Monitoring Blockchain Cryptocurrency Transactions to Improve the Trustworthiness of the Fourth Industrial Revolution (Industry 4.0)
Abstract
1. Introduction
2. Related Works
3. Statistical Modeling of Network and Parameter Estimation
3.1. Notations
3.2. Hidden Markov Multi Linear Tensor Model
4. Monitoring Scheme
5. Performance Evaluation Using Simulation
- (1)
- For to ;
- For and based on the probability of edge creation between nodes i and j generate ;
- Use the MCMC algorithm to estimate vector for the generated network;
- (2)
- For to , calculate based on relation (6);
- (3)
- For to , evaluate the statistics based on relation (7);
- (4)
- For all statistics, find a UCL that the type I error meets.
- (1)
- For to 10000;
- (a)
- Set ;
- (b)
- While < UC;
- Generate a random network based on different probabilities;
- Estimate model parameters with the MCMC algorithm and obtain statistic from relation (7);
- Put ;
- (2)
- Evaluate .
6. Real-World Example
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Notation | Definition |
---|---|
Node index, for i = 1, 2, …, N | |
Node index, j = 1, 2, …, N | |
Number of nodes | |
Time periods, for t = 1, 2, …, T | |
Adjacency matrix | |
Covariate vector for nodes i and j and time t | |
Coefficient vector of covariates | |
Probability distribution of network | |
Number of latent variables | |
Latent node position | |
Node connection rule | |
Error term for nodes i and j and time t | |
matrix with all one elements | |
Hidden state variable | |
Vector of variables for monitoring | |
MEWMA statistic | |
Number of variables for monitoring | |
Vector of smoothing parameters | |
Error type-I |
months | ||||
---|---|---|---|---|
1 | −0.01304 | −0.00098 | −9.13859 | −13.82489 |
2 | 0.00663 | 0.00494 | −24.7135 | 22.90376 |
3 | −0.00139 | 0.00067 | −38.9954 | 35.69328 |
4 | −0.00494 | −0.00208 | −48.2437 | 39.23815 |
5 | −0.00441 | −0.00048 | −38.2289 | −37.16167 |
6 | −0.00497 | −0.00092 | −43.4409 | −36.36019 |
7 | 0.00372 | −0.00384 | −39.5655 | −23.62889 |
8 | 0.00248 | −0.00466 | −41.8008 | −30.24743 |
9 | 0.00484 | −0.00215 | −48.9446 | −33.28495 |
10 | −0.00444 | −0.00082 | −50.1390 | −38.11684 |
11 | 0.00467 | −0.00036 | −51.3839 | −40.68477 |
12 | −0.00546 | −0.00031 | −52.8679 | −45.47404 |
13 | −0.00528 | −0.00035 | −52.0766 | −43.80679 |
14 | 0.00582 | 0.00094 | −48.9130 | 48.70567 |
15 | 0.00468 | −0.00077 | −37.2179 | 40.55287 |
16 | −0.00484 | −0.00048 | −51.1166 | −38.95125 |
17 | 0.00345 | −0.00197 | −67.0583 | −44.05735 |
18 | −0.00316 | −0.00181 | −41.8440 | −42.76087 |
19 | −2.5111 × 10−3 | 2.3869 × 10−5 | −44.2593 | −43.10673 |
20 | −0.00519 | −0.00197 | −39.2207 | 38.30627 |
21 | 0.00457 | 0.00142 | −49.32448 | 58.63748 |
22 | 0.00103 | 0.00155 | −47.7910 | 36.85834 |
23 | 0.00227 | 0.00172 | −57.01123 | 67.6237 |
24 | 0.00260 | −0.00143 | −68.80305 | −44.41586 |
25 | 0.00792 | 0.00158 | −31.07843 | 31.59579 |
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Sabri-Laghaie, K.; Jafarzadeh Ghoushchi, S.; Elhambakhsh, F.; Mardani, A. Monitoring Blockchain Cryptocurrency Transactions to Improve the Trustworthiness of the Fourth Industrial Revolution (Industry 4.0). Algorithms 2020, 13, 312. https://doi.org/10.3390/a13120312
Sabri-Laghaie K, Jafarzadeh Ghoushchi S, Elhambakhsh F, Mardani A. Monitoring Blockchain Cryptocurrency Transactions to Improve the Trustworthiness of the Fourth Industrial Revolution (Industry 4.0). Algorithms. 2020; 13(12):312. https://doi.org/10.3390/a13120312
Chicago/Turabian StyleSabri-Laghaie, Kamyar, Saeid Jafarzadeh Ghoushchi, Fatemeh Elhambakhsh, and Abbas Mardani. 2020. "Monitoring Blockchain Cryptocurrency Transactions to Improve the Trustworthiness of the Fourth Industrial Revolution (Industry 4.0)" Algorithms 13, no. 12: 312. https://doi.org/10.3390/a13120312
APA StyleSabri-Laghaie, K., Jafarzadeh Ghoushchi, S., Elhambakhsh, F., & Mardani, A. (2020). Monitoring Blockchain Cryptocurrency Transactions to Improve the Trustworthiness of the Fourth Industrial Revolution (Industry 4.0). Algorithms, 13(12), 312. https://doi.org/10.3390/a13120312