Paper List
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The Effective Reproduction Number in the Kermack-McKendrick model with age of infection and reinfection
This paper addresses the challenge of accurately estimating the time-varying effective reproduction number ℛ(t) in epidemics by incorporating two crit...
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Covering Relations in the Poset of Combinatorial Neural Codes
This work addresses the core challenge of navigating the complex poset structure of neural codes to systematically test the conjecture linking convex ...
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Collective adsorption of pheromones at the water-air interface
This paper addresses the core challenge of understanding how amphiphilic pheromones, previously assumed to be transported in the gas phase, can be sta...
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pHapCompass: Probabilistic Assembly and Uncertainty Quantification of Polyploid Haplotype Phase
This paper addresses the core challenge of accurately assembling polyploid haplotypes from sequencing data, where read assignment ambiguity and an exp...
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Setting up for failure: automatic discovery of the neural mechanisms of cognitive errors
This paper addresses the core challenge of automating the discovery of biologically plausible recurrent neural network (RNN) dynamics that can replica...
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Influence of Object Affordance on Action Language Understanding: Evidence from Dynamic Causal Modeling Analysis
This study addresses the core challenge of moving beyond correlational evidence to establish the *causal direction* and *temporal dynamics* of how obj...
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Revealing stimulus-dependent dynamics through statistical complexity
This paper addresses the core challenge of detecting stimulus-specific patterns in neural population dynamics that remain hidden to traditional variab...
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Exactly Solvable Population Model with Square-Root Growth Noise and Cell-Size Regulation
This paper addresses the fundamental gap in understanding how microscopic growth fluctuations, specifically those with size-dependent (square-root) no...
Framing local structural identifiability and observability in terms of parameter-state symmetries
Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden | Mathematical Institute, University of Oxford, United Kingdom | School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia | Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden
30秒速读
IN SHORT: This paper addresses the core challenge of systematically determining which parameters and states in a mechanistic ODE model can be uniquely inferred from observed outputs, a fundamental prerequisite for reliable parameter estimation and state reconstruction.
核心创新
- Methodology Introduces a novel subclass of Lie symmetries, termed 'parameter-state symmetries', which simultaneously transform model parameters and states while preserving all observed outputs at every time point.
- Theory Proves a fundamental theorem linking locally structurally identifiable parameter combinations and observable states to the universal invariants of all parameter-state symmetries of a model, providing a rigorous mathematical foundation.
- Methodology Provides a unified framework that simultaneously analyzes local structural identifiability and observability, extending previous work that focused only on identifiability via parameter symmetries of the output system.
主要结论
- Parameter-state symmetries, defined by their preservation of observed outputs (y(t, x, θ) = y(t, x*, θ*)), provide the precise mathematical objects whose invariants correspond to locally identifiable/observable quantities.
- The framework successfully recovers known identifiability results (e.g., from differential algebra methods) and reveals new insights into state observability for canonical models like glucose-insulin regulation and SEI epidemiological models.
- The approach offers a systematic, symmetry-based alternative to established methods (e.g., differential algebra, EAR method) for the joint analysis of two critical structural properties in dynamical systems modeling.
摘要: We introduce a subclass of Lie symmetries, called parameter–state symmetries, to analyse the local structural identifiability and observability of mechanistic models consisting of state-dependent ODEs with observed outputs. These symmetries act on parameters and states while preserving observed outputs at every time point. We prove that locally structurally identifiable parameter combinations and locally structurally observable states correspond to universal invariants of all parameter–state symmetries of a given model. We illustrate the framework on four previously studied mechanistic models, confirming known identifiability results and revealing novel insights into which states are observable, providing a unified symmetry-based approach for analysing structural properties of dynamical systems.