Imagery orientation and vividness: their effect on a motor skill performance.
Pie, Joan S. ; Tenenbaum, Gershon ; Bar-Eli, Michael 等
Two studies were conducted to examine the effect of imagery on a
eye-hand coordination task (throwing a ball in a basket). In the first
study 75 high school students were divided into 3 treatment conditions
and one control. The experimental conditions were comprised of watching
a short video clip of either 15 successful basketball foul shots or 15
unsuccessful shots, or of recreational skiing. Then the subjects were
taught how to experience and feel movement through relaxation and
imagery. In the second study, similar procedures were applied to 20
subjects who were students in a coaching academy. In study 1, the four
shooting trials were performed at one week intervals; in study 2, they
were performed twice a week. In study 1, results indicated that while
imagery vividness remained high and unchanged across four trials in all
groups, performance improved with time as a result of acquaintance with
the task. However, in study 2, external imagery orientation increased
while performance remained unchanged. We conclude that imagery can
contribute to performance only when subjects efficiently master the
task. Accordingly, novice subjects should first practice the task and
only later integrate imagery into their practical programs.
The use of imagery along with physical practice has been found to
enhance performance more than the use of physical practice without
imagery (Smith, 1987; Weinberg, 1982). One recent explanation as to why
physical practice accompanied by mental practice enhances performance,
can be sought through the bioinformational theory (Hecker & Kaczor,
1988; Lang, 1977, 1979). This theory enlightens the relationship between
the athlete's experience level and the physical and psychological
responses to imagery scripts (Hecker & Kaczor, 1988). Because the
athlete has experience with the skills being described during the
imagery training, he/she can then experience the mental practice both
psychologically (mentally creating the situation's sounds,
feelings, etc.) and physically (the feelings of arousal-anxiety, the
muscle movements, the heart rate, etc.). These responses enable the
athlete to further practice the skills needed for their sport, while
being relieved from the constant exertion of physically performing
(Hecker & Kaczor, 1988). However, thus far, more research is needed
to demonstrate the dominance of the bioinformational approach over the
other theories in this domain (Suinn, 1993).
Imagery, observed through self-report, can vary in its vividness.
Vividness is described as being the clarity, color, and realness of the
situation imaged (Smith, 1987). Some studies have suggested that the
more vivid the image, the better the outcome of the performance (Start
& Richardson, 1964). However, Smith (1987) pointed out that it is
unknown whether the elite athlete actually uses imagery (before, during,
and/or after the execution of an action) and if so, whether the
vividness of the images can affect that and/or other performances. Thus,
how performance is affected by these components of imagery is still not
completely understood.
Mental imagery can be classified into two basic cognitive
approaches: internal and external. Internal imagery is where the
performer visualizes the skill as if he/she were actually performing; in
contrast, external imagery is where the performer visualizes him/herself
as if watching from an outside perspective (i.e., watching him/herself
perform on television) (Hall, Rogers, & Barr, 1990). Past research
has found that more experienced athletes have a tendency to use internal
imagery more often than external imagery (Hall, et al., 1990; Mahoney & Avener, 1977). This tendency is in line with the bioinformational
theory, in that internal imagery produces kinesthetic feelings of the
movements being imagined (Jacobson, 1932; Mumford & Hall, 1985).
Since the experienced athlete is more familiar with these movements,
he/she can therefore use internal imagery more efficiently to produce
the feelings and improve the execution of skilled movements (Hecker
& Kaczor, 1988).
Indeed, more experienced athletes (elite level) have been found to
utilize internal imagery more frequently than less experienced athletes
("weekend" type athletes), who tend to use external imagery
more frequently (Epstein, 1980; Smith, 1983). In addition, motor tasks
seem to be more receptive to internal imagery than to external imagery;
in contrast, non-motor tasks tend to be more receptive to external
imagery than to internal imagery (Smith, 1987; Suinn, 1993). In general,
Epstein (1980) has suggested that the combination of both internal and
external imagery is the most effective way of improving performance.
It is unclear whether a person is imaging in the exact manner that
he/she is told (Sheehan, 1967). Disagreement is also found in the
literature as to the amount of time required for imagery to be effective
on performance. Feltz and Landers' (1983) and Smith's (1987)
reviews indicate that more time and trials are needed for each imagery
session when imaging a motor task than when imaging a cognitive task. It
has been suggested that there is an optimal amount of time (yet to be
confirmed) for imagery, just as there is an optimal amount of time for
physical practice to be most effective for the improvement of a skill in
a sport (Twinning, 1949). Mental practice or imagery should also take
into account the nature of the task and the characteristic of the
individual, with the assumption that imagery should be conducted the
same amount of time that it takes to actually perform the task
(Weinberg, 1982).
The present study investigated the effects of imagery orientations
on a motor skill performance. The imagery procedure used here was an
adapted version of the visual motor behavioral rehearsal (VMBR)
originally suggested by Suinn (1976). It was hypothesized that if the
content of an image is controlled through first watching a model of what
is to be imaged and then through instructed Imagery sessions, the
viewing of the model and imagining of that performance is expected to
cause the subject to produce an enhanced performance. This hypothesis
was investigated in two contradictory situations. In the first situation
the subject viewed a successful performance (i.e., a basketball free
throw shot that is successfully completed), and then transferred that
image of success to his/her imagery practice sessions (imaging
him/herself successfully completing a basketball free throw shot). The
second situation consisted of a subject viewing an unsuccessful
situation (i.e., a basketball free throw shot that is unsuccessfully
completed), and then transferring that image of failure to the imagery
practice sessions (imaging him/herself performing an unsuccessful
basketball free throw shot).
The idea to introduce an unsuccessful image was based on the
psychotherapeutic literature, which suggests that it is possible to
extinguish maladaptive behaviors that have been reinforced unknowingly
by others (related to this study, it could be described as "being
afraid of missing a foul shot in front of an audience as it happens even
to the most elite players"). Karoly and Kanfer (1982) introduced
the technique of implosive therapy to describe the extinguishing of
maladaptive behaviors. Implosive therapy is a technique that relies on
the principle of extinction as it focuses on extinguishing the
conditioned avoidance of the anxiety-arousal stimuli (for this study,
the successful and unsuccessful images). In implosion therapy, the
clients are asked to imagine and relive aversive scenes associated with
their source of negative arousal. However, instead of trying to diminish
arousal from the treatment sessions, the therapist deliberately attempts
to elicit a massive "implosion" of negative arousal or
anxiety. With repeated exposure in a "safe" setting, the
stimulus loses its power to elicit arousal and the destructive avoidance
behavior is extinguished.
Woolfolk, Murphy, and Parrish (1983; cited by Suinn, 1993) used
unsuccessful imagery with college students who were divided into groups
according to their golf-putting ability and assigned to one of three
conditions: correct practice imagery, incorrect practice Imagery, and no
training (control). The "correct" condition had subjects
correctly practice putting the ball into a cup; in the
"incorrect" condition, subjects imaged the ball just missing
the cup. This study found significant differences between the
conditions, with the "correct" practice imagery condition
subjects improving by 30.4% from their baseline measurements, the
"incorrect" practice imagery condition subjects deteriorating by 21.1% from their baseline measurements, and the control condition
subjects improving by 9.9% from their baseline measurements. However, no
published study is known in sport psychology to test unsuccessful
imagery based on implosion theory (Suinn, 1993).
Another aspect of imagery is related to the question of whether
images do become stronger (more vivid) over time in regular Imagery
practice sessions. It was assumed that just as learning a new skill or
task, one can also learn to improve his/her imagery skills as well as to
produce more vivid images, and increase the use of internal imagery
(Smith, 1987). Therefore, subjects in the present investigation, who
gained more experience with imagery (whether positive or negative), were
expected not only to improve their performance of the motor skill on top
of the "normal" learning effect being experienced with
practice, but also to increase their frequency of the use of Internal
imagery as well as the vividness of their images.
Method
Study One
Subjects. Four Israeli high school physical education classes
(n=75, age 16.34 + 0.49 years; males and 31 females) took part in Study
1. All students were from the same high school located in Tel Aviv. All
were from moderate to high socioeconomic status families. They were
randomly assigned to one of the following conditions: a successful free
throw treatment (n=20) viewing and imaging a successful basketball free
throw and performing the task (n=20); an unsuccessful free throw
treatment (n=19) - viewing and imaging an unsuccessful basketball free
throw and performing the task; a ski treatment (n=18) - viewing and
imaging a skiing model then performing the task; and a control group
(n=18). Groups were balanced in terms of gender, roughly each group had
equal number of males and females.
Instrumentation and Apparatus
Three 30 minute video cassettes containing a total of eight
minutes of the following were used: (1) General information as to what
the students were about to see and do (two minutes): "Hello and
welcome. You will be participating in the following project, which will
include watching a short video of a sport; then you will be guided
through an imagery session, where you will be performing the sport seen
in the video." (2) A short video (the model) of either 15
successful basketball foul-shots, or 15 unsuccessful basketball
foul-shots, or recreational skiing (each video is two minutes in length;
only one model was used per video). The ski video was used as a neutral
model to control for the possibility of the influence of performing
imagery as such, unrelated to its content. The basketball models
included well known athletes playing on the current championship team of
the Israeli professional basketball league. The ski model was of
professional non-Israeli skiers in a recreational setting; this model
was considered neutral because in Israel, participating in the sport of
skiing is quite rare to near distant. (3) Visual motor behavioral
rehearsal specific to each sport situation viewed in the video model
(four minutes in length; two minutes relaxation, two minutes imagery
rehearsal).
Suinn (1976) introduced VMBR as a type of mental practice that
allows a person to experience imagery as if it were reality, with
feelings of physiological, emotional, and neuromuscular involvement.
VMBR is made up of two steps: (a) relaxation; (b) imagery rehearsal.
This type of mental practice is easily replicated in practice and
research settings because it does not demand special training or skills
and the descriptions used to create the images are very descriptive. In
conjunction with the type of model viewed and imagery rehearsal
practice, the amount of time it takes to complete a basketball foul shot
should be the optimal amount of time needed for the imagery sessions.
In the present study, an adapted version of VMBR was used with
multiple imagery practice sessions, as recommended by Feltz and Landers
(1983) to produce an effect on the performance task. According to Smith
(1987), because of task specificity motor skills such as basketball free
throws should be imaged for five or less minutes. Therefore, the mental
practice sessions in the present study were two minutes in length.
Instructions for the unsuccessful basketball foul-shot were as follows
(in Hebrew): "Imagine yourself standing at the foul line, exactly
as you saw in the video. Now shoot the ball to the basket. Watch it hit
the rim of the basket and miss. Watch the ball fall to the ground. Feel
the disappointment of missing the basket."
Three free throw shooting positions were marked on the basketball
court's key: (a) the actual free throw line, (b) a mark to the left
of the free throw line, and (c) a mark to the right of the free throw
line. Each position was 19 feet from the basket line, which is the same
distance used on regulation sized courts.
Issac, Marks, and Russell's (1986) Vividness of Movement
Imagery Questionnaire (VMIQ) was administered to the subjects. This
questionnaire is used in sport settings and is a valid measure of
imagery vividness. The VMIQ measures both external and internal imagery.
Two different versions were used in the study, each one pertaining to
the model/imagery used in the video seen. One questionnaire was used for
those subjects viewing the successful/unsuccessful basketball foul-shot
models, and the other was for those viewing the ski model. The subjects
who viewed the successful and unsuccessful basketball free throw videos
were asked how vividly they could imagine the basketball, their wrists,
legs, the basket, and their body as they released the ball to the
basket. The subjects rated their legs, hands, head, wrists, and their
whole body as they were skiing down the slopes. The subjects rated their
imagery vividness on a Likert type scale with ratings from one (no image
at all) to five (image perfectly clear and as vivid as normal vision).
Each questionnaire was broken down into three sections, i.e. items
pertaining only to (a) body parts, (b) movement of body parts, and (c)
movement of the whole body. For each of these three parts, the subject
was asked to imagine first from an internal perspective (imagining
him/herself and his/her own body move) and then from an external
perspective (imagining someone else's body and movement). Each part
was measured separately and the averages were recorded. The mean
vividness score was calculated by dividing the vividness score of all
items by the number of items.
Procedure
Each of the four groups performed the imagery and practice
sessions once a week for five consecutive weeks. In the first week, a
baseline measurement of 15 basketball free throws was calculated from
three positions marked on the basketball court. Each subject attempted
five free throws from each of the positions (free throw line, to the
left of the free throw line, and to the right of the free throw line).
The subjects were to randomly shoot one basket at a time at each of the
three positions until all 15 throws were completed. In the first week,
students were randomly assigned to the various baskets on the court, and
returned each week to the same basket with the same group of students.
One student at each basket was asked to record the throws with a
"+" for those baskets made and a "-" for those
throws missed for each student at that basket. Only the total number of
baskets made (+) were recorded.
The second through the fifth weeks consisted of the following
procedures for the three experimental groups: The students were seated
in a classroom with a video cassette recorder and a television watching
and participating with the eight minute group-specific video (described
before). Then these students were given the respective imagery
questionnaire to complete. After completing the questionnaire, the
students went to a gymnasium, where the basketball courts were located,
and completed the same performance task conducted during the baseline
measurement.
The control group underwent the following procedure during the
second week: The students arrived at the gymnasium/basketball courts,
and were asked to answer the following question: "Do you use
imagery when attempting a basketball free throw?" ("Yes"
or "No"). Attached to this question was the same questionnaire
that the successful and unsuccessful basketball free throw imagery
groups responded to. If the student answered "yes" to the
first question, they were told to continue responding to the
questionnaire. If the student answered "no" to the first
question, they were told to stop and not to respond to the remainder of
the questionnaire. Then, the students completed the same performance
task as the other three groups, in line with the baseline measurement.
For the control group, weeks two to five consisted of only arriving to
the gymnasium and completing the performance task (the same task as
during the baseline measurement and the second week).
While Study 1 looked at imagery orientation, vividness, and
performance among high school students for six weeks, Study 2 was
conducted with college aged students, who had more experience with this
particular skill. In Study 2, adapted VMBR procedure and performance
sessions were conducted on a more condensed basis, that is, two times a
week for two weeks.
Study Two
Subjects. Students from the National Israeli School of Coaches
took part in Study 2 (n=20; 14 males and 6 females). Students were
randomly assigned to one of the four treatments as described in Study 1.
The mean age of the students was 23.77 + 2.69 years and they came from
medium socioeconomic status.
Procedure. Instrumentation and apparatus were identical to Study
1. Students also followed the same procedures as in Study 1, but with
the exception that the four imagery and performance sessions were held
twice a week for two weeks, rather than once a week for four weeks as in
Study 1. The baseline performance measures were taken one week prior to
the beginning of imagery and performance sessions. Overall, the students
participated in this study for a total of three weeks and underwent the
same procedures as those students in Study 1. The control group In this
study completed their questionnaire (as described in Study 1) before
their first performance task of the second week. These subjects had more
experience than the high school student sample with the basketball
shooting task, due to the I act that they had just completed a course on
the rules, positions, and techniques of the basketball game.
Results
Study One. Means of the successful basket shots for each of the
three treatment groups and the control for the baseline and four trials
are presented in Figure 1.
[Figure 1 ILLUSTRATION OMITTED]
Repeated Measures (RM) ANCOVA was applied to the data with
treatment as a between subjects factor, four trials as a repeated within
subjects factor, and baseline measure as a covariate (despite the random
assignment, after observing baseline means). The analysis revealed that
only the trial factor reached a statistical significance F(3,21 0)=3.46;
p [is less than] .02. Examination of the trial means across the four
groups has indicated that on the average the performance Improved from
4.68 + 2.68 (first trial) to 5.57 + 3.09 (fourth trial), which is about
a 19% total increase and a 5.93% relative increase [(5.57/15)100 -
(4.68/15)100=5.93%]. Neither the treatment nor Its interaction with the
trial factor were statistically significant.
Examination of the imagery vividness of movement has shown that
all four groups (three experimental treatments plus control group) did
not differ each from the other in the vividness of the imaged movements
(body parts, movement of body parts, movement of the whole body
imagining myself and imagining someone else) for the first trial.
RM-ANOVAs for each of the VMIQ sections (over four trials) have
indicated that the three treatment groups did not differ significantly
from each other during the four trials. Also, the trial effect was found
to be insignificant. Means show that on the average the vividness of the
body parts and movements of the body parts was about 70% of the maximal possible vividness ("almost perfectly clear and as vivid as normal
vision").
Additional analyses were applied to the data in order to detect
possible differences between internal and external (imagery perspective)
vividness in the four trials for the three experimental groups.
Treatment was used as a between subjects factor, and vividness of
imagery perspective (internal-external) was used as the first within
subjects factor, along with the four performance trials within each
factors being used as a second trial factor. The mixed ANOVA design was
applied separately to the vividness of the body parts, movement of the
body parts, and movement of the whole body.
The results revealed significant effects only for the vividness of
the body parts; imagery perspective X performance trials, F(3,129)=4.08;
p [is less than] .008 and treatment X imagery perspective X performance
trials, F(6,129)=2.22; p [is less than] .04. These interactions are
presented in Figure 2.
[Figure 2 ILLUSTRATION OMITTED]
The analysis revealed that subjects exposed to ski imagery,
improved significantly in the imagery perspective of external vividness
of body parts from the first to the fourth trials. The reverse was found
in the successful free throw treatment. This treatment showed a similar,
but insignificant trend for internal vividness of the body parts.
Study 2
Similar analyses to those of Study 1 were applied in Study 2. The
means of the four treatments for each of the four performance trials are
presented in Figure 3.
[Figure 3 ILLUSTRATION OMITTED]
The RM-ANCOVA has indicated that neither the treatment nor the
trial and their interaction were statistically significant (p [is
greater than] .05) for the performance task. All groups remained
consistent in their improvement of performance across the four trials
(about 35% 38% success).
The RM-ANOVAs applied to the VMIQ sections of imaging
one-self's body parts, the movement of body parts, and the movement
of the whole body, have shown trial effects F(3,30)=3.39; p [is less
than] .03, F(3,30)=6.97; p [is less than] .001, and F(3,27)=3.74; p [is
less than] .02 respectively. On the average, the vividness of imagining
one-self's body parts improved by 13%, movement of body parts by
18%, and movement of the whole body by 20%.
Trial effects were also obtained for imagining someone else's
body parts F(3,30)=2.99; p [is less than] .05 and the movement of body
parts F(3,30)=4.23; p [is less than] .01. On the average the vividness
of imagining someone else's body parts improved by 12%, and the
movement of body parts improved by 11%. It should be noted that the
vividness of movement in imagery by the subjects in this study was about
90% of the maximal vividness ("almost perfectly clear and as vivid
as normal vision").
The ANOVA applied to the imagery perspectives (internal-external)
of vividness was similar to those applied in Study 1. This ANOVA
revealed significant effects for imagery perspectives of the body parts,
F(1,10)=9.81; p [is less than]. 01, the movement of body parts,
F(1,10)=8.63; p [is less than] .01, and the movement of the whole body,
F(1,9)=15.93; p [is less than] .003. These effects are shown in Figure
4.
[Figure 4 ILLUSTRATION OMITTED]
It is here that on the average, the vividness of the external
imagery perspective was rated higher than the internal imagery
perspective of the body parts, the movement of body parts, and the
movement of the whole body, The analyses also revealed significant trial
effects for the three components of the VMIQ (across internal/external
imagery perspectives): the body parts, F(3,30)=3.59; p [is less than]
.02; the movement of body parts, F(3,30)=8.48; p [is less than] .00; and
the movement of the whole body F(3,27)=4.55; p [is less than] .01. Thus
the vividness of imagery perspectives (internal-external) of the three
components of the VMIQ increased significantly from the first to the
fourth trial, Figure 5 presents these effects.
[Figure 5 ILLUSTRATION OMITTED]
Discussion
The present studies investigated the question of whether
manipulation of a mental technique such as imagery can enhance a
physical skill such as a basketball throw. Imagery was taught to 3
groups of subjects using three different methods: (1) watching and
imagining successful throws, (2) watching and imagining unsuccessful
throws, and (3) watching and imagining unrelated skills. The subjects in
both studies were inexperienced in the basketball skill and therefore
may be considered novices. It was hypothesized that despite their lack
of experience, experiencing successful throws through imagery would
create a sense of the action and would result in enhanced internal
vividness of the images, which were to enhance physical performance
(Hecker & Kaczor, 1988). The studies were aimed at testing this main
hypothesis, which was based on the bioinformational theory (Hecker &
Kaczor, 1988; Lang, 1977, 1979).
In this investigation, we also attempted to (a) examine whether
imagery of an unsuccessful action has the potential of extinguishing a
maladaptive behavior and enhancing performance, in line with the
implosive therapy applied in the psychotherapeutic domain (Karoly &
Kanfer, 1982) and related findings regarding the physical skill of
golf-putting (Woolfolk et al., 1983, cited by Suinn, 1993); (b) to
examine whether practicing neutral imagery such as skiing may enhance
physical performance similarly or differently from practicing
unsuccessful throws; and (c) to examine whether practicing different
images enhances the vividness of the body parts and their smooth
movement (more internal than external), and consequently enhances
performance through kinesthetic feelings of the movements being imagined
(Jacobson, 1932; Mumford & Hall, 1985).
The findings of the present study suggest that practicing imagery
of a motor skill which is not yet mastered by the subjects may result in
two possible outcomes: Study 1 indicates that while imagery vividness is
sustained following a once a week practice by all the groups, physical
performance which requires eye-hand coordination may increase as a
result of improved acquaintance with the task. However, study 2
indicates that while imagery vividness increased at a high level
following a twice-a-week practice of imagery, physical performance was
sustained at the same level throughout the four trials. This indicates
an improved acquaintance with imagery but not with the eye-hand
coordination task. These two effects are summarized in Table 1.
Table 1 Effects of Practicing Imagery of A Novel Task Which Requires
Eye-hand Coordination
Study Imagery Imagery Motor
Practice Vividness Performance Outcome
1 once a week sustained increased improved
acquaintance
with task
2 twice a week increased sustained improved
acquaintance
with imagery
These two possible outcomes are in disagreement with our a priori expectations. Since progress in shooting throws through four weeks was
similar in the three experimental groups as well as in the control group
(the one not subjected to any imagery manipulation), performance
enhancement may be attributed to better acquaintance with the task.
Neither the bioinformational theory (Lang, 1977, 1979) nor the
principles of implosive therapy (Karoly & Kanfer, 1982) and the
related rationale of Woolfolk et al. (1983) can be used as reasonable
explanations of the present results.
The hypothesis that the high level vividness of the external and
more so of the internal orientation would contribute to some extent to
performance enhancement (Smith, 1987) is not supported by the present
results, because vividness remained consistently high across all four
trials. However, it can be argued that only experienced subjects, who
are well acquainted with the physical task and at the same time feel and
experience the movement through imagery, may improve in such a skill
(Hecker & Kaczor, 1988). It seems that vividness in itself is not
sufficient to improve performance, but mentally experiencing physical
practice may enhance physical performance when the skill is well
mastered. Thus, vividness is needed to support the process, but it
cannot stand by itself. It is possible that subjects exposed to imagery
"saw" the throws to the basket very vividly (from both
internal and external perspectives), but did not feel it. In any case,
substantial experience together with internal feeling of the action are
probably needed to enhance performance. In study 1, neither condition
(experience, feeling the action) was fulfilled.
Study 2 revealed that external orientation of the images
increased, internal images remained consistent across all four trials,
and eye-hand coordination task did not improve whatsoever. These results
may be explained by (a) subjects being novice, that is, they have not
yet sufficiently learned the task; (b) an increase in external vividness
not being necessarily related to physical performance enhancement; (c)
subjects not feeling the action (similar to the subjects in study 1);
(d) short imagery period and insufficient number of trials
The results of study 2 did not confirm the hypothesis that the
more vivid the image, the better the performance outcome (Start &
Richardson, 1964). However, this might be the case with expert athletes
who were found to use internal imagery more often than external imagery
(Hall et al., 1990; Mahoney & Avener, 1977), in comparison to
recreational athletes, who tended to use external imagery more
frequently (Epstein, 1980; Smith, 1983). The fact that motor tasks are
more receptive to internal imagery (Smith, 1987: Suinn. 1993) is
probably true, but this is not a sufficient condition to enhance
performance. It seems that one should actually feel the imaged action in
order to subsequently improve performance of a skilled movement. Thus,
the more the subject is skilled and the more acquainted he or she is
with the physical task, the greater probability of him/her achieving
actual physical progress through internal imagery.
The practicing sport psychologist and the coach should be aware of
the consequences of applying imagery to novice subjects. The three
imagery methods applied in the present research did not decrease
performance, as compared to the groups which did not practice imagery.
However, it seems that more time should be given to imagery and practice
in order to bring about a notable improvement in performance (Smith,
1987; Weinberg, 1982). This applies more to novice athletes, with the
process probably being shorter when skilled athletes are considered. In
any case, the present suggestions call for further research in this
domain.
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