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## 1. chinaXiv:202110.00056 [pdf]

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.

## 2. chinaXiv:202109.00058 [pdf]

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.

## 3. chinaXiv:202004.00005 [pdf]

Subjects: Mathematics >> Applied Mathematics
Subjects: Information Science and Systems Science >> Other Disciplines of Information Science and Systems Science

 本文的目的是建立区块链生态系统中采矿池博弈共识均衡的一般框架，特别是在区块链生态系统中，通过使用一个新的概念“共识博弈（Consensus Game）”，解释与挖掘差距（Gap Games）博弈行为相关的共识均衡存在的意义上的稳定性，这里，区块链生态系统主要是指应用2008年中本聪（Nakamoto）所提出的“工作证明”(Proof of Work) 这一关键共识，将区块链工作的费用、报酬机制和采矿权三类不同因素考虑在内的经济活动。 为了做到这一点，我们首先概述了采矿池游戏共识均衡的一般存在性是如何表述的，然后通过区块链共识框架下共识均衡的存在性来解释比特币缺口博弈 (Gap博弈) 稳定性，然后利用博弈论中矿工的利润函数作为收益，建立了一般矿业缺口博弈一致均衡的一般存在性结果。作为应用，建立了缺口博弈 (Gap博弈)一致均衡的一般存在性结果，这不仅有助于我们在区块链生态系统的一般框架下断言缺口博弈 (Gap博弈) 的一般稳定性的存在性，但也让我们能够说明在研究采矿池博弈时的一些不同现象，这些现象可能是由于采矿者的(Gap博弈)行为与嵌入比特币经济学的情景造成的。 我们对区块链生态系统挖掘缺口博弈稳定性的解释研究表明，共识均衡的概念可能对共识经济学基础理论的发展起到重要作用

## 4. chinaXiv:201907.00015 [pdf]

Subjects: Mathematics >> Applied Mathematics

 研究了一道工序智能加工系统轨道式自动引导车（RGV）调度问题. 该问题为2018年全国大学生数学建模竞赛B题的一部分. 系统由一辆轨道式自动引导车和若干台计算机数控机床(CNC)等部件组成, RGV操控多台CNC完成多个物料加工, RGV调度方案决定了系统的效率. 以 RGV的移动路径为决策变量, 以RGV在CNC上的操作结束时刻为时间节点, 以物料加工剩余时间为状态变量, 给出了问题的数学模型, 但模型中的部分参数以决策变量为下标. 通过定义新的变量和约束, 将模型修改为不含变量下标和分段函数的非线性混合整数规划模型. 最后给出了算例, 说明了模型的正确性和可操作性.

## 5. chinaXiv:201704.00108 [pdf]

Subjects: Mathematics >> Applied Mathematics

 研究了动态围堵嫌犯问题, 假设网络边长相等, 交巡警与嫌犯的速度相等. 建立了嫌犯移动信息更新下的交巡警调度问题的0-1线性整数规划模型, 模型利用点截集条件使调度后的警力形成围堵圈, 并对嫌犯的逃跑行为建模, 由此得到了动态围堵嫌犯问题的动态模拟模型. 算例考虑分割非等边长网络的边, 然后将分割后的网络视为等边长网络.