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

Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical…

Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape…

We introduce the concept of Hypoelliptic Diffusion Maps (HDM), a framework generalizing Diffusion Maps in the context of manifold learning and dimensionality reduction. Standard non-linear dimensionality reduction methods (e.g., LLE,…

Tangent category theory is a well-established categorical framework for differential geometry. A long list of fundamental geometric constructions, such as the tangent bundle functor, vector fields, Euclidean spaces, and vector bundles have…

Fold maps are smooth maps at each singular point of which it is represented as the product map of a Morse function and the identity map. Round fold maps are, in short, such maps the sets of all singular points of which are embedded…

Correspondences between k-tuples of points are key in multiple view geometry and motion analysis. Regular transformations are posed by homographies between two projective planes that serves as structural models for images. Such…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…

With the arrival of digital maps, the ubiquity of maps has increased sharply and new map functionalities have become available such as changing the scale on the fly or displaying/hiding layers. Users can now interact with maps on multiple…

Understanding how brain structure and function interact is key to explaining intelligence yet modeling them jointly is challenging as the structural and functional connectome capture complementary aspects of organization. We introduced…

In this work, we propose "tangent images," a spherical image representation that facilitates transferable and scalable $360^\circ$ computer vision. Inspired by techniques in cartography and computer graphics, we render a spherical image to…

Deep neural networks have become essential for numerous applications due to their strong empirical performance such as vision, RL, and classification. Unfortunately, these networks are quite difficult to interpret, and this limits their…

We consider rationally connected complex projective manifolds M and show that their loop spaces--infinite dimensional complex manifolds--have properties similar to those of M. Furthermore, we give a finite dimensional application concerning…

In this paper, we explain how the abstract notion of a differential bundle in a tangent category provides a new way of thinking about the category of modules over a commutative ring and its opposite category. MacAdam previously showed that…

In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which…

We define formal exponential maps for any graded manifold as maps from the formal tangent bundle (that we also define) into the graded manifold. We show that each such map uniquely determines and is determined by its associated Grothendieck…

The tangential map is a map on the set of smooth planar curves. It satisfies the 3D-consistency property and is closely related to some well-known integrable equations.

We introduce a theoretical framework that connects multi-chart autoencoders in manifold learning with the classical theory of vector bundles and characteristic classes. Rather than viewing autoencoders as producing a single global Euclidean…

Deep functional maps have emerged in recent years as a prominent learning-based framework for non-rigid shape matching problems. While early methods in this domain only focused on learning in the functional domain, the latest techniques…

These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…

Coupling separately developed codes offers an attractive method for increasing the accuracy and fidelity of the computational models. Examples include the earth sciences and fusion integrated modeling. This paper describes the Framework…