Paper List
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An AI Implementation Science Study to Improve Trustworthy Data in a Large Healthcare System
This paper addresses the critical gap between theoretical AI research and real-world clinical implementation by providing a practical framework for as...
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The BEAT-CF Causal Model: A model for guiding the design of trials and observational analyses of cystic fibrosis exacerbations
This paper addresses the critical gap in cystic fibrosis exacerbation management by providing a formal causal framework that integrates expert knowled...
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Hierarchical Molecular Language Models (HMLMs)
This paper addresses the core challenge of accurately modeling context-dependent signaling, pathway cross-talk, and temporal dynamics across multiple ...
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Stability analysis of action potential generation using Markov models of voltage‑gated sodium channel isoforms
This work addresses the challenge of systematically characterizing how the high-dimensional parameter space of Markov models for different sodium chan...
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Approximate Bayesian Inference on Mechanisms of Network Growth and Evolution
This paper addresses the core challenge of inferring the relative contributions of multiple, simultaneous generative mechanisms in network formation w...
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EnzyCLIP: A Cross-Attention Dual Encoder Framework with Contrastive Learning for Predicting Enzyme Kinetic Constants
This paper addresses the core challenge of jointly predicting enzyme kinetic parameters (Kcat and Km) by modeling dynamic enzyme-substrate interaction...
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Tissue stress measurements with Bayesian Inversion Stress Microscopy
This paper addresses the core challenge of measuring absolute, tissue-scale mechanical stress without making assumptions about tissue rheology, which ...
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DeepFRI Demystified: Interpretability vs. Accuracy in AI Protein Function Prediction
This study addresses the critical gap between high predictive accuracy and biological interpretability in DeepFRI, revealing that the model often prio...
Exactly Solvable Population Model with Square-Root Growth Noise and Cell-Size Regulation
Institute for Theoretical Physics, Department of Physics, Utrecht University, Utrecht, Netherlands | Centre for Complex Systems Studies, Utrecht University, Utrecht, Netherlands
30秒速读
IN SHORT: This paper addresses the fundamental gap in understanding how microscopic growth fluctuations, specifically those with size-dependent (square-root) noise, shape population-level fitness and statistics in cell populations, providing an exactly solvable model that contrasts sharply with existing size-independent noise models.
核心创新
- Theory Demonstrates that the asymptotic population growth rate Λ is exactly equal to the mean single-cell growth rate k, independent of noise strength σ and division mechanisms, establishing square-root growth noise as neutral for long-term fitness.
- Methodology Derives exact, closed-form expressions for the steady-state snapshot cell-size distribution, showing it results from a universal one-sided exponential convolution of the deterministic inverse-square-law solution, with kernel width σ².
- Theory Proves that the mean-rescaled population size Nt/⟨Nt⟩ converges to a stationary compound Poisson–exponential distribution determined solely by the growth noise parameter σ, independent of division or partitioning noise.
主要结论
- Population growth rate Λ = k exactly, demonstrating fitness neutrality of square-root noise (contrasting with models where Λ increases with variance of size-independent noise).
- Steady-state population mean cell size shifts by -σ² (e.g., ⟨s⟩pop = 2ln2 - σ² + O(e^{-1/σ²})), while variance is modified only at order σ⁴, showing a hierarchy of decoupling.
- The coefficient of variation of total cell number saturates to √(2σ²), and the full distribution of the mean-rescaled population size is a compound Poisson–exponential, providing concrete, testable signatures.
摘要: We analyze a size-structured branching process in which individual cells grow exponentially according to a Feller square-root process and divide under general size-control mechanisms. We obtain exact expressions for the asymptotic population growth rate, the steady-state snapshot distribution of cell sizes, and the fluctuations of the total cell number. Our first result is that the population growth rate is exactly equal to the mean single-cell growth rate, for all noise strengths and for all division and size-regulation schemes that maintain size homeostasis. Thus square-root growth noise is neutral with respect to long-term fitness, in sharp contrast to models with size-independent stochastic growth rates. Second, we show that the steady-state population cell-size distribution is obtained from the deterministic inverse-square-law solution by a one-sided exponential convolution with kernel width set by the strength of growth fluctuations. Third, the mean-rescaled population size Nt/⟨Nt⟩ converges to a stationary compound Poisson–exponential distribution that depends only on growth noise. This distribution, and hence the long-time shape of population-size fluctuations, is unchanged by division-size noise or asymmetric partitioning. These results identify Feller-type exponential growth with square-root noise as an exactly solvable benchmark for stochastic growth in size-controlled populations and provide concrete signatures that distinguish it from models with size-independent growth-rate noise.