Related papers: 3D Normal Coordinate Systems for Cortical Areas
While neural representations for static 3D shapes are widely studied, representations for deformable surfaces are limited to be template-dependent or lack efficiency. We introduce Canonical Deformation Coordinate Space (CaDeX), a unified…
Neural implicit surface representations have recently emerged as popular alternative to explicit 3D object encodings, such as polygonal meshes, tabulated points, or voxels. While significant work has improved the geometric fidelity of these…
This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also…
Cytoarchitectonic parcellations of the human brain serve as anatomical references in multimodal atlas frameworks. They are based on analysis of cell-body stained histological sections and the identification of borders between brain areas.…
Living systems implement and execute an extraordinary plethora of computational tasks. The inherent degree of large scale coordination emerges as a global property, from the intricate sea of microscopic interactions. The brain, with its…
Advances in optical astrometry allow us to infer the non-radial kinematic structure of the Universe directly from observations. Here I use a supervised machine learning neural network method to predict 1.57 million redshifts based on…
We investigate cortical learning from the perspective of mechanism design. First, we show that discretizing standard models of neurons and synaptic plasticity leads to rational agents maximizing simple scoring rules. Second, our main result…
The cerebrum of mammals spans a vast range of sizes and yet has a very regular structure. The amount of folding of the cortical surface and the proportion of white matter gradually increase with size, but the underlying mechanisms remain…
In this paper we will focus on the potential and on the challenges associated with the development of an integrated brain and spinal cord modelling framework for processing MR neuroimaging data. The aim of the work is to explore how a…
The purpose of this paper is to develop an alternative theory of deuteron stripping to resonance states based on the surface integral formalism of Kadyrov et al. [Ann. Phys. 324, 1516 (2009)] and continuum-discretized coupled channels…
Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based…
Let $\Gamma_g$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We introduce a combinatorial structure of "core surfaces", that represent subgroups of $\Gamma_g$. These structures are (usually)…
The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the~field of applied geometry. An~isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some…
High-dimensional neural activity often reside in a low-dimensional subspace, referred to as neural manifolds. Grid cells in the medial entorhinal cortex provide a periodic spatial code that are organized near a toroidal manifold,…
Criticality in the cortex emerges from the seemingly random interaction of microscopic components and produces higher cognitive functions at mesoscopic and macroscopic scales. Random graphs and percolation theory provide natural means to…
It is a fundamental behavior that different individuals see the world in a largely similar manner. This is an essential basis for humans' ability to cooperate and communicate. However, what are the neuronal properties that underlie these…
A formula for an average connectivity between cortical areas in mammals is derived. Based on comparative neuroanatomical data, it is found, surprisingly, that this connectivity is either only weakly dependent or independent of brain size.…
Building on evidence of structural parallels between brain networks and the cosmic web [1], we apply AI-based geometric analysis to cultured neuronal networks. Isolated neurons self-organize into dendritic lattices shaped by reproducible…
Grid cells, discovered more than a decade ago [5], are neurons in the brain of mammals that fire when the animal is located near certain specific points in its familiar terrain. Intriguingly, these points form, for a single cell, a…
Recent research on learnable neural representations has been widely adopted in the field of 3D scene reconstruction and neural rendering applications. However, traditional feature grid representations often suffer from substantial memory…