Related papers: Complex Functional Maps : a Conformal Link Between…

We study the link between a compact hypersurface in $\P^{n+1}$ and the set of all its tangent planes. In this context, we identify $\P^{n+1}$ to the set of linear subspaces of codimension one by orthogonal complementarity. This gives rise…

Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the development of the basic theory of latent fibrations and…

In the present paper, we establish the uniqueness of tangent maps for general weakly holomorphic and locally approximable maps from an arbitrary almost complex manifold into projective algebraic varieties. As a byproduct of the approach and…

We consider maps which preserve functions which are built out of the invariants of some simple vector fields. We give a reduction procedure, which can be used to derive commuting maps of the plane, which preserve the same symplectic form…

Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…

Developing effective path representations has become increasingly essential across various fields within intelligent transportation. Although pre-trained path representation learning models have shown improved performance, they…

Drawing parallels with hyperplane arrangements, we develop the theory of arrangements of submanifolds. Given a smooth, finite dimensional, real manifold $X$ we consider a finite collection $\mathcal{A}$ of locally flat, codimension-1…

Understanding structure-property relationships in complex materials requires integrating complementary measurements across multiple length scales. Here we propose an interpretable "multimodal" machine learning framework that unifies…

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…

This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…

In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use the convolution to define tangent bundle filters and tangent bundle neural networks…

Given a unipotent bundle of smooth manifolds we construct its secondary transfer map and show that this map determines the higher smooth torsion of the bundle. This approach to higher torsion provides a new perspective on some of its…

Functional connectomes (FCs) contain pairwise estimations of functional couplings based on pairs of brain regions activity. FCs are commonly represented as correlation matrices that are symmetric positive definite (SPD) lying on or inside…

We will consider here some dynamics of the tangent map, weaker than hyperbolicity, and we will discuss if these structures are rich enough to provide a good description of the dynamics from a topological and geometrical point of view. This…

Inspired by the fact that humans use diverse sensory organs to perceive the world, sensors with different modalities are deployed in end-to-end driving to obtain the global context of the 3D scene. In previous works, camera and LiDAR inputs…

Previous work has shown that reverse differential categories give an abstract setting for gradient-based learning of functions between Euclidean spaces. However, reverse differential categories are not suited to handle gradient-based…

An oriented compact closed manifold is called inflexible if the set of mapping degrees ranging over all continuous self-maps is finite. Inflexible manifolds have become of importance in the theory of functorial semi-norms on homology.…

We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.

Accurately following a geometric desired path in a two-dimensional space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to…

Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…