33 citations · 42 across the 4 of their papers we have counts for
5 papers
Liouville integrability in a four-dimensional model of the visual cortex
Ivan Galyaev, Alexey Mashtakov
We consider a natural extension of the Petitot-Citti-Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taking into account such that occ…
Geometrical Optical Illusion via Sub-Riemannian Geodesics in the Roto-Translation Group
Benedetta Franceschiello, Alexey Mashtakov, Giovanna Citti +1
We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual st…
Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to Linear Parabolic and (Hypo-)Elliptic PDEs
Remco Duits, Erik J. Bekkers, Alexey Mashtakov
Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics,…
Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space
Alexey Mashtakov, Anton Popov
For the sub-Riemannian problem on the group of motions of Euclidean space we present explicit formulas for extremal controls in a special case, when one of the initial momenta is f…
Asymptotics of Maxwell time in the plate-ball problem
A. P. Mashtakov, A. Yu. Popov
The problem on rolling of a sphere on a plane without slipping or twisting is considered. One should roll the sphere from one contact configuration to another so that the length of…