Related papers: Identifying cobordisms using kernel persistence
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
Metabolism displays striking and robust regularities in the forms of modularity and hierarchy, whose composition may be compactly described. This renders metabolic architecture comprehensible as a system, and suggests the order in which…
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…
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or,…
Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications…
It is demonstrated in the context of the simple one-dimensional example of a barrier in an infinite well, that highly complex behavior of the time evolution of a wave function is associated with the almost degeneracy of levels in the…
Rooted phylogenetic networks are rooted acyclic digraphs. They are used to model complex evolution where hybridization, recombination and other reticulation events play important roles. A rigorous definition of network compression is…
In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model…
We develop a unified framework based on topological crossed modules for various lifting obstructions for $\Gamma$-kernels. It allows us to identify actions, cocycle actions and $\Gamma$-kernels up to their natural equivalence relations with…
Biological networks provide insight into the complex organization of biological processes in a cell at the system level. They are an effective tool for understanding the comprehensive map of functional interactions, finding the functional…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this…
Persistence diagram (PD) bundles, a generalization of vineyards, were introduced as a way to study the persistent homology of a set of filtrations parameterized by a topological space $B$. In this paper, we present an algorithm for…
We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of…
We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called persistence complex is used to reveal…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal…
In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks. The network approach focuses on pairwise relationships, often…
In many scientific and technological contexts we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal…
Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…