Quantum query complexity of entropy estimation

Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on the number of samples to estimate these entropies have been established in the classical setting, while little is known about their quantum counterparts. In this paper, we give the first quantum algorithms for estimating $\alpha$-R\'enyi entropies (Shannon entropy being 1-Renyi entropy). In particular, we demonstrate a quadratic quantum speedup for Shannon entropy estimation and a generic quantum speedup for $\alpha$-R\'enyi entropy estimation for all $\alpha\geq 0$, including a tight bound for the collision-entropy (2-R\'enyi entropy). We also provide quantum upper bounds for extreme cases such as the Hartley entropy (i.e., the logarithm of the support size of a distribution, corresponding to $\alpha=0$) and the min-entropy case (i.e., $\alpha=+\infty$), as well as the Kullback-Leibler divergence between two distributions. Moreover, we complement our results with quantum lower bounds on $\alpha$-R\'enyi entropy estimation for all $\alpha\geq 0$.Comment: 43 pages, 1 figur

Demystifying Neural Style Transfer

Neural Style Transfer has recently demonstrated very exciting results which catches eyes in both academia and industry. Despite the amazing results, the principle of neural style transfer, especially why the Gram matrices could represent style remains unclear. In this paper, we propose a novel interpretation of neural style transfer by treating it as a domain adaptation problem. Specifically, we theoretically show that matching the Gram matrices of feature maps is equivalent to minimize the Maximum Mean Discrepancy (MMD) with the second order polynomial kernel. Thus, we argue that the essence of neural style transfer is to match the feature distributions between the style images and the generated images. To further support our standpoint, we experiment with several other distribution alignment methods, and achieve appealing results. We believe this novel interpretation connects these two important research fields, and could enlighten future researches.Comment: Accepted by IJCAI 201

Impulsive stabilization of high-order nonlinear retarded differential equations

summary:In this paper, impulsive stabilization of high-order nonlinear retarded differential equations is investigated by using Lyapunov functions and some analysis methods. Our results show that several non-impulsive unstable systems can be stabilized by imposition of impulsive controls. Some recent results are extended and improved. An example is given to demonstrate the effectiveness of the proposed control and stabilization methods

Flipping a Virtual EFL Public Speaking Class Integrated With MOOCs During the COVID-19 Pandemic

This case study explored Chinese undergraduate EFL students’ attitudes to and perceptions of an online English public speaking course, which employs a virtual flipped classroom model and MOOCs during the COVID-19 pandemic outbreak. Since all classes were moved online, a previously flipped public speaking course integrated with MOOCs was converted into a virtual flipped classroom. All 25 participants of the study were undergraduate students in the science, technology, engineering, and mathematics (STEM) field. Zoom, Blackboard, and QQ instant messenger were platforms utilized in instruction. There were weekly two-hour Zoom meetings with learning activities using MOOCs on Blackboard. The study collected and corroborated results from multiple data sources, including surveys, focus group discussions, student presentation videos, and the instructor’s reflective teaching journals. Data was analyzed using Charmaz’s (2006) grounded theory. Survey results indicated that the 25 participants generally felt positive about the virtual learning environment. Students strategically adapted to all three digital platforms (Zoom, Blackboard, and QQ instant messenger), the MOOCs, and the flipped classroom model. They were engaged in exploring a variety of digital platforms, online learning resources, remotely collaborating with peers and interacting with the instructor. Incorporating MOOCs in a virtual flipped classroom allowed for application of theory into practice under the instructor’s supervision, which maximized the students’ speaking and learning opportunities. Recommendations for ELT practitioners and further research are also provided

The Secrets of Salient Object Segmentation

In this paper we provide an extensive evaluation of fixation prediction and salient object segmentation algorithms as well as statistics of major datasets. Our analysis identifies serious design flaws of existing salient object benchmarks, called the dataset design bias, by over emphasizing the stereotypical concepts of saliency. The dataset design bias does not only create the discomforting disconnection between fixations and salient object segmentation, but also misleads the algorithm designing. Based on our analysis, we propose a new high quality dataset that offers both fixation and salient object segmentation ground-truth. With fixations and salient object being presented simultaneously, we are able to bridge the gap between fixations and salient objects, and propose a novel method for salient object segmentation. Finally, we report significant benchmark progress on three existing datasets of segmenting salient objectsComment: 15 pages, 8 figures. Conference version was accepted by CVPR 201