Stimulus and Response: the Law of Initial Value

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Even in the absence of any input, the brain generates complex patterns of spontaneous activity. Fluctuations in this activity affect how the brain responds to the outside world. The electrical activity in the brain — both spontaneous and in response to sensory input — can be measured using electrodes close to the scalp: this measurement is referred to as electroencephalography, or EEG. Spontaneous brain activity takes the form of rhythmic waves, also known as oscillations. In a person who is awake and relaxed, the EEG consists mainly of slow oscillations called alpha and beta waves. Sensory input, such as an image or a sound, triggers changes in brain activity that can be seen in the EEG.

To find out how spontaneous brain activity affects ERPs, Iemi et al. The results showed that the ERP looked different if the stimulus occurred during strong alpha and beta waves. The early part of the ERP — which occurs between 80 and milliseconds after the onset of the stimulus — decreased in size, presumably because it was inhibited by strong alpha and beta waves.

In contrast, the later part of the ERP — which occurs more than milliseconds after stimulus onset — increased in size. This paradox is accounted for by a newly recognized feature of the oscillations, namely that they fluctuate around a non-zero value of the EEG. Thus, two different mechanisms contributed to these opposite changes. The findings add to our understanding of how spontaneous brain activity influences how we perceive the world around us.

Furthermore, spontaneous brain activity differs in a number of disorders, including schizophrenia and autism. Understanding how spontaneous neural oscillations affect how the brain processes information from the senses could provide new insights into these conditions. The brain generates complex patterns of neural activity even in the absence of sensory input or tasks. Numerous studies have shown that such spontaneous neural activity can explain a substantial amount of the trial-by-trial variability in perceptual and cognitive performance e. Yet, the mechanisms by which spontaneous neural activity impacts the processing of sensory information remain unknown.

The mechanisms underlying the effect of prestimulus power on ERP amplitudes are currently unknown, partly because previous studies have been inconsistent regarding the latency and even the directionality of this effect. In this study, we addressed this issue by considering how prestimulus power affects the mechanisms of ERP generation at different latencies: namely, additive and baseline-shift mechanisms. Invasive studies in non-human primates demonstrated that early ERP components are associated with an increase in the magnitude of multi-unit activity MUA in sensory areas Kraut et al.

Non-invasive studies in humans showed that early ERP components e.

Edward Thorndike: The Law of Effect

Low-frequency neural oscillations are thought to set the state of the neural system for information processing Klimesch et al. The vertical line indicates stimulus onset, while the horizontal line indicates zero signal strength. Yellow and blue represent states of strong and weak prestimulus power, respectively. A Non-phase-locked ongoing oscillatory activity with a zero-mean. The oscillations are symmetrical relative to the zero line of the signal A upper panel.

law of initial value

B Non-phase-locked ongoing oscillatory activity with a non-zero-mean. The oscillations are asymmetrical relative to the zero line of the signal. The signal baseline is characterized by a negative offset opaque lines.


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The stronger the power of these oscillations, the stronger the negative offset of the signal baseline B upper panel. During event-related desynchronization ERD , the ongoing oscillations are suppressed to the zero line of the signal. Trial averaging of zero-mean oscillations eliminates prestimulus oscillatory activity that is not time-locked to the stimulus because opposite oscillatory phases cancel out.

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This results in baseline signal at the zero line, which is unaffected by ERD. Therefore, an ERD of zero-mean oscillations does not generate the slow ERP component during the late time window because there is no baseline shift for these oscillations dark gray; A lower panel. Trial averaging of non-zero-mean oscillations does not eliminate non-phase locked ongoing activity.

This results in a prestimulus baseline signal with an offset relative to the zero line. During the ERD, the baseline of the signal gradually approaches the zero line of the signal. When the post-stimulus signal is corrected with the prestimulus non-zero baseline, a slow shift of the ERP signal appears, mirroring the ERD time-course.

Specifically, an ERD of negative positive non-zero mean oscillations shifts the signal upward downward , generating the slow ERP component of positive negative polarity. Crucially, the stronger the prestimulus power, the stronger the ERD, and as a consequence, the stronger the slow shift of the ERP. The baseline-shift account predicts a positive relationship between prestimulus power and the amplitude of the slow ERP during the late time window dark gray; B lower panel.

According to the functional inhibition account, strong prestimulus power attenuates the amplitude of the additive ERP components. The effect of the baseline-shift mechanism on the relationship between prestimulus power and ERP amplitude has never been tested.

In fact, it is generally assumed and not even questioned that neural oscillations are symmetrical around the zero line of the signal. Accordingly, trial averaging is expected to eliminate non-phase-locked oscillations due to phase cancellation assuming a random phase distribution over trials , thereby resulting in a signal baseline with a zero mean.

In contrast to this traditional view, recent studies Nikulin et al. Accordingly, trial averaging does not eliminate non-phase-locked oscillations with a non-zero mean. As a consequence, any amplitude modulation of oscillations with a non-zero mean is expected to change the signal baseline baseline shift , and will therefore affect the ERP amplitude. Specifically, during the event-related desynchronization ERD of low-frequency oscillations, the power suppression is expected to cause a slow shift of the signal baseline toward the zero line. Subtracting the prestimulus non-zero baseline from the post-stimulus signal creates a slow shift, which mirrors the spatio-temporal profile of the ERD.

In particular, an ERD of oscillations with a negative non-zero-mean is expected to generate an upward slow shift of the ERP and viceversa. Accordingly, we predicted that states of strong prestimulus power would yield a strong ERD Min et al. To summarize, states of strong prestimulus power are expected: 1 to suppress the amplitude of additive ERP components during the early time window via functional inhibition ; and 2 to amplify the late ERP component, generated by an event-related modulation of non-zero-mean oscillations via baseline shift.

To test these predictions, we recorded electroencephalography EEG in human participants during rest and during stimulation with identical high-contrast checkerboard stimuli and analyzed the relationship between ERPs, ongoing and event-related oscillations. We find that the effects of prestimulus power on early and late ERP components are consistent with the functional inhibition and baseline-shift accounts, respectively.

Taken together, these results largely resolve apparent inconsistencies in previous literature and specify two distinct mechanisms by which prestimulus neural oscillations modulate visual ERP components. The experiment included stimulation trials with high-contrast checkerboard stimuli presented in the lower LVF; Figure 2A , left panel or upper UVF; Figure 2A , middle panel visual field with equal probability, and fixation-only trials without any checkerboard stimulus Fix; Figure 2A , right panel.

For each participant we quantified the ERP at the electrode with peak activity between 0.

Stimulus and Response

A The stimuli consisted of bilateral checkerboard wedges specifically designed to elicit the C1 component of the visual ERP. The stimuli appeared in the lower left panel, LVF , upper visual field middle panel, UVF , or in no field right panel, Fix with equal probability. Across trials, the participants were instructed to discriminate a central target during stimulus presentation. B Event-related potentials ERP were calculated for the subject-specific electrode with C1-peak activity. The C1 topography illustrates the ERP amplitude averaged at the subject-specific time point of peak activity between 0.

The size of the electrodes in the topography indicates the frequency of the C1-peak electrode in the sample of participants. The C1 is followed by the N, peaking between 0. The N topography illustrates the ERP amplitude averaged between 0. Fix trials do not show any robust additive components during the early time window. The topography of this late component illustrates the ERP amplitude averaged between 0. This late ERP component is present in all trial types. Time 0 indicates stimulus onset.

C Group-level t-statistics maps of event-related oscillations. Negative values blue indicate significant power suppression across participants ERD , while positive values yellow indicate significant power enhancement across participants ERS. The maps are averaged across electrodes of the significant clusters, and masked by a final alpha of 0.

Multiple mechanisms link prestimulus neural oscillations to sensory responses | eLife

The ERD is present in all trial types. Time 0 s indicates stimulus onset. On stimulation trials, the C1 component peaked on average at 0. Following the C1, we observed a N component peaking between 0. The N was followed by a late deflection in the time range between 0. Fix trials showed a late positive deflection with similar timing and topography as on stimulation trials Figure 2B , right panel. For each participant we estimated the event-related synchronization ERS and desynchronization ERD at frequencies between 5 and 30 Hz and at each electrode and time point of the post-stimulus window 0—0.

Ltspice transient analysis initial conditions

The most negative t-statistic was found at 20 Hz, 0. The most positive t-statistic was found at 5 Hz, 0. This test also found two positive clusters indicating ERS. Within this cluster, the most positive t-statistic was found at 5 Hz, 0. Within this cluster, the most positive t-statistic was found at 17 Hz, 0. On Fix trials, the most negative t-statistic was found at 20 Hz, 0.

The functional inhibition account predicts that states of strong prestimulus power reflect neural inhibition, resulting in reduced amplitude specifically of early ERP components generated by the additive mechanism. To test for this mechanism, we classified trials in five bins based on single-trial estimates of oscillatory power at each electrode and each frequency between 5 and 30 Hz averaged over the 0. These total-band power estimates reflect a mixture of both periodic i. Therefore, to determine whether ERP differences between total-band power bins were indeed due to oscillatory activity, we repeated the binning analysis using single-trial estimates of the periodic signal i.

A Group-level t-statistics maps of the difference in ERP amplitude between states of weak Q 1 and strong Q 5 prestimulus power on lower visual field left panel, LVF , upper visual field middle panel, UVF , and fixation-only trials right panel, Fix. Accordingly, positive t-statistics values indicate an enhancement of positive ERP components, and a dampening of negative ERP components, while negative t-statistics values indicate an enhancement of negative ERP components, and a dampening of positive ERP components.