Paper List
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Macroscopic Dominance from Microscopic Extremes: Symmetry Breaking in Spatial Competition
This paper addresses the fundamental question of how microscopic stochastic advantages in spatial exploration translate into macroscopic resource domi...
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Linear Readout of Neural Manifolds with Continuous Variables
This paper addresses the core challenge of quantifying how the geometric structure of high-dimensional neural population activity (neural manifolds) d...
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Theory of Cell Body Lensing and Phototaxis Sign Reversal in “Eyeless” Mutants of Chlamydomonas
This paper solves the core puzzle of how eyeless mutants of Chlamydomonas exhibit reversed phototaxis by quantitatively modeling the competition betwe...
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Cross-Species Transfer Learning for Electrophysiology-to-Transcriptomics Mapping in Cortical GABAergic Interneurons
This paper addresses the challenge of predicting transcriptomic identity from electrophysiological recordings in human cortical interneurons, where li...
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Uncovering statistical structure in large-scale neural activity with Restricted Boltzmann Machines
This paper addresses the core challenge of modeling large-scale neural population activity (1500-2000 neurons) with interpretable higher-order interac...
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Realizing Common Random Numbers: Event-Keyed Hashing for Causally Valid Stochastic Models
This paper addresses the critical problem that standard stateful PRNG implementations in agent-based models violate causal validity by making random d...
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A Standardized Framework for Evaluating Gene Expression Generative Models
This paper addresses the critical lack of standardized evaluation protocols for single-cell gene expression generative models, where inconsistent metr...
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Single Molecule Localization Microscopy Challenge: A Biologically Inspired Benchmark for Long-Sequence Modeling
This paper addresses the core challenge of evaluating state-space models on biologically realistic, sparse, and stochastic temporal processes, which a...
Macroscopic Dominance from Microscopic Extremes: Symmetry Breaking in Spatial Competition
Department of Mathematics, Florida State University | Department of Mathematics and Statistics, Cleveland State University | Institute of Molecular Biophysics, Florida State University
30秒速读
IN SHORT: This paper addresses the fundamental question of how microscopic stochastic advantages in spatial exploration translate into macroscopic resource dominance, revealing that initial discovery and final monopolization are governed by distinct physical mechanisms.
核心创新
- Methodology Introduces a dimensionless scaling parameter χ = (N₂/N₁)8^(d₁-d₂) that completely determines competitive symmetry, showing that a linear spatial disadvantage requires an exponential population advantage to overcome.
- Theory Demonstrates that extreme first-passage statistics govern initial discovery, while non-reciprocal interaction bias (β) controls the sharpness of the competitive phase transition and stability of the absorbing state.
- Biology Reveals a strict hierarchy of symmetry-breaking factors: proximity to resource > population size > interaction bias, with β being necessary but not sufficient for dominance.
主要结论
- Proximity imparts the strongest competitive advantage: a colony with distance d₁ < d₂ requires N₂/N₁ ~ 8^(d₂-d₁) ants to compensate (Equation 3).
- The interaction bias β acts as a phase transition tuner: for β → 0, outcomes remain probabilistic; for large β, the symmetry-breaking boundary sharpens into a step function (Figure 3).
- Discovery and monopolization are decoupled: extreme first-passage statistics govern initial finding (⟨T_i⟩ = d_i + (1-p_i)^(N_i)), while β strictly controls stability of the absorbing state.
摘要: How do competing populations convert a spatial advantage into macroscopic dominance? We introduce a stochastic model for resource competition that decouples the transient discovery phase from monopolization. Initial symmetry breaking is governed by extreme value statistics of first-passage times: a linear spatial disadvantage requires an exponentially larger population to overcome. However, transient superiority cannot stabilize dominance. A non-reciprocal interaction bias is strictly necessary to arrest local fluctuations and drive the system into a robust absorbing state.