Related papers: Spectral Filtrations via Generalized Morphisms
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
Generalizing homogeneous spectra for rings graded by natural numbers, we introduce multihomogeneous spectra for rings graded by abelian groups. Such homogeneous spectra have the same completeness properties as their classical counterparts,…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
We introduce a notion of oriented dialgebra and develop a cohomology theory for oriented dialgebras based on the possibility to mix the standard chain complexes computing group cohomology and associative dialgebra cohomology. We also…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
In this article we construct what we call a higher spectral sequence for any chain complex (or topological space) that is filtered in $n$ compatible ways. For this we extend the previous spectral system construction of the author, and we…
The K-ring of symmetric vector bundles over a scheme X, the so-called Grothendieck-Witt ring of X, can be endowed with the structure of a (special) $\lambda$-ring. The associated $\gamma$-filtration generalizes the fundamental filtration on…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
We want to compute generic $\mathrm{Ext}$-spaces of twisted polynomial functors in relation to the $\mathrm{Ext}$-spaces of the untwisted ones, modulo a parametrisation. Thanks to the study of a spectral sequence we get to a computation in…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization…
We generalize the idea of cofinite groups, due to B. Hartley. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions. The idea of constructing a cofinite graph starts…
We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial…
The recently developed concept of refracting profiles and that of refraction holodiagrams are combined so that the classical Abramson holodiagrams can be generalized taking into account a wider class of wave fronts and refraction at an…
We explain how the approach of Andre and Quillen to defining cohomology and homology as suitable derived functors extends to generalized (co)homology theories, and how this identification may be used to study the relationship between them.…
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix…
In this paper we introduce generalized Spencer cohomology for finite depth Z-graded Lie (super)algebras. We develop a method of finding filtered deformations of such Z-graded Lie (super)algebras based on this cohomology. As an application…
Gaussian filters have applications in a variety of areas in computer science, from computer vision to speech recognition. The collapsing sum is a matrix operator that was recently introduced to study Gaussian filters combinatorially. In…