Öz
A multi-agent singular system is an extension of a traditional multi-agent system. The behavior of neural networks within the brain is crucial for cognitive functions, making it essential to understand the learning processes and the development of potential disorders. This study utilizes the analysis of singular linear systems representing brain neural networks to delve into the complexities of the human brain. In this context, the digraph approach is a powerful method for unraveling the intricate neural interconnections. Directed graphs, or digraphs, provide an intuitive visual representation of the causal and influential relationships among different neural units, facilitating a detailed analysis of network dynamics. This work explores the use of digraphs in analyzing singular linear multi-agent systems that model brain neural networks, emphasizing their significance and potential in enhancing our understanding of cognition and brain function.
Anahtar Kelimeler
Controllability Multi-systens Neural network Singular linear systems
Etik Beyan
It is declared that during the preparation process of this study, scientific and ethical principles were followed and all the studies benefited from are stated in the bibliography.
Teşekkür
The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.
Kaynakça
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- [2] N. Kriegeskorte, Deep neural networks: A new framework for modeling biological vision and brain information processing, Annu. Rev. Vision Sci., 1 (2015), 417–446.
- [3] Y. Yang, H. Cao, Digraph states and their neural network representations, Chin. Phys. B, 31(6) (2022), 060303.
- [4] Z. Li, Z. Duan, G. Chen, L. Huang, Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint, IEEE Trans Circuits Syst I Regul Pap, 57(1), (2009), 213–224.
- [5] A. Proskurnikov, M. Cao, Consensus in multi-agent systems, Wiley Encyclopedia of Electrical and Electronics Engineering, Wiley & Sons. (2016).
- [6] K. S. Narendra, K. Parthasarathy, Neural networks and dynamical systems, Internat. J. Approx. Reason., 6(2) (1992), 109–131.
- [7] M. I. Garcia-Planas, Control properties of multiagent dynamical systems modelling brain neural networks, In 2020 International Conference on Mathematics and Computers in Science and Engineering (MACISE) (106-113), IEEE.(2020, January).
- [8] Sh. Gu, F. Pasqualetti, M. Cieslak, Q. K. Telesford, A. B. Yu, A. E. Kahn, J. D. Medaglia, J. M. Vettel, M. B. Miller, S. T. Grafton, D. S. Bassett, Controllability of structural brain networks, Nat. Commun., 6 (2015), Article: 8414.
- [9] M. L. J. Hautus, Controllability and observability conditions of linear autonomous systems, Nederl. Akad. Wetensch. Proc. Ser. A 72, Indag. Math., 31 (1969), 443–448.
- [10] R. E. Kalman, P. L. Falb, M. A. Arbib, Topics in Mathematical Control Theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London 1969.
- [11] M.I. Garc´ıa-Planas, S. Tarragona, A. Diaz, Controllability of time-invariant singular linear systems, From physics to control through an emergent view, World Scientific, (2010), 112-–117.
- [12] Y. Liu, Y., J. Slotine, A. Barab´asi. Controllability of complex networks, Nature, 473 (2011), 167-–173.
- [13] Z. Yuan, C. Zhao, W.X. Wang, Z. Di, Y.C. Lai, Exact controllability of multiplex networks, New J. Phys., 16(10) (2014), 103036.
- [14] M.I. Garcia-Planas, Exact controllability of linear dynamical systems: A geometrical approach, Appl. Math., 62(1) (2017), 37–47.
- [15] T. Berger, A. Ilchmann, S. Trenn, The quasi-Weierstraß form for regular matrix pencils, Linear Algebra Appl., 436, (2012), 4052–4069.
- [16] G. Ivanyos, M. Karpinski, Y. Qiao, M. Santha, Generalized Wong sequences and their applications to Edmonds’ problems, J. Comput. System Sci., 81(7) (2015), 1373–1386.
- [17] Z.Z. Yuan, C. Zhao, W.X. Wang, Z.R. Di, Y.C. Lai, Exact controllability of multiplex networks, New J. Phys., 16 (2014), 1–24.
- [18] O.I. Abiodun, A. Jantan, A.E. Omolara, K.V. Dada, N.A. Mohamed, H. Arshad, State-of-the-art in artificial neural network applications: A survey, Heliyon, 4(11) (2018), e00938.
Öz
Kaynakça
- [1] L. Xiang, F. Chen, W. Ren, G. Chen. Advances in network controllability, IEEE Circuits Syst. Mag., 19(2) (2019), 8–32.
- [2] N. Kriegeskorte, Deep neural networks: A new framework for modeling biological vision and brain information processing, Annu. Rev. Vision Sci., 1 (2015), 417–446.
- [3] Y. Yang, H. Cao, Digraph states and their neural network representations, Chin. Phys. B, 31(6) (2022), 060303.
- [4] Z. Li, Z. Duan, G. Chen, L. Huang, Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint, IEEE Trans Circuits Syst I Regul Pap, 57(1), (2009), 213–224.
- [5] A. Proskurnikov, M. Cao, Consensus in multi-agent systems, Wiley Encyclopedia of Electrical and Electronics Engineering, Wiley & Sons. (2016).
- [6] K. S. Narendra, K. Parthasarathy, Neural networks and dynamical systems, Internat. J. Approx. Reason., 6(2) (1992), 109–131.
- [7] M. I. Garcia-Planas, Control properties of multiagent dynamical systems modelling brain neural networks, In 2020 International Conference on Mathematics and Computers in Science and Engineering (MACISE) (106-113), IEEE.(2020, January).
- [8] Sh. Gu, F. Pasqualetti, M. Cieslak, Q. K. Telesford, A. B. Yu, A. E. Kahn, J. D. Medaglia, J. M. Vettel, M. B. Miller, S. T. Grafton, D. S. Bassett, Controllability of structural brain networks, Nat. Commun., 6 (2015), Article: 8414.
- [9] M. L. J. Hautus, Controllability and observability conditions of linear autonomous systems, Nederl. Akad. Wetensch. Proc. Ser. A 72, Indag. Math., 31 (1969), 443–448.
- [10] R. E. Kalman, P. L. Falb, M. A. Arbib, Topics in Mathematical Control Theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London 1969.
- [11] M.I. Garc´ıa-Planas, S. Tarragona, A. Diaz, Controllability of time-invariant singular linear systems, From physics to control through an emergent view, World Scientific, (2010), 112-–117.
- [12] Y. Liu, Y., J. Slotine, A. Barab´asi. Controllability of complex networks, Nature, 473 (2011), 167-–173.
- [13] Z. Yuan, C. Zhao, W.X. Wang, Z. Di, Y.C. Lai, Exact controllability of multiplex networks, New J. Phys., 16(10) (2014), 103036.
- [14] M.I. Garcia-Planas, Exact controllability of linear dynamical systems: A geometrical approach, Appl. Math., 62(1) (2017), 37–47.
- [15] T. Berger, A. Ilchmann, S. Trenn, The quasi-Weierstraß form for regular matrix pencils, Linear Algebra Appl., 436, (2012), 4052–4069.
- [16] G. Ivanyos, M. Karpinski, Y. Qiao, M. Santha, Generalized Wong sequences and their applications to Edmonds’ problems, J. Comput. System Sci., 81(7) (2015), 1373–1386.
- [17] Z.Z. Yuan, C. Zhao, W.X. Wang, Z.R. Di, Y.C. Lai, Exact controllability of multiplex networks, New J. Phys., 16 (2014), 1–24.
- [18] O.I. Abiodun, A. Jantan, A.E. Omolara, K.V. Dada, N.A. Mohamed, H. Arshad, State-of-the-art in artificial neural network applications: A survey, Heliyon, 4(11) (2018), e00938.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Sayısal ve Hesaplamalı Matematik (Diğer) |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 20 Kasım 2024 |
| Yayımlanma Tarihi | 9 Aralık 2024 |
| Gönderilme Tarihi | 14 Temmuz 2024 |
| Kabul Tarihi | 18 Kasım 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 7 Sayı: 4 |
Kaynak Göster
Universal Journal of Mathematics and Applications
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