Related papers: Grid Cell Percolation
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
The spiking activity of principal cells in mammalian hippocampus encodes an internalized neuronal representation of the ambient space---a cognitive map. Once learned, such a map enables the animal to navigate a given environment for a long…
The entorhinal-hippocampal circuit plays a critical role in higher brain functions, especially spatial cognition. Grid cells in the medial entorhinal cortex (MEC) periodically fire with different grid spacing and orientation, which makes a…
Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…
The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…
An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable network activations within a limited critical range. In this range, the…
We develop of a line of work initiated by Curto and Itskov towards understanding the amount of information contained in the spike trains of hippocampal place cells via topology considerations. Previously, it was established that simply…
The brain is immensely complex, with diverse components and dynamic interactions building upon one another to orchestrate a wide range of functions and behaviors. Understanding patterns of these complex interactions and how they are…
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's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information is through head direction cells and grid cells. Brains use head direction cells…
We take the testing perspective to understand what the minimal discrimination time between two stimuli is for different types of rate coding neurons. Our main goal is to describe the testing abilities of two different encoding systems:…
The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step…
Many neural systems display cascading behavior characterized by uninterrupted sequences of neuronal firing. This gap precludes an understanding of how variations in network structure manifest in neural dynamics and either support or impinge…
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…
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…
Grid cells in the medial entorhinal cortex (MEC) and place cells in the hippocampus (HC) both form spatial representations. Grid cells fire in triangular grid patterns, while place cells fire at specific locations and respond to contextual…
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…
The macrocolumn is a key component of a neuromorphic computing system that interacts with an external environment under control of an agent. Environments are learned and stored in the macrocolumn as labeled directed graphs where edges…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
Comprehending how the brain interacts with the external world through generated neural data is crucial for determining its working mechanism, treating brain diseases, and understanding intelligence. Although many theoretical models have…