deletions | additions       diff --git a/sectionAim_1__subsec.tex b/sectionAim_1__subsec.tex  index 13322a9..e49a3b4 100644  --- a/sectionAim_1__subsec.tex  +++ b/sectionAim_1__subsec.tex 
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The analysis of Aim 1 assumes that temporal dynamics stay the same, meaning that the nodes of traditionally defined networks such as the default mode network are stationary. Recently, in \cite{Chang_2010}, researchers found that temporal dynamics are not stationary. In particular, they found that the phase and coherence of the posterior cingulate cortex (PCC, a hub of the default mode network) had variable connectivity with other nodes of not only the DMN, but other networks such as the salience and attention networks. Given this finding, it is possible that a disease pathology like MS may change the normal network dynamics in short periods of time, and that dynamic functional connectivity may be more sensitive to these small changes. For Alzheimers disease, researchers used functional dynamics to build a classifier to differentiate between patients with mild cognitive impairment or normal controls \cite{Wee_2015}.  The analysis consists of a sliding window approach outlined in \cite{Chang_2010}, where a graph is estimated from a section of the timeseries, and that section slides across the whole timeseries. In \cite{Wee_2015}, the method was modified to enforce temporal smoothness (meaning that network connectivity strengths and topology cannot change drastically between adjacent sliding windows), which is accomplished using a fused multiple group LASSO. From the graph, network measures, such as the clustering coefficient and small-worldness properties, are estimated\cite{Wee_2015}. The new resulting timeseries (clustering coefficient over time, or small-worldness over time) will then be used as features for a random forest classifier, which will attempt to distinguish between the High and Low NHPT groups. A random forest regressor will be used to estimate groups, and  the high and low  CMCT of the MS patients. groups.  I prefer random forests to SVMs because there are less parameters to go into the model. The dynamic function connectivity analysis already needs the following parameters to tune: 1) the window size, 2) the step size and 3) the regularization parameters for the LASSO optimization. Parameter tuning is done in a nested leave-one-out cross-validation, where the inner cross-validation fold is used to select the parameters and the results from outer fold are reported as the effect size.