How Entorhinal Grid Cells May Learn Multiple Spatial Scales from a Dorsoventral Gradient of Cell Response Rates in a Self-organizing Map
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{"title"=>"How Entorhinal Grid Cells May Learn Multiple Spatial Scales from a Dorsoventral Gradient of Cell Response Rates in a Self-organizing Map", "type"=>"journal", "authors"=>[{"first_name"=>"Stephen", "last_name"=>"Grossberg", "scopus_author_id"=>"7101773583"}, {"first_name"=>"Praveen K.", "last_name"=>"Pilly", "scopus_author_id"=>"24081408000"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "scopus"=>"2-s2.0-84868103019", "sgr"=>"84868103019", "pui"=>"365953613", "doi"=>"10.1371/journal.pcbi.1002648", "pmid"=>"23055909", "issn"=>"1553734X"}, "id"=>"b8a5aead-2a70-3c54-ba6c-889dfc1d3e88", "abstract"=>"Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic \"neural relativity\" that may clarify how episodic memories are learned.", "link"=>"http://www.mendeley.com/research/entorhinal-grid-cells-learn-multiple-spatial-scales-dorsoventral-gradient-cell-response-rates-selfor", "reader_count"=>80, "reader_count_by_academic_status"=>{"Unspecified"=>4, "Professor > Associate Professor"=>6, "Student > Doctoral Student"=>5, "Researcher"=>19, "Student > Ph. D. Student"=>20, "Student > Postgraduate"=>7, "Student > Master"=>10, "Other"=>1, "Student > Bachelor"=>6, "Professor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>4, "Professor > Associate Professor"=>6, "Student > Doctoral Student"=>5, "Researcher"=>19, "Student > Ph. D. Student"=>20, "Student > Postgraduate"=>7, "Student > Master"=>10, "Other"=>1, "Student > Bachelor"=>6, "Professor"=>2}, "reader_count_by_subject_area"=>{"Unspecified"=>5, "Engineering"=>2, "Environmental Science"=>1, "Agricultural and Biological Sciences"=>34, "Medicine and Dentistry"=>7, "Neuroscience"=>11, "Physics and Astronomy"=>4, "Psychology"=>5, "Social Sciences"=>1, "Computer Science"=>9, "Linguistics"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>7}, "Neuroscience"=>{"Neuroscience"=>11}, "Social Sciences"=>{"Social Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>4}, "Psychology"=>{"Psychology"=>5}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>34}, "Computer Science"=>{"Computer Science"=>9}, "Linguistics"=>{"Linguistics"=>1}, "Unspecified"=>{"Unspecified"=>5}, "Environmental Science"=>{"Environmental Science"=>1}}, "reader_count_by_country"=>{"Canada"=>2, "Netherlands"=>1, "United States"=>7, "United Kingdom"=>3, "France"=>3, "Germany"=>2}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/564559"], "description"=>"<p>Simulations of membrane potential (blue curves) and habituative transmitter (red curves) traces in response to constant current injections of different amplitudes for a ventral category cell and for a dorsal category cell , which are shown in the left and right columns, respectively. The three rows provide results for different current amplitudes: (A) and (B) for ; (C) and (D) for ; and (E) and (F) for . The inset in each panel zooms in on the noisy membrane potential fluctuation between 25 s and 27 s to highlight its relative frequency content.</p>", "links"=>[], "tags"=>["membrane", "oscillation"], "article_id"=>235053, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g016", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_membrane_potential_oscillation_traces_/235053", "title"=>"Model membrane potential oscillation traces.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:15:09"}
  • {"files"=>["https://ndownloader.figshare.com/files/563134"], "description"=>"<p>(A) Spatial response of a model stripe cell with a spacing of 20 cm in a 100 cm×100 cm environment. (B) Realistic rat trajectory in the same sized environment used in our simulations (data: <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Sargolini1\" target=\"_blank\">[4]</a>). (C) Small-scale (solid; spacing of 20 cm) and large-scale (dashed; spacing of 35 cm) stripe fields of four spatial phases (colors) along their preferred direction. Note the normalized stripe fields; that is, the area under each stripe field is a constant between the two scales. (D) Depiction of how the bump of activity in each directional ring attractor can be moved by linear movements of an animal with a component along the preferred direction.</p>", "links"=>[], "tags"=>["chemistry", "computer science", "mathematics"], "article_id"=>233630, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g001", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Linear_path_integration_inputs_/233630", "title"=>"Linear path integration inputs.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:07:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/564196"], "description"=>"<p>Case 4 simulations in which the category cells receive projections from input stripe cells of three spacings (20 cm, 35 cm, and 50 cm). Several measures of learned map cells with gridness score >0 in the last trial are shown as a function of response rate : (A) grid spacing, (B) grid field width, (C) gridness score, (D) inter-trial stability, (E) percent of grid cells, and (F) grid orientation. In (A) and (C), the red curves plot the corresponding measures of map cells with gridness score >0.3 in the last trial. The three dashed lines parallel to the x-axis in (A) signify the three potential grid scales. Dashed lines parallel to the x-axis in (C)–(E) signify experimentally measured values for adult dorsal grid cells <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Langston1\" target=\"_blank\">[37]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Wills1\" target=\"_blank\">[38]</a>. Error bars, present in all panels but (E) show SEM.</p>", "links"=>[], "tags"=>["chemistry", "computer science", "mathematics"], "article_id"=>234691, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g012", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Case_4_results_/234691", "title"=>"Case 4 results.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:13:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/564652"], "description"=>"<p>List of experimental evidence for various model components.</p>", "links"=>[], "tags"=>["chemistry", "computer science", "mathematics"], "article_id"=>235145, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.t002", "stats"=>{"downloads"=>7, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_List_of_experimental_evidence_for_various_model_components_/235145", "title"=>"List of experimental evidence for various model components.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-19 22:15:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/563542"], "description"=>"<p>(A, C) Data <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Brun1\" target=\"_blank\">[6]</a> and (B, D) Case 2 simulation results of the distribution of grid field width at different anatomical locations along the dorsoventral axis of MEC. Panels (A) and (B) provide error bar plots of grid field width (mean +/− SEM). In particular, panel (B) shows grid field width of learned map cells with gridness score >0 as a function of response rate in the last trial. In (D), the width of the central peak in the spatial autocorrelogram of the rate map of all model map cells is shown for each response rate. Note that map cells with gridness score >0 are identified by blue squares, and the rest by black squares.</p>", "links"=>[], "tags"=>["width"], "article_id"=>234042, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g005", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Grid_field_width_distributions_/234042", "title"=>"Grid field width distributions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:09:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/564295"], "description"=>"<p>(A, C) Grid spacing and (B, D) grid field width of learned map cells with gridness score >0 in the last trial as a function of response rate for different model and input variations: Case 5 (red curves in (A) and (B)); Case 6 (blue curves in (A) and (B)); Case 7 (green curves in (A) and (B)); Case 8 (blue curves in (C) and (D)); Case 9 (green curves in (C) and (D)); and Case 10 (red curves in (C) and (D)). See the <b>Simulation Settings</b> for detailed description of these various cases. The two dashed lines parallel to the x-axis in (A) and (C) signify the two potential grid scales. Error bars in each panel depict SEM.</p>", "links"=>[], "tags"=>["cases"], "article_id"=>234791, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g013", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Results_for_Cases_5_8211_10_/234791", "title"=>"Results for Cases 5–10.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:13:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/563219"], "description"=>"<p>The Spectral Spacing model responds to the navigational movements of an animal along a realistic trajectory and with stripe cells of multiple spatial scales initially projecting to the population of category learning cells at some location along the dorsoventral axis of MEC. Model simulations were conducted with 25 category cells in each of 10 MEC local populations that differed in the rate of intrinsic cellular dynamics, and with input stripe cells of nine directional preferences, four spatial phases, and up to three spatial scales.</p>", "links"=>[], "tags"=>["chemistry", "computer science", "mathematics"], "article_id"=>233717, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g002", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_depiction_/233717", "title"=>"Model depiction.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:07:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/564389"], "description"=>"<p>Simulations for Case 11 in which it is the habituation rate that is varied with distance along the dorsoventral axis of MEC. Several measures of learned map cells with gridness score >0 in the last trial are shown as a function of habituation rate : (A) grid spacing, (B) grid field width, (C) gridness score, (D) inter-trial stability, (E) percent of grid cells, and (F) peak rate. In (A) and (C), the red curves plot the corresponding measures for map cells with gridness score >0.3 in the last trial. The two dashed lines parallel to the x-axis in (A) signify the two potential grid scales. And the dashed lines parallel to the x-axis in (C)–(E) signify experimentally measured values for adult dorsal grid cells <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Langston1\" target=\"_blank\">[37]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Wills1\" target=\"_blank\">[38]</a>. Note the log10 scale of the x-axis in each panel. Error bars, present in all panels but (E), show SEM.</p>", "links"=>[], "tags"=>["11"], "article_id"=>234883, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g014", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Case_11_results_/234883", "title"=>"Case 11 results.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:14:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/563800"], "description"=>"<p>Simulation results for Case 2 regarding how various measures of learned map cells with gridness score >0 vary as a function of number of learning trials for two representative response rates (dorsal: (green); ventral: (blue)). Reported measures are (A) grid spacing, (B) grid field width, (C) gridness score, and (D) inter-trial stability. Error bars in each panel indicate SEM.</p>", "links"=>[], "tags"=>["grid"], "article_id"=>234302, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g008", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_grid_cell_learning_dynamics_/234302", "title"=>"Model grid cell learning dynamics.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:10:56"}
  • {"files"=>["https://ndownloader.figshare.com/files/563888"], "description"=>"<p>Simulations for Case 2 of the learned spatial fields and synaptic weights from stripe cells of two representative model grid cells, (A) one from a ventral location , and (B) the other from a dorsal location , in the last trial. The top row in each panel shows the corresponding spatial rate map and autocorrelogram, with color coding from blue (min.) to red (max.). Note the gridness score and peak firing rate on the top of the rate map, and the grid spacing on top of the autocorrelogram. And the two dashed circles centered on the central peak in the autocorrelogram signify the two potential grid scales. The bottom row in each panel provides the adapted weights from the stripe cells of the two scales (20 cm, 35 cm) to the corresponding cell. Note the solid curves trace the maximal weight from each directional group of stripe cells, the dashed lines parallel to the x-axis signify the average weight level of the projections from the corresponding scale, and the y-axes for the two spatial scales have different weight scales.</p>", "links"=>[], "tags"=>["weights", "inputs", "multi-scale", "stripe"], "article_id"=>234383, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g009", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pruned_weights_of_inputs_from_multi_scale_stripe_cells_/234383", "title"=>"Pruned weights of inputs from multi-scale stripe cells.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:11:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/563660"], "description"=>"<p>(A, C) Data <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Brun1\" target=\"_blank\">[6]</a> and (B, D) Case 2 simulations regarding the (A, B) peak rates and (C, D) mean rates of grid cells (from their smoothed spatial rate maps) at different anatomical locations along the dorsoventral axis of MEC. Error bars in each panel show SEM. Model results are derived from learned map cells with gridness score >0 in the last trial.</p>", "links"=>[], "tags"=>["firing"], "article_id"=>234160, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g006", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Grid_cell_peak_and_mean_firing_rates_/234160", "title"=>"Grid cell peak and mean firing rates.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:10:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/564678"], "description"=>"<p>Values of model parameters that do not differ across various simulation cases.</p>", "links"=>[], "tags"=>["parameters", "simulation"], "article_id"=>235173, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.t001", "stats"=>{"downloads"=>2, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Values_of_model_parameters_that_do_not_differ_across_various_simulation_cases_/235173", "title"=>"Values of model parameters that do not differ across various simulation cases.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-19 22:15:50"}
  • {"files"=>["https://ndownloader.figshare.com/files/563414"], "description"=>"<p>(A, C) Data <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Brun1\" target=\"_blank\">[6]</a> and (B, D) Case 2 simulation results regarding the distribution of grid spacing at different anatomical locations along the dorsoventral axis of MEC. Panels (A) and (B) provide error bar plots of grid spacing (mean +/− SEM). In (B), blue and red curves show grid spacing of learned map cells with gridness score >0 and those with gridness score >0.3, respectively, as a function of response rate in the last trial. The two dashed lines parallel to the x-axis in (B) signify the two potential grid scales. In (D), grid spacings derived for all model map cells are shown for each response rate. Note that map cells with gridness score >0.3 are identified by red squares, and those among the remaining with gridness score >0 by blue squares, and the rest by black squares.</p>", "links"=>[], "tags"=>["spacing"], "article_id"=>233916, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g004", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Grid_spacing_distributions_/233916", "title"=>"Grid spacing distributions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:08:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/564104"], "description"=>"<p>Case 3 simulations in which the model animal runs along a novel realistic trajectory in each trial. The <b>Simulation Settings</b> subsection in the <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#s2\" target=\"_blank\"><b>Methods</b></a> section describes how various novel trajectories are generated from one realistic rat trajectory. Several measures of learned map cells with gridness score >0 in the last trial are shown as a function of response rate : (A) grid spacing, (B) grid field width, (C) gridness score, (D) inter-trial stability, (E) percent of grid cells, (F) peak rate, and (G) grid orientation. Panel (H) shows the grid orientation distribution of map cells with gridness score >0 in the last trial for the dorsal most MEC population . In (A) and (C), the red curves plot the corresponding measures of map cells with gridness score >0.3 in the last trial. The two dashed lines parallel to the x-axis in (A) signify the two potential grid scales. Dashed lines parallel to the x-axis in (C)–(E) signify experimentally measured values for adult dorsal grid cells <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Langston1\" target=\"_blank\">[37]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Wills1\" target=\"_blank\">[38]</a>. Error bars, present in all panels but (E) and (H) show SEM.</p>", "links"=>[], "tags"=>["chemistry", "computer science", "mathematics"], "article_id"=>234597, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g011", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Case_3_results_/234597", "title"=>"Case 3 results.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:12:33"}
  • {"files"=>["https://ndownloader.figshare.com/files/563990"], "description"=>"<p>Case 2 simulations showing the learned spatial fields of two representative model cells, (A) one from a ventral location , and (B) the other from a dorsal location , across the learning trials. The top and bottom row in each panel show the corresponding spatial rate map and autocorrelogram, respectively. Color coding from blue (min.) to red (max.) is used for these. Note the trial number (e.g., T1 = trial 1) and gridness score on top of each rate map, and grid spacing on top of each associated autocorrelogram.</p>", "links"=>[], "tags"=>["chemistry", "computer science", "mathematics"], "article_id"=>234488, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g010", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spatial_learning_dynamics_of_two_example_model_cells_/234488", "title"=>"Spatial learning dynamics of two example model cells.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:11:55"}
  • {"files"=>["https://ndownloader.figshare.com/files/564479"], "description"=>"<p> (A) Data showing the frequency of subthreshold membrane potential oscillations (MPOs) in the dorsal (filled bars) and ventral (open bars) groups of rat MEC layer II stellate cells at three different mean membrane potentials <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Yoshida1\" target=\"_blank\">[14]</a>. See also Figure 1C in [13]. (B) Simulations of the frequency of MPOs of model category cells as a function of response rate , which is proposed to decrease along the dorsoventral axis of MEC, for current injections of different amplitudes (0.5 (blue); 1 (green); 1.5 (red); 2 (cyan); and 2.5 (magenta)). (C) Simulations of the frequency of MPOs of model category cells as a function of habituation rate for current injections of different amplitudes (0.5 (blue); 1 (green); 1.5 (red)). Error bars in (A–C) indicate SEM.</p>", "links"=>[], "tags"=>["oscillations", "medial", "entorhinal"], "article_id"=>234981, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g015", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Membrane_potential_oscillations_of_medial_entorhinal_cells_/234981", "title"=>"Membrane potential oscillations of medial entorhinal cells.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:14:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/563728"], "description"=>"<p>Simulations for Case 2 of how (A) gridness score, (B) inter-trial stability, (C) percent of grid cells, and (D) grid orientation of learned map cells with gridness score >0 in the last trial vary as a function of response rate . Panel (A) additionally plots gridness score of learned map cells with gridness score >0.3 in the last trial (red curve). Circular mean and standard deviation for grid orientation were calculated over the range [0°, 60°). Error bars in (A), (B), and (D) depict SEM. In (D), the inset provides a polar plot to depict mean grid orientation for various response rates, with the 360° range scaled for the 60° range of orientations. The dashed lines parallel to the x-axis in (A)–(C) signify corresponding experimentally measured values for adult dorsal grid cells <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Langston1\" target=\"_blank\">[37]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002648#pcbi.1002648-Wills1\" target=\"_blank\">[38]</a>.</p>", "links"=>[], "tags"=>["chemistry", "computer science", "mathematics"], "article_id"=>234223, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g007", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Case_2_results_/234223", "title"=>"Case 2 results.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:10:32"}
  • {"files"=>["https://ndownloader.figshare.com/files/563281"], "description"=>"<p>Results of Case 1 in which a single category cell responded to a stripe cell-like input shown in (A). (B) Cell responses defined by for different response rates (: 1 (cyan), 0.5 (red), 0.2 (green), and 0.1 (blue)) in the absence of self-excitatory feedback. Here, cell potential follows: . (C) Cell responses defined by in the presence of self-excitatory feedback that is not habituatively gated. In this case, cell potential follows: . (D) Dynamics of the habituative transmitter in the presence of self-excitatory feedback that is habituatively gated. (E) Cell responses defined by the habituatively gated product for the case in (D). (F) Cell responses defined by for the case in (D). For (D–F), cell potential and habituative transmitter follow and , respectively.</p>", "links"=>[], "tags"=>["chemistry", "computer science", "mathematics"], "article_id"=>233778, "categories"=>["Information And Computing Sciences", "Mathematics", "Chemistry"], "users"=>["Stephen Grossberg", "Praveen K. Pilly"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002648.g003", "stats"=>{"downloads"=>3, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Case_1_results_/233778", "title"=>"Case 1 results.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 22:08:07"}

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Relative Metric

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