Paper List
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Pharmacophore-based design by learning on voxel grids
This paper addresses the computational bottleneck and limited novelty in conventional pharmacophore-based virtual screening by introducing a voxel cap...
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CONFIDE: Hallucination Assessment for Reliable Biomolecular Structure Prediction and Design
This paper addresses the critical limitation of current protein structure prediction models (like AlphaFold3) where high-confidence scores (pLDDT) can...
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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 ...
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Training Dynamics of Learning 3D-Rotational Equivariance
This work addresses the core dilemma of whether to use computationally expensive equivariant architectures or faster symmetry-agnostic models with dat...
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Fast and Accurate Node-Age Estimation Under Fossil Calibration Uncertainty Using the Adjusted Pairwise Likelihood
This paper addresses the dual challenge of computational inefficiency and sensitivity to fossil calibration errors in Bayesian divergence time estimat...
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Few-shot Protein Fitness Prediction via In-context Learning and Test-time Training
This paper addresses the core challenge of accurately predicting protein fitness with only a handful of experimental observations, where data collecti...
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scCluBench: Comprehensive Benchmarking of Clustering Algorithms for Single-Cell RNA Sequencing
This paper addresses the critical gap of fragmented and non-standardized benchmarking in single-cell RNA-seq clustering, which hinders objective compa...
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
The 30-Second View
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.
Innovation (TL;DR)
- 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.
Key conclusions
- 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.
Abstract: 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.