A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems
Abstract
:1. Introduction
1.1. A Suite of Algorithms
- show that full RI and piecewise RI algorithms typically lead to similar groupings
- characterize the performance of the piecewise RI algorithm, introduced in order to speed up the identification of RSs
- characterize the performance of the zI-graph algorithm.
1.2. Knock-Out Experiments
2. The RI Method
2.1. The zI Index
2.2. The Sieving Algorithm
2.3. A Useful Remark
2.4. The Full RI Method
3. The Piecewise RI Method
3.1. Dividing the System into Parts
3.2. Partitioning Based on Equal Size Parts
- A: division into k parts
- B: creation of folders and files related to each single partition
- C: analysis of each partition
- D: collection of the RSs of each analysis
- E: final zI analysis.
3.3. Partitioning Based on Network Analysis
Algorithm 1 Piecewise zI |
N ⇐ List of elements of the system |
G ⇐ Empty graph |
MaxD ⇐ Maximum size of the group under consideration |
for element in N do |
G.add_node(element) |
for couple in combination(2,N) do |
if calcolate_index_value(couple) ≥ threshold then |
G.add_edge(couple) |
Last_round = [] |
for community in G.get_communities() do |
Last_round.append(full_zI(community)) |
full_zI(Last_round) |
3.4. Full/Piecewise RI Comparison
4. The Reconstruction of the Network of Relationships: The zI-Graph Algorithm
5. Gene Knock-Out Analysis
5.1. Introduction
5.2. Artificial Gene Regulatory Networks
5.2.1. The Reconstruction of Artificial Gene Regulatory Networks
5.2.2. Identification and Characterization of Dynamic Groups
5.3. Knock-Outs in Saccharomyces cerevisiae
6. Discussion
- the creation of synthetic models of the same size as the S. cerevisiae, in order to reproduce its dynamic distributions
- the tracing of the biological function of the identified RSs (modules, pathways, …) and the potential discover of new hitherto unknown relationships
- the interpretation of the role of isolated genes
- the analysis of the topology of the connections between the various RSs.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Speed Up of the Piecewise zI Algorithm
Appendix B
Appendix C
Appendix D
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Piecewise zI Strategies vs. Full zI Algorithm | Thelper | CSTR | GreenC | LF ** |
---|---|---|---|---|
Graph ARI = 1.0 (fraction) | 1.00 * | 1.00 * | 0.00 * | 0.95 |
Graph ARI ≥ 0.8 (fraction) | 1.00 * | 1.00 * | 0.00 * | 1.00 |
Graph ARI | 1.00 | 1.00 | 0.686 | 0.99 ± 0.01 |
Homo ARI = 1.0 (fraction) | 0.70 | 0.00 | 0.00 | 0.82 ± 0.02 |
Homo ARI ≥ 0.8 (fraction) | 0.70 | 0.00 | 0.00 | 0.95 ± 0.01 |
Homo Average ARI | 0.82 ± 0.07 | 0.12 ± 0.06 | 0.35 ± 0.01 | 0.93 ± 0.02 |
Piecewise zI vs. Full zI Algorithm | RND | SF | SW |
---|---|---|---|
ARI ≥ 0.8 (fraction) | 0.714 | 1.00 | 1.00 |
Average ARI | 0.83 ± 0.02 | 0.960 ± 0.005 | 0.939 ± 0.006 |
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D’Addese, G.; Casari, M.; Serra, R.; Villani, M. A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems. Mathematics 2021, 9, 1022. https://doi.org/10.3390/math9091022
D’Addese G, Casari M, Serra R, Villani M. A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems. Mathematics. 2021; 9(9):1022. https://doi.org/10.3390/math9091022
Chicago/Turabian StyleD’Addese, Gianluca, Martina Casari, Roberto Serra, and Marco Villani. 2021. "A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems" Mathematics 9, no. 9: 1022. https://doi.org/10.3390/math9091022