A numerical study on mixing of hydrogen injected transversely into a supersonic air stream has been performed by solving Two-Dimensional full Navier-Stokes equations. An explicit Harten-Yee Non-MUSCL Modified-flux-type TVD scheme has been used to solve the system of equations, and a zero-equation algebraic turbulence model to calculate the eddy viscosity coefficient. The main objectives of this...

In this contribution we present a formulation of the 2D3D pose estimation problem using implicit algebraic surfaces. To model the projective mapping, we apply novel Dixon resultant heuristics to deal with the rapidly increasing polynomial degrees of projected image outlines. The advantages as well as disadvantages of using linearised twist coordinates for pose representation are also discussed....

We present a discrete approximation method for planar algebraic curves. This discrete approximation is hierarchical, curvature dependent, and provides eecient algorithms for various primitive geometric operations on algebraic curves. We consider applications on the curve intersections , the distance computations, and the common tangent and convolution computations. We implemented these approxim...

The Hausdorff distance between two sets of curves is a measure for the similarity of these objects and therefore an interesting feature in shape recognition. If the curves are algebraic computing the Hausdorff distance involves computing the intersection points of the Voronoi edges of the one set with the curves in the other. Since computing the Voronoi diagram of curves is quite difficult we c...

We present an algebraic account of the Wasserstein distances Wp on complete metric spaces. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in p, for algebras over metric spaces equipped with probabilistic choice operations. The axioms say that the operations form a barycentric algebra and that the metric...

The quasispecies model introduced by Eigen in 1971 has close connections with the isometry group of the space of binary sequences relative to the Hamming distance metric. Generalizing this observation we introduce an abstract quasispecies model on a finite metric space X together with a group of isometries Γ acting transitively on X . We show that if the domain of the fitness function has a nat...

The construction, estimation of minimum distance, and decoding algorithms of algebraic geometry codes can be explained without using advanced mathematics by the notion of weight domains. We clarify the relation between algebraic geometry codes and linear codes from weight domains. Then we review a systematic construction which yields all weight domains.

Nowadays, a huge amount of genetic information is publicly available. Genomic’s current challenge is to process this information in order to obtain relevant biological conclusions. One possible way of structuring this information is through genome comparison, where we seek similarities and differences among the genomes of two or more organisms. In this context, the area of Genome Rearrangements...

So far in the course, we have seen three types of codes, summarized as follows: 1. Algebraic Codes • Work for worst-case errors. • Have polynomial time encoding and decoding algorithms 2. LDPCs • Work for worst-case errors as well, but a less many errors (smaller distance) compared to the Algebraic Codes. • Have linear time encoding and decoding algorithms and are simpler. 3. Polar Codes • Work...

Minimax single facility location problems in multidimensional space with Chebyshev distance are examined within the framework of idempotent algebra. The aim of the study is twofold: first, to give a new algebraic solution to the location problems, and second, to extend the area of application of idempotent algebra. A new algebraic approach based on investigation of extremal properties of eigenv...