We provide explicit exponential upper bounds for the probabilities of under- and overestimating the interaction graph restricted to the observed set and obtain the strong consistency of the estimator. Our result does not require stationarity nor uniqueness of the invariant measure of the process.
Source Bernoulli , Volume 25, Number 1 , Zentralblatt MATH identifier Keywords biological neural nets graph of interactions interacting chains of variable memory length statistical model selection. Estimating the interaction graph of stochastic neural dynamics. Bernoulli 25 , no. Read more about accessing full-text Buy article.
Abstract Article info and citation First page References Abstract In this paper, we address the question of statistical model selection for a class of stochastic models of biological neural nets. Article information Source Bernoulli , Volume 25, Number 1 , Export citation.
Export Cancel. References  Adrian, E. The discharge of impulses in motor nerve fibres. Part II. The frequency of discharge in reflex and voluntary contractions. London: Christophers. Efficiently learning Ising models on arbitrary graphs. Vertical and horizontal electrooculograms EOGs were recorded simultaneously. Electromagnetic calibration of the coil positions was conducted before each MEG recording session. In this study, the stimuli were made from the same materials as those in the present study. The resulting activations showed similar patterns to the original study, including the clusters of bilateral posterior visual areas the activation foci in the V5, FG, and STS , the right inferior parietal lobule, and the right IFG.
A Basic Introduction To Neural Networks
We adopted these cortical activities as the prior. Threshold-based artifact rejection was also conducted. Trials including artifacts were also excluded on the basis of visual inspection. Before the source reconstruction analysis, we conducted a sensor level analysis to check for data quality by computing the mean-square field strength from the MEG sensors.
The mean-squared responses were then averaged across all participants to create the grand-mean waveforms for each condition and contour maps at representative peaks Supplementary Fig.
The inverse of this normalization transformation was then used to warp a canonical cortical mesh in the MNI space to the individual cortical mesh The cortical mesh described the source locations with 20, vertices i. Next, the MEG sensors were coregistered to the anatomical MRI by matching the positions of three fiducials nasion and R- and L-preauricular points and head shape.
Following inversion of the forward model, we conducted cortical source reconstruction using a parametric empirical Bayesian framework A standard minimum norm inversion was used to compute the cortical source activities on the cortical mesh based on the aforementioned fMRI data as spatial priors on the source localization The use of priors in the current framework imposed only soft not hard constraints The parameters of the inversion were based on SPM default settings, with the exception of not using a Hanning taper for the time series.
The intensity was normalized to the mean over voxels and conditions to reduce inter-participant variance. A non-sphericity correction was used to correct for uneven variance between the factor levels. The observations dependent on the factor levels were also corrected. The ensuing covariance components were estimated using a restricted maximum likelihood procedure and used to adjust the statistics. The low-variance regions, which can cause artificially high statistical values and localization bias, were also adjusted Planned contrasts were performed for each time window.
We tested the main effect of stimulus type dynamic facial expression versus dynamic mosaic and also analyzed the main effect of emotion and the interactions between stimulus type and emotion for descriptive purposes. We used DCM for ERP modeling of electrophysiological data 67 to explore how effective connectivity between brain regions was modulated by dynamic facial expression.
DCM allows us to make inferences about the influence that one neural system exerts over another and how this is affected by experimental contexts We focused on modulation of the cortical network by the presentation of dynamic facial expressions; thus, individual averaged responses were collapsed across the frightened and happy conditions, and the factor of emotion was excluded from the DCM input.
Artificial neural network
Anatomical identification was conducted using the cytoarchitectonic map with the Anatomy Toolbox version 1. The time window was determined because it was the first to show a large deflection during visual inspections of source estimates in this region The V1 search region was derived from the Anatomy Toolbox. The ROIs were restricted to the right hemisphere because this was the only one that showed significant activation in all ROIs. The hypothesized models of neural networks were constructed with the driving input of the visual stimulus into V1.
The modulatory effect of dynamic facial expressions was modeled to modulate each of these bidirectional connections. Based on these criteria, we constructed a total of seven models by changing the locations of the modulatory effects Fig. The first model included no modulatory effect on any connections. The next three models included modulatory effects on forward connections, but differed in terms of the included stages. The last three models included modulation on backward connections, in addition to modulatory effects on all forward connections, and also differed gradually in terms of the included stages.
To select the fittest model, we used random-effects BMS We used the exceedance probability to evaluate the belief that a particular model was more likely than any other given the group data. To clarify the involvement of feedback modulation, we grouped the models into three families: no modulation family, only including the null modulation model; forward modulation only family, including modulatory effects on forward connections alone; and forward and backward modulation family, containing modulatory effects on both forward and backward connections.
We then compared the families using BMS To specify the effect of timing of backward modulation, we further compared the models with and without backward modulation models 4 and 7, respectively, in Fig. How to cite this article : Sato, W. Spatiotemporal neural network dynamics for the processing of dynamic facial expressions. Darwin, C. John Murray, London, Yoshikawa, S. Dynamic facial expressions of emotion induce representational momentum. Anttonen, J. Ballistocardiographic responses to dynamic facial displays of emotion while sitting on the EMFi chair.
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Duarte , Galves , Löcherbach , Ost : Estimating the interaction graph of stochastic neural dynamics
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LZ W. The authors declare no competing financial or other interests. Conceived and designed the experiments: W. Performed the experiments: W.