Norbert wrote:geo wrote:But what about the problem if both signals do not have the same embedding dimension ? Can You still use CRP ?
This is exactly the problem. The purpose of CRPs is to compare the states of two processes, what means that the states represent the same physical process, i.e. the data should have the same unit and the phase space reconstruction must be the same. It doesn't make sense to compare fully different phase space reconstructions, e.g. one from blood pressure and the other one from solar cycle. However, it could be interesting to look for a dependence between such kind of different processes. For such purpose it is more suitable to compare their recurrences, i.e. whether the recurrences of states in both systems separately occur at the same times. This is what the joint recurrence plot is doing. It is simply the element-wise product of the separate recurrence plots. Look at this article of Romano et al, 2005:
http://www.recurrence-plot.tk/bibliography.php?label=romano2005Best regards,
Norbert
Dear Norbert,
I agree completely. Essentially both type of signals are scalar times series reflecting the same" complex proces of "movement regulation" a neurological assembly involving motor cortex, basal ganglia and relying and reverberating frontostriatal loops and feed back mechanisms that regulate motor activity. Defects in these pathways can give raise to increased (fi chorea
and dyskinesia) or reduced motor output (parkinson) to the anterior motor neurones in the spinal cord. Essentially both signals should be measuring the same (complex) process dynamics but the granularity differs. Its is not that we compare unrelated signal sources but the first ones are superficial scalp EEG that pick up a lot of other activity from non motor neurological superficial cortical and deep neuronal processes and where signals are filtered by skin scalp, skull and meninges while the depth electrodes are directly in de subthalamic effector nucleus (picking up the direct motor signal to the thalamus) and not influenced by skull and membrane filters. I could bge that the signals will be modelled in diferent embedding dimensions. I recon that it would be best to measure this first before continuing these speculative questions (:=))) but anyhow even if the embedding dimension for the model should differ could chose the one of the most direct signal as "primairy" . Would that be allowed ?
Otherwise apart from synchrony how could i find out which signal drives which ?
I will do the analysis on the signals first and report back later with the results.
Best regards,
Georges
Dr. G. Otte
Neuropsychiatry+Neurophysiology
PC dr Guislain Neurolab
Ferrerlaan 66A
9000 Gent
Belgium
09 216 33 11