1 citations · 1 across the 5 of their papers we have counts for
5 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…
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…
A ripple in time: a discontinuity in American history
Alexander Kolpakov, Igor Rivin
In this technical note we suggest a novel approach to discover temporal (related and unrelated to language dilation) and personality (authorship attribution) aspects in historical…