Paper List
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SpikGPT: A High-Accuracy and Interpretable Spiking Attention Framework for Single-Cell Annotation
This paper addresses the core challenge of robust single-cell annotation across heterogeneous datasets with batch effects and the critical need to ide...
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Unlocking hidden biomolecular conformational landscapes in diffusion models at inference time
This paper addresses the core challenge of efficiently and accurately sampling the conformational landscape of biomolecules from diffusion-based struc...
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Personalized optimization of pediatric HD-tDCS for dose consistency and target engagement
This paper addresses the critical limitation of one-size-fits-all HD-tDCS protocols in pediatric populations by developing a personalized optimization...
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Realistic Transition Paths for Large Biomolecular Systems: A Langevin Bridge Approach
This paper addresses the core challenge of generating physically realistic and computationally efficient transition paths between distinct protein con...
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Consistent Synthetic Sequences Unlock Structural Diversity in Fully Atomistic De Novo Protein Design
This paper addresses the core pain point of low sequence-structure alignment in existing synthetic datasets (e.g., AFDB), which severely limits the pe...
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MoRSAIK: Sequence Motif Reactor Simulation, Analysis and Inference Kit in Python
This work addresses the computational bottleneck in simulating prebiotic RNA reactor dynamics by developing a Python package that tracks sequence moti...
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On the Approximation of Phylogenetic Distance Functions by Artificial Neural Networks
This paper addresses the core challenge of developing computationally efficient and scalable neural network architectures that can learn accurate phyl...
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EcoCast: A Spatio-Temporal Model for Continual Biodiversity and Climate Risk Forecasting
This paper addresses the critical bottleneck in conservation: the lack of timely, high-resolution, near-term forecasts of species distribution shifts ...
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.