36 research outputs found
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