Paper List
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Ill-Conditioning in Dictionary-Based Dynamic-Equation Learning: A Systems Biology Case Study
This paper addresses the critical challenge of numerical ill-conditioning and multicollinearity in library-based sparse regression methods (e.g., SIND...
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Hybrid eTFCE–GRF: Exact Cluster-Size Retrieval with Analytical pp-Values for Voxel-Based Morphometry
This paper addresses the computational bottleneck in voxel-based neuroimaging analysis by providing a method that delivers exact cluster-size retrieva...
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abx_amr_simulator: A simulation environment for antibiotic prescribing policy optimization under antimicrobial resistance
This paper addresses the critical challenge of quantitatively evaluating antibiotic prescribing policies under realistic uncertainty and partial obser...
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PesTwin: a biology-informed Digital Twin for enabling precision farming
This paper addresses the critical bottleneck in precision agriculture: the inability to accurately forecast pest outbreaks in real-time, leading to su...
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Equivariant Asynchronous Diffusion: An Adaptive Denoising Schedule for Accelerated Molecular Conformation Generation
This paper addresses the core challenge of generating physically plausible 3D molecular structures by bridging the gap between autoregressive methods ...
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Omics Data Discovery Agents
This paper addresses the core challenge of making published omics data computationally reusable by automating the extraction, quantification, and inte...
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Single-cell directional sensing at ultra-low chemoattractant concentrations from extreme first-passage events
This work addresses the core challenge of how a cell can rapidly and accurately determine the direction of a chemoattractant source when the signal is...
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SDSR: A Spectral Divide-and-Conquer Approach for Species Tree Reconstruction
This paper addresses the computational bottleneck in reconstructing species trees from thousands of species and multiple genes by introducing a scalab...
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.