The goal of the present paper is to construct examples of global deformations of vector field Lie algebras in a conceptual way. Fialowski and Schlichermaier [8] constructed global deformations of the infinitesimally and formally rigid Lie algebra of polynomial vector fields on the circle and of its central extension, the Virasoro algebra. The Lie algebra of polynomial vector fields on the circl...

Sweepers is a framework for defining space deformation operations for interactive shape modeling. The artist describes a basic deformation as a path through which a tool is moved. Our tools are simply shapes. So we can use shapes already created as customized tools to make more complex shapes or to simplify the modeling process. When a tool is moved, it causes a deformation of the working shape...

During an image-guided neurosurgery procedure, the neuronavigation system is subject to inaccuracy because of anatomical deformations which induce a gap between the preoperative images and their anatomical reality. Thus, the objective of many research teams is to succeed in quantifying these deformations in order to update preoperative images. Anatomical intraoperative deformations correspond t...

Residual deformations strongly influence the local biomechanical environment in a number of connective tissues. The sclera is known to be biomechanically important in healthy and diseased eyes, such as in glaucoma. Here, we study the residual deformations of the sclera, as well as the adjacent choroid and retina. Using freshly harvested porcine eyes, we developed two approaches of quantifying r...

This paper proposes an approach to effectively representing the statistics of high-dimensional deformations, when relatively few training samples are available, and conventional methods, like PCA, fail due to insufficient training. Based on previous work on scale-space decomposition of deformation fields, herein we represent the space of "valid deformations" as the intersection of three subspac...

We compactify the spaces K(m,n) introduced by Maxim Kontsevich. The initial idea was to construct an L∞ algebra governing the deformations of a (co)associative bialgebra. However, this compactification leads not to a resolution of the PROP of (co)associative bialgebras, but to a new algebraic structure we call here a CROC. It turns out that these constructions are related to the non-commutative...

We develop a hydroelastic model based on a {3,2}-order sandwich composite panel theory and Wagner’s water impact theory for investigating the fluid–structure interaction during the slamming process. The sandwich panel theory incorporates the transverse shear and the transverse normal deformations of the core, while the face sheets are modeled with the Kirchhoff plate theory. The structural mode...

We extend the formality theorem of M. Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes.

We develop a generic framework to build large deformations from a combination of base modules. These modules constitute a dynamical dictionary to describe transformations. The method, built on a coherent sub-Riemannian framework, defines a metric on modular deformations and characterises optimal deformations as geodesics for this metric. We will present a generic way to build local affine trans...