Related papers: On the existence of Parseval frames for vector bun…
The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle $E(B,V,A)$ associated to a quantum principal bundle $P(B,A)$ are in…
We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in…
We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…
Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite…
We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields…
We show that an equivariant vector bundle on a complete toric variety is nef or ample if and only if its restriction to every invariant curve is nef or ample, respectively. Furthermore, we show that nef toric vector bundles have a…
Transformers have recently emerged as a powerful tool for learning visual representations. In this paper, we identify and characterize artifacts in feature maps of both supervised and self-supervised ViT networks. The artifacts correspond…
We develop a theory of \'etale parallel transport for vector bundles with numerically flat reduction on a $p$-adic variety. This construction is compatible with natural operations on vector bundles, Galois equivariant and functorial with…
Let $C$ be a chain-like curve over $\mathbb{C}$. In this paper, we investigate the rationality of moduli spaces of $w$-semistable vector bundles on $C$ of arbitrary rank and fixed determinant by putting some restrictions on the Euler…
Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…
Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All…
Raynaud and Gruson showed that there is a reasonable algebro-geometric notion of family of discrete (infinite-dimensional) vector spaces. The author introduces a notion of family of Tate spaces ("Tate" means "locally linearly compact") and…
We study vector bundles on curves with rational tails and their smoothings and give a sufficient condition for the general fibre to be balanced.
We give a complete classification of globally generated vector bundles of rank 3 on a smooth quadric threefold with $c_1\leq 2$ and extend the result to arbitrary higher rank case. We also investigate the existence of globally generated…
We define the notion of a parahoric group scheme $\mathcal G$ over a smooth projective curve, and formulate four conjectures on the structure of the stack of $\mathcal G$-bundles, which generalize to this case well-known results on…
Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to…