36 citations · 170 across the 43 of their papers we have counts for
49 papers
Machine Learning of the Prime Distribution
Alexander Kolpakov, Aidan Rocke
In the present work we use maximum entropy methods to derive several theorems in probabilistic number theory, including a version of the Hardy-Ramanujan Theorem. We also provide a…
On the impossibility of discovering a formula for primes using AI
Alexander Kolpakov, Aidan Rocke
The present work explores the theoretical limits of Machine Learning (ML) within the framework of Kolmogorov's theory of Algorithmic Probability, which clarifies the notion of entr…
Expansion properties of Whitehead moves on cubic graphs
Laura Grave de Peralta, Alexander Kolpakov
The present note concerns the "graph of graphs" that has cubic graphs as vertices connected by edges represented by the so-called Whitehead moves. Here, we prove that the outer-con…
Robust affine point matching via quadratic assignment on Grassmannians
Alexander Kolpakov, Michael Werman
Robust Affine Matching with Grassmannians (RoAM) is a new algorithm to perform affine registration of point clouds. The algorithm is based on minimizing the Frobenius distance betw…
An approach to robust ICP initialization
Alexander Kolpakov, Michael Werman
In this note, we propose an approach to initialize the Iterative Closest Point (ICP) algorithm to match unlabelled point clouds related by rigid transformations. The method is base…
Infinitely many arithmetic hyperbolic rational homology 3-spheres that bound geometrically
Leonardo Ferrari, Alexander Kolpakov, Alan W. Reid
In this paper we provide the first examples of arithmetic hyperbolic 3-manifolds that are rational homology spheres and bound geometrically either compact or cusped hyperbolic 4-ma…