Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime between three universality classes. It is shown that the statistical properties of level dynamics are in general nonuniversal and strongly depend on the way in...

Weierstrass representation is a classical parameterization of minimal surfaces. However, two functions should be specified to construct the parametric form in Weierestrass representation. In this paper, we propose an explicit parametric form for a class of parametric polynomial minimal surfaces of arbitrary degree. It includes the classical Enneper surface for cubic case. The proposed minimal s...

Parametric-stereo coding is a technique to efficiently code a stereo audio signal as a monaural signal plus a small amount of parametric overhead to describe the stereo image. The stereo properties are analyzed, encoded, and reinstated in a decoder according to spatial psychoacoustical principles. The monaural signal can be encoded using any (conventional) audio coder. Experiments show that the...

In this thesis, all-optical processing for future optical networks is studied by means of parametric processes in optical fibers. Parametric processes are nonlinear effects which arise in optical fibers when high-powered waves are properly placed at specific spectral positions. The properties of parametric processes are defined by the optical fiber characteristics, the power and the wavelength ...

Artificial discontinuity is a kind of singularity at a parametric point in computing the Gröbner basis of a specialized parametric ideal w.r.t. a certain term order. When it occurs, though parameters change continuously at the point and the properties of the parametric ideal have no sudden changes, the Gröbner basis will still have a jump at the parametric point. This phenomenon can cause insta...

Clustering has recently enjoyed progress via spectral methods which group data using only pairwise affinities and avoid parametric assumptions. While spectral clustering of vector inputs is straightforward, extensions to structured data or time-series data remain less explored. This paper proposes a clustering method for time-series data that couples non-parametric spectral clustering with para...

Border polynomial and discriminant variety are two important notions related to parametric polynomial system solving, in particular, for partitioning the parameter values into regions where the solutions of the system depend continuously on the parameters. In this paper, we study the relations between those notions in the case of parametric triangular systems. We also investigate the properties...