Related papers: Hyperbolic planforms in relation to visual edges a…

Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in human-computer interactions. However, their utility is currently limited because EEG decoding…

Brain organoids recapitulate a number of brain properties, including neuronal diversity. However, do they recapitulate brain structure? Using a hydrodynamic description for cell nuclei as particles interacting initially via an effective,…

Tractograms are virtual representations of the white matter fibers of the brain. They are of primary interest for tasks like presurgical planning, and investigation of neuroplasticity or brain disorders. Each tractogram is composed of…

Finding suitable embeddings for connectomes (spatially embedded complex networks that map neural connections in the brain) is crucial for analyzing and understanding cognitive processes. Recent studies have found two-dimensional hyperbolic…

Hyperbolic neural networks can effectively capture the inherent hierarchy of graph datasets, and consequently a powerful choice of GNNs. However, they entangle multiple incongruent (gyro-)vector spaces within a layer, which makes them…

Humans have the capacity to question what we see and to recognize when our vision is unreliable (e.g., when we realize that we are experiencing a visual illusion). Inspired by this capacity, we present MetaCOG: a hierarchical probabilistic…

One of the conspicuous features of real slices of bicritical rational maps is the existence of Tricorn-type hyperbolic components. Such a hyperbolic component is called invisible if the non-bifurcating sub-arcs on its boundary do not…

Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…

Mathematical modeling of visual textures traces back to Julesz's intuition that texture perception in humans is based on local correlations between image features. An influential approach for texture analysis and generation generalizes this…

Primary visual cortex (V1) is the first stage of cortical image processing, and a major effort in systems neuroscience is devoted to understanding how it encodes information about visual stimuli. Within V1, many neurons respond selectively…

We consider the evolution model proposed in [9, 6] to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and differences with the widely used Wilson-Cowan equations [48],…

We introduce the notion of the visual core of a hyperbolic 3-manifold N and explore its basic properties. The visual core can be thought of as a harmonic analysis analogue of the convex core. We investigate circumstances in which the visual…

The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate…

3D-aware visual pretraining has proven effective in improving the performance of downstream robotic manipulation tasks. However, existing methods are constrained to Euclidean embedding spaces, whose flat geometry limits their ability to…

For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…

A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…

Functional magnetic resonance imaging (fMRI) reveals complex brain functional networks with hierarchical topologies crucial for cognitive processing. Standard Euclidean Graph Neural Networks (GNNs) often struggle to represent these…

We show that a neural network, trained on the entanglement spectra of a nearest neighbor Heisenberg chain in a random transverse magnetic field, can be used to efficiently study the ergodic/many-body localized properties of a number of…

For long it has been known that specific patterns of folding are necessary for an optimally functioning brain. For instance, lissencephaly and polymicrogyria can lead to severe mental retardation, short life expectancy, epileptic seizures,…

Negatively curved, or hyperbolic, regions of space in an FRW universe are a realistic possibility. These regions might occur in voids where there is no dark matter with only dark energy present. Hyperbolic space is strange and various…