Continuous Geometry

Furrow geometry nnder surge and continuous flow

Continuous fictitious play via projective geometry

Using insights from the theory of projective geometry one can prove convergence of continuous fictitious play in a certain class of games. As a corollary, we obtain a kind of equilibrium selection result, whereby continuous fictitious play converges to a particular equilibrium contained in a continuum of equivalent equilibria for symmetric 4×4 zero-sum games. Journal of Economic Literature clas...

Quantitative Combinatorial Geometry for Continuous Parameters

The Geometry of Continuous Latent Space Models for Network Data

We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to be conditionally independent given the dyads? unobserved positions in a latent space. In this way, these models provide a probabilistic framework for embeddin...

Molecular distance geometry methods: from continuous to discrete

Distance geometry problems arise from the need to position entities in the Euclidean K-space given some of their respective distances. Entities may be atoms (molecular distance geometry), wireless sensors (sensor network localization), or abstract vertices of a graph (graph drawing). In the context of molecular distance geometry, the distances are usually known because of chemical properties an...