9 papers
A Polynomial Recovery Criterion for Forced Commutativity in the Matrix Square-Root Fiber of a Square-Free Cubic Polynomial
Oleg Kiriukhin
Let be an algebraically closed field of characteristic different from and , and let be square-free. For set . This paper st…
Orbit-Level Transfer Matrix for the 3D Fourier-Galerkin Navier-Stokes System on the Periodic Torus: Explicit Orbit-Triad Incidence Bounds and Deterministic Row-Sum Estimates
Oleg Kiriukhin
I study the cubic Fourier-Galerkin truncation of the three-dimensional (3D) incompressible Navier-Stokes equations on the periodic torus after reduction by the full octahedral symm…
A Strict Gap Between Relaxed and Partition-Constrained Spectral Compression in a Six-State Lumpable Markov Chain
Oleg Kiriukhin
This paper studies a finite reversible lumpable Markov chain for which relaxed spectral compression yields a larger determinant than partition-constrained compression. For a symmet…
Variable-Length Markov Chains on Finite Quivers: Boundary-Window Identifiability, Exact Depth, and Local Rank Comparison
Oleg Kiriukhin
Variable-length Markov chains on finite quivers provide a natural framework for context-dependent stochastic growth under incidence constraints. I study quiver-valued variable-leng…
Entropy-Rate Selection for Partially Observed Processes
Oleg Kiriukhin
I formulate an entropy-rate maximization problem at the observable level for stochastic processes observed through an information-reducing observation map. For a visible stationary…
Orbit-Level Stretching in Cubic Fourier-Galerkin Navier-Stokes: Sharp Incidence, Spectral Decay, and a Continuation Criterion
Oleg Kiriukhin
I study orbit-level enstrophy stretching in a cubic Fourier-Galerkin truncation of the three-dimensional incompressible Navier-Stokes equations, reduced by the full octahedral symm…
Probabilistic Verification of Voice Anti-Spoofing Models
Evgeny Kushnir, Alexandr Kozodaev, Dmitrii Korzh +3
Recent advances in generative models have amplified the risk of malicious misuse of speech synthesis technologies, enabling adversaries to impersonate target speakers and access se…
Towards Robust Speech Deepfake Detection via Human-Inspired Reasoning
Artem Dvirniak, Evgeny Kushnir, Dmitrii Tarasov +5
The modern generative audio models can be used by an adversary in an unlawful manner, specifically, to impersonate other people to gain access to private information. To mitigate t…
Differential invariants of feedback transformations for quasi-harmonic oscillation equations
D. S. Gritsenko, O. M. Kiriukhin
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential e…