simulating the foraging behavior of trigona biroi using

Simulating the Foraging behavior of Trigona Biroi using Multi-agent Systems

Roberto B. Figueroa Jr.Institute of Computer Science

University of the Philippines Los Banos

Los Banos, Laguna+639285034866

[email protected]

Arian J. JacildoInstitute of Computer Science

University of the Philippines Los Banos

Los Banos, Laguna+639202301166

[email protected]

Jomar F. RabajanteInstitute of Mathematical Sciences and

PhysicsUniversity of the Philippines Los

Banos+639165184733

[email protected]

ABSTRACTThis paper presents a multi-agent system for simulating the foraging behavior of stingless bees (Trigona biroi Friese), an endemic species of bees in the Philippines which is currently gaining attention in its potential for increasing the yield of pollinated crops and the production of propolis. The design of the multi-agent system is described using features of the Agents, Groups, Roles (AGR) model and the Markov Decision Process (MDP). To simulate the Optimal Foraging Theory (OFT) or the assumption that bees tend to maximize the amount of food foraged based on varying criteria, the system incorporates the Biroi Preference Algorithm and two implementations of the quasi-random walk process. The system is implemented in NetLogo, a programmable modeling environment for simulating natural and social phenomena. Statistical tests on the results of the simulations verified that the system indeed simulates the OFT.

KeywordsMulti-agent System, NetLogo, Biroi Preference Algorithm, Trigona biroi Friese.

1. INTRODUCTIONIt is believed that most tropical crops depend on insect pollination. Studies show that bees are effective cross-pollinators and are therefore beneficial for better crop production [2][3][4][5][8][12][13]. Since most of these crops are important components of our diet, there is a need for ways of efficiently growing and reproducing them. Gojmerac said that one-third of the world’s food supply is either directly or indirectly dependent on plants pollinated by insects such as bees [7]. This means that bees indirectly contribute to our national food security.

Efforts in harnessing the potential of these wonderful creatures have been made by sectors in the government, the business community and educational institutions. The Bee Program of the Institute of Biological Sciences (IBS), UPLB has been promoting and disseminating information about bees to local government units and the local community as agribusiness opportunities and agents for mitigating climate change [1].

Recently, the Institute of Mathematical Sciences and Physics (IMSP) and the Institute of Computer Science (ICS) have joined IBS through a collaborative effort of modeling the foraging behavior of a species of stingless bees, which is well known for its pollinating potential – the Trigona biroi Friese. Initial attempts for modeling their behavior gave birth to an algorithm that was inspired by the aforementioned species - the Biroi Preference Algorithm, which is based on the Analytical Hierarchy Process (AHP) [10]. Joint efforts continued to improve the model and another aspect of the bees foraging behavior, the Area Restrict Strategy, was modeled as a quasi-random walk process, which

makes the foragers deviate from its original target probabilistically when encountering other food sources along the path [11].

This paper presents the multi-agent design of the system described using features of AGR model and MDP. The AGR is a model used to describe the organizational structure and the interactions of the multi-agent system[6]. The MDP is a model used to describe the general behavior of the individual agents participating in the multi-agent system[14]. This paper also presents the statistical tests that were conducted to verify the logical expectations of the proponents for the simulation that follows the OFT.

Major areas of this study are discussed in the succeeding sections. Section 2 is a discussion of the multi-agent design of the system. Section 3 covers the details of the Biroi Preference Algorithm. Section 4 covers the NetLogo implementations including the static and dynamic probability parameters in the random walk process. Section 5 covers the discussion of the statistical results of simulations. Finally, section 6 contains a summary of conclusions and recommendations.

2. Multi-agent Design of the System

2.1 Organizational DesignThe organizational design provides an overview of the multi-agent system for the simulation. The organizational structure of the agents is described using an interaction diagram taken from the Agents, Groups, Roles model [6]. The diagram and some details regarding its components and interactions are discussed below.

Figure 1. Interaction Diagram of the system's Organizational Structure

The interaction diagram considers three general types of agents: turtle-agents, patch agents, and intangible agents. The turtle agents are further classified into two breeds: scouts and foragers which are roles for the group sets in which the turtles will participate in. Two group sets are defined. The Hive group set involves agents and their interactions inside the hive. An agent taking the role of a scout inside the hive provides information to all other agents inside the hive by storing it into an intangible agent which is the Hive Bank.

The Hive bank is intangible since there is no patch or agent that represents it. Access to it is given once a turtle agent sets foot on a hive patch. An agent taking the role of a forager may deposit food into the Hive Bank, get food source information, or update the information currently stored in the hive bank. The same agents will take the same role in the group set containing agents who are outside the hive. A scout in this group set interacts with a food patch by getting information from it. A forager, on the other hand, gets food from it. It is worth noting that the food information that the forager gets and updates deals with its availability and not its location. It is the role of the scouts to gather and disseminate information regarding the location of a food source.

2.2 Agent DesignFeatures of the Markov Decision Process (MDP) were employed to design the agents that were used for the simulation. Though MDP was originally designed for singular agents, it can be extended for multi-agent systems if the effects of actions of other agents are considered as part of the environment [14]. There are two types of turtle agents that are included in the simulation –the scouts and the foragers. These are the two classifications of the workers. The scouts’ only role is to search for food locations. Once they have found a new food source, they go back and report it to the hive by some sort of waggle-dance behavior communicating the vector of the new food location to the rest of the hive. The foragers are the ones who actually pick up the food from the communicated sources. However, there is usually more than one location in the information base of the hive. That is why they have to choose from the set of information available before going to the food source. The initial choosing is handled by the Biroi Preference Algorithm. The basic behavior of the scouts and foragers are modeled using the Markov Decision Process components in the subsequent discussions.

3.2.1 ScoutsThe design of the scouts involves four combinations of two attribute values. These combinations represent the states of scouts. These attribute values are represented by two-bit numbers. The following illustrates the states and actions. A transition and rewards table follows.

Table 1. Scout's Attributes

Attribute 1 0Bit 1 : Location Outside Hive Inside HiveBit 2: Food Found ? Yes No

Table 2. Scout's States State Bit 1 Bit 2S1 0 0S2 0 1S3 1 0S4 1 1

Table 3. Scout's ActionsAction DescriptionA1 Search for FoodA2 Return to HiveA3 Report Food Info

A transition function for an agent represents the outcome of an agent's action. Since the state of an agent is affected by its actions, then a transition function's parameters are the initial state of an agent, the action that the agent does, and the resulting state after the action was executed. The result of the function is a value between 0 and 1 which is the probability of the resulting state to happen when an action is executed. This is true when the automaton is nondeterministic, which means that there is more than one possible resulting state for an action done by an agent with it's initial state. If there is only one resulting state for an agent doing an action with an initial state, then the result of the transition function is 1.

For the transition Table, the following are defined for reference:

1. Ph : Number of Hive Patches

2. Pf : Number of Food Patches

3. Pt : Total Number of Patches

Table 4. Scout's Transition Table

Si Ak Sj T(si,ak,sj)S1 A1 S1 Ph/PtS1 A1 S3 (Pt – Ph)/PtS2 A3 S1 1.0S3 A1 S3 Pf/ (Pt – Ph)S3 A1 S4 ((Pt - Ph) - Pf) / (Pt – Ph)

S4 A2 S2 Ph/PtS4 A2 S4 (Pt – Ph)/Pt

The Reward function reflects a state's desirability for an agent and may affect its decisions. Since states 2 and 4 represent the state where the scout has successfully gathered new food information, they are given positive values. This means that they are more desirable than the other two states.

Table 5. Scout's Reward FunctionS R(s)

S1 0

S2 2S3 0S4 1

Figure 2. Scout's MDP Automaton

A1:

A3:

A1:A1:

A1:

A2:

A2:

3.2.2 ForagersThe design for foragers included more attributes, some of which are related to the food patches. Some of its states are used as basis for computing the quasi-random walk of foragers in the latter improvements of the simulation.

Table 7. Forager's Attributes

Attribute 1 0Bit 1 : Location Outside Hive Inside HiveBit 2: Food Chosen ? Yes NoBit 3: Carrying Food? Yes NoBit 4: In Food Source Location?

Yes No

Bit 5: Food Source Visited Yes NoBit 6: Memory > 0 Yes No Bit 7: Homebound Yes No

Table 8. Forager's StatesState Bit

1Bit 2

Bit 3

Bit 4

Bit 5

Bit 6

Bit 7

S1 0 0 0 0 0 0 0S2 0 1 0 0 0 1 0S3 0 1 1 0 1 1 1S4 0 1 0 0 1 1 1S5 0 1 0 0 1 0 1S6 0 1 0 0 1 1 0S7 1 1 0 0 DC 1 0S8 1 1 0 DC 1 1 1S9 1 1 1 DC 1 1 1

Table 9. Forager's ActionsAction DescriptionA1 Pick New Food Source A2 Forage Food at Food SourceA3 Go back to Hive A4 Store Food in Hive

For the transition Table, the following are defined for reference:

1. Ph : Number of Hive Patches

2. Pf : Number of Food Patches

3. Pt : Total Number of Patches

4. Mf: Number of Max amount of food

5. Mm: Number of Maximum Memory units

Table 10. Forager's Transition Table

Si Ak Sj T(si,ak,sj)S1 A1 S1 1 - Pf/PtS1 A1 S2 Pf /PtS2 A2 S2 Ph/PtS2 A2 S7 (Pt – Ph)/PtS7 A2 S7 Pf/ (Pt – Ph)S7 A2 S8 ((Pt - Ph) - Pf) / (Pt – Ph)(Mf-1/Mf)S7 A2 S9 ((Pt - Ph) - Pf) / (Pt – Ph)(1-((Mf-1)/Mf))S8 A3 S8 (Pt – Ph)/PtS8 A3 S4 Ph/Pt(Mm-1/Mm)S8 A3 S5 Ph/Pt(1-((Mm-1)/Mm))S4 A2 S6 1S5 A1 S5 1 – Pf/PtS5 A1 S2 Pf/PtS6 A2 S6 Ph/Pt

S6 A2 S7 (Pt – Ph)/PtS9 A3 S9 (Pt – Ph)/PtS9 A3 S3 Ph/PtS3 A4 S4 1

Table 11. Forager's Reward Function S R(s)

S1 0

S2 1

S3 3

S4 1

S5 -1

S6 -2

S7 1

S8 -2

S9 3

The Reward Function table shows that the most favorable states for foragers are S3 and S9, where they are carrying food from the food source. This means that their foraging expedition is successful. The least favorable states are S6 and S8 which means that they are already returning to a food source that has been marked as depleted. A negative value for the reward function means that it is costly to be at that state because an opportunity of being at the right location has been lost to that wrong choice of location.

Since a stingless bee (Trigona biroi Friese) has a relatively slow learning curve, it takes a few more returns to an already depleted food source before it chooses a new one. Hence, S6 and S8 are possible states. However, later on, it can be minimized upon the introduction of an auxiliary algorithm that makes a forager who happen to pass by another food source shift to that food source instead of the original one randomly (implementation 1) or by using a formula based on the MDP (implementation 2). The MDP automaton in Figure 3 summarizes the general behavior of foragers.

Figure 3. Forager's MDP Automaton

3. Biroi Preference AlgorithmMany algorithms based on mathematical models exist for studying the behavior of bees. These algorithms include Ant Colony, Particle Swarm, and the Honeybee Algorithm. The study has employed a newly developed algorithm by the name of Biroi Preference Algorithm which is based upon the assumption that bees follow the Optimal Foraging Theory (OFT). This means that they try to maximize the benefits that can be gained by what they do against the cost of doing those activities.

It utilizes the analytical hierarchy process or AHP, which collects the ranking of bees among different food characteristics from wet lab experiments. Its detailed procedure will be mentioned in the succeeding section. In the model, the scouts communicate the food sources that they have discovered and the colony builds a list based on these discoveries. This will be available to the foragers including some notable properties of these food sources. Based on the AHP, the foragers will rank the food sources and choose to collect from one of them based on the model with some degree of randomness. This, however, is not the only basis for the foragers to choose their food source. Along the path that they will be taking to get to the food source, they will encounter other food sources and based on their knowledge about their target food source and some level of randomness, there is a probability that they will choose the ones they randomly encountered over their original targets. This is called the Quasi-Random walk process for modeling the Area-Restrict Strategy of stingless bees [11].

The basic algorithm of the Biroi Preference Algorithm for modeling the Optimal Foraging Theory is characterized by the following:

Setup Bee Hive and n Food Sources.

Input C1, C2, ..., Cm (criteria to be considered)Input Ai,j where i=1,2,...n; j=1,2,...m (values of each criteria per food source; Ai,j ϵ ℝ⊕ with usual notion of order)Compute W1, W2, ..., Wm using Analytic Hierarchy Process.

Do until i=nDo until j=m

Sj = ∑i=1

nAi,j

Normi,j = Ai,j

S jend do

Weighti=∑

j=1

mNorm

i,j×W

j

end do

Do until i=n

Probabilityi=Weight i

∑d=1

nWeight

d

end doAssign Probabilityi to food source i.

♠Foragers randomly choose among the food sources based on the probabilities (Example: If there are two food sources, say F1 and F2; and F1 has Probability1=0.34 and F2 has Probability2 =0.66, then random numbers s will be assigned to F1 where 0<s<34, and random numbers t will be assigned to F2 where 34<t<100)

Do the Simulation.Compute B1, B2, ..., Bn (number of bees in each food source per simulation tick)Determine E1, E2, ..., En (food collected from food source 1, 2, ..., n, respectively per simulation tick)

4. NetLogo Basic ImplementationThe simulation of the model was implemented in NetLogo, a cross-platform environment for developing models of complex systems. NetLogo both has a modeling environment and a programming language [9].

4.1 Hive and Food SourcesThe simulation involves two types of bees – the scout bees and the forager bees. Patches, which represent environment data, are mainly classified into food patches (of which there are three types), hive patches, and wall patches. These patches are colored to signify their distinction from each other and from the white normal patches (which contain no data). The three food patches are placed variably distanced from the nest (cyan, green, and blue respectively) while the hive patches (purple) are surrounded by the wall patches (pink).

4.2 Scouts and Forager

The outline of each bee is colored to represent its current state. Scouts that are outlined with red signify that they haven't found anything yet, while those that are outlined with pink have successfully found food. White outlined foragers are those that are going to the food source to collect food. Upon returning, they are outlined with green, cyan, or blue to signify which food source they've collected. They can also be colored yellow if they've been to an already empty food source.

As mentioned earlier, the first of the four parameters is implemented as the distance from each food source to the hive. This is done for initially testing the logical accuracy of the AHP model. When all parameters except distance are equal in value and in terms of their ranks in the upper triangular, the model should show that if distance is given top priority by foragers, then the closest food source to the hive will have the most number of visits from the foragers.

Figure 4. Basic Netlogo Implementation

On the left side are switches and sliders that can alter the population of scouts and foragers, the length of delay before each bee leaves after another has left, the loyalty of bees to a tree, the wiggle rate of bees, the learning curve or memory of bees, the probability of food being replenished and its delay, and other debugging related variables for programmers and modelers. The two buttons, “Setup” and “Go” respectively resets the model, and starts the simulation.

4.4 Plots and Monitors

Figure 6. Plots and Monitors

A plot can also be seen at the bottom-right corner of the model where the number of food collected from each source is plotted per tick (the unit of measurement for time used in NetLogo). Monitors of bees in a certain state are also recorded per tick.

5. Quasi-Random Walk ImplementationAnother implementation of the foraging simulation reflects the tendency of a forager to select a new food source that it happens to pass by instead of its original target, which is based on the Biroi Preference Algorithm. It is a behavior that characterizes the area restrict strategy of the stingless bees in this study, which is described by the foragers’ increased flight turns especially when they encounter richer feeding sites. Studies have shown that some insects observe a levy-loop flight pattern which makes the forager’s food collection behavior seem random. However, as shown by previous studies, their seemingly random behavior are affected by recognized patterns and preferences such as the distance of the food source location to the hive or to their current position thereby making it a quasi-random walk process.

The new implementation revised how the foragers move from the hive to the food source and back. It changed the flight of foragers to the food source vector from a straight path into a wave like motion.

Figure 7. Refined Forager Movement

The foragers, which studies have shown to have scouting tendencies as well, have been given sight by the revised simulation where it detects new food sources in a certain radius. The first version based the probability of a forager choosing a new food source that it has encountered instead of its original target on a slider that is included in the NetLogo simulation. The slider is labeled as random-walk probability.

Figure 8. Forager Sensor and Quasi-Random Walk

The second version assigned probabilities using an algorithm that is loosely based on the MDP model of the forager agent, specifically the reward function. The radius of sight is represented by the red splotch marks around each forager. A forager who has decided to choose a newly encountered food patch is highlighted with a bright circle. Figure 8 shows the forager sight and the quasi-random behavior.

6. Results and DiscussionTwo sets of tests were conducted involving 15 scenarios. The first test involved the three food sources tested with different distance values. The scenarios are labeled from 1 to 3. Each scenario was run 100 times and statistical methods were conducted to see trends and patterns. The means of the average number of bees collecting from a certain food source were collected and Analysis of Variance (Anova) together with the Duncan's Multiple Range Test (DMRT) were performed to see if the simulations followed the trend predicted by the AHP matrix.

Figure 9. Scenario 1 Configuration

Figure 10. Scenario 1 AHP matrix and food value sliders

The layout of food sources with respect to the hive is illustrated in figure 9 while a snapshot of the triangular matrix and the food value sliders is illustrated in figure 10.

Results of the 100 runs were collected and the mean values of the average number of bees collecting from the three food sources were plotted into a graph that is illustrated by figure 11.

Figure 11. Graph of mean food collected from a food source in Scenario 1.

The analysis of variance resulted into the value of F being 8.206x104 with a significance of 0 which means that there is a large variance among the means of the average food collected

from each food source. The results from the DMRT in table 12 shows the magnitude of these differences among the means.

Table 12. Duncan's Multiple Range Test on Scenario 1

food N

Subset for alpha = 0.05

1 2 3

3 100 3.2739

2 100 4.3099

1 100 4.4312

Sig. 1.000 1.000 1.000

It showed that the average food collected from food source 1 by foragers was significantly higher than that in the other two food sources. It consequently showed that the average food collected from food source 3 was significantly lower compared to the other two food sources. The graph shows that foragers collected food mostly from food source 1 and the least number of total food collected came from food source 3.

In scenario 2, where the configuration for the simulation is illustrated by figure 12, the distance of all food sources were all set to 50. This time, the second parameter was preferred over all other parameters and food source 3 got the highest value. A snapshot of the AHP matrix and food value sliders is shown in figure 13.

Figure 12. Scenario 2 Configuration


Results of the 100 runs were collected and the mean values of the average number of bees collecting from the three food sources

were plotted into a graph that is illustrated in figure 14. Table 13 shows the DMRT results.



food N


1 2 3

1 100 2.1527

2 100 4.0993

3 100 5.2618

Sig. 1.000 1.000 1.000

With the F-value from Anova amounting to 7.696 x 10 3 and the significance value equal to 0, it was concluded that there is strong variance among the three means, the magnitude of which is characterized by table 14. The trend in the graph and the results from the DMRT shows that on the average, foragers collected mostly from food source 3. The food source with the least amount of visiting foragers on the average in this scenario was food source 1.

The layout of the food sources with respect to the hive in scenario 3 is just the same as that in the first scenario. However, the AHP matrix and the second row of the food value sliders were identical to that in the second scenario. The Layout is illustrated by Figure 9 while the AHP matrix and the food value sliders are shown in Figure 15.


The same statistical methods were performed for this scenario and the graph in figure 16, together with the DMRT results in Table 14 showed the same trend as Scenario 2 with Anova's F-value amounting to 1.044 x 104 and the significance value equal to 0.



food N


1 2 3

1 100 1.7923

2 100 4.3361

3 100 6.9642

Sig. 1.000 1.000 1.000

The second set of tests involved 12 scenarios where the first 9 scenarios labeled 4 to 12 tested the effect of the first version of the quasi-random walk in the average number of bees having no food collected from a source which was represented by yellow bees in the simulation. Meanwhile, the last three scenarios labeled 13 to 15 tested the effect of the second version of the quasi-random walk in the average number of bees having no food collected from a source. All scenarios of the second set were setup with the third scenario's layout and configuration. The scenarios differ from each other in terms of random-walk probability, a variable statically set by the user in the simulation, and the sensitivity radius. Table 15 shows the setup of each scenario in terms of random-walk probability and radius. It should be noted that random-walk probabilities don't apply with scenarios 13 to 15 because the probabilities are dynamically generated in the quasi-random walk algorithm used in them.

Table 15. Scenarios for the Quasi-Random walk implementations

Scenario Implementation Radius Random-walk

Probability

4 Quasi-Random 1 1 10









13 Quasi-Random 2 1 Not Applicable



Table 16. Duncan's Multiple Range Test for scenarios 3 to 15.

Scen.

GROUPS

1 2 3 4 5 6 7 8 9

11 1.73

8 1.78

9 1.88

6 1.88

12 2.19

5 2.25

10 2.43

7 2.67

4 3.10

13 3.66

14 3.81

15 3.82

3 13.42

Sig .111 .981 .051 1.00 1.00 1.00 1.00 .663 1.00

The means of 100 runs were collected and using statistical methods, the scenarios' results in terms of yellow bees were compared to scenario 3's results using the DMRT and Anova. The

DMRT shows that there's a significant difference between scenario 3 and the other scenarios implementing the quasi-random walk algorithm. It shows that the quasi-random walk significantly decreased the average number of failed foraging trips, which simulates the area restrict strategy of foragers to further achieve the optimal foraging theory.

4. CONCLUSIONIn conclusion, the multi-agent system presented in this study can be used to simulate the foraging behavior of stingless bees following the Optimal Foraging Theory. Statistical results verified that the system is able to correctly generate the expected total food gathered from different food sources using the Biroi Preference Algorithm. Furthermore, statistical results also verified that the quasi-random walk process lessens the rate of failed foraging trips which further reinforces the Optimal Foraging Theory.

Future plans for this study mainly deals with feeding the actual data from wet lab experiments to achieve more accurate simulations. There is also ongoing efforts in the 3D version of the system that allows the visualization of height as a parameter of food sources.

5. ACKNOWLEDGMENTSThe authors would like to thank the UPLB Bee Program for the data they have provided, the referees for their suggestions, Mr. Ramir Ramirez for helping us in the statistical analysis and the College of Arts and Sciences of UPLB for the financial support through CAS-TF #8217700.

6. REFERENCES[1] Cervancia, C.R., R.M. Lucero, A. Manila-Fajardo and A.C.

Fajardo, JR. Management of Native Bees (Trigona spp. Apis cerana, Apis dorsata) UP Los Baños. ISBN 978-971-547-272-2

[2] Cervancia, C.R. and E.A. Bergonia. 1991. Insect pollination of cucumber (Cucumis sativus L) in the Philippines. Acta Horticulturae. 228:278-281.

[3] Deyto, R.C. and C.R. Cervancia. 2009. Floral biology and pollination of ampalaya Momordicacharantia L. Philippine Agricultural scientist. 92(1), 8-18.

[4] Escobin,R.P. P.C. Payawal , C.R. Cervancia. 2004. Pollination syndrome of four reforestation tree species in Mt. Makiling, Luzon, Philippines. Pollination syndrome of four reforestation tree species in Mt. Makiling, Luzon, Philippines. Phil. Agr. Scientist. 87(2), 182-190.

[5] Fajardo, A.C., J.R. Medina, O.S. Opina and C.R. Cervancia. 2008. Insect pollinators and floral visitors of mango, Mangifera indica var. “carabao”. Philippine Agricutural Scientist 91(4) , 372-382.

[6] Ferber, J., Gutknetch, O., & Michel, F. (2003). From Agents to Organizations: an Organizational View of Multi-agent Systems. Agent-Oriented Software Engineering IV (pp. 1-18). Melbourne: LNCS, Springer Verlag.

[7] Gojmerac, W. Bees, Beekeeping, Honey and Pollination. Avi Publ. 1980.

[8] Manila-Fajardo A.C., F.C. Pitargue and C.R.Cervancia. 2003. Pollinators and floral characteristics of calamondin (x Citrofortunella microcarpa (Bunge) Wijjnands. Phil. Agric. Scientist 86(2), 131-133.

[9] NetLogo itself: Wilensky, U. NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University. Evanston, IL. 1999.

[10] Rabajante, J., Figueroa, R., & Jacildo A. Simulation of Bee Foraging Behavior using Biroi Preference Algorithm. . 15th BEENET Conference and Techno-fora. 2009

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[14] Vidal, J. M. Fundametals of Multiagent Systems with Netlogo Examples. 2009.

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