Humans and monkeys show similar skill in estimating uncertain outcomes (original) (raw)

Uncertainty is a common feature of daily life, both for humans and for other animals. For example, leaving one food source to travel to another that is both spatially and temporally distant requires some sense on the part of an organism that the latter source will be more profitable than the current one (see, e.g., Stephens & Krebs, 1986). Another area in which uncertainty is relevant pertains to quantity judgment. What one means by saying that a “bird in the hand is worth two in the bush” is that the “two in the bush” are an uncertain outcome, and thus may be less viable than sticking with the quantity that one has.

Some animals appear to deal with uncertainty adaptively by seeking information or refusing to make a choice when the risk of error is high (see, e.g., Call & Carpenter, [2001](/article/10.3758/s13423-012-0218-x#ref-CR9 "Call, J., & Carpenter, M. (2001). Do apes and children know what they have seen? Animal Cognition, 4, 207–220. doi: 10.1007/s100710100078

            "); Hampton, Zivin, & Murray, [2004](/article/10.3758/s13423-012-0218-x#ref-CR13 "Hampton, R. R., Zivin, A., & Murray, E. A. (2004). Rhesus monkeys (Macaca mulatta) discriminate between knowing and not knowing and collect information as needed before acting. Animal Cognition, 7, 239–246. doi:
                10.1007/s10071-004-0215-1
                
              
            "); Kornell, Son, & Terrace, [2007](/article/10.3758/s13423-012-0218-x#ref-CR17 "Kornell, N., Son, L. K., & Terrace, H. S. (2007). Transfer of metacognitive skills and hint seeking in monkeys. Psychological Science, 18, 64–71. doi:
                10.1111/j.1467-9280.2007.01850.x
                
              
            "); Smith, Shields, & Washburn, [2003](/article/10.3758/s13423-012-0218-x#ref-CR19 "Smith, J. D., Shields, W. E., & Washburn, D. A. (2003). The comparative psychology of uncertainty monitoring and metacognition. The Behavioral and Brain Sciences, 26, 317–339. doi:
                10.1017/S0140525X03000086
                
              
            "); Suda-King, [2008](/article/10.3758/s13423-012-0218-x#ref-CR21 "Suda-King, C. (2008). Do orangutans (Pongo pygmaeus) know when they do not remember? Animal Cognition, 11, 21–42. doi:
                10.1007/s10071-007-0082-7
                
              
            ")). However, there are other ways to deal with uncertainty, and one of these is to rely on past experiences to estimate the likelihoods of the current outcomes. For example, one may not know whether the next roll of the roulette wheel will come up black or red, but observations of the table over a long enough period of time will indicate that both outcomes are equally likely. It is the sum of the observations that produces the estimate of likelihood for each outcome, even if one cannot see that the wheel itself has equal slots for each color. This kind of estimation on the basis of summed experience can produce efficient decision making.

Nonhuman animals may well be capable of this kind of tallying behavior. Animals track the rates of return from multiple food sources within foraging bouts (e.g., Stephens & Krebs, 1986). They track the relative reinforcement rates for multiple response schedules (Herrnstein, [1961](/article/10.3758/s13423-012-0218-x#ref-CR15 "Herrnstein, R. J. (1961). Relative and absolute strength of response as a function of frequency of reinforcement. Journal of Experimental Analysis of Behavior, 4, 267–272. doi: 10.1901/jeab.1961.4-267

            ")), often matching responses to the probabilities of reward on those schedules (Herrnstein, [1997](/article/10.3758/s13423-012-0218-x#ref-CR16 "Herrnstein, R. J. (1997). The matching law: Papers in psychology and economics. Cambridge, MA: Harvard University Press."); Sugrue, Corrado, & Newsome, [2004](/article/10.3758/s13423-012-0218-x#ref-CR22 "Sugrue, L. P., Corrado, G. S., & Newsome, W. T. (2004). Matching behavior and the representation of value in the parietal cortex. Science, 304, 1782–1787. doi:
                10.1126/science.1094765
                
              
            ")). Less studied have been circumstances in which animals are given repeated experience with discrete judgments that are each unique along a quantitative dimension. However, these experiences might lead to the formation of an expected value (or some other measure related to the approximate average number of items that they received across these repeated experiences), and thus would be useful in dealing with choices made in circumstances with incomplete information (i.e., uncertainty).

Beran, Evans, and Harris ([2009](/article/10.3758/s13423-012-0218-x#ref-CR4 "Beran, M. J., Evans, T. A., & Harris, E. H. (2009). When in doubt, chimpanzees rely on estimates of past reward amounts. Proceedings of the Royal Society B, 276, 309–314. doi: 10.1098/rspb.2008.1027

            ")) asked whether, in the face of uncertainty, such as when the quantity in one set was unknown, chimpanzees would use information gathered from their own previous responses to deal with that uncertainty. First, chimpanzees made 15 consecutive judgments between two visible food sets that varied in the numbers of items presented across trials. Then they were faced with the same combinations of set sizes for another 15 trials, but only one set was revealed, while the other remained unknown, and the chimpanzees could choose either option. The chimpanzees made selections as if they were using an approximate mean number of items obtained in the first 15 trials to determine whether the known quantity was large enough. Thus, the rate of return from responses in the first phase (when both sets were known) was what guided the chimpanzees’ choices of the unknown set, rather than some specific quantity that acted as a threshold for choosing between the known or the unknown set.

The results with chimpanzees, however, were from highly trained individuals who had extensive experience in judging between quantities. In some cases, this experience had stretched across more than two decades of testing and involved dozens of different kinds of tests, including tests that required counting items, judging discrete and continuous quantities, responding to arithmetic manipulations, and being tested for long-term retention of numeral meaning (see, e.g., Beran, 2009). In addition, there was no way to directly compare their performance with that of humans, as no relevant data were available. The present study offers the first such direct comparison between humans and a nonhuman species. If capuchin monkeys and humans performed similarly, this would indicate that spontaneous, ongoing representations of reward amounts are widespread among primate species, and these representations could support adaptive responding in the face of uncertainty, such as can occur in the natural environments of these species.

Method

Subjects

A group of 6 capuchin monkeys were tested: Griffin (male, 12 years of age), Gabe (male, 11 years of age), Liam (male, 6 years of age), Lily (female, 12 years of age), Nala (female, 7 years of age), and Wren (female, 7 years of age). All were experienced in a variety of cognitive tests, including some judgments of food quantities (e.g., Beran, Evans, Leighty, Harris, & Rice, [2008](/article/10.3758/s13423-012-0218-x#ref-CR5 "Beran, M. J., Evans, T. A., Leighty, K., Harris, E. H., & Rice, D. (2008). Summation and quantity judgments of sequentially presented sets by capuchin monkeys (Cebus apella). American Journal of Primatology, 70, 191–194. doi: 10.1002/ajp.20474

            "); Evans, Beran, Harris, & Rice, [2009](/article/10.3758/s13423-012-0218-x#ref-CR11 "Evans, T. A., Beran, M. J., Harris, E. H., & Rice, D. (2009). Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella). Animal Cognition, 12, 97–105. doi:
                10.1007/s10071-008-0174-z
                
              
            ")). Thus, they had experiences that allowed them to recognize the value of quantity in making judgments, but they had much less experience than the previously tested chimpanzees.

A further group of 39 humans from Georgia State University were tested (19 males, 20 females; mean age = 20.3 years, age range: 18 to 39 years). They performed the experiment for credit as part of various undergraduate class requirements in the psychology department.

Apparatus

The monkeys voluntarily separated from their group mates into individual test enclosures positioned 107 cm off the floor. Food items were hidden under black plastic containers positioned at opposite ends of a shelf (60 cm wide, and 30 cm deep). The shelf was white plastic coated with a perforated black fabric (to keep reward items from rolling out of place). The shelf sat on top of a utility cart (107 cm tall) that allowed us to move both quantities toward a monkey at the same time.

The humans were tested at a table using materials similar to those used with the capuchin monkeys, except that the humans saw pennies instead of food pellets as the items to be quantified.

Design and procedure

Each experimental session consisted of 30 trials. The first 15 trials constituted the training phase. An experimenter placed a blind between the apparatus and the subject, and then placed two quantities of items (food pellets for monkeys, pennies for humans) on opposite ends of the test area and covered them with the containers. The experimenter removed the blind and then lifted the container on the left, allowing the subject to look at the quantity of items underneath for approximately 2 s before re-covering it. The experimenter then revealed and re-covered the other set (on the right) in the same manner. For monkeys, the experimenter closed his eyes and lowered his head (so as not to influence the monkey’s choice) and immediately pushed the bench shelf forward so that the monkey could make a selection by sticking a finger through the cage mesh and pressing one of the containers. A second experimenter, out of view of the monkeys, called out which container was selected so the first experimenter would know which quantity to uncover and give to the monkey. The barrier was then lowered again, and the next trial was prepared. For humans, only one experimenter played the roles of both presenter and recorder of the choice, and the human participants simply pointed to the container that they wanted. Prior to this, the human participants were told:

Thank you for being in this experiment. Your task is to try to collect as many pennies as possible during this experiment. I will put a barrier between us while I set pennies under each of these two containers. Next, I will move the barrier and uncover and re-cover each container one at a time. Then, I will ask you to point to the container you think holds more pennies. I will put the pennies from the set you chose into the cup. I will then replace the barrier and remove the pennies from the set you did not choose.

In the test phase, a second block of 15 trials was presented. The trials were prepared in the same way (out of view of the subject), and the experimenter revealed the first set in the same way. However, the experimenter never revealed the second set. Instead, the experimenter paused for 2 s and allowed the subject to make a choice. This meant that the second set contained a quantity unknown to the subject at the point of the response. All other aspects of trial presentation were the same. Before these trials, human participants were told:

Now, we will do the same thing as before, except I will only show you what is under one container. You must decide whether to take that amount of pennies or choose the other set, which you have not seen. As before, I will put the pennies from the set you chose into the cup and then remove the other pennies after replacing the barrier. And, as before, your job is to try to get the largest amount of pennies on each trial.

These instructions were considered necessary because, during pilot data collection, humans would immediately ask us why or remind us that the second set had not been revealed. Thus, these instructions were more than monkeys could possibly have been given, but the monkeys also had extensive experience in choice tests of various kinds, so there was no way to perfectly equate the testing experiences of the two species.

Each monkey received one session per day for two or three days each week. In each session, six different quantities were presented during trials, and each possible combination was presented one time during the 15 training trials (when both sets were revealed) and one time during the 15 test trials (when only one set was revealed). The order in which these 15 comparisons were presented was randomly determined for both phases, and position of the larger set was randomized in both phases.

We presented three quantity ranges: 1–6 (1, 2, 3, 4, 5, and 6), 2–10 (2, 3, 5, 6, 8, and 10), and 5–12 (5, 6, 7, 8, 10, and 12). This manipulation allowed us to assess how the monkeys varied their selections of the unknown quantity, both as a function of the known quantity and as a function of the overall rate of reward that they had received during the training phase. Each monkey completed three test sessions with each of the three quantity ranges, for a total of nine sessions. The order of completion within a block was randomized for each monkey. Importantly, 80% of the sessions were separated by multiple days, to minimize any carryover of memory for trials from one session to the next.

Of the 39 human participants, 30 completed only a single session of 30 trials (15 training and 15 test trials) from one of the three ranges. The ranges were randomly assigned to these 30 participants, so that 10 participants were assigned to each range. The remaining 9 participants came to the laboratory on three separate days to perform each of the three quantity range tests. The order of the ranges used in the test session was randomized across these participants.

Results

During the training phase, the capuchin monkeys selected the larger quantity on 247 of the 270 trials (91.5%) when the range was from 1 to 6 items, on 246 of 270 trials (91.1%) when the range was from 2 to 10 items, and on 239 of 270 trials (88.5%) when the range was from 5 to 12 items. Humans in the between-subjects design selected the larger quantity on 150 of their 150 trials (100%) when the range was from 1 to 6 items, on 146 of 150 trials (97.3%) when the range was from 2 to 10 items, and on 148 of 150 trials (98.7%) when the range was from 5 to 12 items. Humans in the within-subjects design selected the larger quantity on 130 of 135 trials (96.3%) when the range was from 1 to 6 items, on 132 of 135 trials (97.8%) when the range was from 2 to 10 items, and on 131 of 135 trials (97.0%) when the range was from 5 to 12 items. Each of these performance levels was significantly higher than chance levels of responding, as assessed with a two-tailed binomial test (p < .01).

In the test phase, all trials were combined across monkeys for each known quantity in each of the three conditions. In Fig. 1a, we present the percentages of all test trials in which the monkeys selected the unknown quantity as a function of the known quantity, for each range of values presented during the training phase. Monkeys’ overall selection frequencies of the unknown quantity differed from chance levels (50%) in nearly all cases, because the monkeys were either significantly more likely than chance to choose the unknown quantity or significantly less likely than chance to choose the unknown quantity (all _p_s < .05, as assessed with a two-tailed binomial test). The only exception was for the quantity 6 when the training range was from 2 to 10, in which case the selections did not exceed chance levels between the two choices.

Fig. 1

Fig. 1

The alternative text for this image may have been generated using AI.

Full size image

Percentages of trials on which capuchin monkeys selected the known quantity during the test phase. Each series of bars shows performance for a different range of quantities presented during individual sessions. The horizontal line shows the 50% level, which indicates indifference between the choices. (a) All data combined across monkeys. (b) Data combined across monkeys for the first session only for each quantity range

In Fig. 1b, we present a subset of the monkey data, now only for the first session completed by each monkey with each quantity range. This analysis is offered in comparison to the overall data to demonstrate that the phenomenon emerged very early in the experiment and was not the result of behavior changing with experience. The percentages of choosing the quantities shared across all ranges were significantly different across the three ranges [known quantity 5, χ2(df = 2) = 12.22, _p = ._002; known quantity 6, χ2(df = 2) = 11.43, _p = ._003].

The performance of the humans was highly consistent with that of the monkeys (Fig. 2). Their overall selection frequencies of the unknown quantity also differed from chance levels (50%) in nearly all cases (all _p_s < .05, as assessed with a two-tailed binomial test). The only exceptions for the 30 participants in the between-subjects design were the quantity 4 when the training range was 1–6, the quantity 6 when the training range was 2–10, and the quantity 8 when the range was 5–12. The only exceptions for the 9 participants in the within-subjects design were the quantities 3 and 4 when the training range was 1–6 and the quantities 5 and 6 when the training range was 2–10.

Fig. 2

Fig. 2

The alternative text for this image may have been generated using AI.

Full size image

Percentages of trials on which humans selected the known quantity during the test phase. All of the data are combined across participants. Each series of bars shows performance for a different range of quantities presented during individual sessions. The horizontal line shows the 50% level, which indicates indifference between the choices. (a) Data for the 30 participants in the between-subjects design. (b) Data for the 9 participants in the within-subjects design

Each of the three quantity ranges shared two common known quantities—five items and six items. Thus, we could assess whether either group of subjects had a threshold quantity that determined their choice of the known or the unknown set. For monkeys, the proportions of choice of the known quantities were significantly different across the three ranges [known quantity 5, χ2(df = 2) = 34.05, p < .001; known quantity 6, χ2(df = 2) = 42.19, p < .001]. For humans in the between-subjects design, the proportions of choice also were significantly different across the three ranges [known quantity 5, χ2(df = 2) = 26.88, p < .001; known quantity 6, χ2(df = 2) = 42.48, p < .001]. For humans in the within-subjects design, the proportions of choice were significantly different across the three ranges [known quantity 5, χ2(df = 2) = 18.08, p < .005; known quantity 6, χ2(df = 2) = 32.89, p < .001]. A comparison of the graphs in Fig. 2a and b shows that performance was highly similar for the between-subjects and within-subjects participants in this experiment.

Humans came closer than monkeys to using the mean number of items obtained in the training phase to guide their choice of the unknown quantity. For the range of 1–6 items, the mean number of items obtained per trial, assuming perfect performance in which every trial ended with choice of the larger set, was 4.67 items. Humans showed indifference between the two choices when the known set was four items, whereas capuchins significantly preferred the known set of four items. For the range of 2–10 items, the mean number of items obtained per trial, assuming perfect performance, was 7.53 items. Humans shifted from selecting the unknown quantity to the known quantity between the six- and eight-item known quantities, whereas capuchins already were indifferent between the choices when the known quantity was six items. For the range of 5–12 items, the mean number of items obtained per trial, assuming perfect performance, was 9.53 items. Humans in the between-subjects test shifted from selecting the unknown quantity to the known quantity between the eight- and ten-item known quantities, whereas capuchin monkeys and humans in the within-subjects test significantly preferred receiving the eight items in the known set when it was presented. Thus, in nearly all cases, humans’ indifference points in choosing between the two sets were as close to the mean number of items received during training as could have occurred, given the actual comparisons that were used. Capuchin monkeys consistently underestimated that mean. It should be noted that this pattern for capuchins still holds even if one uses the actual mean number of items obtained during training, rather than the theoretical number. If all correctly completed training trials for the capuchins were used to calculate the mean number of items obtained across the three ranges, those values would drop to 4.53, 7.36, and 9.32, which are all very close to the means obtained assuming perfect performance during the training trials.

Discussion

Monkeys and humans performed very similarly in this experiment when faced with one known and one unknown quantity. Both species showed nearly the same distributions of responses to the two quantities used in all three ranges used in the experiment. This performance matched that of a group of chimpanzees that had previously been tested (Beran et al., [2009](/article/10.3758/s13423-012-0218-x#ref-CR4 "Beran, M. J., Evans, T. A., & Harris, E. H. (2009). When in doubt, chimpanzees rely on estimates of past reward amounts. Proceedings of the Royal Society B, 276, 309–314. doi: 10.1098/rspb.2008.1027

            ")). Because capuchin monkeys are a New World monkey species distantly related to chimpanzees and humans, this shows that the capacity to estimate likely outcomes in uncertain situations is widespread among primate taxa. Furthermore, because the capuchin monkeys live in a similar laboratory setting to the previously tested chimpanzees, but without the enriched rearing that those chimpanzees experienced, this capacity is not reliant on any special training or rearing.

Monkeys and humans, like the previously tested chimpanzees, did not choose between known and unknown quantities on the basis of some absolute, or threshold, amount. This is evidenced by their differential responding to the quantities of 5 and 6 across the three different quantity ranges. Thus, all three species clearly showed that any prediction regarding their choice of an unknown set would need to take into account not only the known quantity or the unknown quantity, but also what had occurred earlier in the test session. Capuchin monkeys and humans were keeping track of the relative rates of return from their selections across the first 15 training trials and using information from those trials to guide responding in the face of uncertainty. Humans were better at this, as their indifference points nearly always fell exactly where they would be predicted if the mean numbers of items obtained during the training trials were used to guide responding. Capuchins consistently underestimated these means. This difference may have been partly the result of using edible items with animals and small-valued symbolic stimuli (pennies) with humans. Had food items or larger-value coins been used, humans might have performed differently, due to increased motivation that might have affected the relative rates of risk aversion responses versus risk-taking responses. However, this seems unlikely, given that the use of different rewards has been shown not to change choice behavior in monkeys or humans in other tasks (see, e.g., Hayden & Platt, [2009](/article/10.3758/s13423-012-0218-x#ref-CR14 "Hayden, B. Y., & Platt, M. L. (2009). Gambling for Gatorade: Risk sensitive decision making for fluid reward in humans. Animal Cognition, 12, 201–207. doi: 10.1007/s10071-008-0186-8

            ")). Thus, humans more likely are better at estimating the relative rates of return from numerous quantity judgments, perhaps due to representations of quantity and number that are more precise than those formed by nonhuman animals (e.g., Gallistel & Gelman, [2000](/article/10.3758/s13423-012-0218-x#ref-CR12 "Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4, 59–65. doi:
                10.1016/S1364-6613(99)01424-2
                
              
            ")).

The task never required that subjects remember anything from one trial to the next during the training phase. Everything was visible, and choices were made with full knowledge of both set sizes. Even beyond that, the entire testing history of these animals followed the same principle. Success or failure in choosing the larger amount in all previous quantity judgment experiments was based solely on what was seen on a given trial. Retaining information about a trial, for possible use in subsequent trials, offered no benefit whatsoever to the animal for any of its previous experiences. Yet, monkeys (and humans) nonetheless spontaneously tracked the cumulative rewards that they obtained throughout those training trials. Doing so clearly served an adaptive role later in the session, even though subjects could not have known this during the training phase. This was true for all sessions with humans tested in the between-groups design, and at least for the first session with monkeys and with humans tested in the within-subjects design. Thus, these judgments in the face of incomplete information were made spontaneously, as this was the first time that these monkeys (and perhaps these humans) had ever been faced with such quantity judgments with incomplete information.

Although learning something about the overall reward structure of a task offers a source of information that could be used in the face of uncertainty, this is not the same kind of learning that occurs through trial and error or via trial-by-trial feedback in terms of rewards or punishments. Instead, it is a kind of “recordkeeping” whereby presently useless information is still tallied and retained. Although this is most likely done implicitly, especially in the nonhuman species, it still occurs, and apparently it occurs across a variety of primates—or at least those with extensive experimental histories. These monkeys used session-by-session information to guide their responses when information was incomplete. Questions remain, however, about whether less experimentally sophisticated animals would show this same pattern, so there needs to be more research in order to assess both the extent to which untested species might also show this phenomenon, as well as to assess the role of previous experiences in performance on this kind of task. It remains to be seen whether nonprimates or experimentally naïve primates would perform similarly to those already tested, but it seems reasonable to assume that they could. Research has indicated that a variety of species, ranging from insects to birds to mammals, perform in highly similar ways when they judge quantities (e.g., Agrillo, Dadda, Serena, & Bisazza [2008](/article/10.3758/s13423-012-0218-x#ref-CR1 "Agrillo, C., Dadda, M., Serena, G., & Bisazza, A. (2008). Do fish count? Spontaneous discrimination of quantity in female mosquitofish. Animal Cognition, 11, 495–503. doi: 10.1007/s10071-008-0140-9

            "); Anderson, Hattori, & Fujita, [2008](/article/10.3758/s13423-012-0218-x#ref-CR2 "Anderson, J. R., Hattori, Y., & Fujita, K. (2008). Quality before quantity: Rapid learning of reverse-reward contingency by capuchin monkeys (Cebus apella). Journal of Comparative Psychology, 122, 445–448. doi:
                10.1037/a0012624
                
              
            "); Boysen & Berntson, [1989](/article/10.3758/s13423-012-0218-x#ref-CR6 "Boysen, S. T., & Berntson, G. G. (1989). Numerical competence in a chimpanzee (Pan troglodytes). Journal of Comparative Psychology, 103, 23–31. doi:
                10.1037/0735-7036.103.1.23
                
              
            "); Brannon & Terrace, [2000](/article/10.3758/s13423-012-0218-x#ref-CR7 "Brannon, E. M., & Terrace, H. S. (2000). Representation of the numerosities 1–9 by rhesus macaques (Macaca mulatta). Journal of Experimental Psychology: Animal Behavior Processes, 26, 31–49. doi:
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            "); Call, [2000](/article/10.3758/s13423-012-0218-x#ref-CR8 "Call, J. (2000). Estimating and operating on discrete quantities in orangutans (Pongo pygmaeus). Journal of Comparative Psychology, 114, 136–147. doi:
                10.1037/0735-7036.114.2.136
                
              
            "); Dacke & Srinivasan, [2008](/article/10.3758/s13423-012-0218-x#ref-CR10 "Dacke, M., & Srinivasan, M. V. (2008). Evidence for counting in insects. Animal Cognition, 11, 683–689. doi:
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            "); Pepperberg, [1994](/article/10.3758/s13423-012-0218-x#ref-CR18 "Pepperberg, I. M. (1994). Numerical competence in an African Grey parrot (Psittacus erithacus). Journal of Comparative Psychology, 108, 36–44. doi:
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            "); Tomonaga, [2007](/article/10.3758/s13423-012-0218-x#ref-CR23 "Tomonaga, M. (2007). Relative numerosity discrimination by chimpanzees (Pan troglodytes): Evidence for approximate numerical representations. Animal Cognition, 11, 43–57. doi:
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            ")). Those skills clearly offer the basis for the type of implicit “calculations” that would support adaptive decision making in the face of uncertain options in this quantity judgment task—decision making like that shown by the primates given such tests so far.

References

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