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Open Access Highly Accessed Research article

Functional two-way analysis of variance and bootstrap methods for neural synchrony analysis

Aldana M González Montoro1*, Ricardo Cao1, Nelson Espinosa2, Javier Cudeiro2 and Jorge Mariño2

Author Affiliations

1 Department of Mathematics, Facultad de Informática, Universidade da Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain

2 Neuroscience and Motor Control Group (NEUROcom), Department of Medicine, Facultad de Ciencias de la Salud, Universidade da Coruña, Campus de Oza s/n, 15006 A Coruña, Spain

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BMC Neuroscience 2014, 15:96  doi:10.1186/1471-2202-15-96

Published: 12 August 2014



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.


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.


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.

Cross-correlation analysis; Bootstrap; Spike-trains; Dependence; Low firing-rate; Functional data