Bipartite graphs can model matching problems, hypergraphs and relations between sets. Studying their surface embeddings is an old tradition, illustrated by the utilities problem. I shall show how such embeddings can be described by pairs of permutations, and how this leads to a classification of the regular (most symmetric) embeddings of complete bipartite graphs. This is joint work with Du, Kw...

Multiview relations such as the Fundamental matrix and the Trilinear tensor provide scene-independent characterization of a combination of views in the form of algebraic constraints. In this paper, we present a number of multiview constraints for collections of primitives, such as a planar shape boundary. The rich domain of Fourier transforms helps us to combine the properties of the collection...

It is generally known that algorithms can be expressed using simple function applications only. In this paper we will show that it is possible to make a systematic translation of algebraic data types and pattern-based function definitions, like they are used in most modern functional programming languages, to function applications. The translated algebraic data types closely resemble the origin...

This paper describes a novel sensor system to estimate the motion of a stereo camera. Local invariant image features are matched between pairs of frames and linked into image trajectories at video rate, providing the so-called visual odometry, i.e., motion estimates from visual input alone. Our proposal conducts two matching sessions: the first one between sets of features associated to the ima...

Algebraic properties such as associativity or distributivity allow the manipulation of a set of mathematically equivalent expressions. However, the cost of evaluating such expressions on a computer is not constant within this domain. We suggest the use of algebraic transformations to improve the performances of computationally intensive applications on modern architecture computers. We claim th...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

cozero maps are generalized forms of cozero elements. two particular cases of cozero maps, slim and regular cozero maps, are significant. in this paper we present methods to construct slim and regular cozero maps from a given  cozero map. the construction of the slim and the regular cozero map from a cozero map are called slimming and regularization of the cozero map, respectively. also, we pro...

the operations in the set of fuzzy numbers are usually obtained bythe zadeh extension principle. but these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. in fact the zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...

Currently, the paradigm of algebraic programming becomes one of the most important paradigms of declarative programming. Algebraic programming is based on methods of term rewriting [1], which are widely used independently and in programming systems based on other paradigms (in functional, logical, object-oriented, and agent-based programming, in computer algebra and systems of theorem proving)....