K. Staňková
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Stackelberg EvolutionaryGame (SEG) theory frames interactions between a rational leader and evolving followers, who play an evolutionary game among themselves. This framework has applications in managing evolving populations, including fisheries management, pest control, and cancer treatment. To manage an evolving systemin question, in the standard practice, the leader usually adopts a constant aggressive strategy, with the aim to either preserve (e.g., fisheries management) or eradicate (e.g., pest control) the evolving system. However, adopting an aggressive constant strategy ignores the evolving nature of the population in question.
In this thesis, we identify leader’s Nash and Stackelberg strategies in the game, assuming that the evolutionary followers have reached their eco-evolutionary equilibrium. We show that the constant aggressive strategy yields the least favorable outcome for the leader compared to the Nash and Stackelberg strategies. Furthermore, we show that the Stackelberg strategy consistently provides equal or better outcomes for the leader compared to the Nash strategy, as measured by the value of the leader’s objective function. We further explore the SEG framework in cancer treatment, where the followers are treatment-sensitive and treatment-resistant cancer cell populations. The resistant population develops treatment-induced resistance as a quantitative trait. We investigate how a physician as the leader can optimize treatment strategies to maximize patient’s quality of life by anticipating the cancer cells’ treatment-induced response. Three treatment strategies are compared: maximum tolerable dose (MTD), which is commonly used as the standard of care; the Nash strategy; and the Stackelberg strategy. The physician uses the Nash strategy when they take the cancer cells’ ecological equilibrium point into account. However, the physician uses the Stackelberg strategy when they take the eco-evolutionary response of cancer cells into account. Our results demonstrate that the Stackelberg strategy achieves the best outcomes, including reduced treatment-induced resistance, lower drug dosage, and improved patient’s quality of life. We show that the quality of life achieved with the Stackelberg strategy is at least as high as that of the Nash strategy, which typically outperforms theMTD approach.
The best strategy for the leader will depend on our understanding of the underlying eco-evolutionary dynamics of the evolutionary followers. To understand what the best evolutionary game for modeling cancer under treatment is, we fit various models to non-small cell lung cancer (NSCLC) in-vitro data analyzed earlier by Kaznatcheev et al. and Soboleva et al.. These experiments measure cell counts of Alectinib-sensitive and Alectinib-resistant cancer cells in environments with and without Alectinib and the presence or absence of cancer-associated fibroblasts (CAFs). We compare logistic, Gompertz, and von Bertalanffy growth models, along with Norton-Simon, linear, and ratiodependent treatment efficacy terms. We also examine how Alectinib and CAFs influence model parameters and, subsequently, the interactions between cancer cells. For monoculture data, our results indicate that the logistic model with ratio-dependent treatment efficacy provides the best fit. We derive inter-type competition coefficients for co-culture data using growth rate and carrying capacity estimates from monoculture. Statistical tests reveal that growth rate and carrying capacity parameters remain largely unaffected by the presence of CAFs. However, cell interactions in co-cultures vary significantly across environments due to changes in competition coefficients and drug efficacy. Specifically, we show that CAFs enable the coexistence of sensitive and resistant cells, whereas Alectinib favors the outcompetition of sensitive cells by resistant ones. This PhD thesis furthers Stackelberg evolutionary games to frame interactions between a rational leader and evolutionary followers. We integrate SEG theory with empirical cancer growth modeling, highlighting the potential of game-theoretic approaches to enhance cancer treatment outcomes. We also discuss the challenges and future opportunities for applying this framework to other domains where managing evolving systems is essential. ...
In this thesis, we identify leader’s Nash and Stackelberg strategies in the game, assuming that the evolutionary followers have reached their eco-evolutionary equilibrium. We show that the constant aggressive strategy yields the least favorable outcome for the leader compared to the Nash and Stackelberg strategies. Furthermore, we show that the Stackelberg strategy consistently provides equal or better outcomes for the leader compared to the Nash strategy, as measured by the value of the leader’s objective function. We further explore the SEG framework in cancer treatment, where the followers are treatment-sensitive and treatment-resistant cancer cell populations. The resistant population develops treatment-induced resistance as a quantitative trait. We investigate how a physician as the leader can optimize treatment strategies to maximize patient’s quality of life by anticipating the cancer cells’ treatment-induced response. Three treatment strategies are compared: maximum tolerable dose (MTD), which is commonly used as the standard of care; the Nash strategy; and the Stackelberg strategy. The physician uses the Nash strategy when they take the cancer cells’ ecological equilibrium point into account. However, the physician uses the Stackelberg strategy when they take the eco-evolutionary response of cancer cells into account. Our results demonstrate that the Stackelberg strategy achieves the best outcomes, including reduced treatment-induced resistance, lower drug dosage, and improved patient’s quality of life. We show that the quality of life achieved with the Stackelberg strategy is at least as high as that of the Nash strategy, which typically outperforms theMTD approach.
The best strategy for the leader will depend on our understanding of the underlying eco-evolutionary dynamics of the evolutionary followers. To understand what the best evolutionary game for modeling cancer under treatment is, we fit various models to non-small cell lung cancer (NSCLC) in-vitro data analyzed earlier by Kaznatcheev et al. and Soboleva et al.. These experiments measure cell counts of Alectinib-sensitive and Alectinib-resistant cancer cells in environments with and without Alectinib and the presence or absence of cancer-associated fibroblasts (CAFs). We compare logistic, Gompertz, and von Bertalanffy growth models, along with Norton-Simon, linear, and ratiodependent treatment efficacy terms. We also examine how Alectinib and CAFs influence model parameters and, subsequently, the interactions between cancer cells. For monoculture data, our results indicate that the logistic model with ratio-dependent treatment efficacy provides the best fit. We derive inter-type competition coefficients for co-culture data using growth rate and carrying capacity estimates from monoculture. Statistical tests reveal that growth rate and carrying capacity parameters remain largely unaffected by the presence of CAFs. However, cell interactions in co-cultures vary significantly across environments due to changes in competition coefficients and drug efficacy. Specifically, we show that CAFs enable the coexistence of sensitive and resistant cells, whereas Alectinib favors the outcompetition of sensitive cells by resistant ones. This PhD thesis furthers Stackelberg evolutionary games to frame interactions between a rational leader and evolutionary followers. We integrate SEG theory with empirical cancer growth modeling, highlighting the potential of game-theoretic approaches to enhance cancer treatment outcomes. We also discuss the challenges and future opportunities for applying this framework to other domains where managing evolving systems is essential. ...
Stackelberg EvolutionaryGame (SEG) theory frames interactions between a rational leader and evolving followers, who play an evolutionary game among themselves. This framework has applications in managing evolving populations, including fisheries management, pest control, and cancer treatment. To manage an evolving systemin question, in the standard practice, the leader usually adopts a constant aggressive strategy, with the aim to either preserve (e.g., fisheries management) or eradicate (e.g., pest control) the evolving system. However, adopting an aggressive constant strategy ignores the evolving nature of the population in question.
In this thesis, we identify leader’s Nash and Stackelberg strategies in the game, assuming that the evolutionary followers have reached their eco-evolutionary equilibrium. We show that the constant aggressive strategy yields the least favorable outcome for the leader compared to the Nash and Stackelberg strategies. Furthermore, we show that the Stackelberg strategy consistently provides equal or better outcomes for the leader compared to the Nash strategy, as measured by the value of the leader’s objective function. We further explore the SEG framework in cancer treatment, where the followers are treatment-sensitive and treatment-resistant cancer cell populations. The resistant population develops treatment-induced resistance as a quantitative trait. We investigate how a physician as the leader can optimize treatment strategies to maximize patient’s quality of life by anticipating the cancer cells’ treatment-induced response. Three treatment strategies are compared: maximum tolerable dose (MTD), which is commonly used as the standard of care; the Nash strategy; and the Stackelberg strategy. The physician uses the Nash strategy when they take the cancer cells’ ecological equilibrium point into account. However, the physician uses the Stackelberg strategy when they take the eco-evolutionary response of cancer cells into account. Our results demonstrate that the Stackelberg strategy achieves the best outcomes, including reduced treatment-induced resistance, lower drug dosage, and improved patient’s quality of life. We show that the quality of life achieved with the Stackelberg strategy is at least as high as that of the Nash strategy, which typically outperforms theMTD approach.
The best strategy for the leader will depend on our understanding of the underlying eco-evolutionary dynamics of the evolutionary followers. To understand what the best evolutionary game for modeling cancer under treatment is, we fit various models to non-small cell lung cancer (NSCLC) in-vitro data analyzed earlier by Kaznatcheev et al. and Soboleva et al.. These experiments measure cell counts of Alectinib-sensitive and Alectinib-resistant cancer cells in environments with and without Alectinib and the presence or absence of cancer-associated fibroblasts (CAFs). We compare logistic, Gompertz, and von Bertalanffy growth models, along with Norton-Simon, linear, and ratiodependent treatment efficacy terms. We also examine how Alectinib and CAFs influence model parameters and, subsequently, the interactions between cancer cells. For monoculture data, our results indicate that the logistic model with ratio-dependent treatment efficacy provides the best fit. We derive inter-type competition coefficients for co-culture data using growth rate and carrying capacity estimates from monoculture. Statistical tests reveal that growth rate and carrying capacity parameters remain largely unaffected by the presence of CAFs. However, cell interactions in co-cultures vary significantly across environments due to changes in competition coefficients and drug efficacy. Specifically, we show that CAFs enable the coexistence of sensitive and resistant cells, whereas Alectinib favors the outcompetition of sensitive cells by resistant ones. This PhD thesis furthers Stackelberg evolutionary games to frame interactions between a rational leader and evolutionary followers. We integrate SEG theory with empirical cancer growth modeling, highlighting the potential of game-theoretic approaches to enhance cancer treatment outcomes. We also discuss the challenges and future opportunities for applying this framework to other domains where managing evolving systems is essential.
In this thesis, we identify leader’s Nash and Stackelberg strategies in the game, assuming that the evolutionary followers have reached their eco-evolutionary equilibrium. We show that the constant aggressive strategy yields the least favorable outcome for the leader compared to the Nash and Stackelberg strategies. Furthermore, we show that the Stackelberg strategy consistently provides equal or better outcomes for the leader compared to the Nash strategy, as measured by the value of the leader’s objective function. We further explore the SEG framework in cancer treatment, where the followers are treatment-sensitive and treatment-resistant cancer cell populations. The resistant population develops treatment-induced resistance as a quantitative trait. We investigate how a physician as the leader can optimize treatment strategies to maximize patient’s quality of life by anticipating the cancer cells’ treatment-induced response. Three treatment strategies are compared: maximum tolerable dose (MTD), which is commonly used as the standard of care; the Nash strategy; and the Stackelberg strategy. The physician uses the Nash strategy when they take the cancer cells’ ecological equilibrium point into account. However, the physician uses the Stackelberg strategy when they take the eco-evolutionary response of cancer cells into account. Our results demonstrate that the Stackelberg strategy achieves the best outcomes, including reduced treatment-induced resistance, lower drug dosage, and improved patient’s quality of life. We show that the quality of life achieved with the Stackelberg strategy is at least as high as that of the Nash strategy, which typically outperforms theMTD approach.
The best strategy for the leader will depend on our understanding of the underlying eco-evolutionary dynamics of the evolutionary followers. To understand what the best evolutionary game for modeling cancer under treatment is, we fit various models to non-small cell lung cancer (NSCLC) in-vitro data analyzed earlier by Kaznatcheev et al. and Soboleva et al.. These experiments measure cell counts of Alectinib-sensitive and Alectinib-resistant cancer cells in environments with and without Alectinib and the presence or absence of cancer-associated fibroblasts (CAFs). We compare logistic, Gompertz, and von Bertalanffy growth models, along with Norton-Simon, linear, and ratiodependent treatment efficacy terms. We also examine how Alectinib and CAFs influence model parameters and, subsequently, the interactions between cancer cells. For monoculture data, our results indicate that the logistic model with ratio-dependent treatment efficacy provides the best fit. We derive inter-type competition coefficients for co-culture data using growth rate and carrying capacity estimates from monoculture. Statistical tests reveal that growth rate and carrying capacity parameters remain largely unaffected by the presence of CAFs. However, cell interactions in co-cultures vary significantly across environments due to changes in competition coefficients and drug efficacy. Specifically, we show that CAFs enable the coexistence of sensitive and resistant cells, whereas Alectinib favors the outcompetition of sensitive cells by resistant ones. This PhD thesis furthers Stackelberg evolutionary games to frame interactions between a rational leader and evolutionary followers. We integrate SEG theory with empirical cancer growth modeling, highlighting the potential of game-theoretic approaches to enhance cancer treatment outcomes. We also discuss the challenges and future opportunities for applying this framework to other domains where managing evolving systems is essential.
Improving Surgical Decision-Making using Artificial Swarm Intelligence
How pancreatic cancer care can be advanced by integrating medical expertise and Artificial Intelligence
In treating patients with pancreatic cancer, multidisciplinary team (MDT) meetings have been established as the clinical standard for discussing patient cases using combined expertise from various specialisations. However, despite the combined expertise, 19%-33% of all pancreatic surgeries is observed to be prematurely abandoned due to locally advanced pancreatic cancer or metastatic disease. Furthermore, MDT meetings typically feature an open discussion format that can be subject to social influence factors affecting the overall objectivity of individual expert opinions. Subsequently, this research explores Artificial Swarm Intelligence (ASI) as a potential technology to overcome the aforementioned issues. Through an experiment, this research tests the use of ASI in a simulated MDT meeting and examines its effects on the accuracy of resectability assessment. Furthermore, a survey is conducted to assess the perceived impact of ASI on social loafing and social bias influences, as well as potential enablers and barriers for the potential implementation of ASI. Based on the experiment results, the use of ASI shows equal assessment accuracy compared to assessing tumor resectability through discussion as with regular MDT meetings. However, with regard to social influ- ence, participants assessed ASI to moderately drive reduction factors that reduce social loafing and social bias - suggesting indirect benefits to the objectivity of the decision process. ...
In treating patients with pancreatic cancer, multidisciplinary team (MDT) meetings have been established as the clinical standard for discussing patient cases using combined expertise from various specialisations. However, despite the combined expertise, 19%-33% of all pancreatic surgeries is observed to be prematurely abandoned due to locally advanced pancreatic cancer or metastatic disease. Furthermore, MDT meetings typically feature an open discussion format that can be subject to social influence factors affecting the overall objectivity of individual expert opinions. Subsequently, this research explores Artificial Swarm Intelligence (ASI) as a potential technology to overcome the aforementioned issues. Through an experiment, this research tests the use of ASI in a simulated MDT meeting and examines its effects on the accuracy of resectability assessment. Furthermore, a survey is conducted to assess the perceived impact of ASI on social loafing and social bias influences, as well as potential enablers and barriers for the potential implementation of ASI. Based on the experiment results, the use of ASI shows equal assessment accuracy compared to assessing tumor resectability through discussion as with regular MDT meetings. However, with regard to social influ- ence, participants assessed ASI to moderately drive reduction factors that reduce social loafing and social bias - suggesting indirect benefits to the objectivity of the decision process.
Police Strategies for Fugitive Interception
A case study in the metro network of Rotterdam
When a crime is committed, catching the offender in the act has several benefits. Among others, it provides evidence of the offender's involvement in the crime, which simplifies the conviction process. However, to capture an offender in the act, the collaboration of multiple police officers is required. When a crime is being reported through the emergency line, it is the responsibility of the police officers in the control room to answer the call. They gather information on the type of crime, the location, a description of the offender, etc. Subsequently, they dispatch police units to the crime scene. The first unit prioritizes reaching the crime scene to ensure the safety of citizens, while the other units are tasked with locating and apprehending the offender.
To adequately respond to reported crimes, police officers in the control room and units on the street rely on intuition, experience, and habit. This leads to the development of individual-specific strategies for handling interception scenarios. Reducing the dependency on these individualized approaches by identifying proven and robust strategies could increase the likelihood of successfully capturing a suspect. However, how the police currently save data on fugitive interception scenarios does not allow for such identification. Hence, alternative approaches to overcome this limitation must be found. Therefore, this paper explores whether simulation and game theoretic analysis are suitable methods for determining robust interception strategies for the police, aiming to increase the catch rate in fugitive interception scenarios.
Classical game theory is the mathematical theory of interactions among rational decision-makers with opposing interests. It offers valuable insights into the decision-making processes, compromises, and strategies the police and offenders may employ in real-world situations. To analyze the fugitive interception scenario with game theory, it is first simulated with an agent-based model. In this simulation model, the police and offender are individual agents with opposing interests and individual decision-making processes. Before modeling, research is conducted to find the current strategies that the police and offenders can potentially adopt.
Given the limited availability of data on fugitive interception scenarios, literature and expert interviews serve as sources for data collection. They provide insights into the behavior and strategies of both agents. Both sources emphasize the nature of the crime as a primary indicator of the offender's escape behavior. Large crimes, such as assassinations or armed robberies, are typically well-planned and characterized by predefined escape routes and rational behavior. During their escape, offenders of large crimes are found to be less susceptible to external factors such as crowd flows or police sightings. On the other hand, smaller crimes are more frequently committed spontaneously and associated with bounded rational behavior. This is depicted by their chaotic and unpredictable escape routes while taking many turns.
For the game theoretic analysis, the results of the simulation model are analyzed. The fugitive interception project is regarded as a non-cooperative zero-sum game. The results are presented in a payoff table, in which Nash equilibria are calculated. Nash equilibria are the points at which no player can single-handedly improve their outcome when the other player does not change strategy.
The pure-strategy Nash equilibrium resulted from the offender strategy where they started at a central metro station and aimed to transfer to a train network. These routes were frequently identified as the shortest compared to other end goals. Conversely, strategies that focused on getting as far away as possible, as quickly as possible, were found to be the least successful.
In determining the success of the police strategy, two factors were found to be crucial. Firstly, strategies where the police conducted surveillance on the metro platforms, as opposed to the station exits, proved significantly more effective. This highlights the importance for the police to strategically position themselves where the offender is most likely to pass, irrespective of assuming it to be the offender's final destination. Secondly, the police's response time served as an indicator for capture success. The quicker the crime is reported, the faster the police can take action to capture the offender, which increases capture chances.
Additionally to the game theoretic analysis, the relationship between the model’s output and its sensitivity to changes in input variables is tested. Results showed that variations in input did not lead to significant changes in output. This can be attributed to the deep uncertainty of this model. To address this challenge, the model must be refined, and done with more iterations.
In conclusion, by combining simulation and game theory new insights can be found beyond what either method can provide individually. By modeling the dynamic nature of a fugitive interception scenario, the success of the offender and police behaviour can be found. This can help the police during decision-making to adopt more robust strategies while considering the dynamic nature of the environment and strategic interactions with the offender.
The study addresses the knowledge gap by simulating offender and police behavior, and analyzing the result with classical game theory. This study has created a simulation model with an intuitively driven agent in a complex dynamic problem. Potential improvements in offender capture chances, with findings informing effective and unbiased police interception strategies. The study aims to contribute to crime reduction and foster increased trust in the Dutch national police. However, before generalizing the results future research must be done to overcome limitations resulting from the simplifications of this simulation model. ...
To adequately respond to reported crimes, police officers in the control room and units on the street rely on intuition, experience, and habit. This leads to the development of individual-specific strategies for handling interception scenarios. Reducing the dependency on these individualized approaches by identifying proven and robust strategies could increase the likelihood of successfully capturing a suspect. However, how the police currently save data on fugitive interception scenarios does not allow for such identification. Hence, alternative approaches to overcome this limitation must be found. Therefore, this paper explores whether simulation and game theoretic analysis are suitable methods for determining robust interception strategies for the police, aiming to increase the catch rate in fugitive interception scenarios.
Classical game theory is the mathematical theory of interactions among rational decision-makers with opposing interests. It offers valuable insights into the decision-making processes, compromises, and strategies the police and offenders may employ in real-world situations. To analyze the fugitive interception scenario with game theory, it is first simulated with an agent-based model. In this simulation model, the police and offender are individual agents with opposing interests and individual decision-making processes. Before modeling, research is conducted to find the current strategies that the police and offenders can potentially adopt.
Given the limited availability of data on fugitive interception scenarios, literature and expert interviews serve as sources for data collection. They provide insights into the behavior and strategies of both agents. Both sources emphasize the nature of the crime as a primary indicator of the offender's escape behavior. Large crimes, such as assassinations or armed robberies, are typically well-planned and characterized by predefined escape routes and rational behavior. During their escape, offenders of large crimes are found to be less susceptible to external factors such as crowd flows or police sightings. On the other hand, smaller crimes are more frequently committed spontaneously and associated with bounded rational behavior. This is depicted by their chaotic and unpredictable escape routes while taking many turns.
For the game theoretic analysis, the results of the simulation model are analyzed. The fugitive interception project is regarded as a non-cooperative zero-sum game. The results are presented in a payoff table, in which Nash equilibria are calculated. Nash equilibria are the points at which no player can single-handedly improve their outcome when the other player does not change strategy.
The pure-strategy Nash equilibrium resulted from the offender strategy where they started at a central metro station and aimed to transfer to a train network. These routes were frequently identified as the shortest compared to other end goals. Conversely, strategies that focused on getting as far away as possible, as quickly as possible, were found to be the least successful.
In determining the success of the police strategy, two factors were found to be crucial. Firstly, strategies where the police conducted surveillance on the metro platforms, as opposed to the station exits, proved significantly more effective. This highlights the importance for the police to strategically position themselves where the offender is most likely to pass, irrespective of assuming it to be the offender's final destination. Secondly, the police's response time served as an indicator for capture success. The quicker the crime is reported, the faster the police can take action to capture the offender, which increases capture chances.
Additionally to the game theoretic analysis, the relationship between the model’s output and its sensitivity to changes in input variables is tested. Results showed that variations in input did not lead to significant changes in output. This can be attributed to the deep uncertainty of this model. To address this challenge, the model must be refined, and done with more iterations.
In conclusion, by combining simulation and game theory new insights can be found beyond what either method can provide individually. By modeling the dynamic nature of a fugitive interception scenario, the success of the offender and police behaviour can be found. This can help the police during decision-making to adopt more robust strategies while considering the dynamic nature of the environment and strategic interactions with the offender.
The study addresses the knowledge gap by simulating offender and police behavior, and analyzing the result with classical game theory. This study has created a simulation model with an intuitively driven agent in a complex dynamic problem. Potential improvements in offender capture chances, with findings informing effective and unbiased police interception strategies. The study aims to contribute to crime reduction and foster increased trust in the Dutch national police. However, before generalizing the results future research must be done to overcome limitations resulting from the simplifications of this simulation model. ...
When a crime is committed, catching the offender in the act has several benefits. Among others, it provides evidence of the offender's involvement in the crime, which simplifies the conviction process. However, to capture an offender in the act, the collaboration of multiple police officers is required. When a crime is being reported through the emergency line, it is the responsibility of the police officers in the control room to answer the call. They gather information on the type of crime, the location, a description of the offender, etc. Subsequently, they dispatch police units to the crime scene. The first unit prioritizes reaching the crime scene to ensure the safety of citizens, while the other units are tasked with locating and apprehending the offender.
To adequately respond to reported crimes, police officers in the control room and units on the street rely on intuition, experience, and habit. This leads to the development of individual-specific strategies for handling interception scenarios. Reducing the dependency on these individualized approaches by identifying proven and robust strategies could increase the likelihood of successfully capturing a suspect. However, how the police currently save data on fugitive interception scenarios does not allow for such identification. Hence, alternative approaches to overcome this limitation must be found. Therefore, this paper explores whether simulation and game theoretic analysis are suitable methods for determining robust interception strategies for the police, aiming to increase the catch rate in fugitive interception scenarios.
Classical game theory is the mathematical theory of interactions among rational decision-makers with opposing interests. It offers valuable insights into the decision-making processes, compromises, and strategies the police and offenders may employ in real-world situations. To analyze the fugitive interception scenario with game theory, it is first simulated with an agent-based model. In this simulation model, the police and offender are individual agents with opposing interests and individual decision-making processes. Before modeling, research is conducted to find the current strategies that the police and offenders can potentially adopt.
Given the limited availability of data on fugitive interception scenarios, literature and expert interviews serve as sources for data collection. They provide insights into the behavior and strategies of both agents. Both sources emphasize the nature of the crime as a primary indicator of the offender's escape behavior. Large crimes, such as assassinations or armed robberies, are typically well-planned and characterized by predefined escape routes and rational behavior. During their escape, offenders of large crimes are found to be less susceptible to external factors such as crowd flows or police sightings. On the other hand, smaller crimes are more frequently committed spontaneously and associated with bounded rational behavior. This is depicted by their chaotic and unpredictable escape routes while taking many turns.
For the game theoretic analysis, the results of the simulation model are analyzed. The fugitive interception project is regarded as a non-cooperative zero-sum game. The results are presented in a payoff table, in which Nash equilibria are calculated. Nash equilibria are the points at which no player can single-handedly improve their outcome when the other player does not change strategy.
The pure-strategy Nash equilibrium resulted from the offender strategy where they started at a central metro station and aimed to transfer to a train network. These routes were frequently identified as the shortest compared to other end goals. Conversely, strategies that focused on getting as far away as possible, as quickly as possible, were found to be the least successful.
In determining the success of the police strategy, two factors were found to be crucial. Firstly, strategies where the police conducted surveillance on the metro platforms, as opposed to the station exits, proved significantly more effective. This highlights the importance for the police to strategically position themselves where the offender is most likely to pass, irrespective of assuming it to be the offender's final destination. Secondly, the police's response time served as an indicator for capture success. The quicker the crime is reported, the faster the police can take action to capture the offender, which increases capture chances.
Additionally to the game theoretic analysis, the relationship between the model’s output and its sensitivity to changes in input variables is tested. Results showed that variations in input did not lead to significant changes in output. This can be attributed to the deep uncertainty of this model. To address this challenge, the model must be refined, and done with more iterations.
In conclusion, by combining simulation and game theory new insights can be found beyond what either method can provide individually. By modeling the dynamic nature of a fugitive interception scenario, the success of the offender and police behaviour can be found. This can help the police during decision-making to adopt more robust strategies while considering the dynamic nature of the environment and strategic interactions with the offender.
The study addresses the knowledge gap by simulating offender and police behavior, and analyzing the result with classical game theory. This study has created a simulation model with an intuitively driven agent in a complex dynamic problem. Potential improvements in offender capture chances, with findings informing effective and unbiased police interception strategies. The study aims to contribute to crime reduction and foster increased trust in the Dutch national police. However, before generalizing the results future research must be done to overcome limitations resulting from the simplifications of this simulation model.
To adequately respond to reported crimes, police officers in the control room and units on the street rely on intuition, experience, and habit. This leads to the development of individual-specific strategies for handling interception scenarios. Reducing the dependency on these individualized approaches by identifying proven and robust strategies could increase the likelihood of successfully capturing a suspect. However, how the police currently save data on fugitive interception scenarios does not allow for such identification. Hence, alternative approaches to overcome this limitation must be found. Therefore, this paper explores whether simulation and game theoretic analysis are suitable methods for determining robust interception strategies for the police, aiming to increase the catch rate in fugitive interception scenarios.
Classical game theory is the mathematical theory of interactions among rational decision-makers with opposing interests. It offers valuable insights into the decision-making processes, compromises, and strategies the police and offenders may employ in real-world situations. To analyze the fugitive interception scenario with game theory, it is first simulated with an agent-based model. In this simulation model, the police and offender are individual agents with opposing interests and individual decision-making processes. Before modeling, research is conducted to find the current strategies that the police and offenders can potentially adopt.
Given the limited availability of data on fugitive interception scenarios, literature and expert interviews serve as sources for data collection. They provide insights into the behavior and strategies of both agents. Both sources emphasize the nature of the crime as a primary indicator of the offender's escape behavior. Large crimes, such as assassinations or armed robberies, are typically well-planned and characterized by predefined escape routes and rational behavior. During their escape, offenders of large crimes are found to be less susceptible to external factors such as crowd flows or police sightings. On the other hand, smaller crimes are more frequently committed spontaneously and associated with bounded rational behavior. This is depicted by their chaotic and unpredictable escape routes while taking many turns.
For the game theoretic analysis, the results of the simulation model are analyzed. The fugitive interception project is regarded as a non-cooperative zero-sum game. The results are presented in a payoff table, in which Nash equilibria are calculated. Nash equilibria are the points at which no player can single-handedly improve their outcome when the other player does not change strategy.
The pure-strategy Nash equilibrium resulted from the offender strategy where they started at a central metro station and aimed to transfer to a train network. These routes were frequently identified as the shortest compared to other end goals. Conversely, strategies that focused on getting as far away as possible, as quickly as possible, were found to be the least successful.
In determining the success of the police strategy, two factors were found to be crucial. Firstly, strategies where the police conducted surveillance on the metro platforms, as opposed to the station exits, proved significantly more effective. This highlights the importance for the police to strategically position themselves where the offender is most likely to pass, irrespective of assuming it to be the offender's final destination. Secondly, the police's response time served as an indicator for capture success. The quicker the crime is reported, the faster the police can take action to capture the offender, which increases capture chances.
Additionally to the game theoretic analysis, the relationship between the model’s output and its sensitivity to changes in input variables is tested. Results showed that variations in input did not lead to significant changes in output. This can be attributed to the deep uncertainty of this model. To address this challenge, the model must be refined, and done with more iterations.
In conclusion, by combining simulation and game theory new insights can be found beyond what either method can provide individually. By modeling the dynamic nature of a fugitive interception scenario, the success of the offender and police behaviour can be found. This can help the police during decision-making to adopt more robust strategies while considering the dynamic nature of the environment and strategic interactions with the offender.
The study addresses the knowledge gap by simulating offender and police behavior, and analyzing the result with classical game theory. This study has created a simulation model with an intuitively driven agent in a complex dynamic problem. Potential improvements in offender capture chances, with findings informing effective and unbiased police interception strategies. The study aims to contribute to crime reduction and foster increased trust in the Dutch national police. However, before generalizing the results future research must be done to overcome limitations resulting from the simplifications of this simulation model.
Spatiotemporal Modeling in Mathematical Oncology
Case Study in Prostate Cancer
Cancer affects a countless number of lives across the world each day. Mathematical oncology develops and studies mathematical models of cancer and its treatment. This thesis focuses on spatiotemporal modeling in mathematical oncology, developing an agent-based model for prostate cancer, with the aim of gaining insights into how the different tumor cells respond to varying testosterone levels and different treatment strategies.
We began by analyzing non-spatial population models, the replicator dynamics and Lotka-Volterra dynamics, proving their equivalence under certain conditions. The study then transitioned to spatial agent-based modeling on a discrete lattice, simulating the interactions between testosterone-dependent and testosterone-independent tumor cells. Through this, we identified a possible phase transition in the testosterone level in the bloodstream, which could influence which tumor cells dominates the grid.
A continuum limit of the discrete model was derived, leading to partial differential equations that describe the tumor's spatial behavior. We applied mathematical tools like non-dimensionalization and linear stability analysis to gain deeper insights into the dynamics of the model. Additionally, we simulated three treatment strategies: (1) testosterone removal from the blood with Lupron, (2) Lupron combined with Abiraterone to stop the testosterone producing cancer cell to grow, and (3) Lupron and Abiraterone alongside high-dose testosterone injections to simulate extinction therapy.
The flexibility of our model allows for its application to other hormonal cancers, and our findings support the promising potential of hormonal manipulation in controlling tumor growth and composition, especially extinction therapy. The mathematical analysis together with simulations provide unique insights into the tumor dynamics. Future research directions include changing assumptions, expanding the model to three dimensions and integrating patient data for more accurate simulations. ...
We began by analyzing non-spatial population models, the replicator dynamics and Lotka-Volterra dynamics, proving their equivalence under certain conditions. The study then transitioned to spatial agent-based modeling on a discrete lattice, simulating the interactions between testosterone-dependent and testosterone-independent tumor cells. Through this, we identified a possible phase transition in the testosterone level in the bloodstream, which could influence which tumor cells dominates the grid.
A continuum limit of the discrete model was derived, leading to partial differential equations that describe the tumor's spatial behavior. We applied mathematical tools like non-dimensionalization and linear stability analysis to gain deeper insights into the dynamics of the model. Additionally, we simulated three treatment strategies: (1) testosterone removal from the blood with Lupron, (2) Lupron combined with Abiraterone to stop the testosterone producing cancer cell to grow, and (3) Lupron and Abiraterone alongside high-dose testosterone injections to simulate extinction therapy.
The flexibility of our model allows for its application to other hormonal cancers, and our findings support the promising potential of hormonal manipulation in controlling tumor growth and composition, especially extinction therapy. The mathematical analysis together with simulations provide unique insights into the tumor dynamics. Future research directions include changing assumptions, expanding the model to three dimensions and integrating patient data for more accurate simulations. ...
Cancer affects a countless number of lives across the world each day. Mathematical oncology develops and studies mathematical models of cancer and its treatment. This thesis focuses on spatiotemporal modeling in mathematical oncology, developing an agent-based model for prostate cancer, with the aim of gaining insights into how the different tumor cells respond to varying testosterone levels and different treatment strategies.
We began by analyzing non-spatial population models, the replicator dynamics and Lotka-Volterra dynamics, proving their equivalence under certain conditions. The study then transitioned to spatial agent-based modeling on a discrete lattice, simulating the interactions between testosterone-dependent and testosterone-independent tumor cells. Through this, we identified a possible phase transition in the testosterone level in the bloodstream, which could influence which tumor cells dominates the grid.
A continuum limit of the discrete model was derived, leading to partial differential equations that describe the tumor's spatial behavior. We applied mathematical tools like non-dimensionalization and linear stability analysis to gain deeper insights into the dynamics of the model. Additionally, we simulated three treatment strategies: (1) testosterone removal from the blood with Lupron, (2) Lupron combined with Abiraterone to stop the testosterone producing cancer cell to grow, and (3) Lupron and Abiraterone alongside high-dose testosterone injections to simulate extinction therapy.
The flexibility of our model allows for its application to other hormonal cancers, and our findings support the promising potential of hormonal manipulation in controlling tumor growth and composition, especially extinction therapy. The mathematical analysis together with simulations provide unique insights into the tumor dynamics. Future research directions include changing assumptions, expanding the model to three dimensions and integrating patient data for more accurate simulations.
We began by analyzing non-spatial population models, the replicator dynamics and Lotka-Volterra dynamics, proving their equivalence under certain conditions. The study then transitioned to spatial agent-based modeling on a discrete lattice, simulating the interactions between testosterone-dependent and testosterone-independent tumor cells. Through this, we identified a possible phase transition in the testosterone level in the bloodstream, which could influence which tumor cells dominates the grid.
A continuum limit of the discrete model was derived, leading to partial differential equations that describe the tumor's spatial behavior. We applied mathematical tools like non-dimensionalization and linear stability analysis to gain deeper insights into the dynamics of the model. Additionally, we simulated three treatment strategies: (1) testosterone removal from the blood with Lupron, (2) Lupron combined with Abiraterone to stop the testosterone producing cancer cell to grow, and (3) Lupron and Abiraterone alongside high-dose testosterone injections to simulate extinction therapy.
The flexibility of our model allows for its application to other hormonal cancers, and our findings support the promising potential of hormonal manipulation in controlling tumor growth and composition, especially extinction therapy. The mathematical analysis together with simulations provide unique insights into the tumor dynamics. Future research directions include changing assumptions, expanding the model to three dimensions and integrating patient data for more accurate simulations.
Design Guidelines for Integrating AI into Mental Healthcare
A Case Study on Posttraumatic Stress Disorder Prediction
Global mental healthcare confronts daunting challenges, notably posttraumatic stress disorder (PTSD), necessitating immediate attention and innovative solutions. Many individuals requiring mental health support face various barriers, including social stigma, low perceived need, and restricted access to care providers — especially prevalent in certain regions — which impedes their quest for professional assistance. Amidst these obstacles, artificial intelligence (AI) emerges as a promising instrument, ushering in its unique challenges and opportunities. This thesis delves into these intricacies, aiming to develop comprehensive and pioneering design guidelines for AI applications within mental healthcare. The research focuses on three pivotal areas: identifying the distinct challenges and opportunities of implementing AI in mental healthcare; adapting existing AI design principles to fit the mental health landscape; and understanding the crucial role of multidisciplinary collaboration and user-centered design in this context. The primary objective is to devise guidelines that address inherent difficulties in mental healthcare, such as stigma and complexity of disorders, while leveraging potential benefits like early support intervention and expanded access to mental healthcare services. The suggested design guidelines embrace a systematic approach, encapsulating problem definition, stakeholder engagement, data acquisition, ethical and legal considerations, model design, system deployment, usage, maintenance, and iterative improvements based on feedback. Grounding these guidelines in a practical context, the thesis introduces AnchorAid, a tool that is designed theoretically and remains hypothetical. This virtual assistant provides post-trauma recovery support by gathering data, generating personalized feedback, recommending symptom management strategies, and assisting clinicians in the patient management processes. Through design guidelines establishment and their implementation via AnchorAid, this thesis lays a solid foundation for AI integration into mental healthcare.
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Global mental healthcare confronts daunting challenges, notably posttraumatic stress disorder (PTSD), necessitating immediate attention and innovative solutions. Many individuals requiring mental health support face various barriers, including social stigma, low perceived need, and restricted access to care providers — especially prevalent in certain regions — which impedes their quest for professional assistance. Amidst these obstacles, artificial intelligence (AI) emerges as a promising instrument, ushering in its unique challenges and opportunities. This thesis delves into these intricacies, aiming to develop comprehensive and pioneering design guidelines for AI applications within mental healthcare. The research focuses on three pivotal areas: identifying the distinct challenges and opportunities of implementing AI in mental healthcare; adapting existing AI design principles to fit the mental health landscape; and understanding the crucial role of multidisciplinary collaboration and user-centered design in this context. The primary objective is to devise guidelines that address inherent difficulties in mental healthcare, such as stigma and complexity of disorders, while leveraging potential benefits like early support intervention and expanded access to mental healthcare services. The suggested design guidelines embrace a systematic approach, encapsulating problem definition, stakeholder engagement, data acquisition, ethical and legal considerations, model design, system deployment, usage, maintenance, and iterative improvements based on feedback. Grounding these guidelines in a practical context, the thesis introduces AnchorAid, a tool that is designed theoretically and remains hypothetical. This virtual assistant provides post-trauma recovery support by gathering data, generating personalized feedback, recommending symptom management strategies, and assisting clinicians in the patient management processes. Through design guidelines establishment and their implementation via AnchorAid, this thesis lays a solid foundation for AI integration into mental healthcare.