TY  - JOUR
AU  - Maletić, Slobodan
AU  - Zhao, Yi
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1925
AB  - Intricacies of the structure of social relations are realized by representing a collection of overlapping opinions as a simplicial complex, thus building latent multidimensional structures, through which agents are, virtually, moving as they exchange opinions. The influence of opinion space structure on the distribution of opinions is demonstrated by modeling consensus phenomena when the opinion exchange between individuals may be affected by the false consensus effect. The results indicate that in the cases with and without bias, the road toward consensus is influenced by the structure of multidimensional space of opinions, and in the biased case, complete consensus is achieved. The applications of proposed modeling framework can easily be generalized, as they transcend opinion formation modeling. (C) 2017 Elsevier B.V. All rights reserved.
T2  - Physica A: Statistical Mechanics and Its Applications
T1  - Hidden multidimensional social structure modeling applied to biased social perception
VL  - 492
SP  - 1419
EP  - 1430
DO  - 10.1016/j.physa.2017.11.069
ER  - 

@article{
author = "Maletić, Slobodan and Zhao, Yi",
year = "2018",
abstract = "Intricacies of the structure of social relations are realized by representing a collection of overlapping opinions as a simplicial complex, thus building latent multidimensional structures, through which agents are, virtually, moving as they exchange opinions. The influence of opinion space structure on the distribution of opinions is demonstrated by modeling consensus phenomena when the opinion exchange between individuals may be affected by the false consensus effect. The results indicate that in the cases with and without bias, the road toward consensus is influenced by the structure of multidimensional space of opinions, and in the biased case, complete consensus is achieved. The applications of proposed modeling framework can easily be generalized, as they transcend opinion formation modeling. (C) 2017 Elsevier B.V. All rights reserved.",
journal = "Physica A: Statistical Mechanics and Its Applications",
title = "Hidden multidimensional social structure modeling applied to biased social perception",
volume = "492",
pages = "1419-1430",
doi = "10.1016/j.physa.2017.11.069"
}

Maletić, S.,& Zhao, Y.. (2018). Hidden multidimensional social structure modeling applied to biased social perception. in Physica A: Statistical Mechanics and Its Applications, 492, 1419-1430.
https://doi.org/10.1016/j.physa.2017.11.069

Maletić S, Zhao Y. Hidden multidimensional social structure modeling applied to biased social perception. in Physica A: Statistical Mechanics and Its Applications. 2018;492:1419-1430.
doi:10.1016/j.physa.2017.11.069 .

Maletić, Slobodan, Zhao, Yi, "Hidden multidimensional social structure modeling applied to biased social perception" in Physica A: Statistical Mechanics and Its Applications, 492 (2018):1419-1430,
https://doi.org/10.1016/j.physa.2017.11.069 . .

TY  - JOUR
AU  - Zhou, Andu
AU  - Maletić, Slobodan
AU  - Zhao, Yi
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7738
AB  - Efficient robustness and fault tolerance of complex network is significantly influenced by its connectivity, commonly modeled by the structure of pairwise relations between network elements, i.e., nodes. Nevertheless, aggregations of nodes build higher-order structures embedded in complex network, which may be more vulnerable when the fraction of nodes is removed. The structure of higher-order aggregations of nodes can be naturally modeled by simplicial complexes, whereas the removal of nodes affects the values of topological invariants, like the number of higher-dimensional holes quantified with Betti numbers. Following the methodology of percolation theory, as the fraction of nodes is removed, new holes appear, which have the role of merger between already present holes. In the present article, relationship between the robustness and homological properties of complex network is studied, through relating the graph-theoretical signatures of robustness and the quantities derived from topological invariants. The simulation results of random failures and intentional attacks on networks suggest that the changes of graph-theoretical signatures of robustness are followed by differences in the distribution of number of holes per cluster under different attack strategies. In the broader sense, the results indicate the importance of topological invariants research for obtaining further insights in understanding dynamics taking place over complex networks.
T2  - Physica A: Statistical Mechanics and Its Applications
T1  - Robustness and percolation of holes in complex networks
VL  - 502
SP  - 459
EP  - 468
DO  - 10.1016/j.physa.2018.02.149
ER  - 

@article{
author = "Zhou, Andu and Maletić, Slobodan and Zhao, Yi",
year = "2018",
abstract = "Efficient robustness and fault tolerance of complex network is significantly influenced by its connectivity, commonly modeled by the structure of pairwise relations between network elements, i.e., nodes. Nevertheless, aggregations of nodes build higher-order structures embedded in complex network, which may be more vulnerable when the fraction of nodes is removed. The structure of higher-order aggregations of nodes can be naturally modeled by simplicial complexes, whereas the removal of nodes affects the values of topological invariants, like the number of higher-dimensional holes quantified with Betti numbers. Following the methodology of percolation theory, as the fraction of nodes is removed, new holes appear, which have the role of merger between already present holes. In the present article, relationship between the robustness and homological properties of complex network is studied, through relating the graph-theoretical signatures of robustness and the quantities derived from topological invariants. The simulation results of random failures and intentional attacks on networks suggest that the changes of graph-theoretical signatures of robustness are followed by differences in the distribution of number of holes per cluster under different attack strategies. In the broader sense, the results indicate the importance of topological invariants research for obtaining further insights in understanding dynamics taking place over complex networks.",
journal = "Physica A: Statistical Mechanics and Its Applications",
title = "Robustness and percolation of holes in complex networks",
volume = "502",
pages = "459-468",
doi = "10.1016/j.physa.2018.02.149"
}

Zhou, A., Maletić, S.,& Zhao, Y.. (2018). Robustness and percolation of holes in complex networks. in Physica A: Statistical Mechanics and Its Applications, 502, 459-468.
https://doi.org/10.1016/j.physa.2018.02.149

Zhou A, Maletić S, Zhao Y. Robustness and percolation of holes in complex networks. in Physica A: Statistical Mechanics and Its Applications. 2018;502:459-468.
doi:10.1016/j.physa.2018.02.149 .

Zhou, Andu, Maletić, Slobodan, Zhao, Yi, "Robustness and percolation of holes in complex networks" in Physica A: Statistical Mechanics and Its Applications, 502 (2018):459-468,
https://doi.org/10.1016/j.physa.2018.02.149 . .

TY  - JOUR
AU  - Maletić, Slobodan
AU  - Zhao, Yi
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1545
AB  - The emergence of complex datasets permeates versatile research disciplines leading to the necessity to develop methods for tackling complexity through finding the patterns inherent in datasets. The challenge lies in transforming the extracted patterns into pragmatic knowledge. In this paper, new information entropy measures for the characterization of the multidimensional structure extracted from complex datasets are proposed, complementing the conventionally-applied algebraic topology methods. Derived from topological relationships embedded in datasets, multilevel entropy measures are used to track transitions in building the high dimensional structure of datasets captured by the stratified partition of a simplicial complex. The proposed entropies are found suitable for defining and operationalizing the intuitive notions of structural relationships in a cumulative experience of a taxi drivers cognitive map formed by origins and destinations. The comparison of multilevel integration entropies calculated after each new added ride to the data structure indicates slowing the pace of change over time in the origin-destination structure. The repetitiveness in taxi driver rides, and the stability of origin-destination structure, exhibits the relative invariance of rides in space and time. These results shed light on taxi drivers ride habits, as well as on the commuting of persons whom he/she drove.
T2  - Entropy
T1  - Multilevel Integration Entropies: The Case of Reconstruction of Structural Quasi-Stability in Building Complex Datasets
VL  - 19
IS  - 4
SP  - 172
DO  - 10.3390/e19040172
ER  - 

@article{
author = "Maletić, Slobodan and Zhao, Yi",
year = "2017",
abstract = "The emergence of complex datasets permeates versatile research disciplines leading to the necessity to develop methods for tackling complexity through finding the patterns inherent in datasets. The challenge lies in transforming the extracted patterns into pragmatic knowledge. In this paper, new information entropy measures for the characterization of the multidimensional structure extracted from complex datasets are proposed, complementing the conventionally-applied algebraic topology methods. Derived from topological relationships embedded in datasets, multilevel entropy measures are used to track transitions in building the high dimensional structure of datasets captured by the stratified partition of a simplicial complex. The proposed entropies are found suitable for defining and operationalizing the intuitive notions of structural relationships in a cumulative experience of a taxi drivers cognitive map formed by origins and destinations. The comparison of multilevel integration entropies calculated after each new added ride to the data structure indicates slowing the pace of change over time in the origin-destination structure. The repetitiveness in taxi driver rides, and the stability of origin-destination structure, exhibits the relative invariance of rides in space and time. These results shed light on taxi drivers ride habits, as well as on the commuting of persons whom he/she drove.",
journal = "Entropy",
title = "Multilevel Integration Entropies: The Case of Reconstruction of Structural Quasi-Stability in Building Complex Datasets",
volume = "19",
number = "4",
pages = "172",
doi = "10.3390/e19040172"
}

Maletić, S.,& Zhao, Y.. (2017). Multilevel Integration Entropies: The Case of Reconstruction of Structural Quasi-Stability in Building Complex Datasets. in Entropy, 19(4), 172.
https://doi.org/10.3390/e19040172

Maletić S, Zhao Y. Multilevel Integration Entropies: The Case of Reconstruction of Structural Quasi-Stability in Building Complex Datasets. in Entropy. 2017;19(4):172.
doi:10.3390/e19040172 .

Maletić, Slobodan, Zhao, Yi, "Multilevel Integration Entropies: The Case of Reconstruction of Structural Quasi-Stability in Building Complex Datasets" in Entropy, 19, no. 4 (2017):172,
https://doi.org/10.3390/e19040172 . .

TY  - JOUR
AU  - Maletić, Slobodan
AU  - Zhao, Yi
AU  - Rajković, Milan
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1115
AB  - Inspired by an early work of Muldoon et al., Physica D 65, 1-16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network. Published by AIP Publishing.
T2  - Chaos
T1  - Persistent topological features of dynamical systems
VL  - 26
IS  - 5
DO  - 10.1063/1.4949472
ER  - 

@article{
author = "Maletić, Slobodan and Zhao, Yi and Rajković, Milan",
year = "2016",
abstract = "Inspired by an early work of Muldoon et al., Physica D 65, 1-16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network. Published by AIP Publishing.",
journal = "Chaos",
title = "Persistent topological features of dynamical systems",
volume = "26",
number = "5",
doi = "10.1063/1.4949472"
}

Maletić, S., Zhao, Y.,& Rajković, M.. (2016). Persistent topological features of dynamical systems. in Chaos, 26(5).
https://doi.org/10.1063/1.4949472

Maletić S, Zhao Y, Rajković M. Persistent topological features of dynamical systems. in Chaos. 2016;26(5).
doi:10.1063/1.4949472 .

Maletić, Slobodan, Zhao, Yi, Rajković, Milan, "Persistent topological features of dynamical systems" in Chaos, 26, no. 5 (2016),
https://doi.org/10.1063/1.4949472 . .