Homesick L\'evy walk: A mobility model having Ichi-go Ichi-e and scale-free properties of human encounters

In recent years, mobility models have been reconsidered based on findings by analyzing some big datasets collected by GPS sensors, cellphone call records, and Geotagging. To understand the fundamental statistical properties of the frequency of serendipitous human encounters, we conducted experiments to collect long-term data on human contact using short-range wireless communication devices which many people frequently carry in daily life. By analyzing the data we showed that the majority of human encounters occur once-in-an-experimental-period: they are Ichi-go Ichi-e. We also found that the remaining more frequent encounters obey a power-law distribution: they are scale-free. To theoretically find the origin of these properties, we introduced as a minimal human mobility model, Homesick L\'evy walk, where the walker stochastically selects moving long distances as well as L\'evy walk or returning back home. Using numerical simulations and a simple mean-field theory, we offer a theoretical explanation for the properties to validate the mobility model. The proposed model is helpful for evaluating long-term performance of routing protocols in delay tolerant networks and mobile opportunistic networks better since some utility-based protocols select nodes with frequent encounters for message transfer.Comment: 8 pages, 10 figure

Similarity and Probability Distribution Functions in Many-body Stochastic Processes with Multiplicative Interactions

Analytical and numerical studies on many-body stochastic processes with multiplicative interactions are reviewed. The method of moment relations is used to investigate effects of asymmetry and randomness in interactions. Probability distribution functions of the processes generally have similarity solutions with power-law tails. Growth rates of the system and power-law exponents of the tails are determined via transcendental equations. Good agreement is achieved between analytical calculations and Monte Carlo simulations.Comment: 8 pages, 4 figures, CN-Kyoto proceeding

Cross-Referencing Method for Scalable Public Blockchain

We previously proposed a cross-referencing method for enabling multiple peer-to-peer network domains to manage their own public blockchains and periodically exchanging the state of the latest fixed block in the blockchain with hysteresis signatures among all the domains via an upper network layer. In this study, we evaluated the effectiveness of our method from three theoretical viewpoints: decentralization, scalability, and tamper resistance. We show that the performance of the entire system can be improved because transactions and blocks are distributed only inside the domain. We argue that the transaction processing capacity will increase to 56,000 transactions per second, which is as much as that of a VISA credit card system. The capacity is also evaluated by multiplying the number of domains by the average reduction in transaction-processing time due to the increase in block size and reduction in the block-generation-time interval by domain partition. For tamper resistance, each domain has evidence of the hysteresis signatures of the other domains in the blockchain. We introduce two types of tamper-resistance-improvement ratios as evaluation measures of tamper resistance for a blockchain and theoretically explain how tamper resistance is improved using our cross-referencing method. With our method, tamper resistance improves as the number of domains increases. The proposed system of 1,000 domains are 3-10 times more tamper-resistant than that of 100 domains, and the capacity is 10 times higher. We conclude that our method enables a more scalable and tamper-resistant public blockchain balanced with decentralization.Comment: (29 pages, 18 figures, Internet of Things 15 (2021) 100419

Asymptotic analysis of the model for distribution of high-tax payers

The z-transform technique is used to investigate the model for distribution of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and others. Our analysis shows an asymptotic power-law of this model with the exponent -5/2 when a total ``mass'' has a certain critical value. Below the critical value, the system exhibits an ordinary critical behavior, and scaling relations hold. Above the threshold, numerical simulations show that a power-law distribution coexists with a huge ``monopolized'' member. It is argued that these behaviors are observed universally in conserved aggregation processes, by analizing an extended model.Comment: 5pages, 3figure