title: Functional two-way analysis of variance and bootstrap methods for neural synchrony analysis.
abstract: BACKGROUND
  Pairwise association between neurons is a key feature in understanding neural coding. Statistical neuroscience provides tools to estimate and assess these associations. In the mammalian brain, activating ascending pathways arise from neuronal nuclei located at the brainstem and at the basal forebrain that regulate the transition between sleep and awake neuronal firing modes in extensive regions of the cerebral cortex, including the primary visual cortex, where neurons are known to be selective for the orientation of a given stimulus. In this paper, the estimation of neural synchrony as a function of time is studied in data obtained from anesthetized cats. A functional data analysis of variance model is proposed. Bootstrap statistical tests are introduced in this context; they are useful tools for the study of differences in synchrony strength regarding 1) transition between different states (anesthesia and awake), and 2) affinity given by orientation selectivity.
  
  
  RESULTS
  An analysis of variance model for functional data is proposed for neural synchrony curves, estimated with a cross-correlation based method. Dependence arising from the experimental setting needs to be accounted for. Bootstrap tests allow the identification of differences between experimental conditions (modes of activity) and between pairs of neurons formed by cells with different affinities given by their preferred orientations. In our test case, interactions between experimental conditions and preferred orientations are not statistically significant.
  
  
  CONCLUSIONS
  The results reflect the effect of different experimental conditions, as well as the affinity regarding orientation selectivity in neural synchrony and, therefore, in neural coding. A cross-correlation based method is proposed that works well under low firing activity. Functional data statistical tools produce results that are useful in this context. Dependence is shown to be necessary to account for, and bootstrap tests are an appropriate method with which to do so.
authors.affiliation: Department of Mathematics, Facultad de Informática, Universidade da Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain. agonzalezmo@udc.es.
authors.forename: Aldana M
authors.initials: AM
authors.lastname: González Montoro
authors.forename: Ricardo
authors.initials: R
authors.lastname: Cao
authors.forename: Nelson
authors.initials: N
authors.lastname: Espinosa
authors.forename: Javier
authors.initials: J
authors.lastname: Cudeiro
authors.forename: Jorge
authors.initials: J
authors.lastname: Mariño
mesh_terms: D000200:Action Potentials; D000465:Algorithms; D000704:Analysis of Variance; D000818:Animals; D066187:Basal Forebrain / Q000502:physiology; D001933:Brain Stem / Q000502:physiology; D002415:Cats; D004558:Electric Stimulation; D008839:Microelectrodes; D008959:Models, Neurological; D015233:Models, Statistical; D009474:Neurons / Q000502:physiology*; D010775:Photic Stimulation; D012815:Signal Processing, Computer-Assisted; D014793:Visual Cortex / Q000502:physiology; D014796:Visual Perception / Q000502:physiology
references.citation: Nature. 1995 Feb 9;373(6514):515-8
references.pmid: 7845462
references.citation: Nature. 1997 Nov 6;390(6655):70-4
references.pmid: 9363891
references.citation: Neural Comput. 2002 Jan;14(1):43-80
references.pmid: 11747534
references.citation: Cereb Cortex. 2009 Sep;19(9):2166-80
references.pmid: 19221143
references.citation: Nat Rev Neurosci. 2008 May;9(5):370-86
references.pmid: 18425091
references.citation: Biophys J. 1967 Jul;7(4):419-40
references.pmid: 4292792
references.citation: J Psychiatry Neurosci. 1994 Nov;19(5):354-8
references.pmid: 7803369
references.citation: Neural Comput. 2003 Jan;15(1):67-101
references.pmid: 12590820
references.citation: Nature. 2000 Mar 9;404(6774):187-90
references.pmid: 10724171
references.citation: Science. 1996 Apr 12;272(5259):225-6
references.pmid: 8602506
references.citation: Nature. 1994 Jul 14;370(6485):140-3
references.pmid: 8022482
references.citation: N Engl J Med. 2010 Dec 30;363(27):2638-50
references.pmid: 21190458
references.citation: J Neurosci. 2003 May 15;23(10):4299-307
references.pmid: 12764118
references.citation: Eur J Neurosci. 2008 Feb;27(3):654-70
references.pmid: 18279318
references.citation: Science. 1969 May 16;164(3881):828-30
references.pmid: 5767782
references.citation: J Physiol. 1962 Jan;160:106-54
references.pmid: 14449617
references.citation: Neuron. 2002 Dec 5;36(5):969-78
references.pmid: 12467599
references.citation: Electroencephalogr Clin Neurophysiol. 1990 Dec;76(6):481-508
references.pmid: 1701118
references.citation: Nat Neurosci. 2005 Feb;8(2):194-201
references.pmid: 15665876
references.citation: J Neurophysiol. 2009 Mar;101(3):1126-40
references.pmid: 19129298
references.citation: J Neurophysiol. 2005 Oct;94(4):2940-7
references.pmid: 16160097
references.citation: J Comp Neurol. 2011 Apr 1;519(5):933-56
references.pmid: 21280045
references.citation: Math Biosci Eng. 2014 Feb;11(1):27-48
references.pmid: 24245679
references.citation: Neural Comput. 2002 Jan;14(1):81-119
references.pmid: 11747535