@gyllingberg.bsky.social
Fulbright scholar and Wallenberg Postdoctoral fellow @uclamath | PhD in applied math from @uppsalauni | Interested in mathematical biology, collective behaviour and complex systems | linneagyllingberg.github.io
Well this is going on the reading list.
07.08.2025 19:54 — 👍 3 🔁 1 💬 1 📌 0
Totally agree on modelling as an art! (Me, @abeba.bsky.social and @soccermatics.bsky.social argued for something similar in this paper, but for the case of models biology, not economics: www.sciencedirect.com/science/arti... )
07.08.2025 19:40 — 👍 10 🔁 2 💬 0 📌 1Wow! Sounds really interesting!
03.08.2025 13:46 — 👍 0 🔁 0 💬 0 📌 0Looks really interesting!
07.07.2025 16:49 — 👍 2 🔁 0 💬 0 📌 0I love the name! 😍
19.06.2025 03:23 — 👍 1 🔁 0 💬 1 📌 0
We argue that currently, the universalist approach dominates and creation of new models, which is inherent to pluralism, is not sufficiently emphasised. This brings us to, in Sections 6 Machine learning cannot replace modelling, 7 Are hybrid models the answer?, a discussion of how mathematical biology has responded with the rise of machine learning. We argue that ML, which emphasises prediction (activity 3), is ill-prepared to deal with complexity without incorporating some form of mechanistic model building. But we also, more controversially for those working in mathematical biology, emphasise how some of the responses to the rise of ML have fallen into the trap of making models of models (or fitting models to data generated by models) rather than innovating by creating new models of biology itself. We conclude that mathematical biology needs less unification and less analysis of existing models, and more creativity and more creation of new models. We should be creative without fear of them being wrong or producing ideas that are mathematically intractable, with an aim of providing a multitude of tools for better understanding of biological systems.
![Instead, the radical definition of complex systems comes from, what is known as, critical complexity. Work by Paul Cilliers and Alicia Juarrero warned against aggrandising models (even supposedly complex systems models) [3], [4]. They emphasise the need to embrace the ambiguous, messy, fluid, non-determinable, contextual, and historical nature of complex systems. They describe complex phenomena as unfinalizible and inexhaustible, which means that we can never capture any given biological system entirety with models [5]. Fig. 1, adapted from Di Paolo et al. (2018), captures the interdependence, fluidly and interactivity of agents and environments in a complex system [2]. Complex systems are open-ended, which means there is no uncontested way of telling whether what we have included in a model is crucial or what we have omitted as irrelevant is indeed so. Models can, according to the critical complexity approach, be contradictory: we can accept two incompatible predictions as both describing the same system.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:26hkfmtr7jrchexamh7hk6rz/bafkreidbtcuxfz7vv53zk3c37lti4el26hankzdt72dlwwiuphmcjjw6ai@jpeg)
Instead, the radical definition of complex systems comes from, what is known as, critical complexity. Work by Paul Cilliers and Alicia Juarrero warned against aggrandising models (even supposedly complex systems models) [3], [4]. They emphasise the need to embrace the ambiguous, messy, fluid, non-determinable, contextual, and historical nature of complex systems. They describe complex phenomena as unfinalizible and inexhaustible, which means that we can never capture any given biological system entirety with models [5]. Fig. 1, adapted from Di Paolo et al. (2018), captures the interdependence, fluidly and interactivity of agents and environments in a complex system [2]. Complex systems are open-ended, which means there is no uncontested way of telling whether what we have included in a model is crucial or what we have omitted as irrelevant is indeed so. Models can, according to the critical complexity approach, be contradictory: we can accept two incompatible predictions as both describing the same system.
![This approach views a model as a snapshot of a system and no single snapshot tells the whole story. For modelling the human body, for example, “a portrait of a person, a store mannequin, and a pig can all be models” [6]. None is a perfect representation, but each can be the best model for a human, depending on whether one wants to remember an old friend, to buy clothes, or to study anatomy. The critical complexity view suggests that theoreticians should avoid specialising in any one modelling approach and try to find the right set of models to understand a particular system in a given context.
There can, of course, be more than one definition of complex systems. Indeed, Cilliers and Juarrero’s approach to complexity encourages a plurality of definitions (after all, there is no single view of a system). We would, though, emphasise that it is the radical definition of complexity – in which systems always resist a complete description, are open and unfinalizable – which is least well understood by mathematical biologists today. It is therefore important to investigate how complexity should be approached in the study of biological systems.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:26hkfmtr7jrchexamh7hk6rz/bafkreicszmjxfslncbz4br2p7rrkcpyqkq6ayjtveaxcbgswc4hneicscu@jpeg)
This approach views a model as a snapshot of a system and no single snapshot tells the whole story. For modelling the human body, for example, “a portrait of a person, a store mannequin, and a pig can all be models” [6]. None is a perfect representation, but each can be the best model for a human, depending on whether one wants to remember an old friend, to buy clothes, or to study anatomy. The critical complexity view suggests that theoreticians should avoid specialising in any one modelling approach and try to find the right set of models to understand a particular system in a given context. There can, of course, be more than one definition of complex systems. Indeed, Cilliers and Juarrero’s approach to complexity encourages a plurality of definitions (after all, there is no single view of a system). We would, though, emphasise that it is the radical definition of complexity – in which systems always resist a complete description, are open and unfinalizable – which is least well understood by mathematical biologists today. It is therefore important to investigate how complexity should be approached in the study of biological systems.
from a 2022 paper with @gyllingberg.bsky.social & @soccermatics.bsky.social
The lost art of mathematical modelling www.sciencedirect.com/science/arti...
Loved writing that paper with you!
07.06.2025 15:58 — 👍 2 🔁 0 💬 1 📌 0We cite that paper in our paper, @abeba.bsky.social! It is Blanchard P., Devaney R.L., Hall G.R.
Differential Equations
Thanks for a great talk, really enjoyed it!
04.03.2025 22:46 — 👍 2 🔁 0 💬 0 📌 0
