Paper List
-
Developing the PsyCogMetrics™ AI Lab to Evaluate Large Language Models and Advance Cognitive Science
This paper addresses the critical gap between sophisticated LLM evaluation needs and the lack of accessible, scientifically rigorous platforms that in...
-
Equivalence of approximation by networks of single- and multi-spike neurons
This paper resolves the fundamental question of whether single-spike spiking neural networks (SNNs) are inherently less expressive than multi-spike SN...
-
The neuroscience of transformers
提出了Transformer架构与皮层柱微环路之间的新颖计算映射，连接了现代AI与神经科学。
-
Framing local structural identifiability and observability in terms of parameter-state symmetries
This paper addresses the core challenge of systematically determining which parameters and states in a mechanistic ODE model can be uniquely inferred ...
-
Leveraging Phytolith Research using Artificial Intelligence
This paper addresses the critical bottleneck in phytolith research by automating the labor-intensive manual microscopy process through a multimodal AI...
-
Neural network-based encoding in free-viewing fMRI with gaze-aware models
This paper addresses the core challenge of building computationally efficient and ecologically valid brain encoding models for naturalistic vision by ...
-
Scalable DNA Ternary Full Adder Enabled by a Competitive Blocking Circuit
This paper addresses the core bottleneck of carry information attenuation and limited computational scale in DNA binary adders by introducing a scalab...
-
ELISA: An Interpretable Hybrid Generative AI Agent for Expression-Grounded Discovery in Single-Cell Genomics
This paper addresses the critical bottleneck of translating high-dimensional single-cell transcriptomic data into interpretable biological hypotheses ...
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.