1 citations · 1 across the 4 of their papers we have counts for
10 papers
Random Knots via Stiefel manifolds
Alexander Kolpakov, Igor Rivin
A fixed simplex, randomly projected into three dimensions and joined in Hamiltonian order, produces a rich and unusually tractable model of random stick knots. We prove that Gaussi…
Discriminant Varieties for Stick Knots and Links
Alexander Kolpakov, Igor Rivin
How many knot types can be built from a fixed budget of straight sticks? We prove that the answer has factorial-scale growth, settling its order for the first time. No previously p…
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…
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…
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…
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…