相关论文: Spectral Synthesis on Continuous Images

In this paper we start studying spectral properties of the Fourier-Stieltjes algebras, largely following Zafran's work on the algebra of measures on a locally compact group. We show that for a large class of discrete groups the Wiener-Pitt…

Motivated by a class of nonlinear equations of interest for string theory, we introduce Sobolev spaces on arbitrary locally compact abelian groups and we examine some of their properties. Specifically, we focus on analogs of the Sobolev…

Let k be an infinite perfect field. We provide a general criterion for a spectrum in the stable homotopy category over k to be effective, i.e. to be in the localizing subcategory generated by the suspension spectra of smooth schemes. As a…

We study the possibility of a continuous extension of a class of mappings to an isolated point on the boundary of a domain. We show that if some characteristic of this mapping is integrable on almost all spheres in the neighborhood of at…

Subspace clustering has become widely adopted for the unsupervised analysis of hyperspectral images (HSIs). Recent model-aware deep subspace clustering methods often use a two-stage framework, involving the calculation of a…

Deep learning has brought an unprecedented progress in computer vision and significant advances have been made in predicting subjective properties inherent to visual data (e.g., memorability, aesthetic quality, evoked emotions, etc.).…

Spectral techniques are popular and robust approaches to data analysis. A prominent example is the use of eigenvectors of a Laplacian, constructed from data affinities, to identify natural data groupings or clusters, or to produce a…

The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type…

We study the algebraic dynamics of endomorphisms of projective varieties. First, we characterize their iterated images, i.e. the intersection of the images of their iterates. Next, we explore the Stein factorizations of the iterates,…

Compositionality of semantic concepts in image synthesis and analysis is appealing as it can help in decomposing known and generatively recomposing unknown data. For instance, we may learn concepts of changing illumination, geometry or…

In this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic $p>0$ is isogenous to another one defined over a finite field. We also show that the category of…

In this paper we provide a framework for quantitative statements on distances and measures when studying algebraic varieties and morphisms of algebraic varieties over local fields. We will concentrate on local fields of the type…

Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…

New advancements for the detection of synthetic images are critical for fighting disinformation, as the capabilities of generative AI models continuously evolve and can lead to hyper-realistic synthetic imagery at unprecedented scale and…

Semantic image synthesis (SIS) aims to generate realistic images that match given semantic masks. Despite recent advances allowing high-quality results and precise spatial control, they require a massive semantic segmentation dataset for…

Recent studies have shown that StyleGANs provide promising prior models for downstream tasks on image synthesis and editing. However, since the latent codes of StyleGANs are designed to control global styles, it is hard to achieve a…

We construct a spectral sequence associated to a stratified space, which computes the compactly supported cohomology groups of an open stratum in terms of the compactly supported cohomology groups of closed strata and the reduced cohomology…

A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on…

The rapid progression of Generative Adversarial Networks (GANs) has raised a concern of their misuse for malicious purposes, especially in creating fake face images. Although many proposed methods succeed in detecting GAN-based synthetic…

We develop criteria for affine varieties to admit uniruled subvarieties of certain dimensions. The measurements are from long exact sequences of versions of symplectic cohomology, which is a Hamiltonian Floer theory for some open symplectic…