Uniqueness in chess studies

Van der Heijden’s ENDGAME STUDY DATABASE IV, HhdbIV, is the definitive collection of 76,132 chess studies. In each one, White is to achieve the stipulated goal, win or draw: study solutions should be essentially unique with minor alternatives at most. In this second note on the mining of the database, we use the definitive Nalimov endgame tables to benchmark White’s moves in sub-7-man chess against this standard of uniqueness. Amongst goal-compatible mainline positions and goal-achieving moves, we identify the occurrence of absolutely unique moves and analyse the frequency and lengths of absolutely-unique-move sequences, AUMSs. We identify the occurrence of equi-optimal moves and suboptimal moves and refer to a defined method for classifying their significance

Optimal Pricing-Based Edge Computing Resource Management in Mobile Blockchain

As the core issue of blockchain, the mining requires solving a proof-of-work puzzle, which is resource expensive to implement in mobile devices due to high computing power needed. Thus, the development of blockchain in mobile applications is restricted. In this paper, we consider the edge computing as the network enabler for mobile blockchain. In particular, we study optimal pricing-based edge computing resource management to support mobile blockchain applications where the mining process can be offloaded to an Edge computing Service Provider (ESP). We adopt a two-stage Stackelberg game to jointly maximize the profit of the ESP and the individual utilities of different miners. In Stage I, the ESP sets the price of edge computing services. In Stage II, the miners decide on the service demand to purchase based on the observed prices. We apply the backward induction to analyze the sub-game perfect equilibrium in each stage for uniform and discriminatory pricing schemes. Further, the existence and uniqueness of Stackelberg game are validated for both pricing schemes. At last, the performance evaluation shows that the ESP intends to set the maximum possible value as the optimal price for profit maximization under uniform pricing. In addition, the discriminatory pricing helps the ESP encourage higher total service demand from miners and achieve greater profit correspondingly.Comment: 7 pages, submitted to one conference. arXiv admin note: substantial text overlap with arXiv:1710.0156

Cloud/fog computing resource management and pricing for blockchain networks

The mining process in blockchain requires solving a proof-of-work puzzle, which is resource expensive to implement in mobile devices due to the high computing power and energy needed. In this paper, we, for the first time, consider edge computing as an enabler for mobile blockchain. In particular, we study edge computing resource management and pricing to support mobile blockchain applications in which the mining process of miners can be offloaded to an edge computing service provider. We formulate a two-stage Stackelberg game to jointly maximize the profit of the edge computing service provider and the individual utilities of the miners. In the first stage, the service provider sets the price of edge computing nodes. In the second stage, the miners decide on the service demand to purchase based on the observed prices. We apply the backward induction to analyze the sub-game perfect equilibrium in each stage for both uniform and discriminatory pricing schemes. For the uniform pricing where the same price is applied to all miners, the existence and uniqueness of Stackelberg equilibrium are validated by identifying the best response strategies of the miners. For the discriminatory pricing where the different prices are applied to different miners, the Stackelberg equilibrium is proved to exist and be unique by capitalizing on the Variational Inequality theory. Further, the real experimental results are employed to justify our proposed model.Comment: 16 pages, double-column version, accepted by IEEE Internet of Things Journa

Sequential Data Mining using Correlation Matrix Memory

This paper proposes a method for sequential data mining using correlation matrix memory. Here, we use the concept of the Logical Match to mine the indices of the sequential pattern. We demonstrate the uniqueness of the method with both the artificial and the real datum taken from the NCBI databank