Related papers: Virtual global generation in higher dimensions

A generalised notion of connection on a fibre bundle E over a manifold M is presented. These connections are characterised by a smooth distribution on E which projects onto a (not necessarily integrable) distribution on M and which, in…

For humans, visual understanding is inherently generative: given a 3D shape, we can postulate how it would look in the world; given a 2D image, we can infer the 3D structure that likely gave rise to it. We can thus translate between the 2D…

Real-world networks evolve over time via additions or removals of vertices and edges. In current network evolution models, vertex degree varies or grows arbitrarily. A recently introduced degree-preserving network growth (DPG) family of…

The aim of this note is to exhibit explicit sufficient criteria ensuring bigness of globally generated, rank-$r$ vector bundles, $r \geqslant 2$, on smooth, projective varieties of even dimension $d \leqslant 4$. We also discuss connections…

There has been an explosion of work in the vision & language community during the past few years from image captioning to video transcription, and answering questions about images. These tasks have focused on literal descriptions of the…

Creating realistic 3D objects and clothed avatars from a single RGB image is an attractive yet challenging problem. Due to its ill-posed nature, recent works leverage powerful prior from 2D diffusion models pretrained on large datasets.…

Visual recognition systems are meant to work in the real world. For this to happen, they must work robustly in any visual domain, and not only on the data used during training. Within this context, a very realistic scenario deals with…

In this paper we construct a model for the classifying space, BVCG, of a crystallographic group G of rank n relative to the family VC of virtually-cyclic subgroups of G. The model is used to show that there exists no other model for the…

Generating future frames given a few context (or past) frames is a challenging task. It requires modeling the temporal coherence of videos and multi-modality in terms of diversity in the potential future states. Current variational…

Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…

A flexible model is developed for multivariate generalized spherical distributions, i.e. ones with level sets that are star shaped. To work in dimension above 2 requires tools from computational geometry and multivariate numerical…

Complex vector modes have become topical of late due to their fascinating properties and the many applications they have found across a broad variety of research fields. Even though such modes can be generated in a wide variety of ways,…

Generating high-quality Scalable Vector Graphics (SVGs) from text remains a significant challenge. Existing LLM-based models that generate SVG code as a flat token sequence struggle with poor structural understanding and error accumulation,…

This paper investigates the projectivization of real vector bundles over small covers. We first give a necessary and sufficient condition for such a projectivization to be a small cover. Then associated with moment-angle manifolds, we…

For domains that involve numerical simulation, it can be computationally expensive to run an ensemble of simulations spanning a parameter space of interest to a user. To this end, an attractive surrogate for simulation is the generative…

The generation of 3D models from real-world objects has often been accomplished through photogrammetry, i.e., by taking 2D photos from a variety of perspectives and then triangulating matched point-based features to create a textured mesh.…

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…

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define…

Graph generation is a crucial task in many fields, including network science and bioinformatics, as it enables the creation of synthetic graphs that mimic the properties of real-world networks for various applications. Graph Generative…

We propose a dual-domain generative model to estimate a texture map from a single image for colorizing a 3D human model. When estimating a texture map, a single image is insufficient as it reveals only one facet of a 3D object. To provide…