Paper List
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GOPHER: Optimization-based Phenotype Randomization for Genome-Wide Association Studies with Differential Privacy
This paper addresses the core challenge of balancing rigorous privacy protection with data utility when releasing full GWAS summary statistics, overco...
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Real-time Cricket Sorting By Sex A low-cost embedded solution using YOLOv8 and Raspberry Pi
This paper addresses the critical bottleneck in industrial insect farming: the lack of automated, real-time sex sorting systems for Acheta domesticus ...
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Training Dynamics of Learning 3D-Rotational Equivariance
This work addresses the core dilemma of whether to use computationally expensive equivariant architectures or faster symmetry-agnostic models with dat...
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Fast and Accurate Node-Age Estimation Under Fossil Calibration Uncertainty Using the Adjusted Pairwise Likelihood
This paper addresses the dual challenge of computational inefficiency and sensitivity to fossil calibration errors in Bayesian divergence time estimat...
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Few-shot Protein Fitness Prediction via In-context Learning and Test-time Training
This paper addresses the core challenge of accurately predicting protein fitness with only a handful of experimental observations, where data collecti...
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scCluBench: Comprehensive Benchmarking of Clustering Algorithms for Single-Cell RNA Sequencing
This paper addresses the critical gap of fragmented and non-standardized benchmarking in single-cell RNA-seq clustering, which hinders objective compa...
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Simulation and inference methods for non-Markovian stochastic biochemical reaction networks
This paper addresses the computational bottleneck of simulating and performing Bayesian inference for non-Markovian biochemical systems with history-d...
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Assessment of Simulation-based Inference Methods for Stochastic Compartmental Models
This paper addresses the core challenge of performing accurate Bayesian parameter inference for stochastic epidemic models when the likelihood functio...
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.