{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T13:57:53Z","timestamp":1761919073771},"reference-count":37,"publisher":"MIT Press - Journals","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2008,2]]},"abstract":"<jats:p> Neurons that sustain elevated firing in the absence of stimuli have been found in many neural systems. In graded persistent activity, neurons can sustain firing at many levels, suggesting a widely found type of network dynamics in which networks can relax to any one of a continuum of stationary states. The reproduction of these findings in model networks of nonlinear neurons has turned out to be nontrivial. A particularly insightful model has been the \u201cbump attractor,\u201d in which a continuous attractor emerges through an underlying symmetry in the network connectivity matrix. This model, however, cannot account for data in which the persistent firing of neurons is a monotonic\u2014rather than a bell-shaped\u2014function of a stored variable. Here, we show that the symmetry used in the bump attractor network can be employed to create a whole family of continuous attractor networks, including those with monotonic tuning. Our design is based on tuning the external inputs to networks that have a connectivity matrix with Toeplitz symmetry. In particular, we provide a complete analytical solution of a line attractor network with monotonic tuning and show that for many other networks, the numerical tuning of synaptic weights reduces to the computation of a single parameter. <\/jats:p>","DOI":"10.1162\/neco.2007.07-06-297","type":"journal-article","created":{"date-parts":[[2007,11,29]],"date-time":"2007-11-29T17:51:42Z","timestamp":1196358702000},"page":"452-485","source":"Crossref","is-referenced-by-count":33,"title":["Design of Continuous Attractor Networks with Monotonic Tuning Using a Symmetry Principle"],"prefix":"10.1162","volume":"20","author":[{"given":"Christian K.","family":"Machens","sequence":"first","affiliation":[{"name":"Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A."}]},{"given":"Carlos D.","family":"Brody","sequence":"additional","affiliation":[{"name":"Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A."}]}],"member":"281","reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.23-34-10852.2003"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1038\/84023"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00337259"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.92.9.3844"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1093\/cercor\/bhg100"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00320393"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1093\/cercor\/10.9.910"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.88.21.9653"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.23-12-05342.2003"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1162\/0899766053630332"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1994.6.4.679"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuron.2006.01.036"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1038\/nn893"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1038\/nn1109"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1126\/science.1104171"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1016\/j.conb.2004.10.017"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1093\/cercor\/bhg101"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1007\/BF00270672"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1152\/jn.1999.82.5.2503"},{"key":"p_23","doi-asserted-by":"publisher","DOI":"10.1016\/0301-0082(79)90005-4"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139900346465"},{"key":"p_26","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.10-06-02008.1990"},{"key":"p_27","doi-asserted-by":"publisher","DOI":"10.1046\/j.1460-9568.2002.01958.x"},{"key":"p_29","doi-asserted-by":"publisher","DOI":"10.1038\/20939"},{"key":"p_30","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.17-15-05900.1997"},{"key":"p_31","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.93.23.13339"},{"key":"p_32","doi-asserted-by":"publisher","DOI":"10.1016\/S0896-6273(00)81155-1"},{"key":"p_33","doi-asserted-by":"publisher","DOI":"10.1162\/08997660360675053"},{"key":"p_34","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.4864-05.2006"},{"key":"p_36","doi-asserted-by":"publisher","DOI":"10.1007\/BF00230390"},{"key":"p_37","doi-asserted-by":"publisher","DOI":"10.1093\/cercor\/bhg102"},{"key":"p_38","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-1063(1999)9:4<481::AID-HIPO14>3.0.CO;2-S"},{"key":"p_39","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.19-21-09587.1999"},{"key":"p_40","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-2236(00)01868-3"},{"key":"p_41","doi-asserted-by":"publisher","DOI":"10.1007\/BF00288786"},{"key":"p_42","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.16-06-02112.1996"},{"key":"p_43","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.13-08-03406.1993"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/neco.2007.07-06-297","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:35:22Z","timestamp":1615584922000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/20\/2\/452-485\/7275"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["10.1162\/neco.2007.07-06-297"],"URL":"https:\/\/doi.org\/10.1162\/neco.2007.07-06-297","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,2]]}}}