Related papers: Spaces and sequences in the hippocampus: a homolog…
In present paper we discuss several approaches to reconstructing the topology of the physical space from neural activity data of CA1 fields in mice hippocampus, in particular, having Cognitome theory of brain function in mind. In our…
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…
Random walks can reveal communities or clusters in networks, because they are more likely to stay within a cluster than leave it. Thus, one family of community detection algorithms uses random walks to measure distance between pairs of…
The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…
The ubiquity of topographic maps in the brain has long been known, and molecular mechanisms for the formation of topographic organization of neural systems have been revealed. Less attention has been given to the question of why are the…
Models of neural networks have proven their utility in the development of learning algorithms in computer science and in the theoretical study of brain dynamics in computational neuroscience. We propose in this paper a spatial neural…
Place cells in the rat hippocampus play a key role in creating the animal's internal representation of the world. During active navigation, these cells spike only in discrete locations, together encoding a map of the environment.…
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…
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…
The hippocampus and the striatum support episodic and procedural memory, respectively, and "place" and "response" learning within spatial navigation. Recently this dichotomy has been linked to "model-based" and "model-free" reinforcement…
Cognitive maps are a proposed concept on how the brain efficiently organizes memories and retrieves context out of them. The entorhinal-hippocampal complex is heavily involved in episodic and relational memory processing, as well as spatial…
We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one…
To understand collective network behavior in the complex human brain, pairwise correlation networks alone are insufficient for capturing the high-order interactions that extend beyond pairwise interactions and play a crucial role in brain…
Complex networks encountered in biology are often characterized by significant structural diversity. Whether it be differences in the three-dimensional structure of allosteric proteins, or the variation among the micro-scale structures of…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…
Our goal in this paper is to leverage the potential of the topological signal processing (TSP) framework for analyzing brain networks. Representing brain data as signals over simplicial complexes allows us to capture higher-order…
In this paper we explain the strikingly regular activity of the 'grid' cells in rodent dorsal medial entorhinal cortex (dMEC) and the spatially localized activity of the hippocampal place cells in CA3 and CA1 by assuming that the…
The neural networks of the human brain act as very efficient parallel processing computers co-ordinating memory related responses to a multitude of input signals from sensory organs. Information storage, update and appropriate retrieval are…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…