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Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…
Application of the noncommutative geometry to several physical models is considered.
We propose a quantum theory of rotating light beams and study some of its properties. Such beams are polychromatic and have either a slowly rotating polarization or a slowly rotating transverse mode pattern. We show there are, for both…
Using the Surface Evolver software, we perform numerical simulations of point-like deformations in a two-dimensional foam. We study perturbations which are infinitesimal or finite, isotropic or anisotropic, and we either conserve or do not…
The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation…
Two variable speed of light models and their physical consequences are investigated.
Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for understanding tissue homeostasis and stable developmental processes. However, numerical simulations…
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
The main goal of this paper is to extend [J. Algebra Appl. 20 (2021), 2150074] to generalized quaternion algebras, even when these algebras are not necessarily division rings. More precisely, in such cases, the image of a multilinear…
Transient imaging has recently made a huge impact in the computer graphics and computer vision fields. By capturing, reconstructing, or simulating light transport at extreme temporal resolutions, researchers have proposed novel techniques…
Following unprecedented success on the natural language tasks, Transformers have been successfully applied to several computer vision problems, achieving state-of-the-art results and prompting researchers to reconsider the supremacy of…
We study the Hessian geometry of toric multi-Taub-NUT metrics and their phase change phenomena via the images of their moment maps. This generalizes an earlier paper on toric Gibbons-Hawking metrics.
We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the…
Blurring of a photographic image by a wrong focus can be modeled by convolution. Is inversion a possible answer? This paper adds complements to a foregoing paper discussing convolution-inversion of some measures.
We describe a racetrack-shaped ring in which the cross-plane coupling can be continuously varied between an uncoupled configuration to a M\"obius configuration, where the transverse planes change role after one turn. Tunes, emittances, and…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
In this note we describe a discrete dynamical system acting on the similarity classes of a plane convex body within the affine class of the body. We find invariant elements in all affine classes, and describe the orbits of bodies in some…
In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…
This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.
When two identical balls collide with equal inital speed on a horizontal groove, one can observe three trajectory types depending on the groove width. To explain this observation, we derive velocity diagrams of the balls motions from…