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of 219
pro vyhledávání: '"Kolpakov, Alexander"'
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 theoretical argument explaining the experimental observations of Yang-
Externí odkaz:
http://arxiv.org/abs/2403.12588
Autor:
Kolpakov, Alexander, Rivin, Igor
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 datasets. We exemplify our approach on the State of the Union addresse
Externí odkaz:
http://arxiv.org/abs/2312.01185
In this note we highlight some connections of UMAP to the basic principles of Information Geometry. Originally, UMAP was derived from Category Theory observations. However, we posit that it also has a natural geometric interpretation.
Comment: 1
Comment: 1
Externí odkaz:
http://arxiv.org/abs/2309.01237
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 entropy as Expected Kolmogorov Complexity and formalizes other fundamental
Externí odkaz:
http://arxiv.org/abs/2308.10817
The present note studies the "graph of graphs" that has cubic graphs as vertices connected by edges represented by the so-called Whitehead moves. We study its conductance and expansion properties, and the adjacency spectrum.
Externí odkaz:
http://arxiv.org/abs/2303.13923
Autor:
Kolpakov, Alexander, Werman, Michael
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 between two elements of the Grassmannian. For this purpose, an indefinite
Externí odkaz:
http://arxiv.org/abs/2303.02698
Autor:
Kolpakov, Alexander, Werman, Michael
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 based on matching the ellipsoids defined by the points' covariance matrice
Externí odkaz:
http://arxiv.org/abs/2212.05332
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-manifolds.
Comment: 19 pages, 1 figure, 1 table; improved expositio
Comment: 19 pages, 1 figure, 1 table; improved expositio
Externí odkaz:
http://arxiv.org/abs/2203.01997
In this paper we study crystallographic sphere packings and Kleinian sphere packings, introduced first by Kontorovich and Nakamura in 2017 and then studied further by Kapovich and Kontorovich in 2021. In particular, we solve the problem of existence
Externí odkaz:
http://arxiv.org/abs/2203.01973
Autor:
Kolpakov, Alexander, Werman, Michael
Publikováno v:
In Pattern Recognition Letters October 2024 186:265-271
