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1. chinaXiv:202107.00011 [pdf]

Properties of several fuzzy set spaces

Huan Huang
Subjects: Mathematics >> Mathematics (General)

This paper discusses the properties the spaces of fuzzy sets in a metric s- pace equipped with the endograph metric and the sendograph metric, re- spectively. We fist discuss the level characterizations of the Γ-convergence and the endograph metric, and point out the elementary relationships among Γ-convergence, endograph metric and the sendograph metric. On the basis of these results, we present the characterizations of total boundedness, rel- ative compactness and compactness in the space of compact positive α-cuts fuzzy sets equipped with the endograph metric, and in the space of com- pact support fuzzy sets equipped with the sendograph metric, respectively. Furthermore, we give completions of these two kinds of spaces, respectively.

submitted time 2021-11-27 Hits6833Downloads440 Comment 0

2. chinaXiv:202105.00070 [pdf]


Subjects: Statistics >> Mathematical Statistics
Subjects: Computer Science >> Computer Application Technology
Subjects: Information Science and Systems Science >> Basic Disciplines of Information Science and Systems Science


submitted time 2021-11-10 Hits13434Downloads1534 Comment 0

3. chinaXiv:202110.00083 [pdf]

Characterizations of compactness in fuzzy set space with Lp metric

Subjects: Mathematics >> Mathematics (General)

In this paper, we give characterizations of compactness in fuzzy set space with Lpmetric. Based on these results, we present completions of fuzzy set spaces with Lpmetric. The fuzzy sets discussed in this paper are fuzzy sets in general metric space. We also point out that the results in this paper generalize the results given in our previous paper.

submitted time 2021-10-25 Hits1588Downloads135 Comment 0

4. chinaXiv:202110.00056 [pdf]

Resonance Algorithm: A New Look at the Shortest Path Problem

Liu, Yu; Lin, Qiguang; Hong, Binbin; Hjerpe, Daniel; Liu, Xiaofeng
Subjects: Mathematics >> Applied Mathematics
Subjects: Information Science and Systems Science >> Other Disciplines of Information Science and Systems Science

The shortest path problem (SPP) is a classic problem and appears in a wide range of applications. Although a variety of algorithms already exist, new advances are still being made, mainly tuned for particular scenarios to have better performances. As a result, they become more and more technically complex and sophisticated. Here we developed a novel nature-inspired algorithm to compute all possible shortest paths between two nodes in a graph: Resonance Algorithm (RA), which is surprisingly simple and intuitive. Besides its simplicity, RA turns out to be much more time-efficient for large-scale graphs than the extended Dijkstra's algorithm (such that it gives all possible shortest paths). Moreover, RA can handle any undirected, directed, or mixed graphs, irrespective of loops, unweighted or positively-weighted edges, and can be implemented in a fully decentralized manner. These good properties ensure RA a wide range of applications.

submitted time 2021-10-11 Hits2728Downloads255 Comment 0

5. chinaXiv:202109.00058 [pdf]

Dating the First Case of COVID-19 Epidemic from a Probabilistic Perspective

Zhouwang Yang; Yunhe Hu; Zhiwei Ding; Tiande Guo
Subjects: Mathematics >> Applied Mathematics

In the early days of the epidemic of coronavirus disease 2019 (COVID-19), due to insufficient knowledge of the pandemic, inadequate nucleic acid tests, lack of timely data reporting, etc., the origin time of the onset of COVID-19 is difficult to determine. Therefore, source tracing is crucial for infectious disease prevention and control. The purpose of this paper is to infer the origin time of pandemic of COVID-19 based on a data and model hybrid driven method. We model the testing positive rate to fit its actual trend, and use the least squares estimation to obtain the optimal model parameters. Further, the kernel density estimation is applied to infer the origin time of pandemic given the specific confidence probability. By selecting 12 representative regions in the United States for analysis, the dates of the first infected case with 50% confidence probability are mostly between August and October 2019, which are earlier than the officially announced date of the first confirmed case in the United States on January 20, 2020. The experimental results indicate that the COVID-19 pandemic in the United States starts to spread around September 2019 with a high confidence probability. In addition, the existing confirmed cases are also used in Wuhan City and Zhejiang Province in China to infer the origin time of COVID-19 and provide the confidence probability. The results show that the spread of COVID-19 pandemic in China is likely to begin in late December 2019.

submitted time 2021-09-22 Hits24886Downloads4516 Comment 0

6. chinaXiv:202108.00116 [pdf]

Some discussions on Hausdorff metric

Subjects: Mathematics >> Mathematics (General)

In this paper, we discuss the properties of functions generated using Hausdorff metric.

submitted time 2021-08-30 Hits2268Downloads256 Comment 0

7. chinaXiv:202108.00117 [pdf]


耿海洋; 李吉星
Subjects: Psychology >> Cognitive Psychology
Subjects: Biology >> Neurobiology


submitted time 2021-08-30 Hits6510Downloads869 Comment 0

8. chinaXiv:202108.00057 [pdf]

Properties of fuzzy set

Subjects: Mathematics >> Mathematics (General)

In this paper, we give some properties related to platform points of a fuzzy set and their applications.

submitted time 2021-08-10 Hits3598Downloads362 Comment 0

9. chinaXiv:202107.00070 [pdf]

A Note on the High-dimensional Sparse Fourier Transform in the Continuous Setting

Subjects: Mathematics >> Theoretical Computer Science

In this paper, we theoretically propose a new hashing scheme to establish the sparse Fourier transform in high-dimensional space. The estimation of the algorithm complexity shows that this sparse Fourier transform can overcome the curse of dimensionality. To the best of our knowledge, this is the first polynomial-time algorithm to recover the high-dimensional continuous frequencies.

submitted time 2021-07-26 Hits3059Downloads236 Comment 0

10. chinaXiv:202105.00069 [pdf]

Copositivity for a class of fourth order symmetric tensors given by scalar dark matter

宋义生; 李旭东
Subjects: Mathematics >> Mathematical Physics

In this paper, we mainly discuss the copositivity of 4th order symmetric tensor defined by scalar dark matter stable under a $\mathbb{Z}_{3}$ discrete group, and obtain an analytically necessary and sufficient condition of the copositivity of such a class of tensors. Furthermore, this analytic expression may be used to verify the vacuum stability for $\mathbb{Z}_{3}$ scalar dark matter.

submitted time 2021-06-16 Hits8357Downloads595 Comment 0

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