Related papers: Some Minimal Shape Decompositions Are Nice
Supercurrents, as introduced by Lagerberg, were mainly motivated as a way to study tropical varieties. Here we will associate a supercurrent to any smooth submanifold of $\R^n$. Positive supercurrents resemble positive currents in complex…
This paper proposes the estimation of a mutual shape from a set of different segmentation results using both active contours and information theory. The mutual shape is here defined as a consensus shape estimated from a set of different…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
An image related question defines a specific visual task that is required in order to produce an appropriate answer. The answer may depend on a minor detail in the image and require complex reasoning and use of prior knowledge. When humans…
We construct Lipschitz $Q$-valued functions which approximate carefully integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the…
In a set of two papers, we propose to study an old-standing problem, namely the electromagnetic interaction for particles of arbitrary spin. Based on the assumption that light-cone helicity at tree level and $Q^2=0$ should be conserved…
In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between…
Idempotents dominate the structure theory of rings. The Peirce decomposition induced by an idempotent provides a natural environment for defining and classifying new types of rings. This point of view offers a way to unify and to expand the…
Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…
The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics and…
The purpose of these notes is to present a fairly complete proof of the classification Theorem for compact surfaces. Other presentations are often quite informal (see the references in Chapter V) and we have tried to be more rigorous. Our…
Particle physics has evolved a coherent model that characterizes forces and particles at the most elementary level. This Standard Model, built from many theoretical and experimental studies, is in excellent accord with almost all current…
The electric field of light induces--in a non centrosymmetric insulator--a dc current, quadratic in the field magnitude, and called "shift current". When addressed from a many-electron viewpoint, the shift current has a simple explanation…
We construct in complete intersection's case, elementary currents which describe the local ideal, and give a decomposition in it for holomorphic function.
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
Real-life man-made objects often exhibit strong and easily-identifiable structure, as a direct result of their design or their intended functionality. Structure typically appears in the form of individual parts and their arrangement.…
We show that a real rational (over $\C$) surfaces are quasi-simple, i.e., that such a surface is determined up to deformation in the class of real surfaces by the topological type of its real structure.
The contribution of this paper is to provide a semantic model (using soft constraints) of the words used by web-users to describe objects in a language game; a game in which one user describes a selected object of those composing the scene,…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
This is a brief reminder, with extensions, from a different angle and for a less specialized audience, of my presentation at WGMP32 in July 2013, to which I refer for more details on the topics hinted at in the title, mainly deformation…