Paper List
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STAR-GO: Improving Protein Function Prediction by Learning to Hierarchically Integrate Ontology-Informed Semantic Embeddings
This paper addresses the core challenge of generalizing protein function prediction to unseen or newly introduced Gene Ontology (GO) terms by overcomi...
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Incorporating indel channels into average-case analysis of seed-chain-extend
This paper addresses the core pain point of bridging the theoretical gap for the widely used seed-chain-extend heuristic by providing the first rigoro...
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Competition, stability, and functionality in excitatory-inhibitory neural circuits
This paper addresses the core challenge of extending interpretable energy-based frameworks to biologically realistic asymmetric neural networks, where...
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Enhancing Clinical Note Generation with ICD-10, Clinical Ontology Knowledge Graphs, and Chain-of-Thought Prompting Using GPT-4
This paper addresses the core challenge of generating accurate and clinically relevant patient notes from sparse inputs (ICD codes and basic demograph...
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Learning From Limited Data and Feedback for Cell Culture Process Monitoring: A Comparative Study
This paper addresses the core challenge of developing accurate real-time bioprocess monitoring soft sensors under severe data constraints: limited his...
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Cell-cell communication inference and analysis: biological mechanisms, computational approaches, and future opportunities
This review addresses the critical need for a systematic framework to navigate the rapidly expanding landscape of computational methods for inferring ...
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Generating a Contact Matrix for Aged Care Settings in Australia: an agent-based model study
This study addresses the critical gap in understanding heterogeneous contact patterns within aged care facilities, where existing population-level con...
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Emergent Spatiotemporal Dynamics in Large-Scale Brain Networks with Next Generation Neural Mass Models
This work addresses the core challenge of understanding how complex, brain-wide spatiotemporal patterns emerge from the interaction of biophysically d...
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.