41m2/s4 StemRegenin 1 solubility or standard deviation of 0.64m/s2. The variances of the other neurons all exceeded this magnitude. Another way to view the high variability of the acceleration is by means of coefficient of variation, which is the ratio of standard deviation over mean. All the absolute values of coefficients of variation exceeded 1.19, indicating high variability in acceleration response. Figure 5 plots the distribution of follower’s acceleration for input vectors

(in the training data set) that had winning neurons at (x = 0, y = 9) and (x = 8, y = 3), respectively. The neuron at (x = 0, y = 9), as reflected in Figure 3, has moderate follower’s velocity, high relative velocity, and moderate gap. In such a condition, most of the followers are expected to respond with acceleration. The accelerations as shown in Figure 5(a) were distributed between [−3.04,3.41] m/s2 with a mean of 0.85m/s2. The neuron at (x = 8, y = 3) belongs

to the input state that has high follower’s velocities, negative relative velocities, and small gaps. Majority of the drivers facing this situation will decelerate to avoid a rear-end collision. As shown in Figure 5(b), the response ranges from [−3.41,2.97] m/s2 with the mean of −0.94m/s2. Moreover, for both neurons, the modes occurred at 0m/s2. This is because the followers may choose not to act at the present time step; they may have responded at an earlier or later time step. Figure 5 Distribution of response for the same stimulus categories. The analysis in this subsection and Figure 5 has shown that, given similar stimuli (input vectors that have the same winning neuron), the follower’s response is not deterministic. The variation in the response may be due to the driving behavior between drivers (interdriver

heterogeneity), the inconsistency of the same driver (intradriver heterogeneity), or when the leaders belong to different types of vehicle (inter-vehicle-type heterogeneity). Note that the term interdriver heterogeneity also implicitly includes the varied acceleration response caused by the different performance characteristics of the same type of vehicle (e.g., cars). GSK-3 These three types of heterogeneities will be demonstrated in the next three subsections. 5.3. Interdriver Heterogeneity To demonstrate interdriver heterogeneity, data from two pairs of passenger cars in test data set I was fed into the trained SOM and the distributions of their responses were compared. Due to limitations on space, we chose two pairs which share the most number of the same winning neurons to demonstrate the interdriver heterogeneity. The first pair was denoted as Pair 1794-1790, in which the follower’s Vehicle Identification Number (VIN) in the NGSIM data set was 1794 and the leader’s VIN was 1790. The second pair was Pair 1852-1847. For each pair of cars, the vehicle trajectories for at least 68 continuous seconds were extracted, resulting in more than 136 vectors at 0.5 second intervals.