Kyoto University
Blockchain Research Center
Mathematical Research
1. Mathematical research on
crypto currencies
・Prediction of bubble formation/collapse by
analyzing transaction networks
・Anomaly detection of fraud/money laundering
by quantum machine learning
2. Solutions to global problems
・International remittance for immigrants
(low cost, quick, reliable)
・Digital ID for medical services for refugees
・Trade in decarbonized energy
(renewable energy and hydrogen)
・Financial inclusion
(non-discriminatory financial services)
・Supply chain management
(global supply chain, commodity market)
・Economic support
(financing, human resource matching)
[1] Motif Analysis of Direct XRP Transaction
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We analyzed the direct XRP transaction recorded from Jan 2013 to Sep 2019, including the bubble period in early 2018 to detect triangular motifs that observed more often than expected by chance.
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Network motif analysis in the Top 300 network showed that Motif 3, Motif 5, Motif 6, Motif 7, Motif 10 and Motif 11 were statistically significant. We found that these significant motifs increased at the bubble period in early 2018..
[2] "Loop - Flow" in Remittance Transaction
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We analyzed the remittance transaction recorded on the XRP ledger for BTC, ETH, USD, and EUR. .We estimated the "loop flows" which is considered an anomaly using the Hodge decomposition. .
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We found the following characteristic differences at the bubble period.
-For ETH, there was significant increase in in the loop-flow. This might be related to Money laundering or Arbitrage.
-USD shows small increase in the loop-flow, while BTC and EUR show no increase in the loop-flow.
[3] XRP Price Burst and Correlation Tensor
A vector for each regular node is obtained by embedding the weekly network. From a set of weekly node vectors, we construct a correlation tensor. A double singular value decomposition of the correlation tensors gives its singular values.
The significance of the singular values is shown by comparing with its randomize counterpart. The evolution of singular values shows a distinctive behavior. The largest singular value shows a significant negative correlation with XRP/USD price.
【4】Three groups in the flow weighted frequency
diagram
Goal: To understand the mechanism of crypto asset price spikes and crashes from the network and flow of transactions.
Results: We found a "three brunch structure" by defining flow-weighted frequency that represents the frequency of outgoing and incoming flows, considering how a player has a role in these flows. We found a correlation between price and the number of each player. For frequently active players, we found the change of position around the price peak.
[5,6] Bitcoin's Crypto Flow Network
Purpose: How crypto flows among Bitcoin users is an important question for understanding the structure and dynamics of the crypto asset at a global scale.
Data: We compiled all the blockchain data of Bitcoin from its genesis to the year 2020, identified users from anonymous addresses of wallets, and constructed monthly snapshots of networks by focusing on regular users as a big players.
Result : We apply the methods of bow-tie structure and Hodge decomposition in order to locate the users in the upstream, downstream, and core of the entire crypto flow. Additionally, we reveal principal components hidden in the flow by using non-negative matrix factorization, which we interpret as a probabilistic model. We show that the model is equivalent to a probabilistic latent semantic analysis in natural language processing, enabling us to estimate the number of such hidden components. Moreover, we find that the bow-tie structure and the principal components are quite stable among those big players.
References
[1]Yuichi Ikeda,
"Characterization of XRP Crypto-Asset Transactions from Networks Scientific Approach".
In: Y.Aruka(eds) "Digital Designs for Money, Markets, and Social Dilemmas". Evolutionary Economics and Social Complexity Science, vol 28. Springer, Singapore (2022).
[2]Yuichi Ikeda, Abhijit Chakraborty,
"Hodge Decomposition of the Remittance Network on the XRP Ledger in the Price Hike of January 2018", arXiv:2212.02048［cs.CR］
[3]Abhijit Chakraborty, Tetsuo Hatsuda, Yuichi Ikeda,
"Projecting XRP price burst by correlation tensor spectra of transaction networks" arXiv:2211.03002［physics.soc-ph］
[4]Aoyama H, Fujiwara Y, Hidaka Y, Ikeda Y (2022), Cryptoasset networks: Flows and regular players in Bitcoin and XRP. PLoS ONE 17(8):e0273068
[5]Islam, R., Fujiwara, Y., Kawata, S. et al. Unfolding identity of financial institutions in bitcoin blockchain by weekly pattern of network flows. Evolut Inst Econ Rev 18, 131-157 (2021)
[6]Yoshi Fujiwara and Rubaiyat Islam, Bitcoin's Crypto Flow Network, JPS Conf.Proc.36, 011002
(2021)