Since its very beginning, linear algebra is a highly algorithmic subject. Let us just mention the famous Gauß Algorithm which was invented before the theory of algorithms has been developed. The purpose of this paper is to link linear algebra explicitly to computable analysis, that is the theory of computable real number functions. Especially, we will investigate in which sense the dimension of...

We investigate the asymptotic behavior, as N grows, of the largest minimal pairwise distance of N points restricted to an arbitrary compact rectifiable set embedded in Euclidean space, and we find the limit distribution of such optimal configurations. For this purpose, we compare best-packing configurations with minimal Riesz s-energy configurations and determine the s-th root asymptotic behavi...

In this paper, the problem of non-rigid shape recognition is viewed from the perspective of metric geometry, and the applicability of diffusion distances within the Gromov-Hausdorff framework is explored. While the commonly used geodesic distance exploits the shortest path between points on the surface, the diffusion distance averages all paths connecting between the points. The diffusion dista...

of a continuum field theory. The Lj are higherdimensional operators. The lattice action is adjusted so that the short-distance Kj coefficients vanish, at least approximately. The Fermilab formalism [4] takes Wilson fermions [2] with the clover action [3] and introduces different couplings for space-like and time-like interactions. Ref. [4] considers operators up to dimension five. Ref. [5] adds...

This paper reports the results obtained in a speaker identification system based in Bhattacharrya distance, which combines LPderived cepstral coefficients, with a nonlinear dynamic feature namely fractal dimension. The nonlinear dynamic analysis starts with the phase espace reconstruction, and the fractal dimension of the correspondent attractor trajectory is estimated. This analysis is perform...

As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes, space-time codes over finite fields, and array codes. We focus on characterizing matrix codes that are both efficient (have high rate) and effective at error correcti...

The range space of dynamic textures spans spatiotemporal phenomena that vary along three fundamental dimensions: spatial texture, spatial texture layout, and dynamics. By describing each dimension with appropriate spatial or temporal features and by equipping it with a suitable distance measure, elementary distances (one for each dimension) between dynamic texture sequences can be computed. In ...

We consider linear error correcting codes associated to higher-dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult questions in combinatorics and algebraic geometry. This is illustrated by codes associated to Schubert varieties in Grassmannians, called Schubert codes, which have...