Model of prison riots

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/229345991 Model of prison riots Article in Physica A: Statistical Mechanics and its Applications · February 2007 DOI: 10.1016/j.physa.2006.08.069 CITATIONS READS 3 33 2 authors: Barbara Pabjan Andrzej Pekalski 24 PUBLICATIONS 25 CITATIONS 117 PUBLICATIONS 936 CITATIONS University of Wroclaw SEE PROFILE University of Wroclaw SEE PROFILE Some of the authors of this publication are also working on these related projects: The power of Collective Memory View project All content following this page was uploaded by Andrzej Pekalski on 29 January 2015. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ARTICLE IN PRESS Physica A 375 (2007) 307–316 www.elsevier.com/locate/physa Model of prison riots Barbara Pabjana, Andrzej P˛ekalskib, a b Institute of Sociology, University of Wroc!aw, ul. Koszarowa 3, 51-149 Wroc!aw, Poland Institute of Theoretical Physics, University of Wroc!aw, pl. M. Borna 9, 50-203 Wroc!aw, Poland Received 22 March 2006; received in revised form 14 August 2006 Available online 26 September 2006 Abstract We present a model of a prison with two types of inmates. One (recidivists) is a better organized and has more influence on the formation of opinions, whereas the second one is more susceptible to the influence of internal and external pressure. We study, via computer simulations, the interplay between well-organized minority and the rest and how the final decision, like e.g. starting a riot, depends on such factors as: fraction of recidivists, their initial support of the riot and possibility of contacts among cells. We find that, as expected, the riot is more likely to start if there is more recidivists favoring it at the beginning. The influence of external factors (media) turned out to have a larger impact on the second group of prisoners. Contrary to a common practice, we show that in order to prevent riots it might be better not to block the inter-cell contacts. r 2006 Elsevier B.V. All rights reserved. Keywords: Monte Carlo simulations; Prison riots; Social modelling 1. Introduction There is a growing interest in the theoretical physicists’ community in applications of statistical physics methods in biology [1–3], economy [4,5] and sociology [6,7] or general collective behavior of individuals [8]. For sociology simulation modelling is very important because it provides the insight into the dynamics of the social process whereas commonly used methods of research not always make it possible. Moreover, such models allow not only to test theory but also they are inspiring and may support constructing new theories in sociology. The most interesting is the possibility to study the dynamics of collective behavior itself and the relationships among variables of interest. There are many papers devoted to study prison crowding (mostly), misconduct of inmates and prison operations [9–11]. These are rather case studies dealing, by their nature, with individual details of the studied prison. A more general point of view on prison order has been presented in the papers by Bottoms [12] and Camp et al. [13]. In the later paper the influence of the environment and the role of various factors, characterizing a prison, upon inmates misconduct, has been studied. An important question, often addressed in sociological papers, is whether prison management could, using available means, create an environment reducing chances for inmates misconduct, in particular catastrophic Corresponding author. Tel.: +48 71 3759354; fax: +48 71 3201409. E-mail addresses: [email protected] (B. Pabjan), [email protected] (A. P˛ekalski). 0378-4371/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2006.08.069 ARTICLE IN PRESS 308 B. Pabjan, A. P˛ekalski / Physica A 375 (2007) 307–316 ones, like riots. In this paper, we propose a simulation model of a prison and we shall determine the influence of the external factors and possible contacts between cells on the behavior of inmates, in particular on a possibility of a riot. Quite recently also sociologists have found that computer-based simulations, called by them Agent Based Models, are very useful tools in describing human populations [14,15]. Simulating social behavior by means of an Ising-type model is, of course, not novel. As far as we know, the papers by Schelling [16] and Galam [17] could be regarded as the pioneering ones. In the model proposed here, also of an Ising-type, we analyze a dynamics of a specific social process— expanding the support for riot in a prison community. This type of community is a specific one; it is of a medium size, relatively closed, it has hierarchical structure and high level of social control. Thus, it is a highly organized social entity-community. Consequently, we assume that we describe in the model a collective action which is the effect of organized activity and it is not similar to mass behavior of the crowd. The latter is based only on imitation of behavior of the others and conformity to the majority. Crowds are not organized and have no structure. Riots in organized community are to some extent planned actions and only in some part they are spontaneous. It is worth to note that the very important features (variables) explaining the dynamics of the riot are used in the model. This approach allows to examine the importance of each element (variable) in the process of developing support for the riot. We have decided to use just a few parameters, nevertheless these variables can be interpreted in other sociological terms such as structure, communication channels, social interests, social control, social ties, group solidarity, etc. As a result of such a translation of meaning it is possible to explain the phenomenon of riot in a broader sociological perspective. The model also combines two levels of social reality: a microsystem and a macrosystem: the prisoners’ group in the cells within the prison community (microsystem) and outside environment (the media as a part of macrosystem). Recidivists are treated here as special type of community, and this category does not have to be interpreted literally. Being a recidivist here means being a member of a better organized community which has a structure, social control and therefore recidivists are more influential. Thus, being a recidivist can be interpreted in other terms as being a member of a gang, an organized crime group or a subculture group, or being a more powerful member of the prison community. Prison authorities usually separate various types of inmates in different sections or cells in prison e.g. recidivism, sexual crime, age, sex are the criteria of spatial segregation in prisons. But let us assume that this variable is an indicator of a higher position and power of individuals in the group. Thus we can examine how the differentiation in the group structure (micro level) influences the behavior in the whole community (macro level). The social characteristics of prison environment are of course more complicated. We have chosen the variables which seem to be crucial for the development of the collective and spontaneous action such as a riot. The interesting feature of the social system is the structure of communication. In the presented model, we can see for example the role of communication channels and influence of structure of power on forming an opinion. To the best of our knowledge similar problems have not been yet considered by physicists. We have in our model some particular features reducing a possibility of a riot. We do not claim that we have found the solution for riots preventing. Our results should be rather treated (as is always the case with such theoretical models) as an indication for further field studies. 2. Model We consider a system (prison) composed of a fixed number of entities (inmates) distributed among a given number ðN ¼ 30Þ of cells. The number of inmates in a cell varies randomly between 3 and 10 and remains constant during the simulations. The inmates are of two kinds—recidivists (called later on R-type inmates) and non-recidivists. The percentage of recidivists, C R , in the system is a parameter of the model. The recidivists are put randomly in the cells. Each inmate has an opinion about the problem we shall investigate here—starting a riot in the prison. The opinion could be either þ1 YES, or 1 NO. In each cell there is a hierarchy—an inmate with higher position has a stronger influence on other inmates and is less susceptible to the opinions of others. These weights are attributed to the inmates at the beginning of the simulation and remain unchanged. The distribution is random, but for the R-type inmates the weights are between 0.5 and 1, while for the others between 0 and 0.5. The choice of the intervals for the weights is, of course, arbitrary. ARTICLE IN PRESS B. Pabjan, A. P˛ekalski / Physica A 375 (2007) 307–316 309 However, such disjoint segments show clearly our points. Moreover, this reflects the fact that recidivists play a more important role in prison cells. The choice of the limits is, of course, arbitrary. We have checked that allowing the limits to overlap (e.g. ½0; 0:6 and ½0:4; 1) or shifting them farther apart (like ½0; 0:4 and ½0:6; 1) does not change the results in any significant way. Each inmate is subject to a pressure (‘‘field’’). This pressure is the prevailing opinion in a given cell and is coming from inside and outside of the cell. The former comes from all the inmates in the same cell, while the later is composed of opinions formed in other cells and by the media. Denoting the weight of an individual j in a cell k by wðk; jÞ and his opinion by oðk; jÞ, we have for the opinion of the cell k X fk ¼ oðk; jÞwðk; jÞ. (1) j This is however not the final field, since we allow for contacts between cells. The intensity (ease) of these contacts is described by the parameter a 2 ½0; 1. Small values of a correspond to weak contacts. We have assumed also, in agreement with the field data, that the effectiveness of the contacts between a given cell and another one, l, is proportional to the density, nR ðlÞ of R-type inmates in the cell l. Therefore the total field (temporal opinion in a cell k) is X Fk ¼ fl nR ðlÞa þ f0 , (2) lak where f0 is the external field (media). Such a field Fk , will remain constant during one Monte Carlo step (MCS), i.e., checking all N cells. Clearly the sign of the field could be either positive (supporting the riot), or negative (against it). Once the fields in all cells are evaluated, we pick consecutively individuals in each cell and check whether his opinion, oðk; jÞ, agrees with the local field Fk . If it does, no action is taken. If it is different (the signs are different), the inmate may change his opinion with a probability pk;j , calculated as   Fk pk;j ¼ exp  . (3) wðk; jÞ The higher the pressure in the cell and the weaker the inmate (his position in the cell), the larger is the chance that he will change his mind. If pk;j is smaller than a random number r 2 ½0; 1, then the inmate changes his opinion oðk; jÞ ¼ oðk; jÞ. After updating the opinions of all inmates, we calculate the global opinion at a given time—MðtÞ XX MðtÞ ¼ oðk; jÞ. k (4) (5) j We allow the R-inmates to have different initial preferences regarding the riot. At the beginning the opinions of the R-type inmates are taken randomly from the interval ½0; SR , where S R is a parameter 2 ½0; 1. S R ¼ 1 means that on average the R-inmates totally support the riot, and SR ¼ 0—that they reject it. The initial support by non-recidivists is always random, i.e., it is equal (on average) 0.5. We want to find out how the global (averaged over all cells) support MðtÞ depends on the percentage of recidivists ðC R Þ, their initial support of the riot ðS R Þ, external field ðf0 Þ and contacts between cells (a). The simulation is run till the system reaches a stationary state, i.e., the global opinion stabilizes. This typically takes about 100 MCS. The runs are repeated with different seeds for the random number generator, but the same values of the parameters. The results presented below were averaged over 1000 such runs. As was mentioned before, it is the influence of chosen social features (variables) on collective behavior and relationship between variables that we analyze in the model. The parameters of the model are important social variables and are often used while describing social behavior in a group. In our model, we apply these variables to describe collective behavior in a specific type of a group, namely a closed group. The initial support for the riot may be related to the division of interests of prisoners. The percentage of recidivists indicates the structure of each cell and the structure of the community of prisoners in the whole prison; easy or ARTICLE IN PRESS B. Pabjan, A. P˛ekalski / Physica A 375 (2007) 307–316 310 difficult contact between prisoners corresponds to the type of communication structure and the spatial distribution of the group. A typical problem in the field of collective behavior is the relation between majority and minority. Whereas the advantage and strength of majority is obvious, the interesting problem is the power of the minority against the majority. An attention-grabbing question is how strong must be the minority to be more powerful and more influential than majority? This is also the issue of power of the elite, as each strong minority is potentially the elite of power. 3. Results and discussion We have decided to simulate the effect of the media by assuming that there is an interest in the media about the situation in the prison and the media are supporting the riot. However, after certain time another hot topic shows up and the interest of the media in the situation in the prison drops to zero. We consider below two cases: in the first one the media are simply absent ðf0 ¼ 0Þ and in the second one the support of the media starts at some time t1 , grows linearly and then disappears at time t2 . In our simulations t1 ¼ 20 MCS and t2 ¼ 60 MCS. Particular values of t1 and t2 are not important. Changing their values will not influence the results in a qualitative way. In Fig. 1, we present the dependence of the global opinion about the riot on concentration of recidivists ðC R Þ in the case when the media are absent. Positive values of the opinion mean support, negative ones—rejection. The presented curves correspond to the case of difficult contact between cells ða ¼ 0:1Þ, however the curves look much the same also for a ¼ 1. We can therefore conclude that in the absence of the media it is the local field within each cell which determines the outcome. The final opinion depends on the initial support of the R-inmates and their concentration. When there are just a few of them, their preferences (SR values) do not matter. However if C R  0:3 the outcome is determined by their initial preferences. Facility of contacts does not play a significant role. In Fig. 2 we show the time dependence of the global opinion in the presence of media, for difficult ða ¼ 0:1Þ contacts between cells and three values of the averaged initial support of the R-inmates 0:25 (rather negative, Fig. 2(a)), 0.50 (random, Fig. 2(b)) and 0.75 (strong, Fig. 2(c)). In the legends, we have indicated the percentage of cases in which the idea of the riot won support (e.g. þð14Þ) and in which it lost (e.g ð86Þ). We see from Fig. 2a that the media have the strongest impact on the non-recidivists, hence the media influence is stronger when C R is small. For example, the media cannot change strong negative attitude when 70% of the inmates are of R-type. An important question here is what kind of external influence (e.g. the media) can shape the opinion of the group and how strong is such an impact of the outside environment. This is one of the most popular issues, 1 SR=0.40 SR=0.45 SR=0.50 SR=0.55 SR=0.60 Final opinion 0.5 0 -0.5 a = 0.1 -1 0 0.1 0.2 0.3 0.4 0.5 CR 0.6 0.7 0.8 0.9 1 Fig. 1. Final opinion as a function of concentration of R-type inmates. Contacts between cells are difficult. Media are absent. ARTICLE IN PRESS B. Pabjan, A. P˛ekalski / Physica A 375 (2007) 307–316 311 1 Opinion 0.5 CR=0.2 + (100) CR=0.5 + ( 14) CR=0.5 -- ( 86) CR=0.7 -- (100) media/2 0 -0.5 a = 0.1, SR = 0.25 -1 20 40 60 80 60 80 Time (a) 1 Opinion 0.5 CR=0.2 + (100) CR=0.5 + ( 92) CR=0.5 -- ( 8) CR=0.7 + (58) CR=0.7 -- (42) 0 -0.5 a = 0.1, SR = 0.50 -1 20 40 Time (b) 1 Opinion 0.5 0 -0.5 CR=0.2 + (100) CR=0.5 + (100) CR=0.7 + (100) media/2 a = 0.1, SR = 0.75 -1 20 (c) 40 60 80 Time Fig. 2. Time dependence of the global opinion MðtÞ: (a) initial support of R-type inmates is small ðSR  SR ¼ 0:25Þ; (b) initial support of R-type inmates is random ðSR ¼ 0:5Þ; (c) initial support of R-type inmates is strong ðSR ¼ 0:75Þ. Contacts between cells are difficult a ¼ 0:1. Changes in the media are shown. ARTICLE IN PRESS 312 B. Pabjan, A. P˛ekalski / Physica A 375 (2007) 307–316 especially on the ground of the common knowledge. The model shows that media (or the outside environment) has a restricted influence on the group knowledge when other features of community are strong enough. The model proves that the strength of the particular social variable can overcome the influence of the media. The sociological interpretation of the result in the model can be as follows: if the C R is strong there is the specific structure of the group where R have higher position, more power and are more influential. As a consequence they have great impact on the group. So the strong C R account for other special characteristics of the group such as high level of in-group conformism and social control, high level of control performed by the particular group (recidivists), or high level of in-group solidarity stimulated by strong leaders and their supporters. It also means that the relations inside the group are more powerful than the relations with the outside environment, e.g. when there are strong and numerous leaders (strong C R ) then they affect the microsystem directly and the pressure of the media (the outside environment) is of no or little importance. This is also seen in Fig. 2b, when the initial preference of all inmates is random. When the concentration of R-type inmates is 70%, the chances of supporting the riot are about fifty-fifty. However when half of the inmates are of the R-type, the chances grow tremendously to about 90%. Analogous dependence, but for easy contacts between cells, is presented in Fig. 3. They may look similar, but there are nevertheless important differences. In Fig. 2(a) two cases (C R ¼ 0:2 and C R ¼ 0:5) may lead to a riot, while only one does it in Fig. 3(a). Also for S R ¼ 0:5 (Figs. 2(b) and 3(b)) the chances for a riot go down when the contacts are easier. There are practically no differences between Figs. 2(c) and 3(c), which correspond to strong initial support from the R-inmates. This result is also interesting, and the interpretation which is adequate here points out that when the group is strong and the communication channels are open (easy contacts) among the powerful members of the group, the conflict of interests may appear and the collective common behavior such as a riot is less possible. Relatively strong C R leads to the splitting up of the community and its leaders. As a result two (or more) opposite groups may appear. It happens very often when leaders fight for power against each other. In such cases, the direct and easy communication enables or even stimulates splitting because it may take form of confrontation, fight, etc. Fig. 4(a) and (b) show the final (in the asymptotic state) opinion versus concentration of the R-inmates, for a ¼ 0:1 and a ¼ 1, respectively. If the concentration C R is either larger than 0.7 or smaller than 0.1, the value of a has nearly no effect on the final decision. Otherwise, if SR p0:5, weaker contacts make the support of the riot more likely. For example for C R ¼ 0:3 and S R ¼ 0:4 the chance for the riot is about 99% for a ¼ 0:1 and only 35% for a ¼ 1. All these features are summarized in Fig. 5, which shows a phase diagram in the ðS R ; C R Þ plane. The surface is divided into two regions—one where the final support is greater than 50% and the second one where it is smaller than 50%. It is evident that if the initial support of the R-inmates is less than 0.5 then in order to prevent a riot it is better to allow for easy contacts between cells. Only when the initial support approaches 0.5, restriction of the contact diminishes slightly the probability of the riot. Analogous phase diagram for the case without the media shows a rather simple feature. As long as the initial support of the R-inmates is less than 0.5 there is practically no chance for the final support. Once it exceeds 0.5, the probability jumps to 1. This result is very interesting not only because of possible predictions of the rising-up riot and practical decisions but also for the examining the role of direct and effective communication in spreading the ideas. This result is in contradiction with common knowledge and practice in prisons. The typical action which is supposed to prevent the riots is to restrict the communication as much as possible. The model suggests that other solution may be more effective; the restricted communication may increase the support for riot because it stimulates the rising of the in-group solidarity and the opposition in case of lack of communication. The lack of direct communication itself does not prevent from forming the strong opinion or support which constitutes the resistance to the system of formal control of information. This result is worth to note because it provides some arguments in the dispute on collective actions, conscience or representation. All collective social phenomena are not reducible to individual constituents which means they create the emergent social order. The interesting issue is to examine the relations between individual and collective levels of social life. We think this result can be also interpreted as an example of the influence of the ‘‘climate’’ of the opinion or public opinion. This social phenomenon is not simply the sum of the opinions of individuals and does not have to be formed just by spreading the information directly from one ARTICLE IN PRESS B. Pabjan, A. P˛ekalski / Physica A 375 (2007) 307–316 313 1 Opinion 0.5 CR=0.2 + (65) CR=0.2 -- (35) CR=0.5 -- (100) CR=0.7 -- (100) 0 -0.5 a=1.0, SR=0.25 -1 20 40 60 80 Time (a) 1 Opinion 0.5 CR=0.2 + (88) CR=0.2 -- (12) CR=0.5 + (64) CR=0.5 -- (36) CR=0.7 + (46) CR=0.7 -- (54) 0 -0.5 a = 1.0, SR = 0.50 -1 20 40 60 80 Time (b) 1 Opinion 0.5 0 -0.5 CR=0.2 + (100) CR=0.5 + (100) CR=0.7 + (100) a = 1.0, SR = 0.75 -1 20 (c) 40 60 80 Time Fig. 3. Time dependence of the global opinion MðtÞ: (a) initial support of R-type inmates is small ðSR ¼ 0:25Þ; (b) initial support of R-type inmates is random ðSR ¼ 0:5Þ; (c) initial support of R-type inmates is strong ðSR ¼ 0:75Þ. Contacts between cells are easy ða ¼ 1Þ. ARTICLE IN PRESS B. Pabjan, A. P˛ekalski / Physica A 375 (2007) 307–316 314 1 SR=0.10 SR=0.20 SR=0.30 SR=0.40 SR=0.45 SR=0.50 Final opinion 0.5 0 -0.5 a = 0.1 -1 0 0.1 0.2 0.3 0.4 (a) 0.5 CR 0.6 0.7 0.8 0.9 1 1 SR=0.10 SR=0.20 SR=0.30 SR=0.40 SR=0.45 SR=0.50 Final opinion 0.5 0 -0.5 a = 1.0 -1 0 (b) 0.1 0.2 0.3 0.4 0.5 CR 0.6 0.7 0.8 0.9 1 Fig. 4. Final global opinion versus concentration of the R-inmates: (a) contacts between cells are difficult a ¼ 0:1; (b) contacts between cells are easy a ¼ 1. individual to the other. Public opinion is a commonly shared collective knowledge based on the previous experience of the group and the history of group relations. This may prove that the face-to-face communication is not necessary to create the common perception of interests or threats. We can also express our model in terms of magnetic moments, treating the inmates as particles with spin 12, which are grouped into clusters of irregular, but restricted size. The particles apart from the spin degree of freedom have also another one—their weight w. They interact inside the clusters with forces proportional to their weights and are susceptible to changes of their spin with a probability which is the inverse of the weight. The local fields, f, created by the interactions sum up to an equivalent of a mean field F. However this mean field is not simply proportional to MðtÞ, but is constructed from microscopic interactions. There is also an external field f0 . 4. Conclusions We have presented a model of a closed system composed of a fixed number of objects organized in closed groups and interacting among themselves and with the external field. The objects were interpreted as inmates and the groups as cells. The external field represented the media. We wanted to estimate the role of strong ARTICLE IN PRESS B. Pabjan, A. P˛ekalski / Physica A 375 (2007) 307–316 315 1 a = 0.1 a = 1.0 0.8 CR. 0.6 SUPPORT < 50 % 0.4 0.2 SUPPORT > 50 % 0 0 0.1 0.2 0.3 SR 0.4 0.5 0.6 Fig. 5. Phase diagram showing for which values of CR and SR out of 1000 runs at least 50% lead to support of the riot. Contacts between cells are difficult a ¼ 0:1 and easy a ¼ 1. leaders inside each cell (recidivists) on a probability of a riot in the prison. Our findings indicate that when the media are absent the crucial role is played by the recidivists—their fraction in the total population and how strong was their initial support of the riot. When we allowed the media to interfere with the opinion of the inmates, it turned out that when the initial support was rather weak riot has a less chance if the contacts were strong and there were more recidivists since the media have stronger effect on non-recidivists than on the recidivists. Our results show that when the fraction of recidivists supporting a riot is high, it is not important whether there are good or poor contacts between cells. However when this fraction is low, the riot is less likely to happen if the contacts are easy. It could be therefore a good policy to keep these channels open. Such a solution seems to be very controversial because it is in contradiction with the common sense and the practice of the correctional policy but it is quite understandable and reasonable from the sociological point of view. There is a gap between theory and practice. The social research of conflicts proves that there is a strong connection between the level of restrictions in the society (social structure, constraint in communication, etc.) and the strength of the conflicts. The conflict of interests is a common feature of societies. It can be resolved in many ways but we can observe some rules: different consequences follow diverse types of conflict resolutions (e.g. it is known that compromise and negotiation can prevent the outburst of violent conflicts). The social conflicts are usually violent when the restrictions are strong, because it means that one of the group wins and the other loses its interest. Concluding, to prevent the explosion of a riot it is better to impose less restricted social relations and free contacts among cells might be the indicator of a less restricted policy in the prisons. One should also note that the situation we describe here and the role of recidivists in creating a riot, is linked to the much more studied problem of the role of minority in opinion spreading (see e.g. Ref. [18]). Our general conclusions are as follows: Combining physics and sociology is a chance to explore the collective action in experimental conditions. What more, the dynamics of the process mimicking real life situations, can be examined more carefully. The interdependence of prisoners has a dynamic character and is one of the advantages of using models to find an explanation of the role of particular factors. We can hope for some the practical usage of the information obtained in the analyzed model. Finally, the model makes clear what is the role of particular elements of the system (e.g. variables describing the social system and social action in the riot). It shows the outcome of a dynamic social process as the result of inferences between variables such as group structure, communication channels, social interests, social control, social ties, group solidarity. The model provides the estimation of the effects of social variables in mutual relations. One could expect a different dependence of the support of a riot on the parameters of the model, if the recidivists are put separately from non-recidivists. In particular, we have found that the lines separating the more and less than 50% support in Fig. 5, start at S R  0:2, go as a more or less straight line to 1 at S R ¼ 0:5. ARTICLE IN PRESS B. Pabjan, A. P˛ekalski / Physica A 375 (2007) 307–316 316 Since the contacts between cells are, in our model, related to the number of recidivists in the cells, the value of the parameter a does not play an essential role. In this paper we discussed the behavior of inmates in a rather small prison. A detailed study of the way in which inmates are located in a prison and the role played by the size of the prison, is the subject of our next paper. We believe this model shows how emergent order e.g. collective (or public) opinion evolves from individual opinions and above all from the very social process such as influence of structure, power and social control. 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