Related papers: Topological decoding of grid cell activity via pat…
About a decade ago grid cells were discovered in the medial entorhinal cortex of rat. Their peculiar firing patterns, which correlate with periodic locations in the environment, led to early hypothesis that grid cells may provide some form…
The properties of complex networked systems arise from the interplay between the dynamics of their elements and the underlying topology. Thus, to understand their behaviour, it is crucial to convene as much information as possible about…
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis,…
Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion).…
Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that…
Grid cells in the medial entorhinal cortex (MEC) of the mammalian brain exhibit a strikingly regular hexagonal firing field over space. These cells are learned after birth and are thought to support spatial navigation but also more abstract…
The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cortex (mEC) show a triangular grid pattern, and once established might be based in part on path-integration mechanisms. Grid axes are tightly…
Persistent homology applied to the activity of grid cells in the Medial Entorhinal Cortex suggests that this activity lies on a toroidal manifold. By analyzing real data and a simple model, we show that neural oscillations play a key role…
This study explores novel activation functions that enhance the ability of neural networks to manipulate data topology during training. Building on the limitations of traditional activation functions like $\mathrm{ReLU}$, we propose…
This paper investigates the conformal isometry hypothesis as a potential explanation for the hexagonal periodic patterns in grid cell response maps. We posit that grid cell activities form a high-dimensional vector in neural space, encoding…
The entorhinal-hippocampal formation is the mammalian brain's navigation system, encoding both physical and abstract spaces via grid cells. This system is well-studied in neuroscience, and its efficiency and versatility make it attractive…
Geographic space is better understood through the topological relationship of the underlying streets (note: entire streets rather than street segments), which enables us to see scaling or fractal or living structure of far more…
Neurodegeneration affects cortical gray matter leading to loss of cortical mantle volume. As a result of such volume loss, the geometrical arrangement of the regions on the cortical surface is expected to be altered in comparison to healthy…
We present a generalised Hanson-Wright inequality and use it to establish new statistical insights into the geometry of data point-clouds. In the setting of a general random function model of data, we clarify the roles played by three…
Grid cells in medial entorhinal cortex are believed to play a key role in path integration. However, the relation between path integration and the grid-like arrangement of their firing field remains unclear. We provide theoretical evidence…
The brain achieves stability and plasticity in a topologically complex, shifting world through Metric-Topology Factorization (MTF), separating discrete topological indexing for context selection from continuous metric condensation for local…
Spatial functional organization is a hallmark of biological brains: neurons are arranged topographically according to their response properties, at multiple scales. In contrast, representations within most machine learning models lack…
The accurate and automatic extraction of roads from satellite imagery is critical for applications in navigation and urban planning, significantly reducing the need for manual annotation. Many existing methods decompose this task into…
The neuronal networks in the mammals cortex are characterized by the coexistence of hierarchy, modularity, short and long range interactions, spatial correlations, and topographical connections. Particularly interesting, the latter type of…
Grid cells in the brain respond when an animal occupies a periodic lattice of "grid fields" during spatial navigation. The grid scale varies along the dorso-ventral axis of the entorhinal cortex. We propose that the grid system minimizes…