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Volume 1, 2018

Mathematical Foundations of Computing (MFC) serves an interdisciplinary forum to promote interaction among mathematicians, computer scientists and statisticians as well as engineers to exchange new ideas and techniques for attacking the pressing challenges in data analysis. The journal aims to provide a place for more understanding and transparency of data analytics in different areas of AI. We welcome high-quality papers in all areas of AI related to the computational and algorithmic aspects of data analysis, with emphasis on innovative theoretical development, methods, and algorithms including, but not restricted to, machine learning, deep learning, and learning theory.

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

AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.

MFC is a joint publication of the American Institute of Mathematical Sciences and Qufu Normal University.

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Cryptographic algorithms for privacy-preserving online applications
Ruinian Li, Yinhao Xiao, Cheng Zhang, Tianyi Song and Chunqiang Hu
2018, 1(4) : 311-330 doi: 10.3934/mfc.2018015 +[Abstract](44) +[HTML](34) +[PDF](994.72KB)
Abstract:

Privacy in online applications has drawn tremendous attention in recent years. With the development of cloud-based applications, protecting users' privacy while guaranteeing the expected service from the server has become a significant issue. This paper surveyed the most popular cryptographic algorithms in privacy-preserving online applications to provide a tutorial-like introduction to researchers in this area. Specifically, this paper focuses on introduction to homomorphic encryption, secret sharing, secure multi-party computation and zero-knowledge proof.

Privacy preserving feature selection and Multiclass Classification for horizontally distributed data
Yunmei Lu, Mingyuan Yan, Meng Han, Qingliang Yang and Yanqing Zhang
2018, 1(4) : 331-348 doi: 10.3934/mfc.2018016 +[Abstract](32) +[HTML](15) +[PDF](1992.06KB)
Abstract:

In the last two decades, a lot of scientific fields have experienced a huge growth in data volume and data complexity, which brings data miners lots of opportunities, as well as many challenges. With the advent of the era of big data, applying data mining techniques on assembling data from multiple parties (or sources) has become a leading trend. However, those data mining tasks may divulge individuals' privacy, which leads to the increased concerns in privacy preserving. In this work, a Privacy Preserving feature selection method (PPFS-IFW) and Multiclass Classification method (PPM2C) are proposed. Experiments had been conducted to validate the performance of the proposed approaches. Both PPFS-IFW and PPM2C were tested on six benchmark datasets. The testing results demonstrate PPFS-IFW's capability in enhancing the classification performance at the level of accuracy by selection informative features. PPFS-IFW can not only preserve private information but also outperform some other state-of-the-art feature selection approaches. Experimental results also show that the proposed PPM2C method is workable and stable. Particularly, It reduces the risk of over-fitting when compared with the regular Support Vector Machine. In the meantime, by employing the Secure Sum Protocol to encrypt data at the bottom layer, users' privacy is preserved.

An effective hybrid firefly algorithm with the cuckoo search for engineering optimization problems
Mohamed A. Tawhid and Ahmed F. Ali
2018, 1(4) : 349-368 doi: 10.3934/mfc.2018017 +[Abstract](25) +[HTML](11) +[PDF](649.23KB)
Abstract:

Firefly and cuckoo search algorithms are two of the most widely used nature-inspired algorithms due to their simplicity and inexpensive computational cost when they applied to solve a wide range of problems. In this article, a new hybrid algorithm is suggested by combining the firefly algorithm and the cuckoo search algorithm to solve constrained optimization problems (COPs) and real-world engineering optimization problems. The proposed algorithm is called Hybrid FireFly Algorithm and Cuckoo Search (HFFACS) algorithm. In the HFFACS algorithm, a balance between the exploration and the exploitation processes is considered. The main drawback of the firefly algorithm is it is easy to fall into stagnation when the new solution is not better than its previous best solution for several generations. In order to avoid this problem, the cuckoo search with Lèvy flight is invoked to force the firefly algorithm to escape from stagnation and to avoid premature convergence. The proposed algorithm is applied to six benchmark constrained optimization problems and five engineering optimization problems and compared against four algorithms to investigate its performance. The numerical experimental results show the proposed algorithm is a promising algorithm and can obtain the optimal or near optimal solution within a reasonable time.

Relay selection based on social relationship prediction and information leakage reduction for mobile social networks
Xiaoshuang Xing, Gaofei Sun, Yong Jin, Wenyi Tang and Xiuzhen Cheng
2018, 1(4) : 369-382 doi: 10.3934/mfc.2018018 +[Abstract](42) +[HTML](15) +[PDF](429.11KB)
Abstract:

Despite the extensive study on relay selection in mobile social networks (MSNs), few work has taken both transmission latency (i.e. efficiency) and information leakage probability (i.e. security) into consideration. Therefore we target on designing an efficient and secure relay selection algorithm to enable communication among legitimate users while reducing the information leakage probability to other users. In this paper, we propose a novel mobility model for MSN users considering both the randomness and the sociality of the movements, based on which the social relationship among users, i.e. the meeting probabilities among the users, are predicted. Taken both efficiency and security into consideration, we design a network formation game based relay selection algorithm by defining the payoff functions of the users, designing the game evolving rules, and proving the stability of the formed network structure. Extensive simulation is conducted to validate the performance of the relay selection algorithm by using both synthetic trace and real-world trace. The results show that our algorithm outperforms other algorithms by trading a balance between efficiency and security.

Constant competitive algorithms for unbounded one-Way trading under monotone hazard rate
Yong Zhang, Francis Y. L. Chin, Francis C. M. Lau, Haisheng Tan and Hing-Fung Ting
2018, 1(4) : 383-392 doi: 10.3934/mfc.2018019 +[Abstract](32) +[HTML](9) +[PDF](320.76KB)
Abstract:

In the one-way trading problem, a seller has some product to be sold to a sequence of buyers in an online fashion, i.e., buyers come one after another. Each buyer has the accepted unit price which is known to the seller on his arrival. To maximize the total revenue, the seller has to carefully decide the amount of products to be sold to each buyer at the then-prevailing prices. In this paper, we study the unbounded one-way trading, i.e., the highest unit price among all buyers is positive and unbounded. We assume that the highest prices of buyers follow some distribution with monotone hazard rate, which is a well-adopted assumption. We investigate two variants, (1) the distribution is on the highest price among all buyers, and (2) the distribution of the highest price of each buyer is independent and identically distributed. To measure the performance of the algorithms, the expected competitive ratios, \begin{document}$ \mathrm{E}[OPT]/\mathrm{E}[ALG] $\end{document} and \begin{document}$ \mathrm{E}[OPT/ALG] $\end{document}, are considered. If the distributions satisfy the monotone hazard rate, for both of the above two variants, constant-competitive algorithms can be achieved.

A survey: Reward distribution mechanisms and withholding attacks in Bitcoin pool mining
Saide Zhu, Wei Li, Hong Li, Chunqiang Hu and Zhipeng Cai
2018, 1(4) : 393-414 doi: 10.3934/mfc.2018020 +[Abstract](80) +[HTML](23) +[PDF](902.32KB)
Abstract:

The past three years have seen the rapid increase of Bitcoin difficulty, which has led to a substantial variance in solo mining. As a result, miners tend to join a large open pool to get a more stable reward. Nowadays, mining pools take up over 98% of Bitcoins total computation power. In a sense, this is a manifestation of Bitcoin that tends to be centralized. Thus, researchers have shown an increased interest in pool mining payoff and security. The purpose of this paper is to review and summarize recent research in Bitcoin pool mining system. We first introduce several common reward distribution schemes, and analyze their advantages and disadvantages with some improvement mechanisms; In the second section, to address pool security problems, we examined the practical utility of some existing and potential attack strategies. To study those malicious attack in details, several defense methods are collected. Finally, we make an outlook on Bitcoin future.

Cryptographic algorithms for privacy-preserving online applications
Ruinian Li, Yinhao Xiao, Cheng Zhang, Tianyi Song and Chunqiang Hu
2018, 1(4) : 311-330 doi: 10.3934/mfc.2018015 +[Abstract](44) +[HTML](34) +[PDF](994.72KB) Cited By(0)
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](906) +[HTML](480) +[PDF](708.5KB) Cited By(0)
Relay selection based on social relationship prediction and information leakage reduction for mobile social networks
Xiaoshuang Xing, Gaofei Sun, Yong Jin, Wenyi Tang and Xiuzhen Cheng
2018, 1(4) : 369-382 doi: 10.3934/mfc.2018018 +[Abstract](42) +[HTML](15) +[PDF](429.11KB) 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](469) +[HTML](525) +[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](1338) +[HTML](1165) +[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](747) +[HTML](450) +[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](980) +[HTML](668) +[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](2384) +[HTML](1880) +[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](438) +[HTML](328) +[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](909) +[HTML](673) +[PDF](609.18KB) 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](4043) +[HTML](2238) +[PDF](3282.55KB) PDF Downloads(579)
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](2384) +[HTML](1880) +[PDF](1032.13KB) PDF Downloads(201)
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](1104) +[HTML](789) +[PDF](2792.87KB) PDF Downloads(108)
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](980) +[HTML](668) +[PDF](1438.97KB) PDF Downloads(98)
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](1338) +[HTML](1165) +[PDF](5025.25KB) PDF Downloads(91)
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](906) +[HTML](480) +[PDF](708.5KB) PDF Downloads(60)
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](909) +[HTML](673) +[PDF](609.18KB) PDF Downloads(48)
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](927) +[HTML](565) +[PDF](653.98KB) PDF Downloads(38)
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](469) +[HTML](525) +[PDF](865.09KB) PDF Downloads(33)
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](710) +[HTML](393) +[PDF](577.4KB) PDF Downloads(32)

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