has significant effect on their thermal comfort by behavioral, physiological and psychological paths. Thus, the running mean air temperature method and aPMV model are recommended for thermal comfort evaluation in free-running space. The research results provide comprehensive understanding of the thermal comfort demand which directly affects the energy needs for heating and cooling purpose. The findings provide scientific evidence to the concept that dynamic thermal comfort temperature range should be considered in the evaluation of indoor thermal environment

Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization

Natural policy gradient (NPG) methods are among the most widely used policy optimization algorithms in contemporary reinforcement learning. This class of methods is often applied in conjunction with entropy regularization -- an algorithmic scheme that encourages exploration -- and is closely related to soft policy iteration and trust region policy optimization. Despite the empirical success, the theoretical underpinnings for NPG methods remain limited even for the tabular setting. This paper develops $\textit{non-asymptotic}$ convergence guarantees for entropy-regularized NPG methods under softmax parameterization, focusing on discounted Markov decision processes (MDPs). Assuming access to exact policy evaluation, we demonstrate that the algorithm converges linearly -- or even quadratically once it enters a local region around the optimal policy -- when computing optimal value functions of the regularized MDP. Moreover, the algorithm is provably stable vis-\`a-vis inexactness of policy evaluation. Our convergence results accommodate a wide range of learning rates, and shed light upon the role of entropy regularization in enabling fast convergence.Comment: v2 adds new proofs and improved results; accepted to Operations Researc