Related papers: Neurogeometry of perception: isotropic and anisotr…
We study the geometry of surfaces in $\mathbb R^5$ by relating it to the geometry of regular and singular surfaces in $\mathbb R^4$ obtained by orthogonal projections. In particular, we obtain relations between asymptotic directions, which…
Action, cognition, emotion and perception can be mapped in the brain by using set of techniques. Translating unimodal concepts from one modality to another is an important step towards understanding the neural mechanisms. This paper…
This article reports on simulations that show how, starting with a form of neural lattice structure, it is possible to reversibly generate many alternative isomers with a lower structural symmetry, which results from twisting two hexagons…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In this work, we combine topological deep generative models and…
The cortical magnification matrix M is introduced founded on a notion similar to that of the scalar cortical magnification factor M. Unlike M, this matrix is suitable to describe anisotropy in cortical magnification, which is of particular…
Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
The analysis of complex networks has revealed patterns of organization in a variety of natural and artificial systems, including neuronal networks of the brain at multiple scales. In this paper, we describe a novel analysis of the…
The geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include media with isotropic, inhomogeneous, chirality. It is found that such media may be described through introducing the…
In a joint paper, Jean Petitot together with the authors of the present paper described the functional geometry of the visual cortex as the symplectization of a contact form to describe the family of cells sensitive to position, orientation…
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. We define the adjacency, incidence and Laplacian matrices of an oriented hypergraph and study each of them. We extend several matrix…
Network models describe the brain as sets of nodes and edges that represent its distributed organization. So far, most discoveries in network neuroscience have prioritized insights that highlight distinct groupings and specialized…
A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…
Current connectivity diagrams of human brain image data are either overly complex or overly simplistic. In this work we introduce simple yet accurate interactive visual representations of multiple brain image structures and the connectivity…
This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This…
The characterisation of the brain as a "connectome", in which the connections are represented by correlational values across timeseries and as summary measures derived from graph theory analyses, has been very popular in the last years.…
The cerebral cortex is composed of multiple cortical areas that exert a wide variety of brain functions. Although human brain neurons are genetically and areally mosaic, the three-dimensional structural differences between neurons in…
Surface analysis of the cortex is ubiquitous in human neuroimaging with MRI, e.g., for cortical registration, parcellation, or thickness estimation. The convoluted cortical geometry requires isotropic scans (e.g., 1mm MPRAGEs) and good…
In neuroscience, functional brain connectivity describes the connectivity between brain regions that share functional properties. Neuroscientists often characterize it by a time series of covariance matrices between functional measurements…