4 papers
DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale
Alexander Kolpakov, Igor Rivin
Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise…
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…
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…