The multidimensional brain

Tozzi, Arturo

doi:10.1016/j.plrev.2018.12.004

Cited by 31 publications

(18 citation statements)

References 106 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, mapping the brain imaging data 13 , 14 to networks involved different types of signals across spatial and temporal scales; consequently, a variety of structural and functional networks have been obtained 15 – 18 . This network mapping enabled getting a new insight into the functional organisation of the brain 19 , 20 , in particular, based on the standard and deep graph theoretic methods 21 – 23 and the algebraic topology of graphs 1 , 24 . The type of network that we consider in this work is the whole-brain network human connectome ; it is mapped from the diffusion tensor imaging data available from the human connectome project 25 , see Methods.…”

Section: Introductionmentioning

confidence: 99%

The topology of higher-order complexes associated with brain hubs in human connectomes

Andjelković

Tadić

Melnik

2020

Sci Rep

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

The topology of higher-order complexes associated with brain hubs in human connectomes

Andjelković

Tadić

Melnik

2020

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Reversely, the dimensionality increase 'unglues' points, and information increases. In more detail, this point of view is presented and illustrated with applications in the review paper [25]. It is necessary to add that for a continuous map f : S n → R n 'almost every' point is glued with another point (just imagine a projection of a 2D sphere on a plane).…”

mentioning

confidence: 99%

The unreasonable effectiveness of small neural ensembles in high-dimensional brain

Gorban

Makarov

Tyukin

2019

Physics of Life Reviews

View full text Add to dashboard Cite

“…It is noteworthy that, apart from the quaternionic maps described in this paper, another method is available to assess higher dimensional activities of nervous networks. Indeed, it has been recently suggested (Tozzi 2019) that hidden spatial dimensions of nervous activity could be tackled in terms of oscillations inside a two-dimensional superlattice equipped with quantum Hall effects. In this peculiar apparatus, the superimposition of waves of different wavelengths gives rise to both (two-dimensional) linear and (four-dimensional) nonlinear dynamics (Lohse et al, 2018;Zilberberg et al, 2018).…”

Section: Discussionmentioning

confidence: 99%

“…It has been stated that "invariances or symmetries afforded by projections onto high dimensional spaces... may not reveal themselves through local scrutiny of the surface data acquired from the brain in action, but may require" the use of higher-dimensional manifolds (Friston, 2017). For a reviewon the multidimensional brain, see Tozzi (2019). In its early formulation, the higherdimensional nervous trajectories have been described as occurring in the four spatial dimensions of a genus-zero hypersphere S 3 , or of a genus-one Clifford torus (Tozzi and Peters, 2016;.…”

mentioning

confidence: 99%

Quaternionic Assessment of EEG Traces on Nervous Multidimensional Hyperspheres

Tozzi

Jaušovec³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

The nervous activity of the brain takes place in higher-dimensional functional spaces. Indeed, recent claims advocate that the brain might be equipped with a phase space displaying four spatial dimensions plus time, instead of the classical three plus time. This suggests the possibility to investigate global visualization methods for exploiting four-dimensional maps of real experimental data sets. Here we asked whether, starting from the conventional neuro-data available in three dimensions plus time, it is feasible to find an operational procedure to describe the corresponding four-dimensional trajectories. In particular, we used quaternion orthographic projections for the assessment of electroencephalographic traces (EEG) from scalp locations. This approach makes it possible to map three-dimensional EEG traces to the surface of a four-dimensional hypersphere, which has an important advantage, since quaternionic networks make it feasible to enlighten temporally far apart nervous trajectories equipped with the same features, such as the same frequency or amplitude of electric oscillations. This leads to an incisive operational assessment of symmetries, dualities and matching descriptions hidden in the very structure of complex neuro-data signals.

show abstract

The multidimensional brain

Cited by 31 publications

References 106 publications

The topology of higher-order complexes associated with brain hubs in human connectomes

The topology of higher-order complexes associated with brain hubs in human connectomes

The unreasonable effectiveness of small neural ensembles in high-dimensional brain

Quaternionic Assessment of EEG Traces on Nervous Multidimensional Hyperspheres

Contact Info

Product

Resources

About