Compositional Modeling with Stock and Flow Diagrams DOI Creative Commons
John C. Baez, Xiaoyan Li,

Sophie Libkind

et al.

arXiv (Cornell University), Journal Year: 2022, Volume and Issue: unknown

Published: Jan. 1, 2022

Stock and flow diagrams are widely used in epidemiology to model the dynamics of populations. Although tools already exist for building these simulating systems they describe, we have created a new package called StockFlow, part AlgebraicJulia ecosystem, which uses ideas from category theory overcome notable limitations existing software. Compositionality is provided by decorated cospans: stock can be composed form larger ones an intuitive way formalized operad undirected wiring diagrams. Our approach also cleanly separates syntax semantics assigned. We consider ordinary differential equations, although others possible. As example, explain code StockFlow that implements simplified version COVID-19 Canada.

Language: Английский

Epidemic dynamics in homes and destinations under recurrent mobility patterns DOI
Yusheng Li, Yichao Yao, Minyu Feng

et al.

Chaos Solitons & Fractals, Journal Year: 2025, Volume and Issue: 195, P. 116273 - 116273

Published: March 19, 2025

Language: Английский

Citations

1
Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations DOI Creative Commons
Jason Dykes, Alfie Abdul‐Rahman, Daniel Archambault

et al.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences, Journal Year: 2022, Volume and Issue: 380(2233)

Published: Aug. 15, 2022

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting reflecting upon knowledge constructs-a series of ideas, approaches methods taken from existing research practice-deployed developed to support modelling the COVID-19 pandemic. Structured independent commentary these efforts is synthesized through iterative reflection develop: evidence effectiveness value in this context; open problems which communities may focus; guidance for future activity type recommendations safeguard achievements promote, advance, secure prepare collaborations kind. In describing comparing a related projects that were undertaken unprecedented conditions, our hope unique report, its rich interactive supplementary materials, will guide scientific community embracing observation, analysis data as well disseminating findings. Equally we encourage engage with impactful science addressing emerging challenges. If are successful, showcase stimulate mutually beneficial engagement complementary expertise address significance epidemiology beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article part theme issue 'Technical challenges real-life epidemics examples overcoming these'.

Language: Английский

Citations

15
Compositional Modeling with Stock and Flow Diagrams DOI Creative Commons
John C. Baez, Xiaoyan Li,

Sophie Libkind

et al.

Electronic Proceedings in Theoretical Computer Science, Journal Year: 2023, Volume and Issue: 380, P. 77 - 96

Published: July 28, 2023

Stock and flow diagrams are widely used in epidemiology to model the dynamics of populations. Although tools already exist for building these simulating systems they describe, we have created a new package called StockFlow, part AlgebraicJulia ecosystem, which uses ideas from category theory overcome notable limitations existing software. Compositionality is provided by decorated cospans: stock can be composed form larger ones an intuitive way formalized operad undirected wiring diagrams. Our approach also cleanly separates syntax semantics assigned. We consider ordinary differential equations, although others possible. As example, explain code StockFlow that implements simplified version COVID-19 Canada.

Language: Английский

Citations

6
Whole-grain Petri Nets and Processes DOI
Joachim Kock

Journal of the ACM, Journal Year: 2022, Volume and Issue: 70(1), P. 1 - 58

Published: Aug. 25, 2022

We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The supports both geometric semantics in the style of Goltz Reisig (processes are maps from graphs) an algebraic Meseguer Montanari, terms free coloured props, allows following unification: P net, Segal space P-processes is shown to be prop-in-groupoids P. There also unfolding \`a la Winskel, which bypasses classical symmetry problems: with new formalism, every net admits universal unfolding, turn has associated event structure Scott domain. Since everything encoded explicit sets, their processes have elements. In particular, individual-token native. (Collective-token emerges rather drastic quotient constructions Best-Devillers, involving taking {\pi}_0 groupoids states.)

Language: Английский

Citations

6
Structured and Decorated Cospans from the Viewpoint of Double Category Theory DOI Creative Commons
Evan Patterson

arXiv (Cornell University), Journal Year: 2023, Volume and Issue: 397, P. 210 - 225

Published: Dec. 14, 2023

Structured and decorated cospans are broadly applicable frameworks for building bicategories or double categories of open systems. We streamline generalize these using central concepts category theory. show that, under mild hypotheses, structured cocartesian (have finite double-categorical coproducts) equipments. The proofs simple as they utilize appropriate universal properties. Maps between studied from the same perspective. then give a new construction recently introduced Grothendieck construction. Besides its conceptual value, this reconstruction leads to natural generalization cospans, which we illustrate through an example motivated by statistical theories other processes.

Language: Английский

Citations

2
A Categorical Framework for Modeling with Stock and Flow Diagrams DOI
John C. Baez, Xiaoyan Li,

Sophie Libkind

et al.

Fields Institute communications, Journal Year: 2023, Volume and Issue: unknown, P. 175 - 207

Published: Jan. 1, 2023

Language: Английский

Citations

2
A diagrammatic view of differential equations in physics DOI Creative Commons
Evan Patterson,

Andrew Baas,

Timothy Hosgood

et al.

Mathematics in Engineering, Journal Year: 2022, Volume and Issue: 5(2), P. 1 - 59

Published: Jan. 1, 2022

Presenting systems of differential equations in the form diagrams has become common certain parts physics, especially electromagnetism and computational physics. In this work, we aim to put such use on a firm mathematical footing, while also systematizing broadly applicable framework reason formally about their solutions. Our main tools are category-theoretic diagrams, which well known, morphisms between have been less appreciated. As an application diagrammatic framework, show how complex, multiphysical can be modularly constructed from basic physical principles. A wealth examples, drawn electromagnetism, transport phenomena, fluid mechanics, other fields, is included.

Language: Английский

Citations

3
Towards Rapid Design of Compartmental Models DOI

Zahra Fiyouzisabah,

Jessie Carbonnel, Marios Fokaefs

et al.

Published: Sept. 22, 2024

Language: Английский

Citations

0
Technical challenges of modelling real-life epidemics and examples of overcoming these DOI Creative Commons
Jasmina Panovska‐Griffiths, William Waites, Graeme J. Ackland

et al.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences, Journal Year: 2022, Volume and Issue: 380(2233)

Published: Aug. 15, 2022

The coronavirus disease 2019 (COVID-19) pandemic has highlighted the importance of mathematical modelling in informing and advising policy decision-making. Effective practice challenges. These can be around technical framework how different techniques are combined, appropriate use formalisms or computational languages to accurately capture intended mechanism process being studied, transparency robustness models numerical code, simulating scenarios via explicitly identifying underlying assumptions about nature simplifying approximations facilitate modelling, correctly quantifying uncertainty model parameters projections, taking into account variable quality data sources, applying established software engineering practices avoid duplication effort ensure reproducibility results. Via a collection 16 papers, this special issue aims address some these challenges alongside showcasing usefulness as applied pandemic. This article is part theme 'Technical real-life epidemics examples overcoming these'.

Language: Английский

Citations

2
Compositional Modeling with Stock and Flow Diagrams DOI Creative Commons
John C. Baez, Xiaoyan Li,

Sophie Libkind

et al.

arXiv (Cornell University), Journal Year: 2022, Volume and Issue: unknown

Published: Jan. 1, 2022

Stock and flow diagrams are widely used in epidemiology to model the dynamics of populations. Although tools already exist for building these simulating systems they describe, we have created a new package called StockFlow, part AlgebraicJulia ecosystem, which uses ideas from category theory overcome notable limitations existing software. Compositionality is provided by decorated cospans: stock can be composed form larger ones an intuitive way formalized operad undirected wiring diagrams. Our approach also cleanly separates syntax semantics assigned. We consider ordinary differential equations, although others possible. As example, explain code StockFlow that implements simplified version COVID-19 Canada.

Language: Английский

Citations

0