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The Journal of Neuroscience, December 15, 1998, 18(24):10688-10699
An Oscillatory Short-Term Memory Buffer Model Can Account for
Data on the Sternberg Task
Ole
Jensen and
John E.
Lisman
Volen Center for Complex Systems, Brandeis University, Waltham,
Massachusetts 02243
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ABSTRACT |
A limited number (7 ± 2) of items can be held in human
short-term memory (STM). We have previously suggested that observed dual (theta and gamma) oscillations could underlie a multiplexing mechanism that enables a single network to actively store up to seven
memories. Here we have asked whether models of this kind can account
for the data on the Sternberg task, the most quantitative measurements
of memory search available. We have found several variants of the
oscillatory search model that account for the quantitative dependence
of the reaction time distribution on the number of items (S) held in
STM. The models differ on the issues of (1) whether theta frequency
varies with S and (2) whether the phase of ongoing oscillations is
reset by the probe. Using these models the frequencies of dual
oscillations can be derived from psychophysical data. The derived
values (f = 6-10 Hz; f = 45-60 Hz) are in
reasonable agreement with experimental values. The exhaustive nature of
the serial search that has been inferred from psychophysical
measurements can be plausibly explained by these oscillatory models.
One argument against exhaustive serial search has been the existence of
serial position effects. We find that these effects can be explained by
short-term repetition priming in the context of serial scanning models.
Our results strengthen the case for serial processing and point to
experiments that discriminate between variants of the serial scanning process.
Key words:
theta; gamma; oscillations; working memory; short-term
memory; Sternberg; brain waves
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INTRODUCTION |
The brain has a limited short-term
memory (STM) capacity (7 ± 2 items) for list items, such as the
digits in a novel phone number (Brener, 1940 ; Miller, 1956). If human
STM is maintained by active firing as observed in prefrontal cortex of
the monkey (Goldman-Rakic, 1995; Fuster, 1997), there is a fundamental
problem of how to keep multiple memories separate. It has been
suggested that this is accomplished by a "buffer" (Atkinson and
Shiffrin, 1968), but the physiological mechanisms that would allow
multiple items to be stored in a buffer are not known. We have proposed (Lisman and Idiart, 1995; Jensen et al., 1996) that a single brain network can separately maintain up to seven memories by a multiplexing mechanism that uses theta (Gundel and Wilson, 1992; Mecklinger et al.,
1992; Nakamura et al., 1992; Iramina et al., 1996; Krause et al., 1996;
Sasaki et al., 1996; Gevins et al., 1997; Klimesch et al., 1997;
Tesche, 1997) and gamma (Galambos et al., 1981; Pantev et al., 1991;
Joliot et al., 1994; Tallon-Baudry et al., 1997, 1998) brain
oscillations for clocking. A memory is represented by groups of neurons
that fire in the same gamma cycle. Individual memories become serially
active in sequential gamma subcycles of a theta cycle (Fig.
1). This pattern of activation repeats on
subsequent theta cycles. We have previously shown that a multiplexing buffer of this kind can be plausibly realized by known biophysical mechanisms (Lisman and Idiart, 1995; Jensen and Lisman, 1996a; Jensen
et al., 1996). A key underlying idea is that a memory is represented by
cells firing within a gamma cycle, and different memory representations
are activated in different gamma cycles. Recent work by Wehr and
Laurent (1996) is consistent with the idea that gamma oscillations
serve as a clock for information processing. They showed that
components of sequences representing odors are active in successive
gamma cycles. Furthermore, modeling work shows that the phase advance
of hippocampal place cells can be quantitatively explained in terms of
expected positions read out in sequential gamma subcycles of a theta
cycle (Jensen and Lisman, 1996b).
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Figure 1.
Seven memories (A-G) are
multiplexed; memory A, represented by a certain spatial
pattern of cell firing (oval inset), is active in the first
gamma subcycle of a theta oscillation, followed by memory B
in the next gamma cycle, etc. After a dead time (d), the
seven memories repeat in the subsequent theta cycle.
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To further test the concept of a multiplexing buffer, we have asked
whether models of this kind can account quantitatively for data from
the Sternberg task (Sternberg, 1966). This task has been extensively
used to explore the timing of retrieval from STM, and there is general
agreement about the central findings. In the task, a list of items is
presented rapidly. A few seconds later, a probe item is presented, and
the subject answers as quickly as possible whether the probe was on the
list. A key finding consistent with serial memory scanning is that the
average reaction time (RT) increases linearly with the number of items
on the list (S). A second key finding is that the increase in RT with S
is the same for "yes" (positive probes) and "no" (negative
probes) answers. This observation led to the suggestion that the search
is exhaustive (Sternberg, 1966): the answer can apparently not be given
until the entire list is scanned.
In our initial effort to link STM to brain oscillations we pointed out
that the increase in RT with each additional item (the "slope" of
the Sternberg curves) approximates the period of one gamma cycle
(Lisman and Idiart, 1995). Furthermore, the number of gamma subcycles
that occur during a theta cycle (Bragin et al., 1995) is close to the
human memory span of 7 ± 2. It was these correspondences that
suggested that an oscillatory model based on theta and gamma
oscillations might organize STM. However, we did not show that an
oscillatory model could quantitatively explain the full RT
distributions and their dependence on S. This is one of the goals of
the current study.
A second goal has been to analyze one of the major objections to serial
scanning. A simple exhaustive scanning model would predict that the RT
is the same for all items stored in STM. However, a strong serial
position effect has been found if the retention interval between the
presentation of the list and the probe is <1.5 sec (Clifton and
Birenbaum, 1970; Burrows and Okada, 1971; Forrin and Cunningham, 1973):
subjects respond faster to items at the end of the list. We have found
that this data can be simply explained by short-term repetition priming
in the context of a serial scanning model.
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RESULTS |
We have sought to find oscillatory models that can account
quantitatively for the details of RT distributions in the Sternberg task. As found by Sternberg (1966), the linear increase in RT with
memory load (S) is ~38 msec/item (Fig.
2). The increment is the same for
negative and positive probes. Sternberg (1964) also found that not only
does the RT increase with S, but the variance and asymmetry (measured
by the third central moment) also increase with S (Fig. 2). The
cumulative RT distributions have been characterized by Ashby et al.
(1993). As seen in Fig. 3, the cumulative
distributions are systematically delayed as S gets larger. Thus the
mean RT increases with S. A final important feature of the Sternberg
data is the effect of serial position: subjects respond faster to a
probe that corresponds to an item late in the list (Forrin and
Cunningham, 1973). However, when the delay between the presentation of
the list and the probe becomes sufficiently long (>1.5 sec), the
serial position effect vanishes (see Fig. 10).
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Figure 2.
Adapting theta model fit (dashed lines)
to experimental data (solid lines) for mean, variance, and
skewness of the RT distribution for the Sternberg task. The data
obtained by Sternberg are responses to negative probes only. The best
fit using Equations 13, 15, and 16 resulted in the parameters
T = 22 msec; pa = 0.88; d = 80.1 msec;  motor = 57 msec;
and t0 = 215 msec. The fit was obtained by first
fitting the slopes of the increases with S and then fitting
motor and t0. Error bars indicate
SEs. Data are average of 10 subjects.
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Figure 3.
Adapting theta model (dashed lines)
fitted to the cumulative RT distribution for both positive and negative
probes (solid lines) measured by Ashby et al. (1993). By
applying a least mean square method the cumulative distributions (Eq. 18) were fitted. The four values of T are
kept constant across subjects and experiments. For simplicity,
motor is kept the same for all subjects.
pa and t0 are allowed to
vary individually. Fitted values for T
(S = 2, 3, 4, and 5) are 96, 119, 135, and 158 msec,
respectively.
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The oscillatory models that we have considered are all based on the
following principles: a memory is represented by a subset of neurons
firing within a gamma cycle (Fig. 1). When multiple memory
representations are being kept active during a retention period, they
are activated in successive gamma subcycles of a theta cycle. This
pattern repeats during each theta cycle (Fig. 4A). We have previously
implemented a physiologically plausible network model of such a buffer
(Lisman and Idiart, 1995; Jensen and Lisman, 1996a; Jensen et al.,
1996). This model is constructed of a network of excitatory and
inhibitory cells. The excitatory cells receive an external oscillatory
drive at theta frequency. Each of the excitatory cells have the
following properties: a cell will remain inactive until it is activated
by an external input triggering an action potential. After the action
potential follows a depolarizing ramp (afterdepolarizing potential),
which repeatedly brings the cell to fire in subsequent theta cycles. This allows the storage of a memory representation by repeated activation at theta rate. Each time a memory representation is activated the inhibitory cells in the network provide a hyperpolarizing feedback. This feedback, which produces the gamma oscillations, serves
to keep multiple memory representation separate in time. Recurrent
collaterals have synaptic weights that encode each item (but not the
unique sequence in the list) and enable the network to reactivate
memories in the correct sequence, even in the presence of noise.
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Figure 4.
Diagrams indicating definition of relevant times
and the concept of adapting theta. A, Three items
(A-C) are loaded; the theta period increases by one
gamma period as each additional item is loaded (Eq 1). After loading,
there is a delay period (tretention) in which
the items are maintained by activity-dependent intrinsic properties of
the neurons coding these items (Lisman and Idiart 1995; Haj-Dahmane and
Andrade, 1997). After probe presentation the items can be scanned,
i.e., compared with the probe as they are activated. Scanning must wait
until a trough of the theta cycle is reached, giving rise to a wait
time (twait). After scanning the motor
response is initiated at the first possible trough, contributing to the
time, tmotor. B, There is a high
probability, pa, that the answer will be
initiated after the first complete scan. If not, scanning will be
repeated and the response initiated at the end of the second scan with
probability pa (1  pa). The figure shows the probability of response
after n scans (a geometric distribution; Eq. 11). This
skipping process is responsible for the increase in skewness (third
moment) of the RT distribution with S.
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The RT in the Sternberg task can be described as the sum of various
components (Fig. 4A). In the Sternberg paradigm a
probe typically arrives 500-3000 msec
(tretention) after the end of item presentation
(typically 0.5-1.2 sec/item). This probe then has to be identified.
After the item is identified, we assume that there is a wait period
(twait) until the beginning (trough) of a theta
cycle. The probe is then serially compared with the items in
the buffer (scanning) as they are activated
(tscan). Finally, at the next trough the
answering process may be initiated as a motor process of duration
tmotor. In the simplest model, oscillations
would be unaffected by presentation of the probe, and theta frequency
would be independent of S. This last assumption means that even if only
two memories are held, there are five "empty" gamma cycles. In this
simple form the model cannot account for the increase in RT with S,
because none of the times depends on S. Alternatively scanning might be
initiated at the trough of a theta cycle and the motor response
delivered at the end of the last active gamma cycle (not at the
trough). In this model twait does not depend on
S but tscan does. This model can correctly reproduce the increase in RT with S, because
tscan depends on S. However, it cannot account
for the increase in variance with S, because the only term that depends
on S is tscan, which equals one theta cycle, and
this by definition has no variance. These examples illustrate how
models can fail to account for the detailed data. The next sections
describe two models that can account for the data. The mathematical
derivations are given in .
Model I: theta frequency depends on the number of memories being
stored (adapting theta model)
Figure 4A describes a model that successfully
accounts for the RT data. The theta period increases with the number of
items (S); i.e., the theta frequency decreases with S. Thus, a key
feature of this model is that there are no "empty" gamma cycles
even if the number of stored items is less than seven. When an
additional item is added to STM, the theta period increases so there is
an additional gamma cycle (up to a limit of seven for digits). Thus a
theta period (T) depends on the number of
gamma periods (T) per theta cycle:
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(1)
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Here d is a "dead time" denoting the part of the
trough of the theta oscillations where no memories are active (Fig. 1). Such "theta adaptation" is plausible given the observed frequency variability of brain theta oscillations: correlations between memory
tasks and oscillations have been observed in the 4-7 Hz band (Gevins
et al., 1997; Klimesch et al., 1997; Sarnthein et al., 1998) and also
at higher frequencies (10-12 Hz) (Krause et al., 1996). Note that in
contrast to the subsequent model, we assume here that the phase of
theta is not reset by the probe. Because T
varies with S, a wait time, twait, described by a uniform distribution (Eq. 8), is introduced. Thus, in this model both
mean and variance increase with S, in accord with the data.
The motor response is described by an exponential distribution with a
constant offset (Eq. 3), contributing tmotor to
the average RT. The motor response gives a constant contribution to the
variance of the RT distribution independent of S.
These assumptions alone predict a symmetrical RT distribution, but the
observed distribution is skewed and has a skewness that increases with
S (Fig. 2). To account for these features, we assumed that the
probability of giving an answer (pa) at the end
of a theta cycle is <1; if no answer is given, scanning is repeated
(Fig. 4B). We term this "skipping." The long RTs
produced by skipping will produce the skewness in the distribution. The longer the theta period, the longer the duration of a skip. Thus, this
effect can account for the increase in skewness with S (it also adds to
the mean and variance of the RT). From these assumptions the full RT
distribution can be derived (Eq. 17), as well as the mean, variance,
and skewness (Eqs. 13, 15, 16). These expressions can be fit to the
experimental data by finding the best parameters T, d, pa,
motor, and t0. The
constant t0 determines the offset of the
cumulative distribution and is defined in Equation 7. The dotted lines
in the graphs of Figure 2 are the best fit of this model and account
well for how the average, variance, and skewness of the RT distribution
increase with S. These data were provided to us by S. Sternberg
(University of Pennsylvania).
The model can also be tested against the data of Ashby et al. (1993),
which provides a complete RT distribution. In Figure 3 we have
replotted the RT distributions from Ashby et al. (1993) as cumulative
distributions. In fitting the data it was assumed for simplicity that
all subjects have the same theta period (T) for a given value of S. The free parameters are
T(S), which depends on
T and d, and
motor, t0, and
pa. The latter two are assumed to be unique for each
subject. The derived cumulative distributions were fit to the data
using a procedure that minimizes the least square error.
The cumulative distributions are well fit by the model for all values
of S and for all subjects (Fig. 3). The derived values of
T as a function of S obtained from the fits
are shown in Figure 5. Note that the
increase in theta with S is linear, even though all the theta values
were fit to individual values of S. As S varies, the theta period
varies from 96 to 158 msec (5.8-12.3 Hz). These numbers are in
plausible agreement with observed values in humans, which show
considerable variability [4-7 Hz (Klimesch et al., 1997), 5.9 Hz
(Gevins et al., 1997), 4-7 Hz (Sarnthein et al., 1998), 10-12 Hz
(Krause et al., 1996)]. The gamma period (T)
is the slope of the increase in T with S, and
the dead time (d) is the intercept (Fig. 5). The frequency of gamma derived in this way is 49 Hz, consistent with typical values
of gamma frequency (Galambos et al., 1981; Pantev et al., 1991;
Joliot et al., 1994; Singer and Gray, 1995; Tallon-Baudry et al.,
1997, 1998). The dead time d is 75.5 msec.
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Figure 5.
Theta values obtained from the fits in Figure 3
increase linearly with S. The slope and intercept of the best fit
(dashed line) determine the gamma frequency and dead time:
T = 20.2 msec; and d = 75.5
msec.
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Note that we obtained all the fits keeping the theta period at each S
(and hence the gamma period) the same for all the subjects. Hence
individual differences were accounted for by variation in t0 and pa, both of which
are assumed to be independent of S. The variations in
t0 might simply reflect individual differences
in the rapidity of motor processes. Individual differences in
attentiveness might explain variations in
pa.
Model II: reset of the slow-wave oscillation
We next asked whether it was possible to find a satisfactory model
in which theta adaptation did not occur. This implies that when the
buffer has fewer items than seven there will be empty "slots" (Fig.
6A). As stated
previously, simple models without theta adaptation do not work. We have
considered the possibility that the phase of ongoing theta oscillations
is "reset" each time a memory set is scanned. There is evidence for
the reset of the theta oscillations in some brain regions (Berger et
al., 1983; Rahn and Basar 1993a,b; Brankack et al., 1996; Brandt 1997).
We assume that the reset is controlled by the external mechanism driving the network at the theta rhythm. We have further assumed that
the reset does not occur during the part of the theta cycle when the
memories are actively being read out, because this would distort order
information. If the probe identification is completed at a time when
memories are being reactivated at gamma frequency, reset has to wait
(twait) until after activation of the last item (Fig. 6B, 1). Otherwise the reset occurs immediately
(Fig. 6B, 2).
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Figure 6.
Reset model for RT in the Sternberg task.
A, As for the adapting theta model, memories are loaded into
the STM and kept active on subsequent theta cycles. In the reset model
the theta frequency is independent of the memory load. After the probe
arrives the theta oscillation is reset before scanning begins.
B, Wait time (twait) of the reset
model. If the probe arrives when memories are actively read out, reset
is delayed until after the last item (1). Otherwise, reset
occurs immediately (2). This principle introduces a wait
time described by Equation 23. The wait time contributes to the
increase in variance with S but also the mean RT. C, As in
the adapting theta model, skipping occurs if an answer is not available
after the first scan trough. In this case the slow-wave oscillation is
reset again, and another scan is initiated. This process is described
by Equation 25 and accounts for the increase in skewness with S.
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After reset, scanning occurs from the trough to the end of the list
(Fig. 6A). Thus, both twait
and tscan depend on S. This gives rise to an
increase in RT with S, which is approximately linear. It further
follows that the wait time (Fig. 6B) increases with S
(Eq. 24). The random variation in twait accounts
for the major part of the increase in variance of RT with S. As in the previous model, a skipping process is assumed to account for the skewness of the distribution. The probability of the answer being given
after the first scan is pa (Fig. 6C).
If for some reason the answer is not given, another scan is initiated
after the theta oscillation has been reset. This produces the
increasing asymmetry of the RT distribution with S (Eq. 25). The
complete expressions for the mean, variance, and asymmetry (third
central moment) are given by Equations 27, 29, and 30, with the free
parameters motor, t0,
pa, T, and d. The
full RT distribution is given by Equation 31. Note that the final
increase in RT with S has a second-order term (Eq. 28) because of the
distribution of the wait time. However, for realistic parameter values,
the increase in RT with S is approximately linear.
The three expressions fit quite well to the data of Sternberg (Fig.
7). The fit is, however, not unique; we
can vary the dead time, d (see Eq. 20), in the interval from
10 to 100 msec and still obtain fits to the Sternberg data within the
SEs. The resulting values for f, f,
and pa are shown in Figure
8. Note that pa
and f do not depend significantly on
d, whereas f does. The dead time
mainly adds to the theta period, but because scanning occurs from the
trough to the end of the list, this does not change the retrieval
properties of the model significantly.
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Figure 7.
Reset model (broken lines) fitted to
the moments (mean, variance, and skewness) of the RT distributions
(solid lines) from the data provided by Sternberg. The best
fit to Equations 27, 29, and 30 resulted in the parameters
T = 143 msec; pa = 0.78; t0 = 300 msec; and motor = 70 msec. d was fixed to 15.0 msec.
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Figure 8.
How varying d influences the
parameters. d was fixed in the interval from 10 to 100 msec,
and the other parameters were fitted to the Sternberg data in Figure 7.
The fits remained well within the experimental SEs. Note that only
f varies strongly on d.
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As for the previous model, we have derived the expressions for the
cumulative RT distributions to fit the data of Ashby et al. (1993)
(Fig. 9). In this case
T and motor are kept the same
for the four subjects, and t0 and
pa are unique for each subject. d was
fixed to 15 msec and Sspan = 7.
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Figure 9.
Reset model (dashed lines; Eq. 31)
fitted to the cumulative RT distribution (solid lines)
provided by Ashby et al. (1993). pa and
t0 varied in between subjects, whereas
motor and T were the same for
all subjects. The dead time was fixed to d = 15.0
msec.
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We conclude that the reset model accounts for the RT data just as well
as the adapting theta model. We are therefore not able to distinguish
between the two models on the basis of the psychophysical data only. As
will be discussed later, electrophysiological recordings on subjects
performing the Sternberg task could be used to distinguish the two models.
Accounting for serial position effect
A major objection to serial scanning has been the existence of
serial position effects: RT is systematically longer for early list
items than late items (Fig. 10,
first panel). Superficially, this is inconsistent
with a scanning process in which each item is handled similarly. An
important hint about the basis of this effect is that it disappears if
the retention interval between list presentation and the probe is >1.5
sec (Fig. 10). This suggests that the serial position effect is not
fundamental to scanning itself. For positive items, the probe is a
repetition of a just-presented item, and we propose that the serial
position effect is a consequence of short-term repetition priming
(Bertelson and Renkin, 1966; Posner and Keele, 1967; Smith et al.,
1973; McKone 1995); the time needed to identify the probe
(tidentify) is decreased if the item has been
presented in the last few seconds. We have assumed that this priming
decays exponentially (prime; Eq. 33, Fig.
11). The time between the presentation
of a memory item and the probe is a function of both the presentation
rate, frate, and the retention interval,
tretention. The average time to identify the
probe (tidentify) is determined by Equation 35.
Figure 10 shows that with a value of prime = 1.2 sec,
this model nicely accounts for the serial position effects for various
retention times.
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Figure 10.
Data from Forrin and Cunningham (1973), showing
that short-term repetition priming can explain serial position effects.
The shorter the delay between presentation of list items and the probe
(tretention), the faster the RT (recency), as
shown by the solid lines. By modeling the priming by a
simple exponential (Fig. 11), recency is fit reasonably well
(broken lines). Best fit (least mean square):
prime = 1181 msec and  = 250 msec. Response times are
plotted relative to serial position 1.
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Figure 11.
Repetition priming is modeled as a single
exponential (Eq. 33). A positive probe is primed by the previous
occurrence of the similar item during presentation. This reduces the
time to identify the probe. Negative probes are not primed.
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Some experiments show that the average response to positive probes is
slightly faster than for negative probes (Burrows and Okada, 1971;
Corballis et al., 1972). This feature can be explained by repetition
priming as well: only positive probes are primed and hence have a
faster RT. Figure 12 shows how the
adapting theta model captures this effect when a 500 msec retention
interval is used. The RT for positive items is ~60-70 msec faster
than for negative items. From Figure 12 it can also be seen that the model predicts that the slope for positive items is 50% higher than
the slope for negative items. According to our model this is a direct
consequence of the priming effect resulting in faster RTs for positive
items late is the list than items earlier in the list. This prediction
is consistent with some experimental data in which fast presentation
rates and short retention intervals were applied. Corballis et al.
(1972) found that positive probes had 49% higher slopes than negative
probes. Burrows and Okada (1971) found the value to be 18%. Many
factors can contribute to the differences in the ratios, such as
presentation rate and training of the subjects.
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Figure 12.
Repetition priming explains why the RT for
positive items is faster than for negative items (which lack priming).
Also, the slope of the RT curve for positive items should be slightly
steeper than for negative items. The graph shows the mean RT calculated
using Equations 21 and 36 for t0. The parameters
from the fit in Figure 7 were used, except t0 = 70 msec. For the priming mechanism we used = 1200 msec and = 250 msec. The presentation rate was frate = 1/1200 msec 1; the probe delay was
tprobe = 500 msec.
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DISCUSSION |
Two oscillatory buffer models explain the RT distributions
We have found two models of a multiplexing buffer that can account
quantitatively for the RT distributions of the Sternberg paradigm.
Retrieval in these models is based on exhaustive serial search. The
models fit both the moments of the RT distributions measured by
Sternberg (1964) and the actual distributions measured by Ashby et al.
(1993). They can account for the changes in these distributions with
memory load and can be applied to different subjects without having to
assume differences in fundamental oscillatory frequencies. The two
models differ with regard to theta adaptation and phase reset. In the
first model (adapting theta) the theta period varies with the number of
items in STM, but there is no reset of the oscillations when the probe
arrives. In the second model, the theta period is constant, but the
oscillation is phase-reset by the probe. We later discuss how these
assumptions can be tested.
Table 1 summarizes the fitted values for
the two models. With respect to the gamma frequency the two models give
values in the same range (46-59 Hz). These values are in good
agreement with experimentally observed data (Galambos et al., 1981;
Pantev et al., 1991; Joliot et al., 1994; Singer and Gray, 1995;
Tallon-Baudry et al., 1997, 1998). In the adapting theta model,
slow-wave frequency depends on S and varies from 6 to 10 Hz, i.e.,
covering both the defined theta and alpha bands. Note that both the
Sternberg and Ashby data sets give rise to very similar values. The
reset model does not strongly constrain the value of the theta
frequency and allows frequencies in the interval from 4 to 7 Hz.
A key feature of the data that determines the value of gamma frequency
is the systematic changes in the rising edge of the cumulative response
time distribution with increasing S (Fig. 3). This is the closest
psychophysics comes to direct detection of gamma frequency. However, an
important conclusion of our work is that deriving gamma from the data
requires a full model. We originally thought that the Sternberg slope
(average increase in reaction time per item) might directly correspond
to the gamma period (Lisman and Idiart, 1995). However, the models
presented here show the correspondence is only approximate. This is
because slope measurements are based on average RT, but this average is determined not only by T but also the wait
time and skipping (Eqs. 13 and 27). Consequently, the slope is
~1.5-2 higher than the gamma period.
The rising edge of the cumulative response distributions of a task
related to the Sternberg paradigm, the speed-accuracy trade-off (SAT) (McElree and Dosher, 1989), does not have a latency
depending on S, whereas the Sternberg task does (Fig. 3). The SAT data
have been taken as an argument against serial scanning. However, the SAT methodology is different from conventional recognition memory paradigms in ways we believe limit the conclusions that can be drawn.
In this test, the subject is urged to respond at some fixed time after
the presentation of the test item by a signal to respond. The presence
of this signal and its processing introduce processing problems not
present in the Sternberg paradigm. Second, although the signal to
respond is given at a precise time, the subsequent time to respond is
not precise. This could be enforced by only considering responses given
with a precise latency but is not. Because of this ambiguity, the
method may not be able to resolve small relevant delays on the order of
30 msec.
Several other models have been proposed that can account for the main
features of the RT distribution and the serial position effects.
Cavanagh (1976) has investigated trace strength models and holographic
models, which both accounted for the increase in RT with S and serial
position effects of the Sternberg paradigm. Ratcliff (1978) and Hockley
and Murdock (1987) suggested decision type models, which also
successfully accounted for the RT distributions and serial position
effects. However, none of these theories has been implemented in a
physiologically realistic way.
Possible rationale for exhaustive search
Sternberg concluded that memory search was exhaustive because RT
depended similarly on S for positive probes as for negative probes (for
which search is necessarily exhaustive). Because it would seem more
efficient for the motor response to begin as soon as a positive match
occurred (i.e., nonexhaustive search), some have argued that exhaustive
search is implausible. Our oscillatory model, however, provides a
plausible explanation for exhaustive search. All that needs to be
assumed is that initiation of the motor response can only occur at the
trough of the theta cycle. There are several examples in the literature
of the importance of theta phase for information processing (Pavlides
et al., 1988; O'Keefe and Recce, 1993; Nicolelis et al., 1995; Huerta
and Lisman, 1996).
Physiological tests for distinguishing between the models
The adapting theta model can be tested by analyzing EEG,
magnetoencephalography (MEG) and/or intracranial recordings on
subjects performing the Sternberg task. Results from imaging studies
suggest that prefrontal and parietal cortex are involved in the active maintenance of STM (Shallice and Vallar, 1990; Cohen et al., 1997a,b; Jonides et al., 1998). We therefore expect to observe the predicted changes in theta and gamma oscillations in these areas. If the model is
correct, the slow-wave oscillation during the retention period should
systematically decrease in frequency with higher memory loads.
Oscillations in the theta band have been identified in humans
performing STM tasks using both EEG and MEG recordings (Gundel and
Wilson, 1992; Mecklinger et al., 1992; Gevins et al., 1997; Klimesch et
al., 1997; Sarnthein et al., 1998). The band in which theta
oscillations have been observed is sufficiently broad to allow the
predicted adaptation with memory loads, but whether these variations
are related to memory load remains to the tested.
The two models make different predictions about the effect of S on
overall neuronal firing and thus on the signals detected by
brain-imaging methods. In the reset model, the fraction of the theta
period being occupied by active memory representations increases with
S. Consequently, the number of activated neurons per theta cycle will
increase linearly with S (Fig. 13). In
contrast, the adapting theta model predicts a sublinear increase with S (Fig. 13). These predictions may be relevant in interpreting the data
of Cohen et al. (1997a,b), which showed that memory load (S) increases
functional MRI signals in prefrontal cortex, parietal areas, and
Broca's area.
View larger version (19K):
[in this window]
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|
Figure 13.
Both of the proposed models predict an increase
in overall neuronal activity with S. The constant theta model predicts
a linear increase attributable to temporal summation of neurons
participating in the memory representation. In the adapting theta
model, a sublinear increase is expected: activation = [T(S 1)]/[T(S 1) + d].
|
|
Examination of the load dependence of EEG amplitude may provide another
way of distinguishing the models. The factors controlling the amplitude
of EEG are unclear, but it seems plausible that amplitude would vary
with the number of neurons that fire within an oscillatory cycle. Hence
one might expect the theta amplitude to increases with S. A study by
Gevins et al. (1997) points in this direction: in an n-back
task a higher power of frontal-midline theta was observed for
n = 3 than for n = 1.
A critical distinction between the adapting theta and reset models may
be made by studying the reset of the slow-wave oscillations after the
arrival of the probe. When S is small, there will be a fairly large
period during which there will be no cells firing. If the end of item
identification occurs during this period, the phase of oscillation will
be reset, and the resulting waveforms will be synchronized with the
probe onset. Although there will also be a less synchronized component
(if identification occurs during firing), the synchronous component
will be identifiable as an oscillation in the averaged EEG, the evoked
potential. Such a signal would not be generated if the adapting theta
model is correct. Several groups (Rahn and Basar, 1993a,b; Brandt,
1997) have reported components in the range of averaged EEG traces after simple stimuli, suggesting reset of the slow-wave oscillations.
Short-term repetition priming can account for serial
position effects
Serial position effects have been used as an argument against
serial scanning. However, if the time for encoding of the probe can be
primed by previous exposure, our model can account quantitatively for
the serial position effect and retain the idea of serial scanning. The
decay of priming with = 1.2 sec explains why the serial position
effect becomes smaller for longer retention intervals. Furthermore,
priming explains why reaction times are shorter for positive than
negative probes, and why the RT slope (increase in RT with S) is
slightly steeper for positive than for negative probes (Fig. 12).
Short-term repetition priming with a duration of a few seconds has been
observed in other psychophysical tests not necessarily related to
memory paradigms (Bertelson and Renkin, 1966; Posner and Keele, 1967;
Smith et al., 1973; McKone, 1995). Monsell (1978) showed that if an
item has been used as a negative probe in the previous trial, the
response time increases in the subsequent trial if the same item is
used as a positive probe. This finding has been used to argue against
priming as an explanation for the serial position effect. However, this
effect occurs over 10-15 sec, whereas repetition priming decays in a
few seconds; hence different mechanisms may be involved.
Our proposal that priming of the encoding of the probe accounts for
serial position effects (Fig. 10) leads to further predictions within
the context of the reset model. A reset of the theta cycle follows the
arrival of the probe. This reset will occur earlier for probes matching
items late in the list compared with items early in the list. It should
thus be interesting to look for the effect of serial position on the
latency of evoked potentials.
In conclusion, we have found that a physiologically realistic model of
serial memory search can account quantitatively for a large body of the
data on STM. Furthermore, we have been able to counter some of the
major objections to exhaustive serial search. Although it is certainly
true that brain computations can occur in parallel, our results suggest
that there may also be an important role for serial processing.
| |
FOOTNOTES |
Received June 9, 1998; revised Sept. 25, 1998; accepted October 1, 1998.
This work was supported by National Science Foundation Grant
IBN-9723466 and the Alfred P. Sloan Foundation. We gratefully acknowledge the support from the W. M. Keck Foundation. We thank Michael Kahana (Brandeis University) and Saul Sternberg (University of
Pennsylvania) for many helpful discussions. Saul Sternberg has kindly
provided us with his data on the moments of the RT distributions
(Sternberg, 1964), and Greg Ashby (University of California, Santa
Barbara) and Jerry Balakrishnan (Purdue University) have
provided us with the full data set of the RT distributions (Ashby et
al., 1993).
Correspondence should be addressed to Dr. John E. Lisman, Volen Center
for Complex Systems, Brandeis University, Waltham, MA 02243.
| |
APPENDIX |
Derivation of RT distribution for model I
In the first model the theta period (T)
depends on the memory load (S) and dead time (d) according
to Equation 1.
The average reaction time (RT) is the sum of the following terms (see
Fig. 4A):
|
(2)
|
The motor response is simply described by an exponential
distribution:
|
(3)
|
where the contribution to RT is the mean of this distribution:
|
(4)
|
The time from presentation of a memory item until it is available
for insertion into the oscillatory buffer is termed
tidentify. This variable is as a
first-assumption constant:
|
(5)
|
For convenience we define
|
(6)
|
where
|
(7)
|
The probe can become available anywhere within a theta cycle and a
wait time is introduced, described by a uniform distribution:
|
(8)
|
with the mean
|
(9)
|
The memories in the buffer are scanned from trough to trough:
|
(10)
|
where T is defined by Equation 1. The
probability that an answer is available after scanning trough the first
possible theta cycle is pa. In case an answer is
not available, another scan has to be performed, and so forth. Hence
the probability that a response is initiated in theta cycle
n is described by a geometric distribution:
![p<SUB><UP>skip</UP></SUB>(t)=p<SUB><UP>a</UP></SUB>(1−p<SUB><UP>a</UP></SUB>)<SUP>n</SUP>, <UP>where</UP> n=[t/T<SUB>&thgr;</SUB>], t>0.](/content/vol18/issue24/fulltext/10688/img011.gif)
|
(11)
|
This contributes to the mean of RT as
|
(12)
|
Finally, the mean of RT is obtained from the sum of Equations 6,
10, 9, and 12:
|
(13)
|
The slope of RT with S is given by
|
(14)
|
The variance of the response time distribution is the sum of
variances from the distributions in Equations 3, 8, and 11:
|
(15)
|
Only Equations 3 and 11 contribute to the third central moment
measuring skewness:
|
(16)
|
By convolving the distributions, Equations 3, 8, and 11, the full
expression for the RT distribution is obtained:
|
(17)
|
The cumulative distributions is:
|
(18)
|
In this paper we calculated the full distribution by numerical
integration. Both the moments (Eqs. 13, 15, and 16) and the expressions for the cumulative distribution (Eq. 18) have been fitted to the psychophysical data. The parameters to determine are
motor, t0, pa, T, and d. To
fit the moments of the Sternberg data (1964), we first obtained the
linear slopes (obtained by regression) of the mean, variance, and third
central moments of both the data and the model. In the fitting
algorithm the differences between the weighted slopes,
|
(19)
|
were minimized by adjusting T, d, and
pa. Then motor and
t0 were adjusted to fit the intercepts of the
moments. The cumulative distributions (18) were directly fitted to the
data of Ashby et al. (1993).
Derivative of RT distribution for model II
In this model the period of the slow-wave oscillation
(T) is constant. It is derived from the
gamma period (Tgamma), dead time (d),
and the maximum memory span, which is set to
Sspan = 7:
|
(20)
|
Again the average reaction time (RT) is the sum of the following
terms:
|
(21)
|
Scanning occurs from the trough to the end of the list, so:
|
(22)
|
Reset of the theta oscillation after arrival of the probe is
assumed. The reset, however, cannot occur when a set of memories are
actively read out, because this will distort order information. This
principle introduces a wait time determined by
|
(23)
|
with the mean
|
(24)
|
 (t) denotes the delta function. The argument for the
skipping mechanism is the same as in Equation 11, with the additional assumption that the theta oscillation is reset after a skip:
![p<SUB><UP>skip</UP></SUB>(t)=p<SUB><UP>a</UP></SUB>(1−p<SUB><UP>a</UP></SUB>)<SUP>n</SUP>, <UP>where</UP> n=[t/t<SUB><UP>scan</UP></SUB>], t>0.](/content/vol18/issue24/fulltext/10688/img025.gif)
|
(25)
|
This contributes to RT as
|
(26)
|
Finally, the mean of the response time distribution is obtained by
Equations 6, 22, 24, and 26:
|
(27)
|
The increase in RT with S takes the form
|
(28)
|
This expression approximates a linear increase with S for
reasonable values of T and
T. The variance of the response time
distribution is the sum of variances from Equations 3, 23, and 25:
|
(29)
|
The third central moment stems from the motor response (Eq. 3) and
skipping (Eq. 25):
|
(30)
|
The parameters to determine are motor,
t0, pa,
d, and T. The fitting method is
the same as for the adapting theta model.
As for the adapting theta model an expression for the full RT
distribution can be obtained by convolving the individual distributions (Eqs. 3, 23, 25):
|
(31)
|
Serial position
The time to identify a positive probe is shortened (primed) by the
recent introduction of the equivalent item during presentation of the
list. The time between the presentation of item i and the probe is given by:
|
(32)
|
where frate is the presentation rate of the
items, and tprobe is the delay between
presentation of the last items and arrival of the probe. We assume that
the time it takes to identify an item is determined by an exponentially
saturating function:
|
(33)
|
where t denotes the time since previous presentation.
Hence the time to identify item i is:
|
(34)
|
The average identification time for a set of S items is then:
|
(35)
|
Note that tidentify = + cprime for negative probes, and
tretention  prime. When
applying the priming mechanism to the models, Equation 6 is rewritten
to:
|
(36)
|
where
|
(37)
|
| |
REFERENCES |
-
Ashby FG,
Tein J,
Balakrishnan JD
(1993)
Response time distributions in memory scanning.
J Math Psychol
37:526-555.
-
Atkinson RC,
Shiffrin RM
(1968)
Human memory: a proposed system and its control processes.
In: The psychology of learning and motivation: advances in research and theory, Vol. 2 (Spence KW,
ed). New York: Academic.
-
Berger TW,
Rinaldi PC,
Weisz DJ,
Thompson RF
(1983)
Single-unit analysis of different hippocampal cell types during classical conditioning of rabbit nictitating membrane response.
J Neurophysiol
50:1197-1219[Abstract/Free Full Text].
-
Bertelson P,
Renkin A
(1966)
Reaction times to new versus repeated signals in a serial task as a function of response-signal time interval.
Acta Psychol
25:132-136.
-
Bragin A,
Jando G,
Nadasdy Z,
Hetke J,
Wise K,
Buzsaki G
(1995)
Gamma (40-100 Hz) oscillation in the hippocampus of the behaving rat.
J Neurosci
15:47-60[Abstract].
-
Brandt ME
(1997)
Visual and auditory evoked phase resetting of the alpha EEG.
Int J Psychophysiol
26:285-298[Web of Science][Medline].
-
Brankack J,
Seidenbecher T,
Muller-Gartner HW
(1996)
Task-relevant late positive component in rats: is it related to hippocampal theta rhythm?
Hippocampus
6:475-482[Web of Science][Medline].
-
Brener R
(1940)
An experimental investigation of memory span.
J Exp Psychol
26:467-482[Web of Science].
-
Burrows D,
Okada R
(1971)
Serial position effects in high-speed memory search.
Percept Psychophys
10:305-308[Web of Science].
-
Cavanagh P
(1976)
Holographic and trace strength models of rehearsal effects in the item recognition task.
Mem Cognit
4:186-199.
-
Clifton C,
Birenbaum S
(1970)
Effects of serial position and delay of probe in memory scan task.
J Exp Psych
86:69-76.
-
Cohen JD,
Nystrom LE,
Sabb FW,
Braver TS,
Noll DC
(1997a)
Tracking the dynamics of fMRI activation in humans under manipulations of duration and intensity of working memory processes.
Soc Neurosci Abstr
23:1678.
-
Cohen JD,
Perlstein WM,
Braver TS,
Nystrom LE,
Noll DC,
Jonides J,
Smith EE
(1997b)
Temporal dynamics of brain activation during a working memory task.
Nature
386:604-608[Medline].
-
Corballis MC,
Kirby J,
Miller A
(1972)
Access to elements of a memorized list.
J Exp Psychol
94:185-190.
-
Forrin B,
Cunningham K
(1973)
Recognition time and serial position of probed item in short-term memory.
J Exp Psychol
99:272-279.
-
Fuster JM
(1997)
Network memory.
Trends Neurosci
20:451-459[Web of Science][Medline].
-
Galambos R,
Makeig S,
Talmachoff PJ
(1981)
A 40-Hz auditory potential recorded from the human scalp.
Proc Natl Acad Sci USA
78:2643-2647[Abstract/Free Full Text].
-
Gevins A,
Smith ME,
McEvoy L,
Yu D
(1997)
High-resolution EEG mapping of cortical activation related to working memory: effects of task difficulty, type of processing, and practice.
Cereb Cortex
7:374-385[Abstract/Free Full Text].
-
Goldman-Rakic PS
(1995)
Cellular basis of working memory.
Neuron
14:477-485[Web of Science][Medline].
-
Gundel A,
Wilson GF
(1992)
Topographical changes in the ongoing EEG related to the difficulty of mental tasks.
Brain Topogr
5:17-25[Medline].
-
Haj-Dahmane S,
Andrade R
(1997)
Calcium-activated cation nonselective current contributes to the fast afterdepolarization in rat prefrontal cortex neurons.
J Neurophysiol
78:1983-1989[Abstract/Free Full Text].
-
Hockley WE,
Murdock Jr BB
(1987)
A decision model for accuracy and response latency in recognition memory.
Psyc Rev
94:341-358.
-
Huerta PT,
Lisman JE
(1996)
Bidirectional synaptic plasticity induced by a single burst during cholinergic theta oscillation in CA1 in vitro.
Neuron
15:1053-1063.
-
Iramina K,
Ueno S,
Matsuoka S
(1996)
MEG and EEG topography of frontal midline theta rhythm and source localization.
Brain Topography
8:329-331[Web of Science][Medline].
-
Jensen O,
Lisman JE
(1996a)
Novel lists of 7 ± 2 known items can be reliably stored in an oscillatory short-term memory network: interaction with long-term memory.
Learn Mem
3:257-263[Abstract/Free Full Text].
-
Jensen O,
Lisman JE
(1996b)
Hippocampal CA3 region predicts memory sequences: accounting for the phase precession of place cells.
Learn Mem
3:279-287[Abstract/Free Full Text].
-
Jensen O,
Idiart MAP,
Lisman JE
(1996)
Physiologically realistic formation of autoassociative memory in networks with theta/gamma oscillations: role of fast NMDA channels.
Learn Mem
3:243-256[Abstract/Free Full Text].
-
Joliot M,
Ribary U,
Llinas R
(1994)
Human oscillatory brain activity near Hz coexists with cognitive temporal binding.
Proc Natl Acad Sci USA
91:11748-11751[Abstract/Free Full Text].
-
Jonides J,
Schumacher EH,
Smith EE,
Koeppe RA,
Awh E,
Reuter-Lorenz PA,
Marshuetz C,
Willis CR
(1998)
The role of parietal cortex in verbal working memory.
J Neurosci
18:5026-5034[Abstract/Free Full Text].
-
Klimesch W,
Doppelmayr M,
Schimke H,
Ripper B
(1997)
Theta synchronization and alpha desynchronization in a memory task.
Psychophysiology
34:169-176[Web of Science][Medline].
-
Krause CM,
Lang AH,
Laine M,
Kuusisto M,
Pörn B
(1996)
Event-related EEG desynchronization and synchronization during an auditory memory task.
Electroencephalogr Clin Neurophysiol
98:319-326[Web of Science][Medline].
-
Lisman JE,
Idiart MAP
(1995)
Storage of 7 ± 2 short-term memories in oscillatory subcycles.
Science
267:1512-1514[Abstract/Free Full Text].
-
McElree B,
Dosher BA
(1989)
Serial position and set size in short-term memory: the time course of recognition.
J Exp Psychol
118:346-373.
-
McKone E
(1995)
Short-term implicit memory for words and nonwords.
J Exp Psychol Learn Mem Cogn
21:1108-1126[Web of Science].
-
Mecklinger A,
Kramer AF,
Strayer DL
(1992)
Event related potentials and EEG components in a semantic memory search task.
Psychophysiology
29:104-119[Web of Science][Medline].
-
Miller GA
(1956)
The magical number seven plus or minus two.
Psychol Rev
63:81-97[Web of Science][Medline].
-
Monsell S
(1978)
Recency, immediate recognition memory, and reaction time.
Cognit Psychol
10:465-501[Web of Science].
-
Nakamura K,
Mikami A,
Kubota K
(1992)
Oscillatory neural activity related to visual short-term memory in monkey temporal pole.
NeuroReport
3:117-120[Web of Science][Medline].
-
Nicolelis MA,
Baccala LA,
Lin RC,
Chapin JK
(1995)
Sensorimotor encoding by synchronous neural ensemble activity at multiple levels of the somatosensory system.
Science
268:1353-1358[Abstract/Free Full Text].
-
O'Keefe J,
Reece ML
(1993)
Phase relationship between hippocampal place units and the EEG theta rhythm.
Hippocampus
3:317-330[Web of Science][Medline].
-
Pantev C,
Makeig S,
Hoke M,
Galambos R,
Hampson S,
Gallen C
(1991)
Human auditory evoked gamma-band magnetic fields.
Proc Natl Acad Sci USA
88:8996-9000[Abstract/Free Full Text].
-
Pavlides C,
Greenstein YJ,
Grudman M,
Winson J
(1988)
Long-term potentiation in the dentate gyrus is induced preferentially on the positive phase of theta-rhythm.
Brain Res
439:383-387[Web of Science][Medline].
-
Posner IP,
Keele SW
(1967)
Decay of visual information from a single letter.
Science
158:137-139[Abstract/Free Full Text].
-
Rahn E,
Basar E
(1993a)
Prestimulus EEG-activity strongly influences the auditory evoked vertex response: a new method for selective averaging.
Int J Neurosci
69:207-220[Medline].
-
Rahn E,
Basar E
(1993b)
Enhancement of visual evoked potentials by stimulation during low prestimulus EEG stages.
Int J Neurosci
72:123-136[Web of Science][Medline].
-
Ratcliff R
(1978)
A theory of memory retrieval.
Psychol Rev
85:59-108[Web of Science].
-
Sarnthein J,
Petsche H,
Rappelsberger P,
Shaw GL,
von Stein A
(1998)
Synchronization between prefrontal and posterior association cortex during human working memory.
Proc Natl Acad Sci USA
95:7092-7096[Abstract/Free Full Text].
-
Sasaki K,
Tsujimoto T,
Nishikawa S,
Nishitani N,
Ishihara T
(1996)
Frontal mental theta wave recorded simultaneously with magnetoencephalography and electroencephalography.
Neurosci Res
26:79-81[Web of Science][Medline].
-
Shallice T,
Vallar G
(1990)
The impairment of auditory-verbal short-term storage.
In: Neuropsychological impairments of short-term memory (Vallar G,
Shallice T,
eds), pp 11-53. Cambridge, UK: Cambridge UP.
-
Singer W,
Gray CM
(1995)
Visual feature integration and the temporal correlation hypothesis.
Annu Rev Neurosci
18:555-586[Web of Science][Medline].
-
Smith EE,
Chase WG,
Smith PG
(1973)
Stimulus and response repetition effects in retrieval from short-term memory.
J Exp Psychol
98:413-422.
-
Sternberg S (1964) Estimating the distribution of additive
reaction-time components. Paper presented at Psychometric Society
Meeting, Ontario, Canada, October.
-
Sternberg S
(1966)
High speed scanning in human memory.
Science
153:652-654[Abstract/Free Full Text].
-
Tallon-Baudry C,
Bertrand O,
Delpuech C,
Pernier J
(1997)
Oscillatory
 -band activity induced by a visual search task in humans.
J Neurosci
17:722-734[Abstract/Free Full Text]. -
Tallon-Baudry C,
Bertrand O,
Peronnet F,
Pernier J
(1998)
Induced -band activity during the delay of a visual short-term memory task in humans.
J Neurosci
18:4244-4254[Abstract/Free Full Text].
-
Tesche CD
(1997)
Non-invasive detection of ongoing neuronal population activity in normal human hippocampus.
Brain Res
749:53-60[Web of Science][Medline].
-
Wehr M,
Laurent G
(1996)
Odor encoding by temporal sequences of firing in oscillating neural assemblies.
Nature
384:162-166[Medline].
Copyright © 1998 Society for Neuroscience 0270-6474/98/182410688-12$05.00/0
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|
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O. Jensen, J. Gelfand, J. Kounios, and J. E. Lisman
Oscillations in the Alpha Band (9-12 Hz) Increase with Memory Load during Retention in a Short-term Memory Task
Cereb Cortex,
August 1, 2002;
12(8):
877 - 882.
[Abstract]
[Full Text]
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E. Fransen, A. A. Alonso, and M. E. Hasselmo
Simulations of the Role of the Muscarinic-Activated Calcium-Sensitive Nonspecific Cation Current INCM in Entorhinal Neuronal Activity during Delayed Matching Tasks
J. Neurosci.,
February 1, 2002;
22(3):
1081 - 1097.
[Abstract]
[Full Text]
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J. B. Caplan, J. R. Madsen, S. Raghavachari, and M. J. Kahana
Distinct Patterns of Brain Oscillations Underlie Two Basic Parameters of Human Maze Learning
J Neurophysiol,
July 1, 2001;
86(1):
368 - 380.
[Abstract]
[Full Text]
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S. Raghavachari, M. J. Kahana, D. S. Rizzuto, J. B. Caplan, M. P. Kirschen, B. Bourgeois, J. R. Madsen, and J. E. Lisman
Gating of Human Theta Oscillations by a Working Memory Task
J. Neurosci.,
May 1, 2001;
21(9):
3175 - 3183.
[Abstract]
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C. D. Tesche and J. Karhu
Theta oscillations index human hippocampal activation during a working memory task
PNAS,
January 18, 2000;
97(2):
919 - 924.
[Abstract]
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Top
Abstract
Introduction
