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  - 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 . .