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As AI systems enter into a growing number of societal domains, these systems increasingly shape and are shaped by user preferences, opinions, and behaviors. However, the design of AI systems rarely accounts for how AI and users shape one…
Agent-based modelling is a valuable approach for systems whose behaviour is driven by the interactions between distinct entities. They have shown particular promise as a means of modelling crowds of people in streets, public transport…
We present an overview of phase field modeling of active matter systems as a tool for capturing various aspects of complex and active interfaces. We first describe how interfaces between different phases are characterized in phase field…
In recent years, promising mathematical models have been suggested which aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully…
The traditional methods of the biology, based on illustrative descriptions and linear logic explanations, are discussed. This work aims to improve this approach by introducing alternative tools to describe and represent complex biological…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
These notes focus on the description of the phases of matter in two dimensions. Firstly, we present a brief discussion of the phase diagrams of bidimensional interacting passive systems, and their numerical and experimental measurements.…
Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…
Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order.…
Living systems, particularly multicellular systems, often seem hopelessly complex. But recent studies have suggested that beneath this complexity, there may be unifying quantitative principles that we are only now starting to unravel. All…
Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as alternatives to physical experiments. Design and analysis of computer experiments have attracted great attention in past…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
A formal but intuitive framework is introduced to bridge the gap between data obtained from empirical studies and that generated by agent-based models. This is based on three key tenets. Firstly, a simulation can be given multiple formal…
In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and…
The fundamental understanding of how cells physically interact with each other and their environment is key to understanding their organisation in living tissues. Over the past decades several computational methods have been developed to…
Generally, multi-particle spring system is an important and widely used physical model. However, with the increase of the number of particles, the difficulty of solving the kinematic trajectory of the particles becomes more and more…
We revisit the behavioral approach to systems theory and make explicit the abstract pattern that governs it. Our end goal is to use that pattern to understand interaction-related phenomena that emerge when systems interact. Rather than…
Active matter, as other types of self-organizing systems, relies on the take-up of energy that can be used for different actions, such as active motion or structure formation. Here we provide an agent-based framework to model these…