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Register a new userMathematical Models of Radicalization and Terrorism
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The rapid spread of radical ideologies has led to a world-wide succession of terrorist attacks in recent years. Understanding how extremist tendencies germinate, develop, and drive individuals to action is important from a cultural standpoint, but also to help formulate response and prevention strategies. Demographic studies, interviews with radicalized subjects, analysis of terrorist databases, reveal that the path to radicalization occurs along progressive steps, where age, social context and peer-to-peer exchanges play major roles. To execute terrorist attacks, radicals must efficiently communicate with one another while maintaining secrecy; they are also subject to pressure from counter-terrorism agencies, public opinion and the need for material resources. Similarly, government entities must gauge which intervention methods are most effective. While a complete understanding of the processes that lead to extremism and violence, and of which deterrents are optimal, is still lacking, mathematical modelers have contributed to the discourse by using tools from statistical mechanics and applied mathematics to describe existing and novel paradigms, and to propose novel counter-terrorism strategies. We review some of their approaches in this work, including compartment models for populations of increasingly extreme views, continuous time models for age-structured radical populations, radicalization as social contagion processes on lattices and social networks, agent based models, game theoretic formulations. We highlight the useful insights offered by analyzing radicalization and terrorism through quantitative frameworks. Finally, we discuss the role of institutional intervention and the stages at which de-radicalization strategies might be most effective.
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We discuss some social contagion processes to describe the formation and spread of radical opinions. The dynamics of opinion spread involves local threshold processes as well as mean field effects. We calculate and observe phase transitions in the dynamical variables resulting in a rapidly increasing number of passive supporters. This strongly indicates that military solutions are inappropriate.
(shortened version) Religions and languages are social variables, like age, sex, wealth or political opinions, to be studied like any other organizational parameter. In fact, religiosity is one of the most important sociological aspects of populations. Languages are also a characteristics of the human kind. New religions, new languages appear though others disappear. All religions and languages evolve when they adapt to the society developments. On the other hand, the number of adherents of a given religion, the number of persons speaking a language is not fixed. Several questions can be raised. E.g. from a macroscopic point of view : How many religions/languages exist at a given time? What is their distribution? What is their life time? How do they evolve?. From a microscopic view point: can one invent agent based models to describe macroscopic aspects? Does it exist simple evolution equations? It is intuitively accepted, but also found through from statistical analysis of the frequency distribution that an attachment process is the primary cause of the distribution evolution : usually the initial religion/language is that of the mother. Later on, changes can occur either due to heterogeneous agent interaction processes or due to external field constraints, - or both. Such cases can be illustrated with historical facts and data. It is stressed that characteristic time scales are different, and recalled that external fields are very relevant in the case of religions, rending the study more interesting within a mechanistic approach
We analyze properties of apportionment functions in context of the problem of allocating seats in the European Parliament. Necessary and sufficient conditions for apportionment functions are investigated. Some exemplary families of apportionment functions are specified and the corresponding partitions of the seats in the European Parliament among the Member States of the European Union are presented. Although the choice of the allocation functions is theoretically unlimited, we show that the constraints are so strong that the acceptable functions lead to rather similar solutions.
Disaffected youth are among the most susceptible in espousing and acting on extremist ideals, as confirmed by demographic studies. To study age-dependent radicalization we introduce a three-stage model where individuals progress through non-radical, activist, and radical states, while also aging. Transitions between stages are modeled as age-dependent interactions that are maximized for individuals of the same age and that are enhanced at early adulthood. For comparison, we also derive the age-independent formulation corresponding to the full age-dependent model. We find that age-dependence leads to more complex dynamics, enhancing radicalization in certain parameter regimes. We also observe waves of radical behavior ebbing and flowing over generational cycles, realizing well known paradigms in political science. While government intervention is most effective when the appropriate ages are targeted, deciding whether preventive or corrective action is preferable depends on the aggressiveness of the radicalization process.
In this survey we consider mathematical models and methods recently developed to control crowd dynamics, with particular emphasis on egressing pedestrians. We focus on two control strategies: The first one consists in using special agents, called leaders, to steer the crowd towards the desired direction. Leaders can be either hidden in the crowd or recognizable as such. This strategy heavily relies on the power of the social influence (herding effect), namely the natural tendency of people to follow group mates in situations of emergency or doubt. The second one consists in modify the surrounding environment by adding in the walking area multiple obstacles optimally placed and shaped. The aim of the obstacles is to naturally force people to behave as desired. Both control strategies discussed in this paper aim at reducing as much as possible the intervention on the crowd. Ideally the natural behavior of people is kept, and people do not even realize they are being led by an external intelligence. Mathematical models are discussed at different scales of observation, showing how macroscopic (fluid-dynamic) models can be derived by mesoscopic (kinetic) models which, in turn, can be derived by microscopic (agent-based) models.
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