Related papers: Successive Spectral Sequences
In homotopy theory, exact sequences and spectral sequences consist of groups and pointed sets, linked by actions. We prove that the theory of such exact and spectral sequences can be established in a categorical setting which is based on…
We propose a novel sequence prediction method for sequential data capturing node traversals in graphs. Our method builds on a statistical modelling framework that combines multiple higher-order network models into a single multi-order…
We study the problem of building generative models of natural source code (NSC); that is, source code written and understood by humans. Our primary contribution is to describe a family of generative models for NSC that have three key…
Spectral clustering is a powerful technique for clustering high-dimensional data, utilizing graph-based representations to detect complex, non-linear structures and non-convex clusters. The construction of a similarity graph is essential…
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 present sufficient conditions for when an ordering of universal cycles $\alpha_1, \alpha_2, \ldots, \alpha_m$ for disjoint sets $\mathbf{S}_1, \mathbf{S}_2, \ldots , \mathbf{S}_m$ can be concatenated together to obtain a universal cycle…
Fourier methods have a long and proven track record as an excellent tool in data processing. As memory and computational constraints gain importance in embedded and mobile applications, we propose to combine Fourier methods and recurrent…
Working over imperfect fields, we give a comprehensive classification of genus-one curves that are regular but not geometrically regular, extending the known case of geometrically reduced curves. The description is given intrinsically, in…
We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural…
This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical systems, topology, and nonlinear analysis. To this end, we…
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference…
In recent years there has been a growing attention on distribution results in the sense of Weyl for the collective behavior of eigenvalues and singular values of matrix-sequences. Starting from the work of Szeg\"o regarding the case of…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when…
The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in…
In this paper, we investigate the behaviour of the Serre spectral sequence with respect to the algebraic structures of string topology in generalized homology theories, specificially with the Chas-Sullivan product and the corresponding…
The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…
The concept of structured occurrence nets is an extension of that of occurrence nets which are directed acyclic graphs that represent causality and concurrency information concerning a single execution of a distributed system. The formalism…
The spectral properties of signed directed graphs, which may be naturally obtained by assigning a sign to each edge of a directed graph, have received substantially less attention than those of their undirected and/or unsigned counterparts.…
Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2 canonical systems). We prove a number of Szeg\H{o}-type theorems for…
Subsequence matching has appeared to be an ideal approach for solving many problems related to the fields of data mining and similarity retrieval. It has been shown that almost any data class (audio, image, biometrics, signals) is or can be…