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Choke or Thrive? The Relation Between Salivary Cortisol and Math
Performance Depends on Individual Differences in
Working Memory and Math-Anxiety
Andrew Mattarella-Micke and Jill Mateo
The University of Chicago Megan N. Kozak
Katherine Foster and Sian L. Beilock
The University of Chicago
In the current study, we explored how a person’s physiological arousal relates to their performance
in a challenging math situation as a function of individual differences in working memory (WM)
capacity and math-anxiety. Participants completed demanding math problems before and after which
salivary cortisol, an index of arousal, was measured. The performance of lower WM individuals did
not depend on cortisol concentration or math-anxiety. For higher WM individuals high in math-
anxiety, the higher their concentration of salivary cortisol following the math task, the worse their
performance. In contrast, for higher WM individuals lower in math-anxiety, the higher their salivary
cortisol concentrations, the better their performance. For individuals who have the capacity to
perform at a high-level (higher WMs), whether physiological arousal will lead an individual to choke
or thrive depends on math-anxiety.
Keywords: math-anxiety, cortisol, working memory, individual differences
Math-anxiety is characterized as an adverse emotional reaction
to math or the prospect of doing math (Richardson & Suinn, 1972).
For math-anxious individuals, opening a math textbook or even
entering a math classroom can trigger a negative emotional re-
sponse. Despite normal performance in other academic areas,
people with math-anxiety perform poorly on measures of math
ability in comparison to their less-math-anxious peers (Hembree,
Why is math-anxiety tied to poor math performance? One
explanation is that math-anxious students are simply less skilled or
practiced at math than their non-math-anxious counterparts. After
all, individuals high in math-anxiety tend to avoid math classes and
receive lower grades in the math classes they do take (Ashcraft &
Kirk, 2001). However, there is an alternative explanation for how
math-anxiety compromises math performance. Namely, in math-
anxious individuals, the anxiety itself causes an online deficit in
math problem solving that contributes to poor math outcomes
(Ashcraft, Kirk, & Hopko, 1998).
Support for the view that people’s anxiety about doing math—
over and above their actual math ability—can impede their math
performance comes from work by Ashcraft and Kirk (2001). These
researchers examined low and high math-anxious individuals’
ability to simultaneously perform a mental addition task and a
memory task involving the short-term maintenance of random
letter strings for later recall. Difficulty levels of both the primary
math task and the secondary memory task were manipulated.
Performance was worst (mainly in the form of increased math task
error rates) in instances in which individuals, regardless of math-
anxiety, performed both a difficult math and memory task simul-
taneously. However, in comparison to less math-anxious individ-
uals, participants high in math-anxiety showed an exaggerated
increase in performance errors under the difficult math and mem-
ory task condition. The authors concluded that performance defi-
cits under demanding dual-task conditions were most pronounced
in high math-anxious individuals because their emotional reaction
diverted attention away from the content of the task. Similar to a
demanding secondary task, this process co-opted the working
memory capacity that might have otherwise been available for
Working memory (WM) is a short-term system involved in
the control, regulation, and active maintenance of a limited
amount of information relevant to the task at hand (Miyake &
Shah, 1999). If anxiety has a disruptive effect on WM, then
performance should suffer when a task relies on this system.
This article was published Online First June 27, 2011.
Andrew Mattarella-Micke, Katherine Foster, and Sian L. Beilock, De-
partment of Psychology, The University of Chicago; Jill Mateo, Depart-
ment of Comparative Human Development, The University of Chicago;
Megan N. Kozak, Department of Psychology, Pace University.
This research was supported by NSF CAREER Grant DRL-0746970 to
Correspondence concerning this article should be addressed to Sian L.
Beilock, Department of Psychology, 5848 South University Avenue, The
University of Chicago, Chicago, IL 60637. E-mail: firstname.lastname@example.org
Emotion © 2011 American Psychological Association
2011, Vol. 11, No. 4, 1000–1005 1528-3542/11/$12.00 DOI: 10.1037/a0023224
Indeed, previous work supports this prediction. Beilock et al.
(2004) have shown that anxiety about performing at an optimal
level selectively affects performance on those math problems
that place the greatest demands on WM, such as problems that
involve a carry operation or the maintenance of large interme-
Moreover, individual differences in WM capacity also pre-
dict who will be most affected by stressful performance situa-
tions (Beilock & Carr, 2005). In particular, higher working
memory individuals (HWMs) are most susceptible to perfor-
mance decrements in stressful situations. This is because
HWMs tend to employ cognitively demanding strategies during
problem solving. These strategies allow HWMs to reach a
greater level of performance relative to lower working memory
individuals (LWMs) who employ cognitively leaner but less
accurate heuristics. Yet, these cognitively demanding strategies
fail when WM is compromised while heuristics yield a low but
consistent level of performance (Beilock & DeCaro, 2007).
Thus, there is considerable evidence to suggest that diversion of
WM, perhaps toward worries about the task, is one mechanism
behind the online deficits associated with math-anxiety
Although anxiety plays an important role in the expression of
poor performance, it may not be the only factor. For instance,
while math-anxious individuals report anxiety in math-related sit-
uations, they also exhibit intense physiological reactions, such as a
pounding heart, sweaty palms and even shaking hands (as in
Ashcraft, 2002), that may be related to their affective response. In
the current work we explore the relation between these physiolog-
ical reactions and math performance.
Two-Factor Theory of Emotion
Our approach is motivated by work in the social psychology
literature (Schachter & Singer, 1962). According to Schachter and
Singer’s two-factor theory, individuals perceive an emotional
event based on a cognitive interpretation of internal physiological
cues. For example, if a person experiences sweating palms and a
racing heart, the two-factor theory argues that one’s interpretation
of these cues discriminates between the subjective feeling of fear
and that of love (see also, Macdowell & Mandler, 1989). Given a
potentially stressful situation such as math problem solving,
whether an individual chokes or thrives may similarly depend on
their interpretation of their physiological state. While many indi-
viduals have heightened physiological responses in a math perfor-
mance situation, math-anxious individuals in particular may be
likely to interpret this physiological reaction negatively and
thus perform poorly. In contrast, nonanxious individuals might
even benefit from a heightened physiological state if they
interpret their physiological reaction to indicate a challenging
In the current work, participants solved a set of difficult math
problems. To assess how our participants might construe this
potentially stressful situation, we also measured their trait math-
anxiety. Because math-anxiety taps into an individual’s explicit
anxiety about math, it is an appropriate gauge of how they would
react to a challenging math situation. We also asked participants to
complete a WM capacity measure. Last, we sampled salivary
cortisol concentrations in our participants both before and after the
math test as an index of their physiological response to performing
We selected the hormone cortisol because it is often associated
with stressors in humans and is thought to have effects on WM
(Duncko, Johnson, Merikangas, & Grillon, 2009; Elzinga & Ro-
elofs, 2005; Lupien, Gillin, & Hauger, 1999). Recent animal
research supports this idea (Roozendaal, McReynolds, &
McGaugh, 2004). In Sprague–Dawley rats, corticosterone (the
analogous hormone in rats) has been shown to act on the prefrontal
cortex to cause a deficit in performance on the delayed response T
maze (a putative measure of WM). Critically, this deficit depends
on input from the basolateral amygdala, a key region in emotional
processing (LeDoux, 2000). When input from this region is in-
terrupted by a lesion or blocked by a receptor antagonist, the
corticosterone-driven deficit disappears. This has lead to the
claim that the negative effects of corticosterone on WM depend
on emotional processing. Although not definitive, this work
suggests cortisol as a potential link between people’s anxiety
about a math situation, their WM capacity, and their math
We used modular arithmetic (Bogomolny, 1996) as our math
task. The object of modular arithmetic (MA) is to judge the
validity of problems such as 51⬅19(mod 4). One way to solve
MA is to subtract the middle number from the first number (i.e.,
51–19) and then divide this difference is by the last number
(32/4). If the dividend is a whole number, the answer is “true.”
MA is a desirable math task because it is novel, challenging,
and its WM demands can be easily manipulated by varying the
size of the numbers and whether or not problems involve a
In summary, the two-factor theory allows us to make specific
predictions about which individuals will choke and which will
thrive in our math performance situation. Individuals that in-
terpret the situation negatively (high math-anxious individuals)
will suffer as the intensity of their physiological response
increases. However, this same physiological intensity might
actually contribute to facilitated performance for those low in
Critically, the relationship between math-anxiety, cortisol, and
performance should depend on individual differences in WM. This
is because the demanding strategies that HMWs often apply in
math performance situations are compromised when WM is im-
paired. If problem solvers interpret their physiological response as
indicative of math-related distress, this interpretation may hinder
one’s ability to execute demanding computations in WM. In con-
trast, because HWMs’ demanding strategies should benefit from
increased availability of WM resources, HWMs may be in a
unique position to gain from a favorable emotional interpretation
of their physiological response.
Participants (N⫽73; 29 male, 44 female) were recruited from
University of Chicago, Roosevelt University, and the local area
(age M⫽23.03, SD ⫽5.42, range ⫽18–42). Participants were
also screened for the use of psychiatric medications and adrenal
Working memory capacity. Participants’ performance on
the automated Reading Span (RSPAN; Conway et al., 2005), a
common WM measure, served as our measure of WM capacity.
In the RSPAN, participants read a series of sentences followed
by letters (e.g., “On warm sunny afternoons, I like to walk in the
park.R”), and judge whether each sentence makes sense by click-
ing either True or False. At the end of a series of two to five
sentence-letter sets, they recall the sequence of letters. Individuals
are tested on three series of each length, 12 in total.
RSPAN scores are calculated based on the total number of
letters recalled in order on any trial, regardless of whether the
entire sequence of letters was correct. This partial-credit scoring
shows high internal consistency and reduces skew (Conway et al.,
Participants performed within the normative range for the
RSPAN task (M⫽59.59, SD ⫽13, Range ⫽19–75), but slightly
higher than reported in a recent latent-variable analysis (M⫽
51.60; Unsworth et al., 2009). RSPAN scores did not differ as a
function of gender t(71) ⫽.19, p⫽.49.
Math-anxiety. Math-anxiety was assessed using the short
Math-anxiety Rating Scale (sMARS). The sMARS (Alexander &
Martray, 1989) measures an individual’s level of anxiety concern-
ing math related situations. Across 25 items, participants rate how
anxious they would be during math activities (e.g., “Listening to
another student explain a math formula”) on a 1–5 scale. The
sMARS is a shortened version of the 98-item MARS (Richardson
& Suinn, 1972). It is highly correlated with the original MARS
(r⫽.96) and exhibits acceptable test–retest reliability. The mean
sMARS score was 32.16 (SD ⫽17.29), slightly lower than that
reported in Ashcraft & Kirk (2001; M⫽36.3, SD ⫽16.3).
Math-anxiety did not differ as a function of gender, t(71) ⫽.03,
Modular arithmetic. MA problems were always of the form
“x ⬅y(mod z)”. The left two operands were selected from num-
bers 2–98, with the constraint that the first number (x) was always
greater than the second number (y). The mod operand (z) ranged
from 2–9. Studies of mental arithmetic have determined that prob-
lems which involve the maintenance of information online, such as
a carry operation, place particular demand on WM (DeStefano &
LeFevre, 2004). In contrast, certain problems lend themselves to
solution via heuristics (e.g., “mod 2” problems which are always
false when the subtraction result is odd). These heuristic solutions
make few demands on WM (DeCaro, Wieth, & Beilock, 2007).
Based on these factors, problems in the math task were divided
into Low and High demand categories corresponding to their
relative recruitment of WM capacity. High Demand problems
always included a carry operation during the subtraction step and
could not be solved via simple heuristic. Low Demand problems
did not have a carry step or could be solved using heuristics (e.g.,
mod 2 problems with an odd subtraction or mod 5 problems
because they could be solved with the simple heuristic that only
subtractions ending in 0 or 5 were true).
Participants completed 30 practice trials, followed by three
experimental blocks of 70 problems, each separated by about a
minute rest. The critical trials consisted of 54 High-Demand prob-
lems, in addition to 186 Low-Demand problems. This proportion
of problems was selected such that participants were not overtaxed
by difficult problems, but had enough time on task for the sluggish
cortisol response to emerge. Order of blocks was counterbalanced
Sessions were scheduled between 11:00 a.m. and 3:00 p.m. to
minimize circadian variation in cortisol concentrations across par-
ticipants. In order to collect proper measurements of salivary
cortisol, participants were instructed not to eat, drink, chew gum,
or brush their teeth for two hours before the session. Participants
were compensated for their involvement.
Participants began by signing informed consent. The first saliva
sample was collected by having individuals spit into a 12 ⫻75 mm
polypropylene tube, which was then capped (Fisher Science; IL,
U.S.A.). Next, all individuals were seated at a computer and
introduced to MA. Participants saw MA problems such as
71 ⬅23(mod 3) on the computer and were asked to judge whether
each problem was true or false as quickly and accurately as
possible. Each trial began with a 500-ms fixation point, screen-
center. This was replaced by a MA problem that remained on the
screen until the participant responded. After response, the word
“Correct” (in black) or “Incorrect” (in red) appeared for 1,000 ms,
providing feedback. The screen then went blank for a 1,000-ms
After the MA task, a second saliva sample was obtained from
participants. This second sample was taken approximately 30
minutes after starting the math task, based on prior research
establishing that salivary cortisol peaks between 21 and 40 minutes
following stressor onset (Dickerson & Kemeny, 2004). Following
the second saliva sample, participants completed the WM tasks.
Last, participants filled out a short packet of questionnaires, in-
cluding sMARS. After the experiment, saliva samples were kept
frozen in the testing room for 2–3 weeks until transport to the lab,
where they were stored until assayed. Samples were assayed in
(MP Biomedicals, CA U.S.A.) and reassayed if the CV was
⬎20%. The sensitivity of the assay is 0.07 g/dL.
Only individuals whose average MA accuracy and cortisol
concentration were within ⫾2SD of the mean of the group were
included in the analyses. This resulted in the removal of four
participants due to accuracy and three participants based on cor-
tisol concentration. Sixty-six participants were retained in the
Self-report data concerning smoking behavior was also collected, how-
ever due to experimenter error this data was only collected for 42 subjects.
Nonetheless, smoking behavior did not correlate with math-anxiety, WM,
or salivary cortisol. Thus it was not included in further analysis.
We also collected Operation Span (OSPAN), a measure of WM that
incorporates math processing. For the purposes of studying the relation of
WM and math-anxiety, OSPAN was not included due to its necessary
relation to math processing.
1002 MATTARELLA-MICKE, MATEO, KOZAK, FOSTER, AND BEILOCK
Modular Arithmetic Accuracy
Overall, participants were fairly accurate on the MA problems
(M⫽90% correct, SD ⫽6%) and completed the problems in
about four seconds on average (M⫽3981 ms, SD ⫽1300). As
expected, the High-Demand problems were performed slower
(M⫽6289 ms, SD ⫽2218) and less accurately (M⫽81%, SD ⫽
12%) than Low-Demand problems (M⫽3232 ms, SD ⫽1126;
M⫽92%, SD ⫽8%), t(65) ⫽17.42, p⬍.0001; t(65) ⫽⫺10.40,
To explore how math-anxiety, individual differences in WM,
and salivary cortisol related to low and high-demand problem
performance, we began by regressing both low and high-demand
math accuracy separately on math-anxiety, WM, post-MA cortisol
(log transformed to reduce skew) and their interactions.
regression approach is preferable to performing a median split and
dichotomizing continuous variables because the latter approach
reduces power (Cohen, 1983) and under certain conditions can
increase the probability of a Type I error (Maxwell & Delaney,
1993). Following Cohen and Cohen (2003), we only considered
regression coefficients as significant if the overall F-statistic was
significant. This procedure protects against Type-I error inflation
associated with testing multiple regression coefficients.
For each regression, the assumptions of normality, homogeneity
and error independence were verified through inspection of the
residuals and a normal q-q plot. Diagnostics of leverage, discrep-
ancy and influence were also considered for each regression to
confirm that the relationships were not the result of a few extreme
or influential cases. DFBETA, a measure of the effect an individ-
ual observation has on a particular beta did not exceed the thresh-
old of ⫾1 (Cohen et al., 2003). Cook’s Distance, a measure of the
effect of a particular observation on overall fit, did not exceed one
for any observation and no residual reached significance as a
regression outlier using the Beckman and Cook (1983) procedure
(␣⫽.05). No leverage values (h*
) differed substantially from the
distribution of values and only four observations (6%) were iden-
tified for further examination (about 5% are expected on average).
Thus, there was no evidence for extreme or influential data in the
regression. Last, we tested for multicollinearity using the variance
inflation factor (VIF). A VIF of 10 is considered strong evidence
for multicollinearity (see Cohen et al., 2003). No predictor VIF
The regression equation predicting high-demand accuracy from
math-anxiety, salivary cortisol, WM and their interactions was
highly significant, F(7, 58) ⫽3.10, p⬍.01. High-demand MA
accuracy was negatively related to overall math-anxiety, ␤⫽
⫺.493, t⫽⫺4.044, p⬍.001. This main effect was qualified by
the predicted three-way interaction between salivary cortisol,
math-anxiety, and WM, ␤⫽⫺.260, t⫽⫺2.15, p⬍.05. The main
effect for cortisol, WM and the two-way interactions did not reach
significance (see Table 1). To fully understand the regression, we
modeled one standard deviation above and below the mean for
WM and math-anxiety. This simplifies interpretation by charac-
terizing the data in terms of high and low WM and math-anxiety
“groups” without actually breaking up the continuous variables
(Aiken & West, 1991). The performance of these modeled groups
on high-demand MA problems is plotted as a function of salivary
cortisol concentration taken after MA in Figure 1.
As seen in Figure 1 (left panel), LWMs’ math accuracy did not
differ as a function of cortisol or math-anxiety. However, for
HWMs, the relation between accuracy and cortisol concentration
depended on their math-anxiety. For low math-anxious individu-
als, increasing cortisol was associated with better MA perfor-
mance. The opposite pattern was found for individuals high in trait
In terms of low-demand MA problems, the full regression model
was not significant, F(7, 58) ⫽1.42, p⫽.22. Because these
problems were specifically selected for their lesser reliance on
WM, this nonsignificant result is an important control. If math-
anxiety or cortisol predicted low-demand performance, this would
suggest that these variables affect performance through another
route apart from their effects on WM.
Modular Arithmetic Reaction Time
The same regressions performed on MA accuracy were also
performed on MA RTs for the high and low-demand problems.
Neither the full equation for high, F(7, 58) ⫽1.54, p⫽.17 nor
low-demand, F(7, 58) ⫽2.01, p⫽.07 reached significance (see
In the current study we explored the relation between an indi-
vidual’s physiological response and their performance on a chal-
lenging math task. We predicted this relation would depend on
whether a person was lower or higher in math-anxiety and thus
their positive or negative construal of the math situation. We
further suggested that this impact might be moderated by individ-
ual differences in WM. Our data showed strong support for these
hypotheses. The relation between cortisol concentration (our mea-
sure of physiological response) and math performance depended
on a participant’s math-anxiety and their WM capacity.
For high math-anxious individuals, increasing cortisol concen-
trations lead to worse math performance. But, for low math-
anxious individuals, this relationship was positive—increasing
concentration of cortisol lead to higher performance. This pattern
of results supports our claim that one’s interpretation of the math
situation helps to determine whether a physiological response will
be disruptive or beneficial.
The effect of cortisol in this scenario was qualified by individual
differences in WM capacity and the WM demands of the math
problems performed. As predicted by previous research (Beilock
& Carr, 2005), low-demand problems were not affected by the
interaction of math-anxiety and cortisol. Moreover, because low
working memory participants (LWMs) often do not rely heavily on
WM to solve mathematical computations (Beilock & DeCaro,
2007), their performance remained unchanged with increasing
concentrations of cortisol even on the high-demand problems. In
contrast, high working memory participants’ (HWMs) math accu-
racy was affected by an interaction between math-anxiety and
As mentioned above, we collected cortisol prior to the math task to
measure individual differences in baseline cortisol. For simplicity, this
variable was not reported in the analysis. However, results remained
significant when cortisol concentrations prior to the math task were in-
cluded as a covariate.
salivary cortisol on high-demand problems. HWMs that were also
high in math-anxiety tended to perform worse on the math task as
cortisol concentrations increased across individuals. However,
HWMs low in math-anxiety excelled on the math task as cortisol
concentrations increased. These results suggest that, given the
cognitive resources and the opportunity to interpret physiological
arousal as a motivational cue, individuals in a challenging envi-
ronment can push themselves to higher levels of performance.
Participants did also exhibit a global difference in performance as
a function of math-anxiety. This is consistent with claims that high
math-anxious individuals possess less experience with math over-
all, contributing to poor performance in addition to their online
affective response (Tobias, 1985).
This work relies on correlational data, thus we draw causal
conclusion cautiously. For instance, placement of the math-anxiety
measure after math performance allows the alternative hypothesis
that math accuracy affected reported math-anxiety (instead of vice
versa). This hypothesis is unlikely, however, because WM mea-
sures separated these two tasks by about 40 minutes. Further,
sMARS is a trait math-anxiety measure, with questions that con-
sider stable anxieties as opposed to one’s current affective state.
Last, an explanation which claims that performance affected re-
ported math-anxiety cannot account for the WM component of our
3-way interaction (i.e., that HWMs, but not LWMs, show a rela-
tionship between performance and math-anxiety).
Second, it is also possible that cortisol concentrations might not
affect performance, but instead may be a byproduct of perfor-
mance outcomes. For instance, perhaps when low math-anxious
individuals notice they are performing well, their cortisol concen-
trations increase; likewise, when high math-anxious individuals
Figure 1. Mean modular arithmetic accuracy on high-demand problems as a function of WM, Math-anxiety
Regression Analyses for Modular Arithmetic Reaction Time and Accuracy
High Demand Low Demand
Accuracy RT Accuracy RT
sMARS ⴚ.49 (ⴚ4.04
).11 ( 0.88) ⫺.34 (⫺2.60
).09 ( 0.66)
RSPAN .09 ( 0.72) ⫺.06 (⫺0.43) .16 ( 1.08) ⫺.05 (⫺0.34)
Cortisol .18 ( 1.51) ⫺.18 (⫺1.39) .06 ( 0.48) ⫺.27 (⫺2.15
Cortisol ⫻sMARS .17 (⫺1.46) .14 ( 1.07) ⫺.02 (⫺0.18) .19 ( 1.54)
sMARS ⫻RSPAN ⫺.01 (⫺0.06) ⫺.01 (⫺0.34) ⫺.02 (⫺0.11) .07 ( 0.50)
RSPAN ⫻Cortisol .11 ( 0.91) .23 ( 1.76) ⫺.03 (⫺0.25) .17 ( 1.37)
sMARS ⫻RSPAN ⫻Cortisol ⴚ.26 (ⴚ2.15
)⫺.20 (⫺1.50) ⫺.21 (⫺1.58) ⫺.20 (⫺1.56)
.19 .07 .05 .07
1.54 1.42 2.01
Note. Adjusted R
, adjusted coefficient of determination; ␤, standardized regression coefficient. Regression
coefficients that exceed ␣⫽.05 for both the overall Ftest and the individual tare indicated in bold along with
their respective adjusted R
1004 MATTARELLA-MICKE, MATEO, KOZAK, FOSTER, AND BEILOCK
notice they are making mistakes, their cortisol increases. However,
a meta-analysis of cortisol studies points to uncontrollable situa-
tions which include potential social-evaluative stress as eliciting
the strongest cortisol response (Dickerson & Kemeny, 2004).
These criteria are consistent with failure on a difficult math task
and thus could explain the experience and performance of highly
math-anxious individuals, but not those lower in math-anxiety.
When considered in tandem with previous experimental manip-
ulations of situation-induced anxiety (Beilock and DeCaro, 2007;
Beilock & Carr, 2005 Dickerson & Kemeny, 2004), these data
support the claim that anxiety affects performance through its
impact on the WM system. The results also suggest that explicit
measures of anxiety alone cannot account for the full impact of
stress on performance. Physiological factors such as cortisol also
play a role. In sum, the results suggest future avenues of research
toward isolating a cognitively (Beilock & Carr, 2005) and biolog-
ically (Roozendaal et al., 2004) plausible mechanism for online
math performance decrements related to anxiety.
Last, the essential role of affect in this ostensibly “cold” cog-
nitive task is of special note. Math performance in adults is most
often studied from a purely cognitive approach (Ashcraft, 1992;
DeStefano & LeFevre, 2004), in which differences in affective
processes are accepted as a necessary source of random variation.
Yet, in the current study, the interaction of affective processes with
cognitive ability account for 25% of the variance in accuracy. This
argues strongly that a cold cognitive task such as math problem
solving can only be understood through a theoretical lens that
includes both affective and cognitive sides of the theoretical coin.
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Received May 21, 2010
Revision received December 13, 2010
Accepted January 5, 2011 䡲