We present a geometric model of social choice among bundles of interdependent elements, that we will call objects. We show that the outcome of the social choice process is highly dependent on the way these bundles are formed. By bundling and unbundling the same set of constituent elements an authority enjoys a vast power of determining the social outcome, as locally or globally stable social op...

The unresolved subtleties of floating point computations in geometric modeling become considerably more difficult in animations and scientific visualizations. Some emerging solutions based upon topological considerations will be presented. A novel geometric seeding algorithm for Newton’s method was used in experiments to determine feasible support for these visualization applications. 1 Computi...

This decade has seen a great deal of progress in the development of information retrieval systems. Unfortunately, we still lack a systematic understanding of the behavior of the systems and their relationship with documents. In this paper we present a completely new approach towards the understanding of the information retrieval systems. Recently, it has been observed that retrieval systems in ...

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into well constrained, over-, and underconstrained subsystems. This paper also gives an efficient method to decompose well constrained systems into irreducible ones....

We present a method for navigating in geometric models and enrich them with additional information. This enables us to adapt geometric models to different purposes and thus to reuse them. We offer dedicated views for the structure and context information as well as for the geometric model, develop strategies to navigate in them and focus on the tight coupling between manipulations in these view...

We present some notes on the definition of mathematical design as well as on the methods of mathematical modeling which are used in the process of the artistic design of the environment and its components. For the first time in the field of geometric modeling, we perform an aesthetic analysis of planar Bernstein-Bézier curves from the standpoint of the laws of technical aesthetics. The shape fe...

Advances in computational geometric modeling, imaging, and simulation let researchers build and test models of increasing complexity, generating unprecedented amounts of data. As recent research in biomedical applications illustrates, visualization will be critical in making this vast amount of data usable; it’s also fundamental to understanding models of complex phenomena. Biomedical Visual Co...

In this paper, we propose an easy-to-use approach to augmenting a panorama with object movies, in such a way that the inserted foreground objects remain visually coherent with the panoramic background. The proposed method is purely image-based in the sense that it does not have to reconstruct the 3D geometric model of the real object to be inserted in the panorama. Based on the proposed method,...

This paper develops a theory of clustering and coding which combines a geometric model with a probabilistic model in a principled way. The geometric model is a Riemannian manifold with a Riemannian metric, gij(x), which we interpret as a measure of dissimilarity. The probabilistic model consists of a stochastic process with an invariant probability measure which matches the density of the sampl...

Card shuffling is an interesting topic to explore because of its complexity. Initially, card shuffling seems simple because it is ubitquitous. The majority of people know how to shuffle a deck of cards but few consider the math behind it. However, when it comes to analyzing the elements of card shuffling, it incorporates linear algebra, group theory, probability theory, and Markov Chains. When ...