# Model comparison via simplicial complexes and persistent homology

@article{Vittadello2021ModelCV, title={Model comparison via simplicial complexes and persistent homology}, author={Sean T. Vittadello and Michael P. H. Stumpf}, journal={Royal Society Open Science}, year={2021}, volume={8} }

In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal statistical model selection to compare and contrast the ability of different mathematical models to describe such data. There is, however, a lack of rigorous methods to compare different models a priori. Here, we develop and illustrate two such approaches that…

## 8 Citations

A group theoretic approach to model comparison with simplicial representations

- Biology
- 2021

An automatable methodology for determining model equivalence using group actions on the simplicial complexes is developed, which greatly simplify and expedite the process of determiningmodel equivalence.

Algebra, Geometry and Topology of ERK Kinetics

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This work studies a polynomial dynamical system describing the dynamics of MEK/ERK with experimental setup, data and known biological information and demonstrates how methods from computational algebraic geometry, differential algebra, Bayesian statistics and computationalgebraic topology can inform the model reduction, identification and parameter inference of MeK variants.

Persistent homology and the shape of evolutionary games

- Computer Science, MedicineJournal of theoretical biology
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The Design Principles of Discrete Turing Patterning Systems.

- MedicineJournal of theoretical biology
- 2021

A large-scale study on all possible two-species networks is performed and it is found that Turing pattern topologies found to be substantially more robust to changes in the parameters of the model than in the continuous case.

Tree Edit Distance with Variables. Measuring the Similarity between Mathematical Formulas

- Computer ScienceArXiv
- 2021

In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the…

Turing pattern design principles and their robustness

- MedicinePhilosophical Transactions of the Royal Society A
- 2021

A review of recent large-scale mathematical analyses that have attempted to narrow down potential design principles for Turing-patterning systems considers robustness in the context of developmental modelling more generally.

What are higher-order networks?

- Computer Science, MathematicsArXiv
- 2021

The goals are to clarify (i) what higher-order networks are, (ii) why these are interesting objects of study, and (iii) how they can be used in applications.

The Design Principles of Discrete Turing Patterning Systems

- Biology, Computer Science
- 2020

A large-scale study on all possible two-species networks is performed and finds the same Turing pattern producing networks as in the continuous framework, but these Turing pattern topologies are found to be substantially more robust to changes in the parameters of the model.

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