Analysis of the Stabilized Supralinear Network
We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to...
Saved in:
| Published in | Neural computation Vol. 25; no. 8; pp. 1994 - 2037 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
One Rogers Street, Cambridge, MA 02142-1209, USA
MIT Press
01.08.2013
MIT Press Journals, The |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the balanced network, which yields only linear behavior. We more exhaustively analyze the two-dimensional case of one excitatory and one inhibitory population. We show that in this case, dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for supersaturation, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing. |
|---|---|
| AbstractList | We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the balanced network, which yields only linear behavior. We more exhaustively analyze the two-dimensional case of one excitatory and one inhibitory population. We show that in this case, dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for supersaturation, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing. We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the balanced network, which yields only linear behavior. We more exhaustively analyze the two-dimensional case of one excitatory and one inhibitory population. We show that in this case, dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for supersaturation, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing. [PUBLICATION ABSTRACT] We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the “balanced network”, which yields only linear behavior. We more exhaustively analyze the 2-dimensional case of 1 excitatory and 1 inhibitory population. We show that in this case dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for “supersaturation”, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing. We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the balanced network, which yields only linear behavior. We more exhaustively analyze the two-dimensional case of one excitatory and one inhibitory population. We show that in this case, dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for supersaturation, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing.We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the balanced network, which yields only linear behavior. We more exhaustively analyze the two-dimensional case of one excitatory and one inhibitory population. We show that in this case, dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for supersaturation, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing. |
| Author | Miller, Kenneth D. Ahmadian, Yashar Rubin, Daniel B. |
| AuthorAffiliation | 4 Kavli Institute for Brain Science, College of Physicians and Surgeons, Columbia University, NY, NY 10032 3 Doctoral Program in Neurobiology and Behavior, College of Physicians and Surgeons, Columbia University, NY, NY 10032 2 Dept. of Neuroscience, College of Physicians and Surgeons, Columbia University, NY, NY 10032 1 Center for Theoretical Neuroscience, College of Physicians and Surgeons, Columbia University, NY, NY 10032 |
| AuthorAffiliation_xml | – name: 3 Doctoral Program in Neurobiology and Behavior, College of Physicians and Surgeons, Columbia University, NY, NY 10032 – name: 2 Dept. of Neuroscience, College of Physicians and Surgeons, Columbia University, NY, NY 10032 – name: 4 Kavli Institute for Brain Science, College of Physicians and Surgeons, Columbia University, NY, NY 10032 – name: 1 Center for Theoretical Neuroscience, College of Physicians and Surgeons, Columbia University, NY, NY 10032 |
| Author_xml | – sequence: 1 givenname: Yashar surname: Ahmadian fullname: Ahmadian, Yashar – sequence: 2 givenname: Daniel B. surname: Rubin fullname: Rubin, Daniel B. – sequence: 3 givenname: Kenneth D. surname: Miller fullname: Miller, Kenneth D. |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/23663149$$D View this record in MEDLINE/PubMed |
| BookMark | eNqFkc1PGzEQxa0KVAL01jNaiQsHlo6_vRekKOKjUgQHitSb5Xi9xXSzTu3dVvDX4yhpFBBVT3OY3zy992Yf7XShcwh9xnCGsSBfbi4mt9poACbJBzTCnEKplPq-g0agqqqUQsg9tJ_SIwAIDPwj2iNUCIpZNUJn4860T8mnIjRF_-CKu97MfOufXV3cDYtoWt85E4sb1_8J8ech2m1Mm9yn9TxA95cX3ybX5fT26utkPC0tB9GXigFzpqYzzITjXBljoJJcVbKpCLO0FlaAnTnghJvGUlU1QmZzuJaGCCnoATpf6S6G2dzV1nV9tqIX0c9NfNLBeP160_kH_SP81gxIzqiywMlaIIZfg0u9nvtkXduazoUh6RyeUb6s4f8olYCJAEIyevwGfQxDzA2uKMIopThTR9vmN67_tp6B0xVgY0gpumaDYNDLp-rtp2acvMGt703vwzK6b_91tE4199su30NfAFYcr7E |
| CODEN | NEUCEB |
| CitedBy_id | crossref_primary_10_1016_j_neuron_2018_01_045 crossref_primary_10_1016_j_neuron_2018_08_032 crossref_primary_10_1113_JP281510 crossref_primary_10_1038_s41467_021_23838_x crossref_primary_10_1016_j_neuron_2023_09_018 crossref_primary_10_1016_j_neuron_2018_04_017 crossref_primary_10_12688_f1000research_7698_1 crossref_primary_10_1162_neco_a_01658 crossref_primary_10_1016_j_neuron_2023_09_010 crossref_primary_10_1038_s41467_024_46484_5 crossref_primary_10_1016_j_conb_2016_01_008 crossref_primary_10_1073_pnas_2216092119 crossref_primary_10_1016_j_neuron_2021_10_017 crossref_primary_10_1073_pnas_2318837121 crossref_primary_10_7554_eLife_18805 crossref_primary_10_1038_s41467_024_51390_x crossref_primary_10_1038_s41467_020_20590_6 crossref_primary_10_1162_NECO_a_00675 crossref_primary_10_1371_journal_pcbi_1012190 crossref_primary_10_1016_j_neuron_2014_04_045 crossref_primary_10_1103_PhysRevE_91_042808 crossref_primary_10_1016_j_neuron_2018_12_002 crossref_primary_10_1016_j_conb_2022_102589 crossref_primary_10_1016_j_neuron_2020_11_013 crossref_primary_10_1038_s41467_019_10327_5 crossref_primary_10_1073_pnas_1700080115 crossref_primary_10_1152_jn_00278_2024 crossref_primary_10_1016_j_neuron_2021_07_031 crossref_primary_10_1038_nn_4128 crossref_primary_10_1523_JNEUROSCI_2386_17_2017 crossref_primary_10_1038_s41593_020_0671_1 crossref_primary_10_1146_annurev_neuro_102320_085825 crossref_primary_10_1371_journal_pcbi_1005583 crossref_primary_10_1038_s41598_022_25708_y crossref_primary_10_1103_PhysRevResearch_5_033023 crossref_primary_10_1016_j_cub_2022_10_063 crossref_primary_10_1103_PhysRevX_14_011021 crossref_primary_10_1109_TAC_2020_3004801 crossref_primary_10_1016_j_neuron_2024_12_019 crossref_primary_10_1038_s41583_020_00390_z crossref_primary_10_1152_jn_00637_2013 crossref_primary_10_1152_jn_00900_2017 crossref_primary_10_7554_eLife_52757 crossref_primary_10_1016_j_neuron_2022_10_001 crossref_primary_10_1073_pnas_2207032119 crossref_primary_10_7554_eLife_71263 crossref_primary_10_1146_annurev_neuro_072116_031005 crossref_primary_10_1371_journal_pcbi_1008958 crossref_primary_10_1371_journal_pcbi_1011097 crossref_primary_10_1371_journal_pcbi_1008916 crossref_primary_10_7554_eLife_55130 crossref_primary_10_1371_journal_pcbi_1006816 crossref_primary_10_1016_j_neuron_2023_11_005 crossref_primary_10_1523_JNEUROSCI_0963_17_2017 crossref_primary_10_1371_journal_pcbi_1008836 crossref_primary_10_1016_j_celrep_2019_03_102 crossref_primary_10_1016_j_neuroscience_2017_07_054 crossref_primary_10_1371_journal_pcbi_1005498 crossref_primary_10_1371_journal_pcbi_1008165 crossref_primary_10_1016_j_isci_2022_104984 crossref_primary_10_1162_jocn_a_00574 crossref_primary_10_1371_journal_pcbi_1005576 crossref_primary_10_1016_j_neuron_2014_12_026 crossref_primary_10_1073_pnas_2311040121 crossref_primary_10_1073_pnas_2305326121 crossref_primary_10_1016_j_neunet_2017_03_003 crossref_primary_10_1016_j_conb_2019_06_007 crossref_primary_10_1007_s10827_024_00877_z crossref_primary_10_1103_PhysRevResearch_6_043179 crossref_primary_10_1113_JP282755 crossref_primary_10_7554_eLife_54875 crossref_primary_10_1126_sciadv_abl5865 crossref_primary_10_1162_netn_a_00219 crossref_primary_10_1103_PhysRevResearch_4_013162 crossref_primary_10_1371_journal_pbio_3001666 crossref_primary_10_1371_journal_pcbi_1010590 crossref_primary_10_1523_ENEURO_0356_17_2018 crossref_primary_10_1016_j_conb_2014_01_017 crossref_primary_10_1016_j_conb_2020_08_001 crossref_primary_10_1038_s41583_024_00795_0 crossref_primary_10_1103_PhysRevX_12_011044 crossref_primary_10_1371_journal_pcbi_1006893 crossref_primary_10_1016_j_neuron_2022_01_023 crossref_primary_10_1038_s41598_018_27099_5 crossref_primary_10_1371_journal_pcbi_1008192 |
| Cites_doi | 10.1016/j.conb.2011.06.003 10.1007/BF00582601 10.1016/j.conb.2011.02.003 10.1152/jn.00692.2001 10.1016/j.neuron.2007.02.029 10.1017/S0952523805221120 10.1152/jn.00425.2001 10.1523/JNEUROSCI.22-12-05118.2002 10.1007/PL00005751 10.1162/089976698300017214 10.1016/j.neuron.2009.12.005 10.1126/science.1179850 10.1016/j.neuron.2011.09.027 10.1152/jn.1987.57.3.773 10.1038/35372 10.1152/jn.00425.2006 10.1152/jn.1985.54.3.651 10.1152/jn.00165.2011 10.1146/annurev.neuro.23.1.441 10.1152/jn.00255.2002 10.1152/jn.2000.84.2.909 10.1167/7.6.13 10.1371/journal.pcbi.1001078 10.1016/j.neuron.2004.12.024 10.1126/science.274.5293.1724 10.1038/nn1391 10.1007/978-0-387-87708-2 10.1113/jphysiol.2001.012776 10.1038/11197 10.1017/CBO9780511815706 10.1016/j.neuron.2009.03.028 10.1016/0042-6989(85)90183-X 10.1038/nature09086 10.1038/nn1660 10.1093/cercor/bhm057 10.1523/JNEUROSCI.06-05-01284.1986 10.1523/JNEUROSCI.17-11-04382.1997 10.1038/nn.2815 10.1038/nn1310 10.1152/jn.00512.2009 10.1126/science.290.5498.1968 10.1523/JNEUROSCI.21-06-02104.2001 10.1152/jn.2001.86.4.1803 10.1038/nrc3398 |
| ContentType | Journal Article |
| Copyright | Copyright MIT Press Journals Aug 2013 |
| Copyright_xml | – notice: Copyright MIT Press Journals Aug 2013 |
| DBID | AAYXX CITATION CGR CUY CVF ECM EIF NPM 7SC 8FD JQ2 L7M L~C L~D 7X8 5PM |
| DOI | 10.1162/NECO_a_00472 |
| DatabaseName | CrossRef Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional MEDLINE - Academic PubMed Central (Full Participant titles) |
| DatabaseTitle | CrossRef MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional MEDLINE - Academic |
| DatabaseTitleList | MEDLINE Computer and Information Systems Abstracts CrossRef Computer and Information Systems Abstracts MEDLINE - Academic |
| Database_xml | – sequence: 1 dbid: NPM name: PubMed url: https://proxy.k.utb.cz/login?url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: EIF name: MEDLINE url: https://proxy.k.utb.cz/login?url=https://www.webofscience.com/wos/medline/basic-search sourceTypes: Index Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1530-888X |
| EndPage | 2037 |
| ExternalDocumentID | PMC4026108 3001586231 23663149 10_1162_NECO_a_00472 neco_a_00472.pdf |
| Genre | Research Support, Non-U.S. Gov't Journal Article Research Support, N.I.H., Extramural |
| GrantInformation_xml | – fundername: NEI NIH HHS grantid: R01 EY11001 – fundername: NEI NIH HHS grantid: R01 EY011001 – fundername: NIGMS NIH HHS grantid: T32 GM007367 – fundername: NIGMS NIH HHS grantid: T32-GM007367 |
| GroupedDBID | --- -~X .4S .DC 0R~ 123 36B 4.4 6IK AAJGR AALMD AAPBV ABDBF ABDNZ ABIVO ABPTK ACGFO ADIYS AEGXH AENEX AFHIN AIAGR ALMA_UNASSIGNED_HOLDINGS ARCSS AVWKF AZFZN BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EAP EAS EBC EBD EBS ECS EDO EJD EMB EMK EMOBN EPL EPS EST ESX F5P FEDTE FNEHJ HZ~ I-F IPLJI JAVBF MCG MINIK MKJ O9- OCL P2P PK0 PQQKQ RMI SV3 TUS WG8 WH7 XJE ZWS 41~ 53G AAFWJ AAYOK AAYXX ABAZT ABEFU ABJNI ABVLG ACUHS ACYGS ADMLS AEILP AMVHM CAG CITATION COF HVGLF H~9 CGR CUY CVF ECM EIF NPM 7SC 8FD JQ2 L7M L~C L~D 7X8 5PM |
| ID | FETCH-LOGICAL-c506t-8404ead3b146e558aaa0975897f924c3d6c60cbe0525afc389f670611d7a26763 |
| ISSN | 0899-7667 1530-888X |
| IngestDate | Thu Aug 21 14:32:28 EDT 2025 Fri Jul 11 02:13:01 EDT 2025 Thu Jul 10 18:34:21 EDT 2025 Mon Jun 30 06:39:41 EDT 2025 Mon Jul 21 05:44:59 EDT 2025 Tue Jul 01 01:19:52 EDT 2025 Thu Apr 24 22:52:38 EDT 2025 Fri Oct 27 04:04:33 EDT 2023 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 8 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c506t-8404ead3b146e558aaa0975897f924c3d6c60cbe0525afc389f670611d7a26763 |
| Notes | August, 2013 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 ObjectType-Article-2 ObjectType-Feature-1 These authors contributed equally to this work. |
| PMID | 23663149 |
| PQID | 1370243331 |
| PQPubID | 37252 |
| PageCount | 44 |
| ParticipantIDs | proquest_miscellaneous_1494353663 crossref_citationtrail_10_1162_NECO_a_00472 crossref_primary_10_1162_NECO_a_00472 proquest_journals_1370243331 pubmedcentral_primary_oai_pubmedcentral_nih_gov_4026108 proquest_miscellaneous_1370126022 mit_journals_10_1162_NECO_a_00472 pubmed_primary_23663149 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2013-08-01 |
| PublicationDateYYYYMMDD | 2013-08-01 |
| PublicationDate_xml | – month: 08 year: 2013 text: 2013-08-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | One Rogers Street, Cambridge, MA 02142-1209, USA |
| PublicationPlace_xml | – name: One Rogers Street, Cambridge, MA 02142-1209, USA – name: United States – name: Cambridge |
| PublicationTitle | Neural computation |
| PublicationTitleAlternate | Neural Comput |
| PublicationYear | 2013 |
| Publisher | MIT Press MIT Press Journals, The |
| Publisher_xml | – name: MIT Press – name: MIT Press Journals, The |
| References | B20 B42 B21 B43 B22 B44 B23 B45 B24 B46 B47 B48 B27 B49 B28 B29 Rubin D. B. (B38) 2010 B30 B31 B10 B32 B11 B33 B12 B34 B13 B35 B14 B36 B15 B37 B16 B17 B18 Miller K. D. (B26) 2011 B19 B1 B2 B3 B4 B5 B6 B8 B9 Dayan P. (B7) 2001 B40 B41 4024474 - Vision Res. 1985;25(6):755-66 9348122 - Exp Brain Res. 1997 Sep;116(2):216-28 9468134 - Nature. 1998 Feb 5;391(6667):580-4 17685796 - J Vis. 2007;7(6):13 11110664 - Science. 2000 Dec 8;290(5498):1968-72 12424292 - J Neurophysiol. 2002 Nov;88(5):2530-46 19477158 - Neuron. 2009 May 28;62(4):578-92 11826034 - J Neurophysiol. 2002 Feb;87(2):653-9 15629708 - Neuron. 2005 Jan 6;45(1):133-45 4045542 - J Neurophysiol. 1985 Sep;54(3):651-67 20596024 - Nature. 2010 Jul 1;466(7302):123-7 16855109 - J Neurophysiol. 2006 Oct;96(4):1755-64 17494058 - Cereb Cortex. 2008 Feb;18(2):331-6 21353526 - Curr Opin Neurobiol. 2011 Apr;21(2):269-74 3559701 - J Neurophysiol. 1987 Mar;57(3):773-86 11600641 - J Neurophysiol. 2001 Oct;86(4):1803-15 3711980 - J Neurosci. 1986 May;6(5):1284-301 15665876 - Nat Neurosci. 2005 Feb;8(2):194-201 16520737 - Nat Neurosci. 2006 Apr;9(4):552-61 21390280 - PLoS Comput Biol. 2011 Feb;7(2):e1001078 22017986 - Neuron. 2011 Oct 20;72(2):231-43 10938316 - J Neurophysiol. 2000 Aug;84(2):909-26 10845071 - Annu Rev Neurosci. 2000;23:441-71 22108672 - Nat Rev Neurosci. 2012 Jan;13(1):51-62 21723114 - Curr Opin Neurobiol. 2011 Oct;21(5):701-8 6473083 - Pflugers Arch. 1984 Jul;401(3):304-14 15338009 - Nat Neurosci. 2004 Oct;7(10):1113-22 20152117 - Neuron. 2010 Jan 14;65(1):107-21 21552274 - Nat Neurosci. 2011 Jun;14(6):775-82 20110507 - Science. 2010 Jan 29;327(5965):587-90 11927690 - J Physiol. 2002 Apr 1;540(Pt 1):321-33 15842744 - Vis Neurosci. 2005 Jan-Feb;22(1):87-99 10412063 - Nat Neurosci. 1999 Aug;2(8):733-9 17408583 - Neuron. 2007 Apr 5;54(1):137-52 8939866 - Science. 1996 Dec 6;274(5293):1724-6 21753021 - J Neurophysiol. 2011 Oct;106(4):1888-900 9151754 - J Neurosci. 1997 Jun 1;17(11):4382-8 11245694 - J Neurosci. 2001 Mar 15;21(6):2104-12 19657084 - J Neurophysiol. 2009 Oct;102(4):2069-83 12077207 - J Neurosci. 2002 Jun 15;22(12):5118-28 12466456 - J Neurophysiol. 2002 Dec;88(6):3398-408 9698348 - Neural Comput. 1998 Aug 15;10(6):1321-71 |
| References_xml | – ident: B4 doi: 10.1016/j.conb.2011.06.003 – ident: B21 doi: 10.1007/BF00582601 – ident: B12 doi: 10.1016/j.conb.2011.02.003 – ident: B6 doi: 10.1152/jn.00692.2001 – ident: B11 doi: 10.1016/j.neuron.2007.02.029 – ident: B19 doi: 10.1017/S0952523805221120 – ident: B27 doi: 10.1152/jn.00425.2001 – ident: B15 doi: 10.1523/JNEUROSCI.22-12-05118.2002 – ident: B41 doi: 10.1007/PL00005751 – volume-title: Theoretical neuroscience year: 2001 ident: B7 – ident: B49 doi: 10.1162/089976698300017214 – ident: B14 doi: 10.1016/j.neuron.2009.12.005 – ident: B37 doi: 10.1126/science.1179850 – ident: B17 doi: 10.1016/j.neuron.2011.09.027 – ident: B43 doi: 10.1152/jn.1987.57.3.773 – volume-title: Balanced amplification and normalization in a simple circuit model of visual cortex explain multiple aspects of attentional modulation year: 2011 ident: B26 – ident: B33 doi: 10.1038/35372 – ident: B20 doi: 10.1152/jn.00425.2006 – ident: B29 doi: 10.1152/jn.1985.54.3.651 – ident: B46 doi: 10.1152/jn.00165.2011 – ident: B10 doi: 10.1146/annurev.neuro.23.1.441 – ident: B16 doi: 10.1152/jn.00255.2002 – ident: B1 doi: 10.1152/jn.2000.84.2.909 – ident: B31 doi: 10.1167/7.6.13 – ident: B32 doi: 10.1371/journal.pcbi.1001078 – ident: B34 doi: 10.1016/j.neuron.2004.12.024 – ident: B48 doi: 10.1126/science.274.5293.1724 – ident: B23 doi: 10.1038/nn1391 – ident: B8 doi: 10.1007/978-0-387-87708-2 – ident: B24 doi: 10.1113/jphysiol.2001.012776 – ident: B40 doi: 10.1038/11197 – ident: B13 doi: 10.1017/CBO9780511815706 – ident: B30 doi: 10.1016/j.neuron.2009.03.028 – ident: B47 doi: 10.1016/0042-6989(85)90183-X – ident: B22 doi: 10.1038/nature09086 – ident: B35 doi: 10.1038/nn1660 – ident: B44 doi: 10.1093/cercor/bhm057 – ident: B9 doi: 10.1523/JNEUROSCI.06-05-01284.1986 – ident: B45 doi: 10.1523/JNEUROSCI.17-11-04382.1997 – ident: B28 doi: 10.1038/nn.2815 – ident: B36 doi: 10.1038/nn1310 – ident: B42 doi: 10.1152/jn.00512.2009 – ident: B2 doi: 10.1126/science.290.5498.1968 – volume-title: Normalization in a nonlinear circuit model of V1 year: 2010 ident: B38 – ident: B3 doi: 10.1523/JNEUROSCI.21-06-02104.2001 – ident: B18 doi: 10.1152/jn.2001.86.4.1803 – ident: B5 doi: 10.1038/nrc3398 – reference: 9151754 - J Neurosci. 1997 Jun 1;17(11):4382-8 – reference: 16855109 - J Neurophysiol. 2006 Oct;96(4):1755-64 – reference: 11245694 - J Neurosci. 2001 Mar 15;21(6):2104-12 – reference: 11110664 - Science. 2000 Dec 8;290(5498):1968-72 – reference: 15629708 - Neuron. 2005 Jan 6;45(1):133-45 – reference: 19477158 - Neuron. 2009 May 28;62(4):578-92 – reference: 9698348 - Neural Comput. 1998 Aug 15;10(6):1321-71 – reference: 21353526 - Curr Opin Neurobiol. 2011 Apr;21(2):269-74 – reference: 4024474 - Vision Res. 1985;25(6):755-66 – reference: 17685796 - J Vis. 2007;7(6):13 – reference: 17494058 - Cereb Cortex. 2008 Feb;18(2):331-6 – reference: 21723114 - Curr Opin Neurobiol. 2011 Oct;21(5):701-8 – reference: 10845071 - Annu Rev Neurosci. 2000;23:441-71 – reference: 12466456 - J Neurophysiol. 2002 Dec;88(6):3398-408 – reference: 15665876 - Nat Neurosci. 2005 Feb;8(2):194-201 – reference: 3711980 - J Neurosci. 1986 May;6(5):1284-301 – reference: 12077207 - J Neurosci. 2002 Jun 15;22(12):5118-28 – reference: 4045542 - J Neurophysiol. 1985 Sep;54(3):651-67 – reference: 9348122 - Exp Brain Res. 1997 Sep;116(2):216-28 – reference: 15842744 - Vis Neurosci. 2005 Jan-Feb;22(1):87-99 – reference: 9468134 - Nature. 1998 Feb 5;391(6667):580-4 – reference: 20152117 - Neuron. 2010 Jan 14;65(1):107-21 – reference: 12424292 - J Neurophysiol. 2002 Nov;88(5):2530-46 – reference: 10412063 - Nat Neurosci. 1999 Aug;2(8):733-9 – reference: 20596024 - Nature. 2010 Jul 1;466(7302):123-7 – reference: 21753021 - J Neurophysiol. 2011 Oct;106(4):1888-900 – reference: 6473083 - Pflugers Arch. 1984 Jul;401(3):304-14 – reference: 10938316 - J Neurophysiol. 2000 Aug;84(2):909-26 – reference: 21552274 - Nat Neurosci. 2011 Jun;14(6):775-82 – reference: 11927690 - J Physiol. 2002 Apr 1;540(Pt 1):321-33 – reference: 21390280 - PLoS Comput Biol. 2011 Feb;7(2):e1001078 – reference: 22108672 - Nat Rev Neurosci. 2012 Jan;13(1):51-62 – reference: 22017986 - Neuron. 2011 Oct 20;72(2):231-43 – reference: 16520737 - Nat Neurosci. 2006 Apr;9(4):552-61 – reference: 8939866 - Science. 1996 Dec 6;274(5293):1724-6 – reference: 3559701 - J Neurophysiol. 1987 Mar;57(3):773-86 – reference: 11826034 - J Neurophysiol. 2002 Feb;87(2):653-9 – reference: 11600641 - J Neurophysiol. 2001 Oct;86(4):1803-15 – reference: 20110507 - Science. 2010 Jan 29;327(5965):587-90 – reference: 15338009 - Nat Neurosci. 2004 Oct;7(10):1113-22 – reference: 19657084 - J Neurophysiol. 2009 Oct;102(4):2069-83 – reference: 17408583 - Neuron. 2007 Apr 5;54(1):137-52 |
| SSID | ssj0006105 |
| Score | 2.4405873 |
| Snippet | We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater... |
| SourceID | pubmedcentral proquest pubmed crossref mit |
| SourceType | Open Access Repository Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1994 |
| SubjectTerms | Brain Comparative analysis Dynamics Feedback, Physiological Humans Models, Neurological Nerve Net - physiology Neural Inhibition - physiology Neural networks Neural Networks (Computer) Neurons Neurons - physiology Nonlinear Dynamics Visual Cortex - cytology Visual Cortex - physiology |
| Title | Analysis of the Stabilized Supralinear Network |
| URI | https://direct.mit.edu/neco/article/doi/10.1162/NECO_a_00472 https://www.ncbi.nlm.nih.gov/pubmed/23663149 https://www.proquest.com/docview/1370243331 https://www.proquest.com/docview/1370126022 https://www.proquest.com/docview/1494353663 https://pubmed.ncbi.nlm.nih.gov/PMC4026108 |
| Volume | 25 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1La9tAEF5a59JL3w-naVGgPRW5sh4r6eikNqGkDhQbfBOr1QoHGjk08iW_Pt9oV9K6OKHtxRhpkOWd2dlvdme-YeyTksChgYjdsiyUG5ahxJxTpYvVpsAEVHFeUKD4Y87PluH3VbTqCRWa6pI6H8nbvXUl_6NVXINeqUr2HzTbPRQX8B36xSc0jM-_0rHNKEIAEsiRcl1vCURur2kLoyKenrlO9bZxKHFyNMwg1NNh5zB-sr5q6Aoa3yxu1qLL3v25zTXhgC5L7_s19_WEpsrHpBGbzQRq7JDYmwlwlzr1oz0MN6lKyvZKaerGXPfQGKnWa3ouQumV7VZ1PbMxn8TykcRGvN95cyKDnU9PLzKRNTSW_SLVHszPL7LZ8vw8W0xXi927ek0mDIggjSrrD3xEDv6AHUxOvp3MuuWZm7zW9n-01RDc_2r_9A5OeXx1We8LQf7MpLWgyeI5e2oG0ZloA3nBHqnqJXvW9utwjPt-xUatvTib0oG9OL29OJa9OMZeXrPlbLo4PXNNvwxXRh6vXcTqIRxDkGP1U1GUCCG8FPFgGpeIsmVQcMk9mStqXShKCaha8hjjMS5i4XMsNG_YoNpU6h1zOJcSkUGcq2Qc5ngMYEyapLwMIq8A5hyyL-3oZNKQyVNPk19ZE1RyP7PHcsg-d9LXmkTlHrljDHRmZtjNPTJHrRoswSAmZs2AXuy4uw1HSadfolKbrZYZI3r3_QdkwhThQwAUPmRvtWa7F_bpMgSGLN7ReSdARO27d6rLdUPYHtJGh5ccPvzq79mTfkoesUH9e6s-APHW-Udjw3fMiqnY |
| linkProvider | EBSCOhost |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Analysis+of+the+Stabilized+Supralinear+Network&rft.jtitle=Neural+computation&rft.au=Ahmadian%2C+Yashar&rft.au=Rubin%2C+Daniel+B&rft.au=Miller%2C+Kenneth+D&rft.date=2013-08-01&rft.pub=MIT+Press+Journals%2C+The&rft.issn=0899-7667&rft.eissn=1530-888X&rft.volume=25&rft.issue=8&rft.spage=1994&rft_id=info:doi/10.1162%2FNECO_a_00472&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=3001586231 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0899-7667&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0899-7667&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0899-7667&client=summon |