Related papers: Gabor frames from contact geometry in models of th…
A Gabor system generated by a window function $g\in L^2(\mathbb{R}^d)$ and a separable set $\Lambda\times \Gamma \subset \mathbb{R}^{2d}$ is the collection of time-frequency shifts of $g$ given by $\mathcal G(g, \Lambda\times \Gamma) =…
Wood is a volumetric material with a very large appearance gamut that is further enlarged by numerous finishing techniques. Computer graphics has made considerable progress in creating sophisticated and flexible appearance models that allow…
We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…
In this paper we consider the Gabor wave front set of ultradistributions in the frame of ultradifferentiable functions. We prove that such a wave front set, defined through a Gabor frame on a regular lattice, is not affected by…
In this paper, we investigate the robustness of structured frames to measurement noise and erasures, with the focus on Gabor frames $(g, \Lambda)$ with arbitrary sets of time-frequency shifts $\Lambda$. This property of frames is important…
We study the folding of the regular two-dimensional triangular lattice embedded in the regular three-dimensional Face-Centred Cubic lattice, a discrete model for the crumpling of membranes. Possible folds are complete planar folds, folds…
Eyeglasses play an important role in the perception of identity. Authentic virtual representations of faces can benefit greatly from their inclusion. However, modeling the geometric and appearance interactions of glasses and the face of…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
This work uses fiber bundles as a framework to describe some effects of number scaling on gauge theory and some geometric quantities. A description of number scaling and fiber bundles over a flat space time manifold, M, is followed by a…
A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with the functional architecture of the primary visual cortex (V1). Particularly the local…
Bound states of two interacting particles moving on a lattice can exhibit remarkable features that are not captured by the underlying single-particle picture. Inspired by this phenomenon, we introduce a novel framework by which genuine…
Let $K\subset \Bbb R^d$ be a set with positive and finite Lebesgue measure. Let $\Lambda=M(\Bbb Z^{2d})$ be a lattice in $\Bbb R^{2d}$ with density dens$(\Lambda)=1$. It is well-known that if $M$ is a diagonal block matrix with diagonal…
Gabor frames have interested many mathematicians and physicists due to their potential applications in time-frequency analysis, in particular, signal processing. A Gabor system is a collection of vectors which is obtained by applying…
Recent experiments have revealed that the meniscus formed near a surface-piercing barrier can significantly alter the propagation and scattering of capillary-gravity surface waves, beyond what classic flat-surface models predict. In…
We construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition. The lattice…
k-Contact geometry is a generalisation of contact geometry to analyse field theories. We develop an approach to k-contact geometry based on distributions that are distributionally maximally non-integrable and admit, locally, k commuting…
An experimental study is reported which investigates the head-on collision of a laminar vortex ring of diameter D (Re{\Gamma}= 3000) on a fakir-like surface composed of circular posts of height h*=0.068 located on a planar bed. Lattices of…
The famous question of Mark Kac "Can one hear the shape of a drum?" addressing the unique connection between the shape of a planar region and the spectrum of the corresponding Laplace operator can be legitimately extended to scattering…
We present an optical study of various device designs for electrically contactable circular Bragg grating cavities in labyrinth geometries. To create an electrical connection between the central disk and the surrounding membrane, which are…
In this work we derive a simple argument which shows that Gabor systems consisting of odd functions of $d$ variables and symplectic lattices of density $2^d$ cannot constitute a Gabor frame. In the 1--dimensional, separable case, this is a…