Euclidean space is the fabric of the world we live in. Whether and how geometric experience shapes our spatial-temporal representations of the world remained unknown. We deprived male rats of experience with crucial features of Euclidean geometry by rearing them inside spheres, and compared activity of large hippocampal neuronal ensembles during navigation and sleep with that of cuboid cage-reared controls. Sphere-rearing from birth permitted emergence of accurate neuronal ensemble spatial codes and preconfigured and plastic time-compressed neuronal sequences. However, sphere-rearing led to diminished individual place cell tuning, more similar neuronal mapping of different track ends/corners, and impaired pattern separation and plasticity of multiple linear tracks, coupled with reduced preconfigured sleep network repertoires. Subsequent experience with multiple linear environments over four days largely reversed these effects. Thus, early-life experience with Euclidean geometry enriches the hippocampal repertoire of preconfigured neuronal patterns selected toward unique representation and discrimination of multiple linear environments.
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http://dx.doi.org/10.1038/s41467-024-52758-9 | DOI Listing |
PLoS One
December 2024
Department of Mathematics & Statistics, Jordan University of Science and Technology, Irbid, Jordan.
This study presents a novel approach to metric spaces through the lens of geometric calculus, redefining traditional structures with new operations and properties derived from non-Newtonian measures. Specifically, we develop and prove geometric versions of the Hölder and Minkowski inequalities, which provide foundational support for applying these spaces in analysis. Additionally, we establish key relationships between geometric and classical metric spaces, examining concepts such as openness, closedness, and separability within this geometric framework.
View Article and Find Full Text PDFBioinformatics
December 2024
Independent Scientist, Reading, MA 01867, United States.
Motivation: Beta turns are the most common type of secondary structure in proteins after alpha helices and beta sheets and play many key structural and functional roles. Turn backbone (BB) geometry has been classified at multiple levels of precision, but the current picture of side chain (SC) structure and interaction in turns is incomplete, because the distribution of SC conformations associated with each sequence motif has commonly been represented only by a static image of a single, typical structure for each turn BB geometry, and only motifs which specify a single amino acid (e.g.
View Article and Find Full Text PDFJ Acoust Soc Am
December 2024
Key Laboratory for Polar Acoustics and Application of Ministry of Education (Harbin Engineering University), Ministry of Education, Harbin, 150001, China.
Matched-field processing (MFP) achieves underwater source localization by measuring the correlation between the array and replica signals, with traditional MFP being equivalent to estimating the Euclidean distance between the data cross-spectral density matrix (CSDM) and replica matrices. However, in practical applications, random inhomogeneities in the marine environment and inaccurate estimation of CSDM reduce MFP performance. The traditional minimum variance matched-field processor with environmental perturbation constraints perturbs a priori environment parameters to obtain linear constraints and yields the optimal weight vectors as the replica vectors.
View Article and Find Full Text PDFOpen Mind (Camb)
November 2024
Laboratory for Developmental Studies, Department of Psychology, Harvard University, Cambridge, MA, USA.
iScience
December 2024
Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, La Jolla, CA, USA.
Recent studies have demonstrated the significance of hyperbolic geometry in uncovering low-dimensional structure within complex hierarchical systems. We developed a Bayesian formulation of multi-dimensional scaling (MDS) for embedding data in hyperbolic spaces that allows for a principled determination of manifold parameters such as curvature and dimension. We show that only a small amount of data are needed to constrain the manifold, the optimization is robust against false minima, and the model is able to correctly discern between Hyperbolic and Euclidean data.
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