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Sustainability is not merely an academic topic. It is an urgent matter that requires making personal and collective decisions about how we live.
Since 'sustainability' is used in so many ways, the module presents it from a variety of perspectives. We will address both the problem of defining sustainability and the challenges that need to be met in order to achieve it. This will require engaging with issues that could range over science, philosophy, law, political economics and other subjects. This is why an interdisciplinary approach is ideal. The aim is to make you aware of work outside your own subjects so you can develop your own views.
Welcome to the new module on Border Controls, Citizenship, and the State!
During the next term, we will explore the historical and contemporary intertwining of migration controls and criminal justice through different interdisciplinary lens -sociology, law, criminology, politics, anthropology, migration studies, philosophy.
We will study this intertwine in light of key questions in criminology and the sociology of punishment: what is crime? who are criminals? and what is the purpose of punishment?
As migration and citizenship are becoming key in the exercise of state powers under contemporary conditions, we will discuss the implications of the merging of criminal justice and border controls functions.
• Relational family: hypergraphs, simplicial complexes and hierachical hypergraphs.Overview
In this lecture will learn how to start the modelling process by thinking about the model's static structure, which then in a dynamic model gives rise to the choice of variables. Finally, with the dive into mathematical learning theories, the students will understand that a mathematical model is never finished, but needs recursive learning steps to improve its parametrisation and even structure.
A very important aspect of the lecture is the smooth transition from static to dynamic stochastic models with the help of rule-based system descriptions which have evolved from the modelling of chemical reactions.Weekly Overview
Week 1: Mathematical Modelling, Past, Present and Future
• What is Mathematical Modelling?
• Why Complex Systems?..
• Philosophy of Science, Empirical Data and Prediction.
• About this course.
Part I Structural Modelling
Week 2: Relational Structures
• Graph characteristics, examples from real world complex systems (social science, infrastructure, economy, biology, internet).
• Introduction to algebraic and computational graph theory.
Week 3: Transformations of Relational Models
• Connections between graphs, hypergraphs, simplicial complexes and hierachical hypergraphs.
• Applications of hierachical hypergraphs.
• Stochastic processes of changing relational model topologies.
Part II Dynamic Modelling
Week 4: Stochastic Processes
• Basic concepts, Poisson Process.
• Opinion formation: relations and correlations.
• Master eqation type-rule based stochastic collision processes.
Week 5: Applications of type-rule based stochastic collision processes
• Chemical reactions and Biochemistry.
• Covid-19 Epidemiology.
• Economics and Sociology, Agent-based modelling.
Week 6: Dynamical Systems (single compartment)
• Basic concepts, examples.
• Relation between type-rule-based stochastic collision processes in single compartments and ODE
• Applications, connections between dynamical systems and structural modelling (from Part I), the interaction graph, feedback loops.
• Time scales: evolutionary outlook.
Week 7: Spatial processes and Partial Differential Equations:
• Type-rule-based multi-compartment models.
• Reaction-Diffusion Equations.
• Applications.
Part III Data Analysis and Machine Learning
Week 8: Statistics and Mathematical Modelling
• Statistical Models and Data.
• Classification.
• Parametrisation.
Week 9: Machine Learning and Mathematical Modelling:
• Mathematical Learning Theory.
• Bayesian Networks.
• Bayesian Model Selection.
Week 10: Neural Networks and Deep Learning:
• Basic concepts.
• Neural Networks and Machine Learning.
• Discussion and outlook.
https://www.mathematical-modelling.science/index.php/lectures/warwick-2020-2021