Related papers: Filtrations induced by continuous functions

The computational cost of persistent homology is often dominated by the growth of the underlying simplicial filtrations. Many different filtrations exist, each with its own assumptions and trade-offs, but all face some form of this growth…

We consider the space of real-valued continuously differentiable functions on a compact subset of a euclidean space. We characterize the completeness of this space and prove that the space of restrictions of continuously differentiable…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

In this paper, we consider a model of classical linear logic based on coherence spaces endowed with a notion of totality. If we restrict ourselves to total objects, each coherence space can be regarded as a uniform space and each linear map…

In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.

We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…

Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove…

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…

We establish necessary and sufficient conditions for suspension flows over certain families of shift spaces to be topologically mixing. We also show the similarities and differences between this case and the smooth measure theoretic setting…

Skorokhod's J1 and M1 topologies are standard tools in proving limit theorems for stochastic processes. Motivated by applications, we extend these topologies so that they are capable of describing the convergence of a sequence of functions…

We define the motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions…

The inevitable noise in real measurements motivates the problem to continuously quantify the similarity between rigid objects such as periodic time series and proteins given by ordered points and considered up to isometry maintaining…

This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…

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…

We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal hypothesis from the result established by the two last-named…

We describe the cosmological dynamics of perfect fluids within the framework of effective field theories. The effective action is a derivative expansion whose terms are selected by the symmetry requirements on the relevant long-distance…

Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…

A d.c. (delta-convex) function on a normed linear space is a function representable as a difference of two continuous convex functions. We show that an infinite dimensional analogue of Hartman's theorem on stability of d.c. functions under…