{"id":1016,"date":"2018-01-17T12:29:55","date_gmt":"2018-01-17T02:29:55","guid":{"rendered":"https:\/\/www.cognav.net\/?p=1016"},"modified":"2018-01-17T15:10:08","modified_gmt":"2018-01-17T05:10:08","slug":"how-to-determine-the-instantaneous-head-direction-by-a-population-vector-scheme","status":"publish","type":"post","link":"https:\/\/braininspirednavigation.com\/?p=1016","title":{"rendered":"How to determine the instantaneous head direction by a population vector scheme?"},"content":{"rendered":"<p>The excerpt note is from the Song et al., 2005 paper. The example code is implemented by Fangwen. The whole example code is <a href=\"https:\/\/www.braininspirednavigation.com\/?p=1010\">here<\/a>.<\/p>\n<p style=\"text-align: justify;\">Pengcheng Song, and Xiao-Jing Wang. &#8220;<strong>Angular path integration by moving &#8220;hill of activity&#8221;: a spiking neuron model without recurrent excitation of the head-direction system<\/strong>.&#8221; Journal of Neuroscience 25, no. 4 (2005): 1002-1014.<\/p>\n<p style=\"text-align: justify;\">In the model, the peak location of the bell-shaped activity profile of the excitatory population provides a natural choice of the internal representation of the animal&#8217;s instantaneous head direction. It was determined by a population vector scheme (Georgopoulos et al., 1986), as follows:<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011718_0229_Howtodeterm1.png\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">Where <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011718_0229_Howtodeterm2.png\" alt=\"\" \/> is the firing rate of neuron <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011718_0229_Howtodeterm3.png\" alt=\"\" \/> , of which the preferred direction is <img decoding=\"async\" src=\"https:\/\/www.braininspirednavigation.com\/wp-content\/uploads\/2018\/01\/011718_0229_Howtodeterm4.png\" alt=\"\" \/> . When a &#8220;hill of activity&#8221; moves at a constant propagation speed, the latter was used as a natural internal representation of the animal&#8217;s angular head velocity (AHV).<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #222222; font-family: Arial; font-size: 12pt;\"><span style=\"background-color: white;\">Georgopoulos, Apostolos P., Andrew B. Schwartz, and Ronald E. Kettner. &#8220;<\/span><span style=\"color: #4a88c2;\"><strong>Neuronal population coding of movement direction<\/strong><span style=\"color: #222222;\"><span style=\"background-color: white;\">.&#8221;\u00a0<\/span><em>Science<\/em><span style=\"background-color: white;\">\u00a0(1986): 1416-1419.<\/span><\/span><\/span><\/span><\/p>\n<pre lang=\u201dLANGUAGE\u201d line=\u201d1\u2033>\r\n[value, z] = max(HDCELLS);\r\nz_HDCELLS=zeros(1,HD_DIMENSION_THETA);\r\nz_HDCELLS(HD_AVG_TH_WRAP(z:z+HD_CELLS_TO_AVG*2)) = HDCELLS(HD_AVG_TH_WRAP(z:z+HD_CELLS_TO_AVG*2));\r\nout_theta = mod(atan2(sum(HD_TH_SUM_SIN_LOOKUP*(z_HDCELLS')), sum(HD_TH_SUM_COS_LOOKUP * (z_HDCELLS')))\/HD_CELL_SIZE_THETA, HD_DIMENSION_THETA);\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>The excerpt note is from the Song et al., 2005 paper. The example code is implemented by Fangwen. The whole example code is here. Pengcheng Song, and Xiao-Jing Wang. &#8220;Angular path integration by moving &#8220;hill of activity&#8221;: a spiking neuron model without recurrent excitation of the head-direction system.&#8221; Journal of Neuroscience 25, no. 4 (2005): [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[114,96,257],"tags":[274,273,272,239,275,242],"_links":{"self":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/1016"}],"collection":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1016"}],"version-history":[{"count":13,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/1016\/revisions"}],"predecessor-version":[{"id":1042,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=\/wp\/v2\/posts\/1016\/revisions\/1042"}],"wp:attachment":[{"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1016"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1016"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/braininspirednavigation.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}