title: A generative spike train model with time-structured higher order correlations.
abstract: Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem. Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures. We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs. We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics.
authors.affiliation: Department of Mathematics, University of Houston Houston, TX, USA.
authors.forename: James
authors.initials: J
authors.lastname: Trousdale
authors.forename: Yu
authors.initials: Y
authors.lastname: Hu
authors.forename: Eric
authors.initials: E
authors.lastname: Shea-Brown
authors.forename: Krešimir
authors.initials: K
authors.lastname: Josić
keywords: correlations; cumulant; neuronal modeling; neuronal network model; neuronal networks; point processes; spiking neurons
references.citation: Proc Natl Acad Sci U S A. 2011 Jun 7;108(23):9679-84
references.pmid: 21602497
references.citation: J Neurosci. 2008 Jan 9;28(2):505-18
references.pmid: 18184793
references.citation: Neural Comput. 2004 Jun;16(6):1105-36
references.pmid: 15130244
references.citation: Neural Comput. 2008 Sep;20(9):2133-84
references.pmid: 18439140
references.citation: Nat Rev Neurosci. 2005 May;6(5):399-407
references.pmid: 15861182
references.citation: J Neurosci. 2001 Mar 1;21(5):1676-97
references.pmid: 11222658
references.citation: Neuron. 2012 Nov 8;76(3):590-602
references.pmid: 23141070
references.citation: Nat Rev Neurosci. 2001 Aug;2(8):539-50
references.pmid: 11483997
references.citation: J Comp Physiol Psychol. 1948 Feb;41(1):35-9
references.pmid: 18904764
references.citation: PLoS One. 2007 Mar 21;2(3):e299
references.pmid: 17375185
references.citation: Neuron. 1998 Dec;21(6):1235-8
references.pmid: 9883717
references.citation: Phys Rev Lett. 2009 Apr 3;102(13):138101
references.pmid: 19392405
references.citation: J Physiol Paris. 2012 May-Aug;106(3-4):120-7
references.pmid: 22115900
references.citation: Nat Neurosci. 2008 Jun;11(6):713-20
references.pmid: 18432198
references.citation: J Neurosci. 1998 May 15;18(10):3870-96
references.pmid: 9570816
references.citation: Nature. 2010 Jul 29;466(7306):617-21
references.pmid: 20601940
references.citation: Proc Natl Acad Sci U S A. 2007 Jan 2;104(1):347-52
references.pmid: 17185420
references.citation: Proc Natl Acad Sci U S A. 2011 Nov 29;108(48):19383-8
references.pmid: 22080608
references.citation: Nature. 2012 Dec 13;492(7428):247-51
references.pmid: 23143335
references.citation: J Neurosci Methods. 1997 Apr 25;73(1):69-79
references.pmid: 9130680
references.citation: Neural Comput. 2009 Jun;21(6):1642-64
references.pmid: 19191596
references.citation: J Neurophysiol. 1996 May;75(5):1806-14
references.pmid: 8734581
references.citation: Neuron. 1999 Sep;24(1):49-65, 111-25
references.pmid: 10677026
references.citation: Neuron. 2010 Nov 4;68(3):362-85
references.pmid: 21040841
references.citation: Nat Rev Neurosci. 2006 May;7(5):358-66
references.pmid: 16760916
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jan;81(1 Pt 1):011916
references.pmid: 20365408
references.citation: Neural Netw. 2001 Jul-Sep;14(6-7):715-25
references.pmid: 11665765
references.citation: Science. 2004 Apr 23;304(5670):559-64
references.pmid: 15105494
references.citation: Nat Neurosci. 2010 Mar;13(3):369-78
references.pmid: 20173745
references.citation: Neural Comput. 2013 Feb;25(2):289-327
references.pmid: 23148409
references.citation: J Neurophysiol. 2010 May;103(5):2912-30
references.pmid: 20032244
references.citation: J Neurosci. 2006 Sep 20;26(38):9673-82
references.pmid: 16988038
references.citation: J Neurosci. 2011 Nov 30;31(48):17514-26
references.pmid: 22131413
references.citation: J Physiol Paris. 1996;90(3-4):243-7
references.pmid: 9116676
references.citation: Nat Neurosci. 2012 Nov;15(11):1498-505
references.pmid: 23001062
references.citation: J Neurosci. 2006 Feb 15;26(7):2088-100
references.pmid: 16481442
references.citation: J Physiol Paris. 1996;90(3-4):249-50
references.pmid: 9116677
references.citation: Neural Comput. 2006 Feb;18(2):245-82
references.pmid: 16378515
references.citation: Nature. 2010 Jan 7;463(7277):98-102
references.pmid: 20054397
references.citation: Phys Rev Lett. 2011 May 20;106(20):208102
references.pmid: 21668265
references.citation: Nature. 1998 May 21;393(6682):268-72
references.pmid: 9607764
references.citation: J Neurosci. 2006 Aug 9;26(32):8254-66
references.pmid: 16899720
references.citation: J Neurosci. 2013 Jan 23;33(4):1684-95
references.pmid: 23345241
references.citation: Neural Comput. 2003 Jan;15(1):127-42
references.pmid: 12590822
references.citation: Nature. 2006 Apr 20;440(7087):1007-12
references.pmid: 16625187
references.citation: Nature. 2008 Aug 21;454(7207):995-9
references.pmid: 18650810
references.citation: J Comput Neurosci. 2010 Aug;29(1-2):327-350
references.pmid: 19862611
references.citation: Front Neurosci. 2011 Apr 28;5:58
references.pmid: 21687787
references.citation: Nat Neurosci. 2006 Mar;9(3):420-8
references.pmid: 16474393
references.citation: Brain Res. 2013 May 20;1511:33-45
references.pmid: 23523914
references.citation: Neuron. 2012 Oct 18;76(2):435-49
references.pmid: 23083744
references.citation: Science. 2010 Sep 24;329(5999):1671-5
references.pmid: 20705816
references.citation: J Neurophysiol. 2012 Nov;108(9):2383-92
references.pmid: 22896720
references.citation: J Neurosci. 2009 Apr 15;29(15):5022-31
references.pmid: 19369571
references.citation: PLoS Comput Biol. 2009 May;5(5):e1000380
references.pmid: 19424487
references.citation: Neuron. 2011 Mar 10;69(5):885-92
references.pmid: 21382549
references.citation: Neural Comput. 2003 Jan;15(1):67-101
references.pmid: 12590820
references.citation: Nature. 2002 Jun 13;417(6890):738-41
references.pmid: 12066184
references.citation: Neuron. 1999 Mar;22(3):435-50
references.pmid: 10197525
references.citation: Neural Comput. 2009 Feb;21(2):397-423
references.pmid: 19196233
references.citation: PLoS Comput Biol. 2012;8(3):e1002385
references.pmid: 22412358
references.citation: Nature. 1995 Jul 6;376(6535):33-6
references.pmid: 7596429
references.citation: Neural Comput. 2009 Jan;21(1):188-215
references.pmid: 19431282
references.citation: Front Comput Neurosci. 2010 Apr 19;4:9
references.pmid: 20485451