Related papers: On the stratification of combinatorial spectra
The scale and complexity of modern data sets and the limitations associated with testing large numbers of hypotheses underline the need for feature selection methods. Spectral techniques rank features according to their degree of…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
For binary mixtures with fixed concentrations of the species, various relationships between the surface tensions and the concentrations are briefly reviewed.
The combinatorial theory of species developed by Joyal provides a foundation for enumerative combinatorics of objects constructed from finite sets. In this paper we develop an analogous theory for the enumerative combinatorics of objects…
We prove that the set of proper ideals of a monoid endowed with coarse lower topology is a spectral space.
We define a right Cartan-Eilenberg structure on the category of Kan's combinatorial spectra, and the category of sheaves of such spectra, assuming some conditions. In both structures, we use the geometric concept of homotopy equivalence as…
We first develop a general framework for Laplace operators defined in terms of the combinatorial structure of a simplicial complex. This includes, among others, the graph Laplacian, the combinatorial Laplacian on simplicial complexes, the…
In this survey we discuss some combinatorial aspects of higher cluster categories.
The aim of these notes is to introduce the intuition motivating the notion of a "complicial set", a simplicial set with certain marked "thin" simplices that witness a composition relation between the simplices on their boundary. By varying…
The long hunt for a symmetric monoidal category of spectra finally ended in success with the simultaneous discovery of the third author's discovery of symmetric spectra and the Elmendorf-Kriz-Mandell-May category of S-modules. In this paper…
We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
Approaches to automated grouping in singular spectrum analysis are considered. A new method for the identification of periodic components is proposed. The possibilities of extensions to multivariate time series and images are discussed.
We establish an equivalence of homotopy theories between symmetric monoidal bicategories and connective spectra. For this, we develop the theory of $\Gamma$-objects in 2-categories. In the course of the proof we establish strictfication…
We recapture Douglas' framework for twisted parametrized stable homotopy theory in the language of $\infty$- categories. A twisted spectrum is essentially a section of a bundle of presentable stable $\infty$-categories whose fiber is the…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
In here we define the concept of fibered symmetric bimonoidal categories. These are roughly speaking fibered categories D->C whose fibers are symmetric monoidal categories parametrized by C and such that both D and C have a further…
In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In the last decade, several of these have been constructed,…
In this paper, we examine an analogue of the recently solved spectrum conjecture by Fujita in the setting of Fine polyhedral adjunction theory. We present computational results for lower-dimensional polytopes, which lead to a complete…
We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in…