Cortico-striatal Circuits and Interval Timing: Coincidence Detection of Oscillatory Processes
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Journal:: “Brain Research. Cognitive Brain Research”
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Abstract
Humans and other animals demonstrate the ability to perceive and respond to temporally relevant information with characteristic behavioral properties. For example, the response time distributions in peak-interval timing tasks are well described by Gaussian functions, and superimpose when scaled by the criterion duration. This superimposition has been referred to as the scalar property and results from the fact that the standard deviation of a temporal estimate is proportional to the duration being timed. Various psychological models have been proposed to account for such responding. These models vary in their success in predicting the temporal control of behavior as well as in the neurobiological feasibility of the mechanisms they postulate. A review of the major interval timing models reveals that no current model is successful on both counts. The neurobiological properties of the basal ganglia, an area known to be necessary for interval timing and motor control, suggests that this set of structures act as a coincidence detector of cortical and thalamic input. The hypothesized functioning of the basal ganglia is similar to the mechanisms proposed in the beat frequency timing model [R.C. Miall, Neural Computation 1 (1989) 359-371], leading to a reevaluation of its capabilities in terms of behavioral prediction. By implementing a probabilistic firing rule, a dynamic response threshold, and adding variance to a number of its components, simulations of the striatal beat frequency model were able to produce output that is functionally equivalent to the expected behavioral response form of peak-interval timing procedures.
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Page 154
Due to the unique bi-stable characteristics of these striatal spiny neurons, uncorrelated cortical inputs are ineffective at driving these neurons into the up-state, let alone causing them to fire. Wilson [194] has simulated the properties of these spiny neurons and demonstrated that approximately 150 simultaneous inputs are required to move the neuron into its up-state. As such, these striatal spiny neurons may essentially act as largescale coincidence detectors.
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There is evidence that suggests that phasic dopamine modulates the direction of synaptic strength change, thereby serving the role of a reinforcement mechanism for patterns of cortical activity that are relevant to an animal [193]
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This functional description of the basal ganglia coincides extremely well with Miall’s beat frequency model of interval timing, which utilizes the coincident activation of a series of high frequency oscillators to code for extended durations [136].
Need to check on this
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As shown in Fig. 2, cortical (and thalamic) neurons would function as the oscillators of the beat frequency model. The striatal spiny neuron is envisioned to function as the coincidence detector (integrator) of the beat frequency model
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Burst-mode dopaminergic input from the SNPC serves as the reinforcement signal, allowing a particular criterion duration to be represented in cortico-striatal synaptic strengths, and following learning, may also serve as a temporal starting gun, effectively resetting the striatal membrane potential.
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Additionally, non-burst dopaminergic input, as well as input from other striatal interneurons, could serve as threshold modulators via their basal efflux onto striatal spiny neurons.
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To avoid confusion between the original beat frequency model (BF [136]) and the adapted version presented below, we will distinguish them by referring to the revised model as the striatal beat frequency model (SBF).
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Our replication is shown in Fig. 3A with parameters that are similar to those used in Miall’s data (1000 pacemakers, 10F1.6 Hz oscillations, 6-s criterion, 0.999 oscillation threshold, 100 Hz integration, synaptic weights at +1 if the neuron fired at the 6-s criterion time and 0 otherwise), plotted over 2.5 times the criterion duration in order to show the activity levels following the reinforced time.
there is a clear peak of neuronal activity around the time of reinforcement, as well as at the fundamentals of the criterion interval (e.g., at one-third, one-half, and twice the trained interval) because the model codes time in a manner Fig. 3. Coherent input to a simulated neuron from an array of cortical oscillators. In all cases, the input strength of each oscillator is weighted depending upon whether it fired during the criterion time. (A) A replication of Miall’s original simulation showing a peak of coherent activity at the reinforced time of 6 s, and additional peaks at the fundamentals (1/3, 1/2, 2 ). (B) Same as A, except that parameters were adjusted to reflect input onto a weighted striatal neuron (i.e., a 25-ms integration factor). (C) Same as B, but with 15,000 oscillating inputs. These results clearly do not match the desired Gaussian peak function. M.S. Matell, W.H. Meck / Cognitive Brain Research 21 (2004) 139–170 15
Least common multiple showing up!
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similar to the calculation of a least common multiple.
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we are interested in the pattern of input that would cause a striatal neuron to fire (i.e., neurons do not simply integrate moment by moment, but rather they integrate over time)
Are they talking about eligibility traces here?
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In a simplistic implementation of this time constant, we utilized a running mean of the cortical input stream over 25 ms.
A more defined version
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synaptic weighting was performed if the cortico-striatal neuron fired in the first 25 ms following the criterion time (rather than precisely at the criterion time, due to the striatal membrane time constant), and was then weighted as +1, otherwise it was given 0 weight.
So still need to understand how they are modifying the weights here as this only describes accumulation
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the simulations were conducted at 1000 Hz
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The addition of a small amount of variability resulted in a reasonable level of discriminability, (e.g., Fig. 4A—standard deviation=1% of the oscillation period, approximate range of 97–103 ms for the 10 Hz oscillator), whereas higher levels of variability caused results to become much less discriminable (e.g., Fig. 4B—3% of the period; Fig. 4C—5% of the period).
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This flattening of the output function with seemingly low levels of oscillatory variability suggests that the model as currently implemented is too reliant on spike time precision.
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We also investigated other neurally based modifications (e.g., probabilistic firing at the peak of each oscillation, insertion of noise, dynamic twostate membrane potential for the striatal neuron, global variance in oscillation speed, and striatal firing thresholds). However, in no case did the model capture the essential features of a scalar, Gaussian temporal response distribution that resembled the behavioral data. As such, we decided to investigate whether we could avoid these problems by using an alternative implementation of cortical firing times.
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As an alternative to cortical activity that spikes only at the peak of every oscillation (or at a constant rate for a proportion of the oscillation phase), we reasoned that oscillatory activity in the cortex might be more realistically described as probabilistic, with cortical neurons being most likely to fire during the positive phase of the sinusoid, and least likely to fire during the negative phase [4].
Maybe I should give the sinusoids a negative value
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If a group of neurons are all firing with the same underlying membrane potential oscillation period, the summed output of these neurons will be sinusoidal. As such, we evaluated the effect of using sinusoidally varying cortical activity as input to the striatal spiny neuron. Such ensemble oscillations are the necessary underpinnings of the various EEG rhythms recorded from the scalp.
The basis for our sinusoidal activity
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Our parameters for these simulations consisted of 300 different cortical oscillator ensembles with periods uniFig. 4. Simulated striatal input function resulting from adding variance to the cortical oscillation times within a trial. Coherent activity is still maximal at the criterion duration, but discriminability rapidly decreases as the variance increases from 1% (A) to 3% (B) to 5% (C). M.S. Matell, W.H. Meck / Cognitive Brain Research 21 (2004) 139–170 15
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formly distributed between 8.5 and 11.5 Hz (i.e., 8.50, 8.51,…,11.50).
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Synaptic strengths of the ensembles were based on the cosine of the oscillation at the criterion time (adjusted so that actual strengths ranged from 0 to +1).
Sooooo…. just sinusoidal? wtf is goin on here? do they reinforce them or not?
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In other words, maximal synaptic weights were applied to those ensembles that had the highest firing probabilities at the criterion time.
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Our initial simulations showed a substantial difference in the summed cortical output function as compared to the precise spike time model (Fig. 5A).
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There was a high level of activity immediately upon trial onset, which decreased over the first couple seconds. The striatal input stayed at a baseline level until time approached the criterion time, at which point it rose to a maximum and then decreased back to baseline in a slightly skewed manner for the remainder of the trial.
Can we match this? I think we already do
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Of particular interest is the fact that there are no peaks at the fundamentals of the criterion duration, a result that plagued the earlier simulations.
Do we not want this?
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To assess the effect of oscillator frequencies, we tested the model at different ranges. Increases in the range of oscillation frequencies led to a sharpening of the coherence peak (Fig. 5B—range=5–15 Hz), whereas decreases in the frequency range produced wider coherence functions (Fig. 5C—range=9.8–10.2 Hz).
This seems important.
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Fig. 6A–C shows the effects of greater or fewer oscillators within an 8.5–11.5 Hz range. Increasing coverage led to a slightly broader and fuller coherence function (Fig. 6A). In contrast, as can be seen in Fig. 6B and C, decreasing the coverage of the oscillators resulted in peaks at harmonics of the criterion time.
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The model was quite sensitive to variance in the oscillation periods when each ensemble was allowed to vary separately from the others (e.g., the 8.5-Hz oscillator sped up and the 8.6-Hz oscillator slowed down). With variance in the oscillators as low as 0.3% of their period, the model showed only a slight discrimination (Fig. 7A).
What does this mean?
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Thus, the model remains highly susceptible to within-trial, desynchronized oscillator variance. In contrast, discrimination was extremely robust if the oscillation speeds varied globally
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Fig. 7B shows the effect when all oscillator periods were doubled (after synaptic weighting), whereas Fig. 7C shows the effect when all oscillator periods were halved.
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As can be seen in Fig 7B and C, proportional global variation caused the peaks to move systematically in the anticipated direction, and the function became sharper/wider as would be expected from changes in clock speed. As such, the present model appears to have features strongly suggestive of scalar timing.
Not sure about this either.
But represents a target goal for reproduction
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In order to fully explore the development of cortical coherence, we allowed the synaptic strengths to vary between 1 and 1, rather than adjusting the cosine values from 0 to 1. In other words, we allowed cortico-striatal synapses to be inhibitory as well as excitatory.
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Adding inhibition dramatically altered the cortical coherence pattern; activation at trial onset was completely blocked, while activation associated with the criterion time was broadened.
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This activation is shown in Fig. 8A. As can be seen, the striatal input function rose and fell in a nearly symmetrical manner around the criterion time, without any aberrant activity anywhere else in time. Such activity is very similar to the peak functions we are trying to duplicate, and such a systematic firing pattern is a major criterion of an interval timing model.
Evidence for using a EIO model?
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As the second major criterion of an interval timing model is the ability to produce the scalar property, the simulations were rerun using criterion times of 12 and 18 s (Fig. 8Band C, respectively). As can be seen, there was no change in the width of the coherence function over these times, indicating a clear violation of the scalar property. Thus, the model needs sources of variance added to it that will enable the scalar property.
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As seen in Fig. 7B and C, variations in global oscillation frequency led to scalar behavior in the cortical coherence function.
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Adding a response threshold (i.e., a striatal firing threshold) simply requires setting a coherence level (Fig. 9A) that would lead to striatal firing every time the threshold is crossed. Adding a constant threshold results in symmetric striatal firing around the criterion time (Fig. 9B), and will obviously fail to induce scalar responding if applied to the results of Fig. 8A–C.
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In order to more closely match the properties of a striatal neuron, we simulated the dynamic threshold changes of striatal spiny neurons, which effectively decrease the firing threshold following a increase in the membrane potential from the down-state to the up-state (from 90 to 60 mV).
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Specifically, a slowly inactivating potassium current that develops at depolarized potentials (e.g., 60 mV), effectively decreases the threshold for striatal firing following current inactivation.
current inactivation?
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This current inactivates at different rates depending upon the depolarizing current (e.g., ~400 ms with 0.5 nA), whereas it recovers from inactivation with a time constant of approximately 2 s [145].
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This inactivation current was modeled in a simplified manner by providing a linear decrease of up to 30% over 400 ms in the threshold of cortical coherence required to spike, building as a function of threshold crossing.
Ok so how they actually did it
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if no spikes occur, recovery was modeled as a linear increase back to the original threshold over 2 s.
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variability in other components may produce an increase in the spread of the cortical coherence function, and a dynamic threshold may then lead to a greater effect. In addition, it has been suggested that two separate thresholds are necessary to explain the correlations between start responding and stop responding times on single trials in the peak-interval procedure [36].
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As this dynamic threshold will reside at different levels as a function of time in the trial, it may be viewed as being similar to this multiple threshold idea.
Not sure what to do with this
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we can easily implement between-trials clock speed variance (global variance in oscillation frequencies) in the current model. Adding normally distributed clock speed variance (10% of oscillator speed=1 standard deviation), allows the model to produce peak-shaped functions in its output that increase in width as a function of time (Fig. 10A).
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However, plotting these functions after they are normalized by their criterion durations of 6, 12, and 18 s shows that they do not superimpose (Fig. 10B).
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Thus, the model in its present state does not lead to the scalar property.
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The reason for this failure in scalar timing is the constant width of the cortical coherence function (Fig. 8A–C), which exerts too large of an influence on the striatal output function at short durations (i.e., 6 s), thereby overwhelming the scalar effects of clock speed variability. As such, we need to introduce a scalar component into the model prior to the development of the cortical coherence function
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Interestingly, this action of dopamine would be specific to training, as this is the only time that the delivery of reinforcement is temporally unpredictable. Once the time of reinforcement becomes predictable, no changes in dopaminergic activity are seen in response to reinforcement [83]. Instead, the pulse of SNPC dopamine occurs in response to the earliest predictor of subsequent reward.
How RPE will work
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In the case of the peak procedure, the discriminative stimulus that indicates the trial has started and reward will be available after a certain amount of time serves as the earliest predictor of reinforcement, and we would expect a dopamine pulse to occur in response to this cue. While the same LTP-inducing processes would be expected to occur at stimulus onset, the dopamine pulse would not lead to substantial synaptic changes, as the conditioned stimulus would not be predictable in time, and different cortical-striatal synapses would therefore be strengthened or weakened over trials.
Why would we not reinforce the Dop hit with ini stim?
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The unexpected delivery of food during a trial, which would also be expected to cause a phasic burst of dopamine [139], causes a complete reset of a rat’s production of a temporal interval [117].
Why we expect reset, however I want to “tie” the ini stim and uncond stim together, by the periodicity of the reinforced osc
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In the present model, resynchronizing the cortical oscillations is considerably more important than resetting the temporal integrator, as starting the integration process with striatal neurons in random states does not dramatically alter the striatal activity function (data not shown).
hmmmmm
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By way of contrast, scalar expectancy theory [68] would be completely unimpaired by failing to reset the temporal signal as it is proposed to run continuously, but temporally accurate behavior would be dramatically affected by failure to reset the integration stage.
Fuck am I doing something closer to SET? Nope. SET uses an accumulator
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Dopamine clearly serves a third role, that of modulating clock speed [113,114,116,119,122,125]. Despite this frequently found effect, the temporal dynamics of dopaminergic clock speed modulation remain unclear.
Ok so this will be an interesting thing to try implementing at some point
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Clock speed alterations may be the result of phasically released dopamine as described above, or it may be a function of tonic levels of dopamine, which are relatively unaffected by phasic bursts, due to the rapid elimination of synaptic dopamine by the reuptake transporter [70].
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As dopaminergic mediated clock speed alterations are evidenced as horizontal shifts across the entire response distribution [122,125], these changes are likely due to consistent increases/decreases in dopaminergic function over the course of the trial, thereby implicating a tonic, rather than phasic, mode of activity.
What does this mean
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Given the multi-faceted role we are proposing for dopamine, one obvious question is what level of interaction occurs between LTP induction, clock resetting, and clock speed modulation.
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Clock speed alterations also appear to result when attention is shared between timing and other processes [16,18,53,54], and such results may also be tied to the mechanisms of SBF.
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Figure 2
Fig. 2. A graphic representation of an oscillatory-based timing circuit. The top of the figure shows three different frequency oscillating signals (cortical ensembles) and the unweighted summation of their output (striatal input) over time. As can be seen, the output periodicity is greater than that of the inputs, demonstrating the potential of this type of model to bridge the millisecond time scale of the brain to the second to minute time scale of interval timing. The lower half of the figure shows information flow through the cortico-striatal-thalamo-cortical loop. Arrows indicate the direction of information flow. Red arrows are GABAergic, green arrows are glutamatergic, blue arrows are dopaminergic. The dopaminergic input to the striatal neuron provides a reinforcement signal to selectively weight cortical and thalamic inputs. Different striatal neurons participate in direct and indirect pathways.
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Figure 2
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Figure 3
Fig. 3. Coherent input to a simulated neuron from an array of cortical oscillators. In all cases, the input strength of each oscillator is weighted depending upon whether it fired during the criterion time. (A) A replication of Miall’s original simulation showing a peak of coherent activity at the reinforced time of 6 s, and additional peaks at the fundamentals (1/3, 1/2, 2 ). (B) Same as A, except that parameters were adjusted to reflect input onto a weighted striatal neuron (i.e., a 25-ms integration factor). (C) Same as B, but with 15,000 oscillating inputs. These results clearly do not match the desired Gaussian peak function.
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Figure 3
Figure
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Figure 5
Fig. 5. Simulated striatal input over time resulting from the use of a sinusoid as opposed to a single spike at the peak of each cortical oscillation. Synaptic weights were proportional to probability of firing at the criterion time, scaled from 0 to 1. Note the symmetrical peak at the criterion time without activity at the fundamentals. However, extensive activity is still seen early in the trial. The width of coherent activity varies depending on the range of sinusoid frequencies utilized. (A) Three hundred oscillators uniformly distributed between 8.5 and 11.5 Hz. (B) One thousand oscillators uniformly distributed between 5 and 15 Hz. (C) Forty oscillators uniformly distributed between 9.8 and 10.2 Hz.
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Figure 5
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Fig 6
Fig. 6. Simulated striatal input over time utilizing different degrees of oscillator coverage across the 8.5–11.5 Hz. range: (A) 600 oscillators; (B) 100 oscillators; (C) 60 oscillators.
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Fig 6
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Fig 7
Fig. 7. Simulated striatal input over time following the addition of variance into each ensembles oscillation frequency. (A) Disruption in discriminability resulted from small amounts of variance applied separately to each ensemble (i.e., one oscillator sped up, while another slowed down). In contrast, when all oscillator frequencies are proportionally increased (Bdoubled in speed) or decreased (C—halved in speed), discriminability is unchanged. Note that these global changes in clock speed lead to scalar contraction and expansion in the coherence function serving as striatal input.
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Fig 7
[!]
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Fig. 8. Simulated striatal input rises and falls symmetrically around the criterion time when the cortico-striatal synaptic weights are allowed to vary from 1 to 1. However, the spread of the input pattern does not broaden at all as the criterion time moves from 6 s (A) to 12 s (B) to 18 s (C).
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