8 papers
Homonym Sense Disambiguation in the Georgian Language
Davit Melikidze, Alexander Gamkrelidze
This research proposes a novel approach to the Word Sense Disambiguation (WSD) task in the Georgian language, based on supervised fine-tuning of a pre-trained Large Language Model…
Approximation of Discs by Octagons on Pixel-Plane via Jaccards Proximity Criterion: Theoretical Approach and Experimental Results Analysis
Irakli Dochviri, Alexander Gamkrelidze, Revaz Kurdiani
In the present paper we study approximation of discs by octagons on the pixel plane. To decide which octagon approximates better the given disc we use Jaccard's distance. The table…
On the notion of a basis of a finite dimensional vector space
Alexander Gamkrelidze, Grigori Giorgadze
In this Note we show that the notion of a basis of a finite-dimensional vector space could be introduced by an argument much weaker than Gauss' reduction method. Our aim is to give…
Affine hom-complexes
M. Bakuradze, A. Gamkrelidze, J. Gubeladze
For two general polytopal complexes the set of face-wise affine maps between them is shown to be a polytopal complex in an algorithmic way. The resulting algorithm for the affine h…
New Invariants for the Graph Isomorphism Problem
Alexander Gamkrelidze, Gunter Hotz, Levan Varamashvili
In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph inv…
Numerical comparison of different algorithms for construction of wavelet matrices
Nika Salia, Alexander Gamkrelidze, Lasha Ephremidze
Factorization of compact wavelet matrices into primitive ones has been known for more than 20 years. This method makes it possible to generate wavelet matrix coefficients and also…
An approximation of Daubechies wavelet matrices by perfect reconstruction filter banks with rational coefficients
Lasha Ephremidze, Aleksander Gamkrelidze, Edem Lagvilava
It is described how the coefficients of Daubechies wavelet matrices can be approximated by rational numbers in such a way that the perfect reconstruction property of the filter ban…
Algorithms for Low-Dimensional Topology
Alexander Gamkrelidze
In this article, we re-introduce the so called "Arkaden-Faden-Lage" (AFL for short) representation of knots in 3 dimensional space introduced by Kurt Reidemeister and show how it c…