Related papers: Gabor frames from contact geometry in models of th…
In this abstract we describe recent [4,7] and latest work on the determination of affordances in visually perceived 3D scenes. Our method builds on the hypothesis that geometry on its own provides enough information to enable the detection…
Estimating the geometry level of human-scene contact aims to ground specific contact surface points at 3D human geometries, which provides a spatial prior and bridges the interaction between human and scene, supporting applications such as…
Predicting the alignment of non-spherical particles in dense granular flows under shear remains a central challenge in soft matter physics. We demonstrate that the first-order behavior of granular fabric,the anisotropic distribution of…
The mean-field treatment of the Bose-Hubbard model predicts properties of lattice-trapped gases to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number $z$. We test this scaling…
The cortical magnification matrix M is introduced founded on a notion similar to that of the scalar cortical magnification factor M. Unlike M, this matrix is suitable to describe anisotropy in cortical magnification, which is of particular…
The construction of finite tight Gabor frames plays an important role in many applications. These applications include significant ones in signal and image processing. We explore when constant amplitude zero autocorrelation (CAZAC)…
We follow our general model in Ref. [3] and analyze the formation of retinotopic projections for the biologically relevant situation of spherical geometries. To this end we elaborate both a linear and a nonlinear synergetic analysis which…
This paper considers aspects of 4-manifold topology from the point of view of the null cone of a neutral metric, a point of view we call neutral causal topology. In particular, we construct and investigate neutral 4-manifolds with null…
Certain signal classes such as audio signals call for signal representations with the ability to adapt to the signal's properties. In this article we introduce the new concept of quilted frames, which aim at adaptivity in time-frequency…
We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the one dominating in the literature, serves also for non-trivial contact structures. In this approach Hamiltonians are no longer functions on the contact…
Currently, Markov-Gibbs random field (MGRF) image models which include high-order interactions are almost always built by modelling responses of a stack of local linear filters. Actual interaction structure is specified implicitly by the…
We derive frame estimates for vector-valued Gabor systems with window functions belonging to Schwartz space. The main result provides frame bound estimates for windows composed of Hermite functions. The proof is based on a recently…
We describe how to design a large class of always on spin-1 interactions between polar molecules trapped in an optical lattice. The spin degrees of freedom correspond to the hyperfine levels of a ro-vibrational ground state molecule.…
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…
In studying structural inter-connections in the human brain, it is common to first estimate fiber bundles connecting different regions of the brain relying on diffusion MRI. These fiber bundles act as highways for neural activity and…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
We investigate what can be learned about a population of distant KBOs by studying the statistical properties of their light curves. Whereas others have successfully inferred the properties of individual, highly variable KBOs, we show that…
This survey offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice. The goal is to collect the most important characterizations of Gabor frames and offer a systematic exposition…
In this paper a large class of universal windows for Gabor frames (Weyl-Heisenberg frames) is constructed. These windows have the fundamental property that every overcritical rectangular lattice generates a Gabor frame. Likewise, every…