Paper List
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Macroscopic Dominance from Microscopic Extremes: Symmetry Breaking in Spatial Competition
This paper addresses the fundamental question of how microscopic stochastic advantages in spatial exploration translate into macroscopic resource domi...
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Linear Readout of Neural Manifolds with Continuous Variables
This paper addresses the core challenge of quantifying how the geometric structure of high-dimensional neural population activity (neural manifolds) d...
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Theory of Cell Body Lensing and Phototaxis Sign Reversal in “Eyeless” Mutants of Chlamydomonas
This paper solves the core puzzle of how eyeless mutants of Chlamydomonas exhibit reversed phototaxis by quantitatively modeling the competition betwe...
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Cross-Species Transfer Learning for Electrophysiology-to-Transcriptomics Mapping in Cortical GABAergic Interneurons
This paper addresses the challenge of predicting transcriptomic identity from electrophysiological recordings in human cortical interneurons, where li...
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Uncovering statistical structure in large-scale neural activity with Restricted Boltzmann Machines
This paper addresses the core challenge of modeling large-scale neural population activity (1500-2000 neurons) with interpretable higher-order interac...
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Realizing Common Random Numbers: Event-Keyed Hashing for Causally Valid Stochastic Models
This paper addresses the critical problem that standard stateful PRNG implementations in agent-based models violate causal validity by making random d...
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A Standardized Framework for Evaluating Gene Expression Generative Models
This paper addresses the critical lack of standardized evaluation protocols for single-cell gene expression generative models, where inconsistent metr...
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Single Molecule Localization Microscopy Challenge: A Biologically Inspired Benchmark for Long-Sequence Modeling
This paper addresses the core challenge of evaluating state-space models on biologically realistic, sparse, and stochastic temporal processes, which a...
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.