1 citations · 3 across the 11 of their papers we have counts for
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Multiplicative Turing Ensembles, Pareto's Law, and Creativity
Alexander Kolpakov, Aidan Rocke
We study integer-valued multiplicative dynamics driven by i.i.d. prime multipliers and connect their macroscopic statistics to universal codelengths. We introduce the Multiplicativ…
Lagrangians, Renormalization, and Quantization in Prefix Coding
Alexander Kolpakov, Aidan Rocke
We develop a statistical mechanics framework for prefix coding based on variational principles, renormalization, and quantization. A Lagrangian formulation of entropy-optimal encod…
Fast Geometric Embedding for Node Influence Maximization
Alexander Kolpakov, Igor Rivin
Computing classical centrality measures such as betweenness and closeness is computationally expensive on large-scale graphs. In this work, we introduce an efficient force layout a…
Dimensionality reduction for homological stability and global structure preservation
Alexander Kolpakov, Igor Rivin
We propose DiRe, a force-directed dimensionality reduction framework designed to preserve global structure and homological features while remaining practical on modern hardware. Th…
Benford's Law from Turing Ensembles and Integer Partitions
Alexander Kolpakov, Aidan Rocke
We develop two complementary generative mechanisms that explain when and why Benford's first-digit law arises. First, a probabilistic Turing machine (PTM) ensemble induces a geomet…