This article shows how a (linear) scale-space representation can be de ned for discrete signals of arbitrary dimension. The treatment is based upon the assumptions that (i) the scale-space representation should be de ned by convolving the original signal with a one-parameter family of symmetric smoothing kernels possessing a semi-group property, and (ii) local extrema must not be enhanced when ...

We consider equidistant discrete splines S(j), j ∈ Z, which may grow as O(|j|s) as |j| → ∞. Such splines present a relevant tool for digital signal processing. The Zak transforms of Bsplines yield the integral representation of discrete splines. We define the wavelet space as a weak orthogonal complement of the coarse-grid space in the fine-grid space. We establish the integral representation o...

This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a ...

We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z2n). It acts in a natural way on the coordinates of the non-commutative 2-torus, T2n and thus is relevant for noncommutative field theories as well as theories of quantum space-time. The class of operators may also be usefu...

We introduce a new class of paraxial optical beams exhibiting discrete-like diffraction patterns reminiscent to those observed in periodic evanescently coupled waveguide lattices. It is demonstrated that such paraxial beams are analytically described in terms of generalized Bessel functions. Such effects are elucidated via pertinent examples.

Probabilistic planning with observability restrictions, as formalized for example as partially observable Markov decision processes (POMDP), has a wide range of applications, but it is computationally extremely difficult. For POMDPs, the most general decision problems about existence of policies satisfying certain properties are undecidable. We consider a computationally easier form of planning...

The maximum distance bound for ultrahigh energy cosmic rays (UHECR) with energies above the Greisen-Zatsepin-Kuzmich cutoff ∼ 10 eV relaxes significantly if there is some mechanism that forces UHECR to propagate in discrete intervals, rather than continuously, through intergalactic space. In particular, intervals as small as a femtometer relax the bound for protons by an order of magnitude and ...

A new approach for the effective computation of geodesic regression curves in shape spaces is presented. Here, one asks for a geodesic curve on the shape manifold that minimizes a sum of dissimilarity measures between given twoor three-dimensional input shapes and corresponding shapes along the regression curve. The proposed method is based on a variational time discretization of geodesics. Cur...

We discuss briefly discrete space effects and show that this leads to space reflection asymmetry and also a minor modification of Einstein’s energy-mass formula. Snyder[1] had shown how it is possible to consider discrete space time consistently with the Lorentz transformation. Discrete space time continues to receive attention over the years from several scholars (Cf. for example [2, 3, 4, 5, ...