A generalization of Serre's conjecture and some related issues

AbstractSeveral topics concerned with multivariate polynomial matrices like unimodular matrix completion, matrix determinantal or primitive factorization, matrix greatest common factor existence and subsequent extraction along with relevant primeness and coprimeness issues are related to a conjecture which may be viewed as a type of generalization of the original Serre problem (conjecture) solved nonconstructively in 1976 and constructively, more recently. This generalized Serre conjecture is proved to be equivalent to several other unsettled conjectures and, therfore, all these conjectures constitute a complete set in the sense that solution to any one also solves all the remaining

Optimal feature selection for learning-based algorithms for sentiment classification

Sentiment classification is an important branch of cognitive computation—thus the further studies of properties of sentiment analysis is important. Sentiment classification on text data has been an active topic for the last two decades and learning-based methods are very popular and widely used in various applications. For learning-based methods, a lot of enhanced technical strategies have been used to improve the performance of the methods. Feature selection is one of these strategies and it has been studied by many researchers. However, an existing unsolved difficult problem is the choice of a suitable number of features for obtaining the best sentiment classification performance of the learning-based methods. Therefore, we investigate the relationship between the number of features selected and the sentiment classification performance of the learning-based methods. A new method for the selection of a suitable number of features is proposed in which the Chi Square feature selection algorithm is employed and the features are selected using a preset score threshold. It is discovered that there is a relationship between the logarithm of the number of features selected and the sentiment classification performance of the learning-based method, and it is also found that this relationship is independent of the learning-based method involved. The new findings in this research indicate that it is always possible for researchers to select the appropriate number of features for learning-based methods to obtain the best sentiment classification performance. This can guide researchers to select the proper features for optimizing the performance of learning-based algorithms. (A preliminary version of this paper received a Best Paper Award at the International Conference on Extreme Learning Machines 2018.)Accepted versio

Constant Sequence Extension for Fast Search Using Weighted Hamming Distance

Representing visual data using compact binary codes is attracting increasing attention as binary codes are used as direct indices into hash table(s) for fast non-exhaustive search. Recent methods show that ranking binary codes using weighted Hamming distance (WHD) rather than Hamming distance (HD) by generating query-adaptive weights for each bit can better retrieve query-related items. However, search using WHD is slower than that using HD. One main challenge is that the complexity of extending a monotone increasing sequence using WHD to probe buckets in hash table(s) for existing methods is at least proportional to the square of the sequence length, while that using HD is proportional to the sequence length. To overcome this challenge, we propose a novel fast non-exhaustive search method using WHD. The key idea is to design a constant sequence extension algorithm to perform each sequence extension in constant computational complexity and the total complexity is proportional to the sequence length, which is justified by theoretical analysis. Experimental results show that our method is faster than other WHD-based search methods. Also, compared with the HD-based non-exhaustive search method, our method has comparable efficiency but retrieves more query-related items for the dataset of up to one billion items

Exploratory Study of Promotional Videos in the 10 Major Tourist Destinations in China: A Content Analysis

Since the mid 1990s, both domestic and international tourism in China has grown rapidly evidenced in many destinations. In particular, tourism plays an important role as a major destination in regional economic development. This article reviews promotional videos of the main destinations in China as research data, analyzes the common content elements, orientations, presentation methods, persuasion methods, time patterns, and the use of sound, music and volume in Beijing, Nanjing, Chengdu, Chongqing, Xi’an, Qingdao, Shanghai, Shenzhen, Xiamen, and Hangzhou. Finally, the authors make suggestions regarding the images of promotional videos, reflecting on the subjects, contents and techniques of shooting the videos, and study the content and techniques of the photographers. Moreover, the authors put forward suggestions on improving promotional videos of destinations from the perspective of the subjects, contents and techniques of shooting