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We will mathematically express as a fiber bundle the hypercolumnar organization of this cortical area, first modelled by Georgopoulos (Georgopoulos et\u00a0al.,\u00a01982; Georgopoulos,\u00a02015). On this structure, we will consider the selective tuning of M1 neurons of kinematic variables of positions and directions of movement. We will then extend this model to encode the notion of fragments introduced by Hatsopoulos et\u00a0al. (2007) which describes the selectivity of neurons to movement direction varying in time. This leads to consider a higher dimensional geometrical structure where fragments are represented as integral curves. A comparison with the curves obtained through numerical simulations and experimental data will be presented. Moreover, neural activity shows coherent behaviours represented in terms of movement trajectories pointing to a specific pattern of movement decomposition Kadmon\u00a0Harpaz et\u00a0al. (2019). Here, we will recover this pattern through a spectral clustering algorithm in the subriemannian structure we introduced, and compare our results with the neurophysiological one of Kadmon\u00a0Harpaz et\u00a0al. (2019).<\/jats:p>","DOI":"10.1007\/s10827-023-00850-2","type":"journal-article","created":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T02:02:13Z","timestamp":1686103333000},"page":"299-327","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Functional architecture of M1 cells encoding movement direction"],"prefix":"10.1007","volume":"51","author":[{"given":"Caterina","family":"Mazzetti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Sarti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giovanna","family":"Citti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,7]]},"reference":[{"key":"850_CR1","doi-asserted-by":"crossref","unstructured":"Abend, W., Bizzi, E., & Morasso,\u00a0P. 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