TY  - JOUR
AU  - Maletić, Slobodan
AU  - Anđelković, Miroslav
PY  - 2024
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12716
AB  - The interest in induced higher-order relational and multidimensional structures embedded in the financial complex dataset is considered within the applied algebraic topology framework. The aim is to transcend the binary correlations when the interactions of the underlying system are stored in the entries of the cross-correlation matrix. By applying different criteria, we examined aggregations of firms through higher-order clustering of the financial system. The outcome is the extraction of patterns that appear in assemblages of firms due to their multidimensional properties embedded in the cross-correlation matrices. Results are compatible with classifying firms into clusters due to the industry they belong to. Furthermore, the novel and mixed collections of firms are revealed based on the applied mathematical approach. In the broader context, results shed light on the higher-order organization of interactions embedded in the cross-correlation matrix and, as a consequence, extract patterns of collective behavior within a complex system.
T2  - Chaos: An Interdisciplinary Journal of Nonlinear Science
T1  - Higher-order clustering patterns in simplicial financial systems
VL  - 34
IS  - 1
DO  - 10.1063/5.0185845
ER  - 

@article{
author = "Maletić, Slobodan and Anđelković, Miroslav",
year = "2024",
abstract = "The interest in induced higher-order relational and multidimensional structures embedded in the financial complex dataset is considered within the applied algebraic topology framework. The aim is to transcend the binary correlations when the interactions of the underlying system are stored in the entries of the cross-correlation matrix. By applying different criteria, we examined aggregations of firms through higher-order clustering of the financial system. The outcome is the extraction of patterns that appear in assemblages of firms due to their multidimensional properties embedded in the cross-correlation matrices. Results are compatible with classifying firms into clusters due to the industry they belong to. Furthermore, the novel and mixed collections of firms are revealed based on the applied mathematical approach. In the broader context, results shed light on the higher-order organization of interactions embedded in the cross-correlation matrix and, as a consequence, extract patterns of collective behavior within a complex system.",
journal = "Chaos: An Interdisciplinary Journal of Nonlinear Science",
title = "Higher-order clustering patterns in simplicial financial systems",
volume = "34",
number = "1",
doi = "10.1063/5.0185845"
}

Maletić, S.,& Anđelković, M.. (2024). Higher-order clustering patterns in simplicial financial systems. in Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(1).
https://doi.org/10.1063/5.0185845

Maletić S, Anđelković M. Higher-order clustering patterns in simplicial financial systems. in Chaos: An Interdisciplinary Journal of Nonlinear Science. 2024;34(1).
doi:10.1063/5.0185845 .

Maletić, Slobodan, Anđelković, Miroslav, "Higher-order clustering patterns in simplicial financial systems" in Chaos: An Interdisciplinary Journal of Nonlinear Science, 34, no. 1 (2024),
https://doi.org/10.1063/5.0185845 . .

TY  - CONF
AU  - Maletić, Slobodan
AU  - Anđelković, Miroslav
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12421
AB  - Detecting pertinent patterns in the collective behavior of complex system elements is challenging for the practical, as well as theoretical, understanding of a system’s dynamics. To date, complex network research set a convenient framework for modeling the complexity of systems formed by elements linked through pairwise interactions. However, this approach may neglect the effects of non-pairwise interactions [1], which produce higher-order structures that underlie complex systems [2], and higher-order interactions among large groups of elements are essential in the system’s functioning and dynamics. On the other hand, one of the ways to capture pairwise weighted interactions of system elements is the formation of the cross- correlation matrix. Nevertheless, extracting grouped interactions of elements as higher-order correlations from pairwise is a rather challenging task [3] due to the nonlinearity of collective behavior which characterizes the system. Toward overcoming this problem, and as an approximation, we propose a framework for extracting collective behavior embedded in connectivity patterns based on pairwise interaction by aggregating elements into higher-order structures called simplices. These objects build non-trivial, complex, layered structures and display rich structural properties. In a nutshell, the development of a system reconstruction from correlations between its elements, using the algebraic topological approach, begins by mapping the system onto a multidimensional object called a simplicial complex [4]. We use the case of the financial system to exemplify the outcomes of the approach. Within this context, the k-order connected clusters of elements within the correlation structure represent aggregations of system elements (i.e., firms) under the criteria of induced multidimensional similarity, hence transcending the binary correlations. For example, 2nd order connected clusters of correlation structure represent groups of firms that form connected chains of elements where two successive firms are significantly correlated to three common firms. The interpretation of the results of these aggregations suits the qualitative classification of firms into groups due to the industry they belong. Furthermore, the novel and mixed collections of firms are revealed based on the algebraic topological approach applied. Our approach sheds light on the higher-order organization of interactions embedded in the cross-correlation matrix and, as a consequence, extracts patterns of collective behavior within a complex system.
C3  - SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts
T1  - Higher-order Connectivity Patterns in the Correlation Structure of Complex Systems
SP  - 64
EP  - 64
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12421
ER  - 

@conference{
author = "Maletić, Slobodan and Anđelković, Miroslav",
year = "2023",
abstract = "Detecting pertinent patterns in the collective behavior of complex system elements is challenging for the practical, as well as theoretical, understanding of a system’s dynamics. To date, complex network research set a convenient framework for modeling the complexity of systems formed by elements linked through pairwise interactions. However, this approach may neglect the effects of non-pairwise interactions [1], which produce higher-order structures that underlie complex systems [2], and higher-order interactions among large groups of elements are essential in the system’s functioning and dynamics. On the other hand, one of the ways to capture pairwise weighted interactions of system elements is the formation of the cross- correlation matrix. Nevertheless, extracting grouped interactions of elements as higher-order correlations from pairwise is a rather challenging task [3] due to the nonlinearity of collective behavior which characterizes the system. Toward overcoming this problem, and as an approximation, we propose a framework for extracting collective behavior embedded in connectivity patterns based on pairwise interaction by aggregating elements into higher-order structures called simplices. These objects build non-trivial, complex, layered structures and display rich structural properties. In a nutshell, the development of a system reconstruction from correlations between its elements, using the algebraic topological approach, begins by mapping the system onto a multidimensional object called a simplicial complex [4]. We use the case of the financial system to exemplify the outcomes of the approach. Within this context, the k-order connected clusters of elements within the correlation structure represent aggregations of system elements (i.e., firms) under the criteria of induced multidimensional similarity, hence transcending the binary correlations. For example, 2nd order connected clusters of correlation structure represent groups of firms that form connected chains of elements where two successive firms are significantly correlated to three common firms. The interpretation of the results of these aggregations suits the qualitative classification of firms into groups due to the industry they belong. Furthermore, the novel and mixed collections of firms are revealed based on the algebraic topological approach applied. Our approach sheds light on the higher-order organization of interactions embedded in the cross-correlation matrix and, as a consequence, extracts patterns of collective behavior within a complex system.",
journal = "SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts",
title = "Higher-order Connectivity Patterns in the Correlation Structure of Complex Systems",
pages = "64-64",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12421"
}

Maletić, S.,& Anđelković, M.. (2023). Higher-order Connectivity Patterns in the Correlation Structure of Complex Systems. in SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts, 64-64.
https://hdl.handle.net/21.15107/rcub_vinar_12421

Maletić S, Anđelković M. Higher-order Connectivity Patterns in the Correlation Structure of Complex Systems. in SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts. 2023;:64-64.
https://hdl.handle.net/21.15107/rcub_vinar_12421 .

Maletić, Slobodan, Anđelković, Miroslav, "Higher-order Connectivity Patterns in the Correlation Structure of Complex Systems" in SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts (2023):64-64,
https://hdl.handle.net/21.15107/rcub_vinar_12421 .

TY  - JOUR
AU  - Anđelković, Miroslav
AU  - Maletić, Slobodan
AU  - Tomanović, Ivan
PY  - 2022
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10603
AB  - Although its uninterrupted supply is essential for everyday life, the electricity occasionally experiences disruptions and outages. The work presented in the current paper aims to initiate the research to design a strategy based on advanced approaches of algebraic topology to prevent such malfunctions in a power grid network. Simplicial complexes are constructed to identify higher-order structures embedded in a network and, alongside a new algorithm for identifying delegates of the simplicial complex, are intended to pinpoint each element of the power grid network to its natural layer. Results of this methodology for analysis of a power grid network can single out its elements that are at risk to cause cascade problems which can result in unintentional islanding and blackouts. Further development of the outcomes of research can find implementation in the algorithms of the energy informatics research applications.
T2  - Thermal Science
T1  - Identifiers for structural warnings of malfunction in power grid networks
VL  - 26
IS  - 6 part B
SP  - 5043
EP  - 5051
DO  - 10.2298/TSCI220616115A
ER  - 

@article{
author = "Anđelković, Miroslav and Maletić, Slobodan and Tomanović, Ivan",
year = "2022",
abstract = "Although its uninterrupted supply is essential for everyday life, the electricity occasionally experiences disruptions and outages. The work presented in the current paper aims to initiate the research to design a strategy based on advanced approaches of algebraic topology to prevent such malfunctions in a power grid network. Simplicial complexes are constructed to identify higher-order structures embedded in a network and, alongside a new algorithm for identifying delegates of the simplicial complex, are intended to pinpoint each element of the power grid network to its natural layer. Results of this methodology for analysis of a power grid network can single out its elements that are at risk to cause cascade problems which can result in unintentional islanding and blackouts. Further development of the outcomes of research can find implementation in the algorithms of the energy informatics research applications.",
journal = "Thermal Science",
title = "Identifiers for structural warnings of malfunction in power grid networks",
volume = "26",
number = "6 part B",
pages = "5043-5051",
doi = "10.2298/TSCI220616115A"
}

Anđelković, M., Maletić, S.,& Tomanović, I.. (2022). Identifiers for structural warnings of malfunction in power grid networks. in Thermal Science, 26(6 part B), 5043-5051.
https://doi.org/10.2298/TSCI220616115A

Anđelković M, Maletić S, Tomanović I. Identifiers for structural warnings of malfunction in power grid networks. in Thermal Science. 2022;26(6 part B):5043-5051.
doi:10.2298/TSCI220616115A .

Anđelković, Miroslav, Maletić, Slobodan, Tomanović, Ivan, "Identifiers for structural warnings of malfunction in power grid networks" in Thermal Science, 26, no. 6 part B (2022):5043-5051,
https://doi.org/10.2298/TSCI220616115A . .

TY  - JOUR
AU  - Maletić, Slobodan
AU  - Anđelković, Miroslav
AU  - Rajković, Milan
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10109
AB  - Complex networks display an organization of elements into nontrivial structures at versatile inherent scales, imposing challenges on a more complete understanding of their behavior. The interest of the research presented here is in the characterization of potential mesoscale structures as building blocks of generalized communities in complex networks, with an integrated property that goes beyond the pairwise collections of nodes. For this purpose, a simplicial complex is obtained from a mathematical graph, and indirectly from time series, producing the so-called clique complex from the complex network. As the higher-order organizational structures are naturally embedded in the hierarchical strata of a simplicial complex, the relationships between aggregation of nodes are stored in the higher-order combinatorial Laplacian. Based on the postulate that aggregation of nodes represents integrated configuration of information, the observability parameter is defined for the characterization of potential configurations, computed from the entries of the combinatorial Laplacian matrix. The framework introduced here is used to characterize nontrivial inherent organizational patterns embedded in two real-world complex networks and three complex networks obtained from heart rate time series recordings of three different subject’s meditative states
T2  - Chaos
T1  - Potential grouping of nodes induced by higher-order structures in complex networks
VL  - 31
IS  - 12
SP  - 123115
DO  - 10.1063/5.0069444
ER  - 

@article{
author = "Maletić, Slobodan and Anđelković, Miroslav and Rajković, Milan",
year = "2021",
abstract = "Complex networks display an organization of elements into nontrivial structures at versatile inherent scales, imposing challenges on a more complete understanding of their behavior. The interest of the research presented here is in the characterization of potential mesoscale structures as building blocks of generalized communities in complex networks, with an integrated property that goes beyond the pairwise collections of nodes. For this purpose, a simplicial complex is obtained from a mathematical graph, and indirectly from time series, producing the so-called clique complex from the complex network. As the higher-order organizational structures are naturally embedded in the hierarchical strata of a simplicial complex, the relationships between aggregation of nodes are stored in the higher-order combinatorial Laplacian. Based on the postulate that aggregation of nodes represents integrated configuration of information, the observability parameter is defined for the characterization of potential configurations, computed from the entries of the combinatorial Laplacian matrix. The framework introduced here is used to characterize nontrivial inherent organizational patterns embedded in two real-world complex networks and three complex networks obtained from heart rate time series recordings of three different subject’s meditative states",
journal = "Chaos",
title = "Potential grouping of nodes induced by higher-order structures in complex networks",
volume = "31",
number = "12",
pages = "123115",
doi = "10.1063/5.0069444"
}

Maletić, S., Anđelković, M.,& Rajković, M.. (2021). Potential grouping of nodes induced by higher-order structures in complex networks. in Chaos, 31(12), 123115.
https://doi.org/10.1063/5.0069444

Maletić S, Anđelković M, Rajković M. Potential grouping of nodes induced by higher-order structures in complex networks. in Chaos. 2021;31(12):123115.
doi:10.1063/5.0069444 .

Maletić, Slobodan, Anđelković, Miroslav, Rajković, Milan, "Potential grouping of nodes induced by higher-order structures in complex networks" in Chaos, 31, no. 12 (2021):123115,
https://doi.org/10.1063/5.0069444 . .

TY  - JOUR
AU  - Tadić, Bosiljka
AU  - Anđelković, Miroslav
AU  - Šuvakov, Milovan
AU  - Rodgers, Geoff J.
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8930
AB  - Functional designs of nanostructured materials seek to exploit the potential of complex morphologies and disorder. In this context, the spin dynamics in disordered antiferromagnetic materials present a significant challenge due to induced geometric frustration. Here we analyse the processes of magnetisation reversal driven by an external field in generalised spin networks with higher-order connectivity and antiferromagnetic defects. Using the model in (Tadić et al. Arxiv:1912.02433), we grow nanonetworks with geometrically constrained self-assemblies of simplexes (cliques) of a given size n, and with probability p each simplex possesses a defect edge affecting its binding, leading to a tree-like pattern of defects. The Ising spins are attached to vertices and have ferromagnetic interactions, while antiferromagnetic couplings apply between pairs of spins along each defect edge. Thus, a defect edge induces n − 2 frustrated triangles per n-clique participating in a larger-scale complex. We determine several topological, entropic, and graph-theoretic measures to characterise the structures of these assemblies. Further, we show how the sizes of simplexes building the aggregates with a given pattern of defects affects the magnetisation curves, the length of the domain walls and the shape of the hysteresis loop. The hysteresis shows a sequence of plateaus of fractional magnetisation and multiscale fluctuations in the passage between them. For fully antiferromagnetic interactions, the loop splits into two parts only in mono-disperse assemblies of cliques consisting of an odd number of vertices n. At the same time, remnant magnetisation occurs when n is even, and in poly-disperse assemblies of cliques in the range n ∈ [ 2 , 10 ] . These results shed light on spin dynamics in complex nanomagnetic assemblies in which geometric frustration arises in the interplay of higher-order connectivity and antiferromagnetic interactions.
T2  - Entropy
T1  - Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques
VL  - 22
IS  - 3
SP  - 336
DO  - 10.3390/e22030336
ER  - 

@article{
author = "Tadić, Bosiljka and Anđelković, Miroslav and Šuvakov, Milovan and Rodgers, Geoff J.",
year = "2020",
abstract = "Functional designs of nanostructured materials seek to exploit the potential of complex morphologies and disorder. In this context, the spin dynamics in disordered antiferromagnetic materials present a significant challenge due to induced geometric frustration. Here we analyse the processes of magnetisation reversal driven by an external field in generalised spin networks with higher-order connectivity and antiferromagnetic defects. Using the model in (Tadić et al. Arxiv:1912.02433), we grow nanonetworks with geometrically constrained self-assemblies of simplexes (cliques) of a given size n, and with probability p each simplex possesses a defect edge affecting its binding, leading to a tree-like pattern of defects. The Ising spins are attached to vertices and have ferromagnetic interactions, while antiferromagnetic couplings apply between pairs of spins along each defect edge. Thus, a defect edge induces n − 2 frustrated triangles per n-clique participating in a larger-scale complex. We determine several topological, entropic, and graph-theoretic measures to characterise the structures of these assemblies. Further, we show how the sizes of simplexes building the aggregates with a given pattern of defects affects the magnetisation curves, the length of the domain walls and the shape of the hysteresis loop. The hysteresis shows a sequence of plateaus of fractional magnetisation and multiscale fluctuations in the passage between them. For fully antiferromagnetic interactions, the loop splits into two parts only in mono-disperse assemblies of cliques consisting of an odd number of vertices n. At the same time, remnant magnetisation occurs when n is even, and in poly-disperse assemblies of cliques in the range n ∈ [ 2 , 10 ] . These results shed light on spin dynamics in complex nanomagnetic assemblies in which geometric frustration arises in the interplay of higher-order connectivity and antiferromagnetic interactions.",
journal = "Entropy",
title = "Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques",
volume = "22",
number = "3",
pages = "336",
doi = "10.3390/e22030336"
}

Tadić, B., Anđelković, M., Šuvakov, M.,& Rodgers, G. J.. (2020). Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques. in Entropy, 22(3), 336.
https://doi.org/10.3390/e22030336

Tadić B, Anđelković M, Šuvakov M, Rodgers GJ. Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques. in Entropy. 2020;22(3):336.
doi:10.3390/e22030336 .

Tadić, Bosiljka, Anđelković, Miroslav, Šuvakov, Milovan, Rodgers, Geoff J., "Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques" in Entropy, 22, no. 3 (2020):336,
https://doi.org/10.3390/e22030336 . .

TY  - JOUR
AU  - Anđelković, Miroslav
AU  - Tadić, Bosiljka
AU  - Melnik, Roderick
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9677
AB  - Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human connectome can be crucial for the brain complex dynamics. In this context, the best-connected brain areas, designated as hub nodes, play a central role in supporting integrated brain function. Here, we study the structure of simplicial complexes attached to eight global hubs in the female and male connectomes and identify the core networks among the affected brain regions. These eight hubs (Putamen, Caudate, Hippocampus and Thalamus-Proper in the left and right cerebral hemisphere) are the highest-ranking according to their topological dimension, defined as the number of simplexes of all orders in which the node participates. Furthermore, we analyse the weight-dependent heterogeneity of simplexes. We demonstrate changes in the structure of identified core networks and topological entropy when the threshold weight is gradually increased. These results highlight the role of higher-order interactions in human brain networks and provide additional evidence for (dis)similarity between the female and male connectomes.
T2  - Scientific Reports
T1  - The topology of higher-order complexes associated with brain hubs in human connectomes
VL  - 10
IS  - 1
SP  - 17320
DO  - 10.1038/s41598-020-74392-3
ER  - 

@article{
author = "Anđelković, Miroslav and Tadić, Bosiljka and Melnik, Roderick",
year = "2020",
abstract = "Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human connectome can be crucial for the brain complex dynamics. In this context, the best-connected brain areas, designated as hub nodes, play a central role in supporting integrated brain function. Here, we study the structure of simplicial complexes attached to eight global hubs in the female and male connectomes and identify the core networks among the affected brain regions. These eight hubs (Putamen, Caudate, Hippocampus and Thalamus-Proper in the left and right cerebral hemisphere) are the highest-ranking according to their topological dimension, defined as the number of simplexes of all orders in which the node participates. Furthermore, we analyse the weight-dependent heterogeneity of simplexes. We demonstrate changes in the structure of identified core networks and topological entropy when the threshold weight is gradually increased. These results highlight the role of higher-order interactions in human brain networks and provide additional evidence for (dis)similarity between the female and male connectomes.",
journal = "Scientific Reports",
title = "The topology of higher-order complexes associated with brain hubs in human connectomes",
volume = "10",
number = "1",
pages = "17320",
doi = "10.1038/s41598-020-74392-3"
}

Anđelković, M., Tadić, B.,& Melnik, R.. (2020). The topology of higher-order complexes associated with brain hubs in human connectomes. in Scientific Reports, 10(1), 17320.
https://doi.org/10.1038/s41598-020-74392-3

Anđelković M, Tadić B, Melnik R. The topology of higher-order complexes associated with brain hubs in human connectomes. in Scientific Reports. 2020;10(1):17320.
doi:10.1038/s41598-020-74392-3 .

Anđelković, Miroslav, Tadić, Bosiljka, Melnik, Roderick, "The topology of higher-order complexes associated with brain hubs in human connectomes" in Scientific Reports, 10, no. 1 (2020):17320,
https://doi.org/10.1038/s41598-020-74392-3 . .

TY  - JOUR
AU  - Tadić, Bosiljka
AU  - Šuvakov, Milovan
AU  - Anđelković, Miroslav
AU  - Rodgers, Geoff J.
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9683
AB  - Recently, the importance of higher-order interactions in the physics of quantum systems and nanoparticle assemblies has prompted the exploration of new classes of networks that grow through geometrically constrained simplex aggregation. Based on the model of chemically tunable self-assembly of simplexes [Šuvakov et al., Sci. Rep. 8, 1987 (2018)], here we extend the model to allow the presence of a defect edge per simplex. Using a wide distribution of simplex sizes (from edges, triangles, tetrahedrons, etc., up to 10-cliques) and various chemical affinity parameters, we investigate the magnitude of the impact of defects on the self-assembly process and the emerging higher-order networks. Their essential characteristics are treelike patterns of defect bonds, hyperbolic geometry, and simplicial complexes, which are described using the algebraic topology method. Furthermore, we demonstrate how the presence of patterned defects can be used to alter the structure of the assembly after the growth process is complete. In the assemblies grown under different chemical affinities, we consider the removal of defect bonds and analyze the progressive changes in the hierarchical architecture of simplicial complexes and the hyperbolicity parameters of the underlying graphs. Within the framework of cooperative self-assembly of nanonetworks, these results shed light on the use of defects in the design of complex materials. They also provide a different perspective on the understanding of extended connectivity beyond pairwise interactions in many complex systems.
T2  - Physical Review E
T1  - Large-scale influence of defect bonds in geometrically constrained self-assembly
VL  - 102
IS  - 3
SP  - 032307
DO  - 10.1103/PhysRevE.102.032307
ER  - 

@article{
author = "Tadić, Bosiljka and Šuvakov, Milovan and Anđelković, Miroslav and Rodgers, Geoff J.",
year = "2020",
abstract = "Recently, the importance of higher-order interactions in the physics of quantum systems and nanoparticle assemblies has prompted the exploration of new classes of networks that grow through geometrically constrained simplex aggregation. Based on the model of chemically tunable self-assembly of simplexes [Šuvakov et al., Sci. Rep. 8, 1987 (2018)], here we extend the model to allow the presence of a defect edge per simplex. Using a wide distribution of simplex sizes (from edges, triangles, tetrahedrons, etc., up to 10-cliques) and various chemical affinity parameters, we investigate the magnitude of the impact of defects on the self-assembly process and the emerging higher-order networks. Their essential characteristics are treelike patterns of defect bonds, hyperbolic geometry, and simplicial complexes, which are described using the algebraic topology method. Furthermore, we demonstrate how the presence of patterned defects can be used to alter the structure of the assembly after the growth process is complete. In the assemblies grown under different chemical affinities, we consider the removal of defect bonds and analyze the progressive changes in the hierarchical architecture of simplicial complexes and the hyperbolicity parameters of the underlying graphs. Within the framework of cooperative self-assembly of nanonetworks, these results shed light on the use of defects in the design of complex materials. They also provide a different perspective on the understanding of extended connectivity beyond pairwise interactions in many complex systems.",
journal = "Physical Review E",
title = "Large-scale influence of defect bonds in geometrically constrained self-assembly",
volume = "102",
number = "3",
pages = "032307",
doi = "10.1103/PhysRevE.102.032307"
}

Tadić, B., Šuvakov, M., Anđelković, M.,& Rodgers, G. J.. (2020). Large-scale influence of defect bonds in geometrically constrained self-assembly. in Physical Review E, 102(3), 032307.
https://doi.org/10.1103/PhysRevE.102.032307

Tadić B, Šuvakov M, Anđelković M, Rodgers GJ. Large-scale influence of defect bonds in geometrically constrained self-assembly. in Physical Review E. 2020;102(3):032307.
doi:10.1103/PhysRevE.102.032307 .

Tadić, Bosiljka, Šuvakov, Milovan, Anđelković, Miroslav, Rodgers, Geoff J., "Large-scale influence of defect bonds in geometrically constrained self-assembly" in Physical Review E, 102, no. 3 (2020):032307,
https://doi.org/10.1103/PhysRevE.102.032307 . .

TY  - JOUR
AU  - Tadić, Bosiljka
AU  - Anđelković, Miroslav
AU  - Melnik, Roderick
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8451
AB  - Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and edges indicate the occurrence of fiber tracts between them, has enabled an objective graph-theoretic analysis of human connectomes. However, the latent structure on higher-order interactions remains unexplored, where many brain regions act in synergy to perform complex functions. Here we use the simplicial complexes description of human connectome, where the shared simplexes encode higher-order relationships between groups of nodes. We study consensus connectome of 100 female (F-connectome) and of 100 male (M-connectome) subjects that we generated from the Budapest Reference Connectome Server v3.0 based on data from the Human Connectome Project. Our analysis reveals that the functional geometry of the common F&M-connectome coincides with the M-connectome and is characterized by a complex architecture of simplexes to the 14th order, which is built in six anatomical communities, and linked by short cycles. The F-connectome has additional edges that involve different brain regions, thereby increasing the size of simplexes and introducing new cycles. Both connectomes contain characteristic subjacent graphs that make them 3/2-hyperbolic. These results shed new light on the functional architecture of the brain, suggesting that insightful differences among connectomes are hidden in their higher-order connectivity. © 2019, The Author(s).
T2  - Scientific Reports
T1  - Functional Geometry of Human Connectomes
VL  - 9
IS  - 1
SP  - 12060
DO  - 10.1038/s41598-019-48568-5
ER  - 

@article{
author = "Tadić, Bosiljka and Anđelković, Miroslav and Melnik, Roderick",
year = "2019",
abstract = "Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and edges indicate the occurrence of fiber tracts between them, has enabled an objective graph-theoretic analysis of human connectomes. However, the latent structure on higher-order interactions remains unexplored, where many brain regions act in synergy to perform complex functions. Here we use the simplicial complexes description of human connectome, where the shared simplexes encode higher-order relationships between groups of nodes. We study consensus connectome of 100 female (F-connectome) and of 100 male (M-connectome) subjects that we generated from the Budapest Reference Connectome Server v3.0 based on data from the Human Connectome Project. Our analysis reveals that the functional geometry of the common F&M-connectome coincides with the M-connectome and is characterized by a complex architecture of simplexes to the 14th order, which is built in six anatomical communities, and linked by short cycles. The F-connectome has additional edges that involve different brain regions, thereby increasing the size of simplexes and introducing new cycles. Both connectomes contain characteristic subjacent graphs that make them 3/2-hyperbolic. These results shed new light on the functional architecture of the brain, suggesting that insightful differences among connectomes are hidden in their higher-order connectivity. © 2019, The Author(s).",
journal = "Scientific Reports",
title = "Functional Geometry of Human Connectomes",
volume = "9",
number = "1",
pages = "12060",
doi = "10.1038/s41598-019-48568-5"
}

Tadić, B., Anđelković, M.,& Melnik, R.. (2019). Functional Geometry of Human Connectomes. in Scientific Reports, 9(1), 12060.
https://doi.org/10.1038/s41598-019-48568-5

Tadić B, Anđelković M, Melnik R. Functional Geometry of Human Connectomes. in Scientific Reports. 2019;9(1):12060.
doi:10.1038/s41598-019-48568-5 .

Tadić, Bosiljka, Anđelković, Miroslav, Melnik, Roderick, "Functional Geometry of Human Connectomes" in Scientific Reports, 9, no. 1 (2019):12060,
https://doi.org/10.1038/s41598-019-48568-5 . .

TY  - JOUR
AU  - Tadić, Bosiljka
AU  - Anđelković, Miroslav
AU  - Šuvakov, Milovan
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1953
AB  - Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are delta-hyperbolic with delta(max) = 1 and the graph diameter D = 3 in each brain. While the emergent hyperbolicity in the two-brain networks varies satisfying delta(max)/D/2 LT = 1 and can be attributed to the topology of the subgraph formed around the cross-brains linking channels. We identify these subgraphs in each studied two-brain network and decompose their structure into simple geometric descriptors ( triangles, tetrahedra and cliques of higher orders) that contribute to hyperbolicity. Considering topologies that exceed two separate brain networks as a measure of coordination synergy between the brains, we identify different neural correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listeners self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior.
T2  - Frontiers in Physics
T1  - Origin of Hyperbolicity in Brain-to-Brain Coordination Networks
VL  - 6
DO  - 10.3389/fphy.2018.00007
ER  - 

@article{
author = "Tadić, Bosiljka and Anđelković, Miroslav and Šuvakov, Milovan",
year = "2018",
abstract = "Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are delta-hyperbolic with delta(max) = 1 and the graph diameter D = 3 in each brain. While the emergent hyperbolicity in the two-brain networks varies satisfying delta(max)/D/2 LT = 1 and can be attributed to the topology of the subgraph formed around the cross-brains linking channels. We identify these subgraphs in each studied two-brain network and decompose their structure into simple geometric descriptors ( triangles, tetrahedra and cliques of higher orders) that contribute to hyperbolicity. Considering topologies that exceed two separate brain networks as a measure of coordination synergy between the brains, we identify different neural correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listeners self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior.",
journal = "Frontiers in Physics",
title = "Origin of Hyperbolicity in Brain-to-Brain Coordination Networks",
volume = "6",
doi = "10.3389/fphy.2018.00007"
}

Tadić, B., Anđelković, M.,& Šuvakov, M.. (2018). Origin of Hyperbolicity in Brain-to-Brain Coordination Networks. in Frontiers in Physics, 6.
https://doi.org/10.3389/fphy.2018.00007

Tadić B, Anđelković M, Šuvakov M. Origin of Hyperbolicity in Brain-to-Brain Coordination Networks. in Frontiers in Physics. 2018;6.
doi:10.3389/fphy.2018.00007 .

Tadić, Bosiljka, Anđelković, Miroslav, Šuvakov, Milovan, "Origin of Hyperbolicity in Brain-to-Brain Coordination Networks" in Frontiers in Physics, 6 (2018),
https://doi.org/10.3389/fphy.2018.00007 . .

TY  - CONF
AU  - Tadić, Bosiljka
AU  - Anđelković, Miroslav
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/11012
AB  - Recently, the study of graphs representing various complex systems has been extended beyond the standard graphtheoretic measures. The use of methods of algebraic topology enabled revealing the higher organized structures and related hidden geometries that can appear in the graph. More specifically, the Q-analysis based on the algebraic topology of graphs identifies elementary geometric shapes or simplexes (triangles, tetrahedrons and higher order cliques) and how they connect to make more substantial structures or simplicial complexes. The original composition of these basic geometry descriptors is unique for a particular network; furthermore, it can induce emergent hyperbolicity or negative curvature, a measure of nodes proximity in the graph-metric space, which often associates with an improved function of the network. However, how the hyperbolic geometry evolves [T3] to support the network’s capacity remains a challenging issue, depending on the nature of the complex system in question. In this lecture, we discuss such hidden structures in conjunction with the functional properties of different types of human brain networks. More specifically, we consider the network structures that are originating from the aggregated fNMR imaging data recently described in [C1,C2], and the graphs mapping the brain activity patterns during social communications recorded by EEG [E1,T1,T2]. Using the generalized 4-point Gromov hyperbolicity criterion for graphs, we demonstrate that these brain networks are hyperbolic, and by performing Q-analysis, we determine the structure of underlying simplicial complexes in them. By comparing brain networks obtained from selected sets of data in conjunction with various resolution, female/male participants, and the level of cross-brain coordination, we attempt to find out how these hidden geometries vary, which may suggest the potential neuro-dynamical origin of the observed negative curvature.
PB  - Department of Biology and Ecology : Faculty of Sciences University of Novi Sad
C3  - Biologia Serbica : Belgrade BioInformatics Conference : BelBi2018 : program and the book of abstracts; June 18-22
T1  - Why Human Brain Networks are Hyperbolic?
VL  - 40
IS  - 1
SP  - 58
UR  - https://hdl.handle.net/21.15107/rcub_vinar_11012
ER  - 

@conference{
author = "Tadić, Bosiljka and Anđelković, Miroslav",
year = "2018",
abstract = "Recently, the study of graphs representing various complex systems has been extended beyond the standard graphtheoretic measures. The use of methods of algebraic topology enabled revealing the higher organized structures and related hidden geometries that can appear in the graph. More specifically, the Q-analysis based on the algebraic topology of graphs identifies elementary geometric shapes or simplexes (triangles, tetrahedrons and higher order cliques) and how they connect to make more substantial structures or simplicial complexes. The original composition of these basic geometry descriptors is unique for a particular network; furthermore, it can induce emergent hyperbolicity or negative curvature, a measure of nodes proximity in the graph-metric space, which often associates with an improved function of the network. However, how the hyperbolic geometry evolves [T3] to support the network’s capacity remains a challenging issue, depending on the nature of the complex system in question. In this lecture, we discuss such hidden structures in conjunction with the functional properties of different types of human brain networks. More specifically, we consider the network structures that are originating from the aggregated fNMR imaging data recently described in [C1,C2], and the graphs mapping the brain activity patterns during social communications recorded by EEG [E1,T1,T2]. Using the generalized 4-point Gromov hyperbolicity criterion for graphs, we demonstrate that these brain networks are hyperbolic, and by performing Q-analysis, we determine the structure of underlying simplicial complexes in them. By comparing brain networks obtained from selected sets of data in conjunction with various resolution, female/male participants, and the level of cross-brain coordination, we attempt to find out how these hidden geometries vary, which may suggest the potential neuro-dynamical origin of the observed negative curvature.",
publisher = "Department of Biology and Ecology : Faculty of Sciences University of Novi Sad",
journal = "Biologia Serbica : Belgrade BioInformatics Conference : BelBi2018 : program and the book of abstracts; June 18-22",
title = "Why Human Brain Networks are Hyperbolic?",
volume = "40",
number = "1",
pages = "58",
url = "https://hdl.handle.net/21.15107/rcub_vinar_11012"
}

Tadić, B.,& Anđelković, M.. (2018). Why Human Brain Networks are Hyperbolic?. in Biologia Serbica : Belgrade BioInformatics Conference : BelBi2018 : program and the book of abstracts; June 18-22
Department of Biology and Ecology : Faculty of Sciences University of Novi Sad., 40(1), 58.
https://hdl.handle.net/21.15107/rcub_vinar_11012

Tadić B, Anđelković M. Why Human Brain Networks are Hyperbolic?. in Biologia Serbica : Belgrade BioInformatics Conference : BelBi2018 : program and the book of abstracts; June 18-22. 2018;40(1):58.
https://hdl.handle.net/21.15107/rcub_vinar_11012 .

Tadić, Bosiljka, Anđelković, Miroslav, "Why Human Brain Networks are Hyperbolic?" in Biologia Serbica : Belgrade BioInformatics Conference : BelBi2018 : program and the book of abstracts; June 18-22, 40, no. 1 (2018):58,
https://hdl.handle.net/21.15107/rcub_vinar_11012 .

TY  - JOUR
AU  - Šuvakov, Milovan
AU  - Anđelković, Miroslav
AU  - Tadić, Bosiljka
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1931
AB  - Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and compatibility of the building blocks are decisive factors. Therefore, a comprehensive understanding of these processes is essential for the design of assemblies of desired properties. Here, we introduce a computational model for cooperative self-assembly with the simultaneous attachment of structured groups of particles, which can be described by simplexes (connected pairs, triangles, tetrahedrons and higher order cliques) to a growing network. The model incorporates geometric rules that provide suitable nesting spaces for the new group and the chemical affinity of the system to accept excess particles. For varying chemical affinity, we grow different classes of assemblies by binding the cliques of distributed sizes. Furthermore, we characterize the emergent structures by metrics of graph theory and algebraic topology of graphs, and 4-point test for the intrinsic hyperbolicity of the networks. Our results show that higher Q-connectedness of the appearing simplicial complexes can arise due to only geometric factors and that it can be efficiently modulated by changing the chemical potential and the polydispersity of the binding simplexes.
T2  - Scientific Reports
T1  - Hidden geometries in networks arising from cooperative self-assembly
VL  - 8
IS  - 1
SP  - 1987
DO  - 10.1038/s41598-018-20398-x
ER  - 

@article{
author = "Šuvakov, Milovan and Anđelković, Miroslav and Tadić, Bosiljka",
year = "2018",
abstract = "Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and compatibility of the building blocks are decisive factors. Therefore, a comprehensive understanding of these processes is essential for the design of assemblies of desired properties. Here, we introduce a computational model for cooperative self-assembly with the simultaneous attachment of structured groups of particles, which can be described by simplexes (connected pairs, triangles, tetrahedrons and higher order cliques) to a growing network. The model incorporates geometric rules that provide suitable nesting spaces for the new group and the chemical affinity of the system to accept excess particles. For varying chemical affinity, we grow different classes of assemblies by binding the cliques of distributed sizes. Furthermore, we characterize the emergent structures by metrics of graph theory and algebraic topology of graphs, and 4-point test for the intrinsic hyperbolicity of the networks. Our results show that higher Q-connectedness of the appearing simplicial complexes can arise due to only geometric factors and that it can be efficiently modulated by changing the chemical potential and the polydispersity of the binding simplexes.",
journal = "Scientific Reports",
title = "Hidden geometries in networks arising from cooperative self-assembly",
volume = "8",
number = "1",
pages = "1987",
doi = "10.1038/s41598-018-20398-x"
}

Šuvakov, M., Anđelković, M.,& Tadić, B.. (2018). Hidden geometries in networks arising from cooperative self-assembly. in Scientific Reports, 8(1), 1987.
https://doi.org/10.1038/s41598-018-20398-x

Šuvakov M, Anđelković M, Tadić B. Hidden geometries in networks arising from cooperative self-assembly. in Scientific Reports. 2018;8(1):1987.
doi:10.1038/s41598-018-20398-x .

Šuvakov, Milovan, Anđelković, Miroslav, Tadić, Bosiljka, "Hidden geometries in networks arising from cooperative self-assembly" in Scientific Reports, 8, no. 1 (2018):1987,
https://doi.org/10.1038/s41598-018-20398-x . .

TY  - JOUR
AU  - Tadić, Bosiljka
AU  - Anđelković, Miroslav
AU  - Šuvakov, Milovan
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1243
AB  - Charge transport in the Coulomb blockade regime of two-dimensional nanoparticle arrays exhibits nonlinear I-V characteristics, where the level of nonlinearity strongly associates with the arrays architecture. Here, we use different mathematical techniques to investigate the collective behavior of the charge transport and quantify its relationship to the structure of the nanoparticle assembly. First, we simulate single-electron tunneling conduction in a class of nanoparticle networks with a controlled variation of the structural characteristics (branching, extended linear segments) which influence the local communication among the conducting paths between the electrodes. Further, by applying an innovative approach based on the algebraic topology of graphs, we analyze the structure of connections in the manifolds, which map the fractal time series of charge fluctuations in the phase space. By tracking the I-V curves in different nanoparticle networks together with the indicators of collective dynamics and the topology of the phase space manifolds, we show that the increased I-V nonlinearity is fully consistent with the enhanced aggregate fluctuations and higher connection complexity among the participating states. Also, by determining shifts in the topology and cooperative transport features, we explore the impact of the size of electrodes and local charge disorder. The results are relevant for designing the nanoparticle devices with improved conduction; they also highlight the significance of topological descriptions for a broader understanding of the nature of fluctuations at the nanoscale.
T2  - Journal of Coupled Systems and Multiscale Dynamics
T1  - The influence of architecture of nanoparticle networks on collective charge transport revealed by the fractal time series and topology of phase space manifolds
VL  - 4
IS  - 1
SP  - 30
EP  - 42
DO  - 10.1166/jcsmd.2016.1094
ER  - 

@article{
author = "Tadić, Bosiljka and Anđelković, Miroslav and Šuvakov, Milovan",
year = "2016",
abstract = "Charge transport in the Coulomb blockade regime of two-dimensional nanoparticle arrays exhibits nonlinear I-V characteristics, where the level of nonlinearity strongly associates with the arrays architecture. Here, we use different mathematical techniques to investigate the collective behavior of the charge transport and quantify its relationship to the structure of the nanoparticle assembly. First, we simulate single-electron tunneling conduction in a class of nanoparticle networks with a controlled variation of the structural characteristics (branching, extended linear segments) which influence the local communication among the conducting paths between the electrodes. Further, by applying an innovative approach based on the algebraic topology of graphs, we analyze the structure of connections in the manifolds, which map the fractal time series of charge fluctuations in the phase space. By tracking the I-V curves in different nanoparticle networks together with the indicators of collective dynamics and the topology of the phase space manifolds, we show that the increased I-V nonlinearity is fully consistent with the enhanced aggregate fluctuations and higher connection complexity among the participating states. Also, by determining shifts in the topology and cooperative transport features, we explore the impact of the size of electrodes and local charge disorder. The results are relevant for designing the nanoparticle devices with improved conduction; they also highlight the significance of topological descriptions for a broader understanding of the nature of fluctuations at the nanoscale.",
journal = "Journal of Coupled Systems and Multiscale Dynamics",
title = "The influence of architecture of nanoparticle networks on collective charge transport revealed by the fractal time series and topology of phase space manifolds",
volume = "4",
number = "1",
pages = "30-42",
doi = "10.1166/jcsmd.2016.1094"
}

Tadić, B., Anđelković, M.,& Šuvakov, M.. (2016). The influence of architecture of nanoparticle networks on collective charge transport revealed by the fractal time series and topology of phase space manifolds. in Journal of Coupled Systems and Multiscale Dynamics, 4(1), 30-42.
https://doi.org/10.1166/jcsmd.2016.1094

Tadić B, Anđelković M, Šuvakov M. The influence of architecture of nanoparticle networks on collective charge transport revealed by the fractal time series and topology of phase space manifolds. in Journal of Coupled Systems and Multiscale Dynamics. 2016;4(1):30-42.
doi:10.1166/jcsmd.2016.1094 .

Tadić, Bosiljka, Anđelković, Miroslav, Šuvakov, Milovan, "The influence of architecture of nanoparticle networks on collective charge transport revealed by the fractal time series and topology of phase space manifolds" in Journal of Coupled Systems and Multiscale Dynamics, 4, no. 1 (2016):30-42,
https://doi.org/10.1166/jcsmd.2016.1094 . .

TY  - JOUR
AU  - Anđelković, Miroslav
AU  - Tadić, Bosiljka
AU  - Mitrović Dankulov, Marija
AU  - Rajković, Milan
AU  - Melnik, Roderick
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1085
AB  - The communication processes of knowledge creation represent a particular class of human dynamics where the expertise of individuals plays a substantial role, thus offering a unique possibility to study the structure of knowledge networks from online data. Here, we use the empirical evidence from questions-and-answers in mathematics to analyse the emergence of the network of knowledge contents (or tags) as the individual experts use them in the process. After removing extra edges from the network-associated graph, we apply the methods of algebraic topology of graphs to examine the structure of higher-order combinatorial spaces in networks for four consecutive time intervals. We find that the ranking distributions of the suitably scaled topological dimensions of nodes fall into a unique curve for all time intervals and filtering levels, suggesting a robust architecture of knowledge networks. Moreover, these networks preserve the logical structure of knowledge within emergent communities of nodes, labeled according to a standard mathematical classification scheme. Further, we investigate the appearance of new contents over time and their innovative combinations, which expand the knowledge network. In each network, we identify an innovation channel as a subgraph of triangles and larger simplices to which new tags attach. Our results show that the increasing topological complexity of the innovation channels contributes to networks architecture over different time periods, and is consistent with temporal correlations of the occurrence of new tags. The methodology applies to a wide class of data with the suitable temporal resolution and clearly identified knowledge-content units.
T2  - PLOS One
T1  - Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers
VL  - 11
IS  - 5
DO  - 10.1371/journal.pone.0154655
ER  - 

@article{
author = "Anđelković, Miroslav and Tadić, Bosiljka and Mitrović Dankulov, Marija and Rajković, Milan and Melnik, Roderick",
year = "2016",
abstract = "The communication processes of knowledge creation represent a particular class of human dynamics where the expertise of individuals plays a substantial role, thus offering a unique possibility to study the structure of knowledge networks from online data. Here, we use the empirical evidence from questions-and-answers in mathematics to analyse the emergence of the network of knowledge contents (or tags) as the individual experts use them in the process. After removing extra edges from the network-associated graph, we apply the methods of algebraic topology of graphs to examine the structure of higher-order combinatorial spaces in networks for four consecutive time intervals. We find that the ranking distributions of the suitably scaled topological dimensions of nodes fall into a unique curve for all time intervals and filtering levels, suggesting a robust architecture of knowledge networks. Moreover, these networks preserve the logical structure of knowledge within emergent communities of nodes, labeled according to a standard mathematical classification scheme. Further, we investigate the appearance of new contents over time and their innovative combinations, which expand the knowledge network. In each network, we identify an innovation channel as a subgraph of triangles and larger simplices to which new tags attach. Our results show that the increasing topological complexity of the innovation channels contributes to networks architecture over different time periods, and is consistent with temporal correlations of the occurrence of new tags. The methodology applies to a wide class of data with the suitable temporal resolution and clearly identified knowledge-content units.",
journal = "PLOS One",
title = "Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers",
volume = "11",
number = "5",
doi = "10.1371/journal.pone.0154655"
}

Anđelković, M., Tadić, B., Mitrović Dankulov, M., Rajković, M.,& Melnik, R.. (2016). Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers. in PLOS One, 11(5).
https://doi.org/10.1371/journal.pone.0154655

Anđelković M, Tadić B, Mitrović Dankulov M, Rajković M, Melnik R. Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers. in PLOS One. 2016;11(5).
doi:10.1371/journal.pone.0154655 .

Anđelković, Miroslav, Tadić, Bosiljka, Mitrović Dankulov, Marija, Rajković, Milan, Melnik, Roderick, "Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers" in PLOS One, 11, no. 5 (2016),
https://doi.org/10.1371/journal.pone.0154655 . .

TY  - JOUR
AU  - Tadić, Bosiljka
AU  - Anđelković, Miroslav
AU  - Boshkoska, Biljana Mileva
AU  - Levnajić, Zoran
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1322
AB  - Human behaviour in various circumstances mirrors the corresponding brain connectivity patterns, which are suitably represented by functional brain networks. While the objective analysis of these networks by graph theory tools deepened our understanding of brain functions, the multi-brain structures and connections underlying human social behaviour remain largely unexplored. In this study, we analyse the aggregate graph that maps coordination of EEG signals previously recorded during spoken communications in two groups of six listeners and two speakers. Applying an innovative approach based on the algebraic topology of graphs, we analyse higher-order topological complexes consisting of mutually interwoven cliques of a high order to which the identified functional connections organise. Our results reveal that the topological quantifiers provide new suitable measures for differences in the brain activity patterns and inter-brain synchronisation between speakers and listeners. Moreover, the higher topological complexity correlates with the listeners concentration to the story, confirmed by self-rating, and closeness to the speakers brain activity pattern, which is measured by network-to-network distance. The connectivity structures of the frontal and parietal lobe consistently constitute distinct clusters, which extend across the listeners group. Formally, the topology quantifiers of the multi-brain communities exceed the sum of those of the participating individuals and also reflect the listeners rated attributes of the speaker and the narrated subject. In the broader context, the presented study exposes the relevance of higher topological structures ( besides standard graph measures) for characterising functional brain networks under different stimuli.
T2  - PLOS One
T1  - Algebraic Topology of Multi-Brain Connectivity Networks Reveals Dissimilarity in Functional Patterns during Spoken Communications
VL  - 11
IS  - 11
DO  - 10.1371/journal.pone.0166787
ER  - 

@article{
author = "Tadić, Bosiljka and Anđelković, Miroslav and Boshkoska, Biljana Mileva and Levnajić, Zoran",
year = "2016",
abstract = "Human behaviour in various circumstances mirrors the corresponding brain connectivity patterns, which are suitably represented by functional brain networks. While the objective analysis of these networks by graph theory tools deepened our understanding of brain functions, the multi-brain structures and connections underlying human social behaviour remain largely unexplored. In this study, we analyse the aggregate graph that maps coordination of EEG signals previously recorded during spoken communications in two groups of six listeners and two speakers. Applying an innovative approach based on the algebraic topology of graphs, we analyse higher-order topological complexes consisting of mutually interwoven cliques of a high order to which the identified functional connections organise. Our results reveal that the topological quantifiers provide new suitable measures for differences in the brain activity patterns and inter-brain synchronisation between speakers and listeners. Moreover, the higher topological complexity correlates with the listeners concentration to the story, confirmed by self-rating, and closeness to the speakers brain activity pattern, which is measured by network-to-network distance. The connectivity structures of the frontal and parietal lobe consistently constitute distinct clusters, which extend across the listeners group. Formally, the topology quantifiers of the multi-brain communities exceed the sum of those of the participating individuals and also reflect the listeners rated attributes of the speaker and the narrated subject. In the broader context, the presented study exposes the relevance of higher topological structures ( besides standard graph measures) for characterising functional brain networks under different stimuli.",
journal = "PLOS One",
title = "Algebraic Topology of Multi-Brain Connectivity Networks Reveals Dissimilarity in Functional Patterns during Spoken Communications",
volume = "11",
number = "11",
doi = "10.1371/journal.pone.0166787"
}

Tadić, B., Anđelković, M., Boshkoska, B. M.,& Levnajić, Z.. (2016). Algebraic Topology of Multi-Brain Connectivity Networks Reveals Dissimilarity in Functional Patterns during Spoken Communications. in PLOS One, 11(11).
https://doi.org/10.1371/journal.pone.0166787

Tadić B, Anđelković M, Boshkoska BM, Levnajić Z. Algebraic Topology of Multi-Brain Connectivity Networks Reveals Dissimilarity in Functional Patterns during Spoken Communications. in PLOS One. 2016;11(11).
doi:10.1371/journal.pone.0166787 .

Tadić, Bosiljka, Anđelković, Miroslav, Boshkoska, Biljana Mileva, Levnajić, Zoran, "Algebraic Topology of Multi-Brain Connectivity Networks Reveals Dissimilarity in Functional Patterns during Spoken Communications" in PLOS One, 11, no. 11 (2016),
https://doi.org/10.1371/journal.pone.0166787 . .

TY  - DATA
AU  - Anđelković, Miroslav
AU  - Tadić, Bosiljka
AU  - Mitrović Dankulov, Marija
AU  - Rajković, Milan
AU  - Melnik, Roderick
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9420
AB  - Names of the first twenty tags ordered according to their topological dimension in the network of tags before filtering and after filtering at the indicated confidence level p has been performed.
T2  - PLOS One
T1  - Names of the first twenty tags ordered according to their topological dimension in the network of tags before filtering and after filtering at the indicated confidence level p has been performed
DO  - 10.1371/journal.pone.0154655.t002
ER  - 

@misc{
author = "Anđelković, Miroslav and Tadić, Bosiljka and Mitrović Dankulov, Marija and Rajković, Milan and Melnik, Roderick",
year = "2016",
abstract = "Names of the first twenty tags ordered according to their topological dimension in the network of tags before filtering and after filtering at the indicated confidence level p has been performed.",
journal = "PLOS One",
title = "Names of the first twenty tags ordered according to their topological dimension in the network of tags before filtering and after filtering at the indicated confidence level p has been performed",
doi = "10.1371/journal.pone.0154655.t002"
}

Anđelković, M., Tadić, B., Mitrović Dankulov, M., Rajković, M.,& Melnik, R.. (2016). Names of the first twenty tags ordered according to their topological dimension in the network of tags before filtering and after filtering at the indicated confidence level p has been performed. in PLOS One.
https://doi.org/10.1371/journal.pone.0154655.t002

Anđelković M, Tadić B, Mitrović Dankulov M, Rajković M, Melnik R. Names of the first twenty tags ordered according to their topological dimension in the network of tags before filtering and after filtering at the indicated confidence level p has been performed. in PLOS One. 2016;.
doi:10.1371/journal.pone.0154655.t002 .

Anđelković, Miroslav, Tadić, Bosiljka, Mitrović Dankulov, Marija, Rajković, Milan, Melnik, Roderick, "Names of the first twenty tags ordered according to their topological dimension in the network of tags before filtering and after filtering at the indicated confidence level p has been performed" in PLOS One (2016),
https://doi.org/10.1371/journal.pone.0154655.t002 . .

TY  - DATA
AU  - Anđelković, Miroslav
AU  - Tadić, Bosiljka
AU  - Mitrović Dankulov, Marija
AU  - Rajković, Milan
AU  - Melnik, Roderick
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9421
AB  - The graph-level measures for tags networks for four consecutive periods, filtered at confidence p = 0.1
T2  - PLOS One
T1  - The graph-level measures for tags networks for four consecutive periods, filtered at confidence p = 0.1
DO  - 10.1371/journal.pone.0154655.t001
ER  - 

@misc{
author = "Anđelković, Miroslav and Tadić, Bosiljka and Mitrović Dankulov, Marija and Rajković, Milan and Melnik, Roderick",
year = "2016",
abstract = "The graph-level measures for tags networks for four consecutive periods, filtered at confidence p = 0.1",
journal = "PLOS One",
title = "The graph-level measures for tags networks for four consecutive periods, filtered at confidence p = 0.1",
doi = "10.1371/journal.pone.0154655.t001"
}

Anđelković, M., Tadić, B., Mitrović Dankulov, M., Rajković, M.,& Melnik, R.. (2016). The graph-level measures for tags networks for four consecutive periods, filtered at confidence p = 0.1. in PLOS One.
https://doi.org/10.1371/journal.pone.0154655.t001

Anđelković M, Tadić B, Mitrović Dankulov M, Rajković M, Melnik R. The graph-level measures for tags networks for four consecutive periods, filtered at confidence p = 0.1. in PLOS One. 2016;.
doi:10.1371/journal.pone.0154655.t001 .

Anđelković, Miroslav, Tadić, Bosiljka, Mitrović Dankulov, Marija, Rajković, Milan, Melnik, Roderick, "The graph-level measures for tags networks for four consecutive periods, filtered at confidence p = 0.1" in PLOS One (2016),
https://doi.org/10.1371/journal.pone.0154655.t001 . .

TY  - JOUR
AU  - Anđelković, Miroslav
AU  - Tadić, Bosiljka
AU  - Maletić, Slobodan
AU  - Rajković, Milan
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/648
AB  - In online communications, patterns of conduct of individual actors and use of emotions in the process can lead to a complex social graph exhibiting multilayered structure and meso-scopic communities. Using simplicial complexes representation of graphs, we investigate in-depth topology of the online social network constructed from MySpace dialogs which exhibits original community structure. A simulation of emotion spreading in this network leads to the identification of two emotion-propagating layers. Three topological measures are introduced, referred to as the structure vectors, which quantify graphs architecture at different dimension levels. Notably, structures emerging through shared links, triangles and tetrahedral faces, frequently occur and range from tree-like to maximal 5-cliques and their respective complexes. On the other hand, the structures which spread only negative or only positive emotion messages appear to have much simpler topology consisting of links and triangles. The nodes structure vector represents the number of simplices at each topology level in which the node resides and the total number of such simplices determines what we define as the nodes topological dimension. The presented results suggest that the nodes topological dimension provides a suitable measure of the social capital which measures the actors ability to act as a broker in compact communities, the so called Simmelian brokerage. We also generalize the results to a wider class of computer-generated networks. Investigating components of the nodes vector over network layers reveals that same nodes develop different socio-emotional relations and that the influential nodes build social capital by combining their connections in different layers. (C) 2015 Elsevier B.V. All rights reserved.
T2  - Physica A: Statistical Mechanics and Its Applications
T1  - Hierarchical sequencing of online social graphs
VL  - 436
SP  - 582
EP  - 595
DO  - 10.1016/j.physa.2015.05.075
ER  - 

@article{
author = "Anđelković, Miroslav and Tadić, Bosiljka and Maletić, Slobodan and Rajković, Milan",
year = "2015",
abstract = "In online communications, patterns of conduct of individual actors and use of emotions in the process can lead to a complex social graph exhibiting multilayered structure and meso-scopic communities. Using simplicial complexes representation of graphs, we investigate in-depth topology of the online social network constructed from MySpace dialogs which exhibits original community structure. A simulation of emotion spreading in this network leads to the identification of two emotion-propagating layers. Three topological measures are introduced, referred to as the structure vectors, which quantify graphs architecture at different dimension levels. Notably, structures emerging through shared links, triangles and tetrahedral faces, frequently occur and range from tree-like to maximal 5-cliques and their respective complexes. On the other hand, the structures which spread only negative or only positive emotion messages appear to have much simpler topology consisting of links and triangles. The nodes structure vector represents the number of simplices at each topology level in which the node resides and the total number of such simplices determines what we define as the nodes topological dimension. The presented results suggest that the nodes topological dimension provides a suitable measure of the social capital which measures the actors ability to act as a broker in compact communities, the so called Simmelian brokerage. We also generalize the results to a wider class of computer-generated networks. Investigating components of the nodes vector over network layers reveals that same nodes develop different socio-emotional relations and that the influential nodes build social capital by combining their connections in different layers. (C) 2015 Elsevier B.V. All rights reserved.",
journal = "Physica A: Statistical Mechanics and Its Applications",
title = "Hierarchical sequencing of online social graphs",
volume = "436",
pages = "582-595",
doi = "10.1016/j.physa.2015.05.075"
}

Anđelković, M., Tadić, B., Maletić, S.,& Rajković, M.. (2015). Hierarchical sequencing of online social graphs. in Physica A: Statistical Mechanics and Its Applications, 436, 582-595.
https://doi.org/10.1016/j.physa.2015.05.075

Anđelković M, Tadić B, Maletić S, Rajković M. Hierarchical sequencing of online social graphs. in Physica A: Statistical Mechanics and Its Applications. 2015;436:582-595.
doi:10.1016/j.physa.2015.05.075 .

Anđelković, Miroslav, Tadić, Bosiljka, Maletić, Slobodan, Rajković, Milan, "Hierarchical sequencing of online social graphs" in Physica A: Statistical Mechanics and Its Applications, 436 (2015):582-595,
https://doi.org/10.1016/j.physa.2015.05.075 . .

TY  - JOUR
AU  - Anđelković, Miroslav
AU  - Gupte, Neelima
AU  - Tadić, Bosiljka
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/563
AB  - We introduce an approach based on algebraic topological methods that allow an accurate characterization of jamming in dynamical systems with queues. As a prototype system, we analyze the traffic of information packets with navigation and queuing at nodes on a network substrate in distinct dynamical regimes. A temporal sequence of traffic density fluctuations is mapped onto a mathematical graph in which each vertex denotes one dynamical state of the system. The coupling complexity between these states is revealed by classifying agglomerates of high-dimensional cliques that are intermingled at different topological levels and quantified by a set of geometrical and entropy measures. The free-flow, jamming, and congested traffic regimes result in graphs of different structure, while the largest geometrical complexity and minimum entropy mark the edge of the jamming region.
T2  - Physical Review E
T1  - Hidden geometry of traffic jamming
VL  - 91
IS  - 5
DO  - 10.1103/PhysRevE.91.052817
ER  - 

@article{
author = "Anđelković, Miroslav and Gupte, Neelima and Tadić, Bosiljka",
year = "2015",
abstract = "We introduce an approach based on algebraic topological methods that allow an accurate characterization of jamming in dynamical systems with queues. As a prototype system, we analyze the traffic of information packets with navigation and queuing at nodes on a network substrate in distinct dynamical regimes. A temporal sequence of traffic density fluctuations is mapped onto a mathematical graph in which each vertex denotes one dynamical state of the system. The coupling complexity between these states is revealed by classifying agglomerates of high-dimensional cliques that are intermingled at different topological levels and quantified by a set of geometrical and entropy measures. The free-flow, jamming, and congested traffic regimes result in graphs of different structure, while the largest geometrical complexity and minimum entropy mark the edge of the jamming region.",
journal = "Physical Review E",
title = "Hidden geometry of traffic jamming",
volume = "91",
number = "5",
doi = "10.1103/PhysRevE.91.052817"
}

Anđelković, M., Gupte, N.,& Tadić, B.. (2015). Hidden geometry of traffic jamming. in Physical Review E, 91(5).
https://doi.org/10.1103/PhysRevE.91.052817

Anđelković M, Gupte N, Tadić B. Hidden geometry of traffic jamming. in Physical Review E. 2015;91(5).
doi:10.1103/PhysRevE.91.052817 .

Anđelković, Miroslav, Gupte, Neelima, Tadić, Bosiljka, "Hidden geometry of traffic jamming" in Physical Review E, 91, no. 5 (2015),
https://doi.org/10.1103/PhysRevE.91.052817 . .