Related papers: On integer sequences for rendering limit sets of K…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
Saliency maps are widely used in the computer vision community for interpreting neural network classifiers. However, due to the randomness of training samples and optimization algorithms, the resulting saliency maps suffer from a…
We show how to implement quantum computation on a system with an intrinsic Hamiltonian by controlling a limited subset of spins. Our primary result is an efficient control sequence on a nearest-neighbor XY spin chain through control of a…
The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient param-eterized algorithms, this method…
The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic…
We propose several procedures for creating new families of integer sequences based on the method of Cantor diagonalization. Then we modify and generalize this method. The paper includes explicit formulas for most proposed families of…
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
We provide new examples of the asymptotic counting for the number of subsets on groups of given size which are free of certain configurations. These examples include sets without solutions to equations in non-abelian groups, and linear…
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gr\"obner and Border bases are fundamental but suffer from high…
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…
We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…
Our purpose is to visualize the pronilpotent completion of a finitely generated free group as a certain subgroup in the free Lie group.
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…
We examine the internal geometry of a Kleinian surface group and its relations to the asymptotic geometry of its ends, using the combinatorial structure of the complex of curves on the surface. Our main results give necessary conditions for…
We present a method for large-mask pluralistic image inpainting based on the generative framework of discrete latent codes. Our method learns latent priors, discretized as tokens, by only performing computations at the visible locations of…
Neural compression offers a domain-agnostic approach to creating codecs for lossy or lossless compression via deep generative models. For sequence compression, however, most deep sequence models have costs that scale with the sequence…
Sentence compression is a Natural Language Processing (NLP) task aimed at shortening original sentences and preserving their key information. Its applications can benefit many fields e.g. one can build tools for language education. However,…
Stein's method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the…
Language models typically tokenize text into subwords, using a deterministic, hand-engineered heuristic of combining characters into longer surface-level strings such as 'ing' or whole words. Recent literature has repeatedly shown the…
We develop a computational framework for the statistical characterization of Galois characters with finite image, with application to characterizing Galois groups and establishing equivalence of characters of finite images of…