Zobrazeno 1 - 10
of 37
pro vyhledávání: '"KALTCHENKO, ALEXEI"'
Autor:
Kaltchenko, Alexei
This paper investigates the uncertainty of Generative Pre-trained Transformer (GPT) models in extracting mathematical equations from images of varying resolutions and converting them into LaTeX code. We employ concepts of entropy and mutual informati
Externí odkaz:
http://arxiv.org/abs/2412.01221
Autor:
Kaltchenko, Alexei
We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the context o
Externí odkaz:
http://arxiv.org/abs/2110.05937
Autor:
Kaltchenko, Alexei
We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/2109.01960
Autor:
KALTCHENKO, ALEXEI1
Publikováno v:
i-Manager's Journal on Mathematics. Jun2024, Vol. 13 Issue 1, p1-10. 10p.
Autor:
Timofeev, Evgeniy, Kaltchenko, Alexei
Publikováno v:
Advances in Mathematics of Communications, 2014, 8(2): 119-127
A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak metrics, a new n
Externí odkaz:
http://arxiv.org/abs/1205.5856
Autor:
Kaltchenko, Alexei
Publikováno v:
Phys.Rev.A. 78 (2008) 022311
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide an alterna
Externí odkaz:
http://arxiv.org/abs/0805.0328
Autor:
Kaltchenko, Alexei
After reviewing unnormalized and normalized information distances based on incomputable notions of Kolmogorov complexity, we discuss how Kolmogorov complexity can be approximated by data compression algorithms. We argue that optimal algorithms for da
Externí odkaz:
http://arxiv.org/abs/cs/0404039
Autor:
Kaltchenko, Alexei, Yang, En-Hui
For a real number $r>0$, let $F(r)$ be the family of all stationary ergodic quantum sources with von Neumann entropy rates less than $r$. We prove that, for any $r>0$, there exists a blind, source-independent block compression scheme which compresses
Externí odkaz:
http://arxiv.org/abs/quant-ph/0302174
Invariance of Stationary and Ergodic Properties of a Quantum Source under Memoryless Transformations
Autor:
Kaltchenko, Alexei, Yang, En-Hui
We prove that the stationarity and the ergodicity of a quantum source are preserved by any trace-preserving completely positive linear map of the tensor product form ${\cal E}^{\otimes m}$, where a copy of ${\cal E}$ acts locally on each spin lattice
Externí odkaz:
http://arxiv.org/abs/quant-ph/0211034
Autor:
Donkor, Eric, Hayduk, Michael, Frey, Michael R., Lomonaco, Samuel J., Myers, John M., Kaltchenko, Alexei
Publikováno v:
Proceedings of SPIE; May 2022, Vol. 12093 Issue: 1 p120930E-120930E-6, 1088377p