eISSN:
 2577-8838

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Volume 1, 2018

Mathematical Foundations of Computing (MFC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not conform to these standards will be rejected.

Areas covered include analysis of algorithms,automata, computational complexity,theoretical computer science,geometry in computer science,discrete algorithms,secure computing,privacy-aware computing,distributed computing and networking,computational probability,statistical computation and simulation,computational intelligence,computational social network,computational biology, coding theory, graph theory,computational learning theory,probability and statistics in computer science, combinatorial optimization in computer science,logic and semantics in computer science,numerical analysis in computer science, numerical algebra in computer science and symbolic computation / computer algebra, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in computer science are welcome.

More detailed indication of the journal's scope is given by the subject interests of the members of the board of editors.

All papers will undergo a thorough peer reviewing process unless the subject matter of the paper does not fit the journal; in this case, the author will be informed promptly. Every effort will be made to secure a decision in three months and to publish accepted papers within six months.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • MFC will publish four issues starting from 2018 in February, May, August and November.
  • MFC is a joint publication of the American Institute of Mathematical Sciences and Qufu Normal University. All rights reserved.

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Influence analysis: A survey of the state-of-the-art
Meng Han and Yingshu Li
2018, 1(3) : 201-253 doi: 10.3934/mfc.2018010 +[Abstract](954) +[HTML](720) +[PDF](2792.87KB)
Abstract:

Online social networks have seen an exponential growth in number of users and activities recently. The rapid proliferation of online social networks provides rich data and infinite possibilities for us to analyze and understand the complex inherent mechanism which governs the evolution of the new online world. This paper summarizes the state-of-art research results on social influence analysis in a broad sense. First, we review the development process of influence analysis in social networks based on several basic conceptions and features in a social aspect. Then the online social networks are discussed. After describing the classical models which simulate the influence spreading progress, we give a bird's eye view of the up-to-date literatures on influence diffusion models and influence maximization approaches. Third, we present the applications including web services, marketing, and advertisement services which based on the influence analysis. At last, we point out the research challenges and opportunities in this area for both industry and academia reference.

Total $\{k\}$-domination in special graphs
Haisheng Tan, Liuyan Liu and Hongyu Liang
2018, 1(3) : 255-263 doi: 10.3934/mfc.2018011 +[Abstract](334) +[HTML](228) +[PDF](337.78KB)
Abstract:

For a positive integer \begin{document}$k$\end{document} and a graph \begin{document}$G = (V,E)$\end{document}, a function \begin{document}$f:V \to \{0,1,...,k\}$\end{document} is called a total \begin{document}$\{k\}$\end{document}-dominating function of \begin{document}$G$\end{document} if \begin{document}$\sum_{u∈ N_G(v)}f(u)≥ k$\end{document} for each \begin{document}$v∈ V$\end{document}, where \begin{document}$N_G(v)$\end{document} is the neighborhood of \begin{document}$v$\end{document} in \begin{document}$G$\end{document}. The total \begin{document}$\{k\}$\end{document}-domination number of \begin{document}$G$\end{document}, denoted by \begin{document}$\gamma _t^{\left\{ k \right\}}\left( G \right)$\end{document}, is the minimum weight of a total \begin{document}$\{k\}$\end{document}-dominating function \begin{document}$G$\end{document}, where the weight of \begin{document}$f$\end{document} is \begin{document}$\sum_{v∈ V}f(v)$\end{document}. In this paper, we determine the exact values of the total \begin{document}$\{k\}$\end{document}-domination number for several commonly-encountered classes of graphs including cycles, paths, wheels, and pans.

Discrete heat transfer search for solving travelling salesman problem
Poonam Savsani and Mohamed A. Tawhid
2018, 1(3) : 265-280 doi: 10.3934/mfc.2018012 +[Abstract](390) +[HTML](438) +[PDF](865.09KB)
Abstract:

Within the academic circle the Traveling Salesman Problem (TSP), this is one of the most major NP-hard problems that have been a primary topic of discussion for years. Developing efficient algorithms to solve TSP have been the goal of many individuals, and so this has been addressed efficiently in this article. Here, a discrete heat transfer search (DHTS) is proposed to solve TSP. DHTS uses three distinct phases to update the city tours namely, conduction, convection, and radiation. Each phase performs a certain function as the conduction phase is a replica of the 2-Opt local search technique, the convection phase exchanges the random city with the finest city tour, and the radiation phase exchanges the random city among two separate city tours without compromising the basics of HTS algorithm. Bench test problems taken from TSPLIB successfully test the algorithm and demonstrate the fact that the proposed algorithm can attain results near the optimal values, and do so within an acceptable duration.

Improve symmetry of arbiter in APUF
Yang Xu, Huansheng Ning, Lingfeng Mao, Youzhong Li and Lijun Zhang
2018, 1(3) : 281-294 doi: 10.3934/mfc.2018013 +[Abstract](361) +[HTML](250) +[PDF](1737.1KB)
Abstract:

Arbiter-based physical unclonable function (APUF) is a classical kind of physical unclonable function (PUF). In APUF-based device authentication, the fairness of traditional APUF is insufficient due to setup time of arbiter. To solve this problem, in this paper we design an arbiter and conduct Monte Carlo simulations to test the performance of the new arbiter. In addition, we present some new evaluation metrics to evaluate the new arbiter quantitatively. Finally, we certify that the new arbiter can work continuously with both one stage racing paths and eight stages racing paths. The new arbiter has good performance in correct rate, stability and fairness. Particularly, it mitigates the setup time problem by reducing the Asymmetry.

A real-time aggregate data publishing scheme with adaptive ω-event differential privacy
Chengtao Yong, Yan Huo, Chunqiang Hu, Yanfei Lu and Guanlin Jing
2018, 1(3) : 295-309 doi: 10.3934/mfc.2018014 +[Abstract](328) +[HTML](311) +[PDF](1304.61KB)
Abstract:

Although massive real-time data collected from users can provide benefits to improve the quality of human daily lives, it is possible to expose users' privacy. \begin{document}$\epsilon$\end{document}-differential privacy is a notable model to provide strong privacy preserving in statistics. The existing works highlight \begin{document}$ω$\end{document}-event differential privacy with a fixed window size, which may not be suitable for many practical scenarios. In view of this issue, we explore a real-time scheme with adaptive \begin{document}$ω$\end{document}-event for differentially private time-series publishing (ADP) in this paper. In specific, we define a novel notion, Quality of Privacy (QoP) to measure both the utility of the released statistics and the performance of privacy preserving. According to this, we present an adaptive \begin{document}$ω$\end{document}-event differential privacy model that can provide privacy protection with higher accuracy and better privacy protection effect. In addition, we also design a smart grouping mechanism to improve the grouping performance, and then improve the availability of publishing statistics. Finally, comparing with the existing schemes, we exploit real-world and synthetic datasets to conduct several experiments to demonstrate the superior performance of the ADP scheme.

Network(graph) data research in the coordinate system
Liu Hui, Lin Zhi and Waqas Ahmad
2018, 1(1) : 1-10 doi: 10.3934/mfc.2018001 +[Abstract](831) +[HTML](433) +[PDF](708.5KB) Cited By(0)
Discrete heat transfer search for solving travelling salesman problem
Poonam Savsani and Mohamed A. Tawhid
2018, 1(3) : 265-280 doi: 10.3934/mfc.2018012 +[Abstract](390) +[HTML](438) +[PDF](865.09KB) Cited By(0)
How convolutional neural networks see the world --- A survey of convolutional neural network visualization methods
Zhuwei Qin, Fuxun Yu, Chenchen Liu and Xiang Chen
2018, 1(2) : 149-180 doi: 10.3934/mfc.2018008 +[Abstract](1207) +[HTML](1053) +[PDF](5025.25KB) Cited By(0)
L(2, 1)-labeling of the Cartesian and strong product of two directed cycles
Zehui Shao, Huiqin Jiang and Aleksander Vesel
2018, 1(1) : 49-61 doi: 10.3934/mfc.2018003 +[Abstract](684) +[HTML](398) +[PDF](392.27KB) Cited By(0)
CP_ABSC: An attribute-based signcryption scheme to secure multicast communications in smart grids
Chunqiang Hu, Jiguo Yu, Xiuzhen Cheng, Zhi Tian, Kemal Akkaya and and Limin Sun
2018, 1(1) : 77-100 doi: 10.3934/mfc.2018005 +[Abstract](897) +[HTML](598) +[PDF](1438.97KB) Cited By(0)
Application of learning algorithms in smart home IoT system security
Jian Mao, Qixiao Lin and Jingdong Bian
2018, 1(1) : 63-76 doi: 10.3934/mfc.2018004 +[Abstract](2157) +[HTML](1668) +[PDF](1032.13KB) Cited By(0)
Improve symmetry of arbiter in APUF
Yang Xu, Huansheng Ning, Lingfeng Mao, Youzhong Li and Lijun Zhang
2018, 1(3) : 281-294 doi: 10.3934/mfc.2018013 +[Abstract](361) +[HTML](250) +[PDF](1737.1KB) Cited By(0)
Hybrid binary dragonfly enhanced particle swarm optimization algorithm for solving feature selection problems
Mohamed A. Tawhid and Kevin B. Dsouza
2018, 1(2) : 181-200 doi: 10.3934/mfc.2018009 +[Abstract](785) +[HTML](580) +[PDF](609.18KB) Cited By(0)
\begin{document}$\{k\}$\end{document}-domination in special graphs">Total $\{k\}$-domination in special graphs
Haisheng Tan, Liuyan Liu and Hongyu Liang
2018, 1(3) : 255-263 doi: 10.3934/mfc.2018011 +[Abstract](334) +[HTML](228) +[PDF](337.78KB) Cited By(0)
Influence analysis: A survey of the state-of-the-art
Meng Han and Yingshu Li
2018, 1(3) : 201-253 doi: 10.3934/mfc.2018010 +[Abstract](954) +[HTML](720) +[PDF](2792.87KB) Cited By(0)
A survey on security and privacy issues of blockchain technology
Archana Prashanth Joshi, Meng Han and Yan Wang
2018, 1(2) : 121-147 doi: 10.3934/mfc.2018007 +[Abstract](3543) +[HTML](1963) +[PDF](3282.55KB) PDF Downloads(517)
Application of learning algorithms in smart home IoT system security
Jian Mao, Qixiao Lin and Jingdong Bian
2018, 1(1) : 63-76 doi: 10.3934/mfc.2018004 +[Abstract](2157) +[HTML](1668) +[PDF](1032.13KB) PDF Downloads(189)
Influence analysis: A survey of the state-of-the-art
Meng Han and Yingshu Li
2018, 1(3) : 201-253 doi: 10.3934/mfc.2018010 +[Abstract](954) +[HTML](720) +[PDF](2792.87KB) PDF Downloads(99)
CP_ABSC: An attribute-based signcryption scheme to secure multicast communications in smart grids
Chunqiang Hu, Jiguo Yu, Xiuzhen Cheng, Zhi Tian, Kemal Akkaya and and Limin Sun
2018, 1(1) : 77-100 doi: 10.3934/mfc.2018005 +[Abstract](897) +[HTML](598) +[PDF](1438.97KB) PDF Downloads(97)
How convolutional neural networks see the world --- A survey of convolutional neural network visualization methods
Zhuwei Qin, Fuxun Yu, Chenchen Liu and Xiang Chen
2018, 1(2) : 149-180 doi: 10.3934/mfc.2018008 +[Abstract](1207) +[HTML](1053) +[PDF](5025.25KB) PDF Downloads(85)
Network(graph) data research in the coordinate system
Liu Hui, Lin Zhi and Waqas Ahmad
2018, 1(1) : 1-10 doi: 10.3934/mfc.2018001 +[Abstract](831) +[HTML](433) +[PDF](708.5KB) PDF Downloads(55)
Hybrid binary dragonfly enhanced particle swarm optimization algorithm for solving feature selection problems
Mohamed A. Tawhid and Kevin B. Dsouza
2018, 1(2) : 181-200 doi: 10.3934/mfc.2018009 +[Abstract](785) +[HTML](580) +[PDF](609.18KB) PDF Downloads(44)
Exploring timeliness for accurate recommendation in location-based social networks
Yi Xu, Qing Yang and Dianhui Chu
2018, 1(1) : 11-48 doi: 10.3934/mfc.2018002 +[Abstract](817) +[HTML](482) +[PDF](653.98KB) PDF Downloads(34)
Discrete heat transfer search for solving travelling salesman problem
Poonam Savsani and Mohamed A. Tawhid
2018, 1(3) : 265-280 doi: 10.3934/mfc.2018012 +[Abstract](390) +[HTML](438) +[PDF](865.09KB) PDF Downloads(32)
Web services recommendation leveraging semantic similarity computing
Boran Hu, Zehui Cheng and Zhangbing Zhou
2018, 1(2) : 101-119 doi: 10.3934/mfc.2018006 +[Abstract](623) +[HTML](336) +[PDF](577.4KB) PDF Downloads(31)

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