Related papers: Spectral Filtrations via Generalized Morphisms
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…
We introduce generalized filtration with which we can represent situations such as some agents forget information at some specific time. The filtration is defined as a functor to a category Prob whose objects are all probability spaces and…
We propose an approach to integrated optical spectral filtering that allows arbitrary programmability, can compensate automatically for imperfections in filter fabrication, allows multiple simultaneous and separately programmable filter…
We prove the existence of a sequence of commutative diagrams generalizing existing results on the cohomology of the Borel-Serre boundary and well-rounded retract to the context of the well-tempered complex. Our main theorem provides a…
We classify filtered quantizations of conical symplectic singularities and use this to show that all filtered quantizations of symplectic quotient singularities are spherical Symplectic reflection algebras of Etingof and Ginzburg. We…
We present in this paper a framework which leverages the underlying topology of a data set, in order to produce appropriate coordinate representations. In particular, we show how to construct maps to real and complex projective spaces,…
Classical splines feature prominently in approximation theory and numerical analysis, while GKM theory arises in the study of equivariant cohomology. More recently, generalized splines have been studied which simultaneously generalize both…
We introduce a new cohomology-theoretic method for classifying generic immersed curves in closed compact surfaces by using Gauss codes. This subsumes a result of J.S. Carter on classifying immersed curves in oriented compact surfaces, and…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
Graphs constructed to translate some graph problem into another graph problem are usually called auxiliary graphs. Specifically total graphs of simple graphs are used to translate the total colouring problem of the original graph into a…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
In this paper we present a unifying framework for continuous optimization methods grounded in the concept of generalized convexity. Utilizing the powerful theory of $\Phi$-convexity, we propose a conceptual algorithm that extends the…
We study the preservation of semisimplicity for holonomic D-modules with respect to the direct and inverse image of mainly finite maps $\pi : X \to Y$ of smooth varieties. A natural filtration of the direct image $\pi_+({\mathcal O}_X)$ is…
In this paper we give a generalization of the normal holomorphic frames in the symplectic manifolds and find conditions for the integrability of complex structures.
We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respect to sublevel persistence modules. This relation is…
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…
Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…