COMPUTING SYSTEMS AND NETWORKS
INTELLIGENCE SYSTEMS AND TECHNOLOGIES
APPLIED ASPECTS OF COMPUTER SCIENCE
SOFTWARE ENGINEERING
DATA PROCESSING AND ANALYSIS
MATHEMATICAL MODELING
MATHEMATICAL FOUNDATIONS OF INFORMATION TECHNOLOGY
A. S. Semenov Tensor Models of Fractal Graphs for Elastic Networks
A. S. Semenov Tensor Models of Fractal Graphs for Elastic Networks
Abstract.

The article presents the results of research on fractal (self-similar) graphs in relation to elastic computing. A characteristic feature of such graphs is their ability to unfold (increase dimensionality) and fold (decrease dimensionality). Two approaches to forming fractal graphs are considered: based on Kronecker product and fractal algebra. The interrelationship of algebraic operations of forming fractal graphs (linear graphs, grids, hypercubes, and trees) with tensor operations and tensor representation based on the integration of adjacency matrices and event vectors of elastic systems is presented. Definitions of corresponding types of dynamically changing tensors are introduced. An analysis of the properties of elastic fractal graphs and related tensor models is conducted

Keywords: 

Kronecker graphs, fractal graphs, fractal algebra, elastic networks, tensor models.

PP. 133-142.

DOI 10.14357/20718632230412 

EDN SSMYLI
 
References

1. Becker S., Brataas G., and Lehrig S. (Eds.). Engineering Scalable, Elastic, and Cost-Efficient Cloud Computing Applications. The CloudScale Method, Springer International Publishing AG 2017, 187p.
2. Semenov A.S. 2017. Fractal Petri Nets [4th Int. Conf. Control, Decision and Information Technologies. Proceedings] Barcelona, Spain, 2017, pp. 1174 – 1179.
3. Semenov A.S. 2020. Graph-based Dynamic Analysis of Elastic Systems. [7th Int. Conf. Control, Decision and Information Technologies. vol 1 Conf. Paper] Publisher: IEEE pp. 65-70, doi: 10.1109/CoDIT49905.2020.9263986.
4. Semenov A.S. Fractal Analysis and Programming of Elastic Systems Using Container-Component Model. 2021. [Smart Innovation, Systems and Technologies, Jain, L. C., Margarita N. Favorskaya, Ilia S. Nikitin, and Dmitry L. Reviznikov, Eds. Springer Nature EBook], 2021, pp. 307-320.
https://doi.org/10.1007/978-981-33-4826-4.
5. Laub, A. J. Matrix Analysis for Scientists and Engineers. Calofornia, Devis SIAM, 2005, pp. 139-144.
6. Liu Y., Liu J., Long Z., Zhu C., Tensor Computation for Data Analysis. Springer Nature Switzerland AG 2022.
7. Leskovec J., Chakrabarti D., Kleinberg J., Faloutsos C., Ghahramani Z., "Kronecker Graphs: An Approach to Modeling. [Journal of Machine Learning Research] 11, 2010. pp. 985-1042.
8. Semenov A.S. Prototype based Programming with Fractal Algebra, [AIP Conf. Proc.] vol.. 2181-1, 2019.
https://doi.org/10.1063/1.5135669.
9. Semenov A,S. Essentials of Fractal programming, [ Smart Innovation, Systems and Technologies] L. C. Jain et al. (eds.), Advances in Theory and Practice of Computational Mechanics, Springer-Verlag, 173, 2020, pp. 373-386.
https://doi.org/10.1007/978-981-15-2600-8_25.
10. R.B. Bapat, Graphs and Matrices. New York: Springer, 2010.
11. Mortveit, H., and C. Reidys. An Introduction to Sequential Dynamical Systems. NY, NY: Springer. 2007.
12. Kuhlman, K., Mortveit, H., et al. A general-purpose graph dynamical system modeling framework,[Proc. of the 2011 Winter Simulation Conf]
13. Papineni, K., Worah, P. A Dynamical System on Bipartite Graphs, [Proc. of the 27th ACM Int. Conf. on Information and Knowledge Management], 2018, Torino, Italy. pp. 1479-1482.
14. Sizemore, A.E., Bassett, D.S. Dynamic graph metrics: Tutorial, toolbox, and tale. [Journal of the NeuroImage. Elsevier] vol. 180, 2018. pp. 417–427. www.elsevier.com/locate/neuroimage
15. Pignolet, Y.,A., et al. The Many Faces of Graph Dynamics. [Social and Information Networks] 2017. arXiv:1506.01565
16. Despreaux, S., Maignan. A. Dynamical Systems Based on Dynamic Graphs. 2009. https://www.researchgate.net/publication/ 254740120
17. Leskovec, J., Faloutsos, C. Scalable Modeling of Real Graphs using Kronecker Multiplication, [Proc. of the 24 th Int. Conf. on Machine Learning] Corvallis, OR, 2007.
18. Charu Aggarwal and Karthik Subbian. Evolutionary network analysis: A survey, [ACM Comput. Surv.] vol 47,1.
2014. DOI: http://dx.doi.org/10.1145/2601412
19. Heckel, R., Taentzer, G. (Eds.). Graph Transformation, Specifications, and Nets. Springer International Publishing AG, part of Springer Nature. 2018. 331p.
20. Fridtjov I. Tensor Analysis. Springer Nature Switzerland AG 2019
 

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