Paper List
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Formation of Artificial Neural Assemblies by Biologically Plausible Inhibition Mechanisms
This work addresses the core limitation of the Assembly Calculus model—its fixed-size, biologically implausible k-WTA selection process—by introducing...
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How to make the most of your masked language model for protein engineering
This paper addresses the critical bottleneck of efficiently sampling high-quality, diverse protein sequences from Masked Language Models (MLMs) for pr...
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Module control in youth symptom networks across COVID-19
This paper addresses the core challenge of distinguishing whether a prolonged societal stressor (COVID-19) fundamentally reorganizes the architecture ...
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JEDI: Jointly Embedded Inference of Neural Dynamics
This paper addresses the core challenge of inferring context-dependent neural dynamics from noisy, high-dimensional recordings using a single unified ...
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ATP Level and Phosphorylation Free Energy Regulate Trigger-Wave Speed and Critical Nucleus Size in Cellular Biochemical Systems
This work addresses the core challenge of quantitatively predicting how the cellular energy state (ATP level and phosphorylation free energy) governs ...
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Packaging Jupyter notebooks as installable desktop apps using LabConstrictor
This paper addresses the core pain point of ensuring Jupyter notebook reproducibility and accessibility across different computing environments, parti...
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SNPgen: Phenotype-Supervised Genotype Representation and Synthetic Data Generation via Latent Diffusion
This paper addresses the core challenge of generating privacy-preserving synthetic genotype data that maintains both statistical fidelity and downstre...
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Continuous Diffusion Transformers for Designing Synthetic Regulatory Elements
This paper addresses the challenge of efficiently generating novel, cell-type-specific regulatory DNA sequences with high predicted activity while min...
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.