Paper List
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Translating Measures onto Mechanisms: The Cognitive Relevance of Higher-Order Information
This review addresses the core challenge of translating abstract higher-order information theory metrics (e.g., synergy, redundancy) into defensible, ...
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Emergent Bayesian Behaviour and Optimal Cue Combination in LLMs
This paper addresses the critical gap in understanding whether LLMs spontaneously develop human-like Bayesian strategies for processing uncertain info...
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Vessel Network Topology in Molecular Communication: Insights from Experiments and Theory
This work addresses the critical lack of experimentally validated channel models for molecular communication within complex vessel networks, which is ...
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Modulation of DNA rheology by a transcription factor that forms aging microgels
This work addresses the fundamental question of how the transcription factor NANOG, essential for embryonic stem cell pluripotency, physically regulat...
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Imperfect molecular detection renormalizes apparent kinetic rates in stochastic gene regulatory networks
This paper addresses the core challenge of distinguishing genuine stochastic dynamics of gene regulatory networks from artifacts introduced by imperfe...
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PanFoMa: A Lightweight Foundation Model and Benchmark for Pan-Cancer
This paper addresses the dual challenge of achieving computational efficiency without sacrificing accuracy in whole-transcriptome single-cell represen...
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Beyond Bayesian Inference: The Correlation Integral Likelihood Framework and Gradient Flow Methods for Deterministic Sampling
This paper addresses the core challenge of calibrating complex biological models (e.g., PDEs, agent-based models) with incomplete, noisy, or heterogen...
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Contrastive Deep Learning for Variant Detection in Wastewater Genomic Sequencing
This paper addresses the core challenge of detecting viral variants in wastewater sequencing data without reference genomes or labeled annotations, ov...
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.