Related papers: Topological simplification guided by forbidden reg…

The rings of linear continuous operators on the topological spaces of $\mathfrak{G}$-zero maps were described, where $\mathfrak{G}$ is a filter on a set with an involution. This applies to modules of formal series with well ordered support…

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which…

Text simplification (TS) is the process of generating easy-to-understand sentences from a given sentence or piece of text. The aim of TS is to reduce both the lexical (which refers to vocabulary complexity and meaning) and syntactic (which…

Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…

We study a discrete-time asynchronous midpoint dynamics on the circle in which, at each step, a uniformly chosen neighboring pair moves to the midpoint along the shortest arc. Although the update rule is locally contractive, we show that…

In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…

Topological Signal Processing (TSP) over simplicial complexes is a framework that has been recently proposed, as a generalization of graph signal processing (GSP), to extend GSP to analyzing signals defined over sets of any order (i.e., not…

Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…

Feature space topology refers to the organization of samples within the feature space. Modifying this topology can be beneficial in machine learning applications, including dimensionality reduction, generative modeling, transfer learning,…

Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this type of network, we intend to reduce the number of network…

In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…

Matrix reduction is the standard procedure for computing the persistent homology of a filtered simplicial complex with $m$ simplices. Its output is a particular decomposition of the total boundary matrix, from which the persistence diagrams…

Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we…

Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…

Sentence simplification is the task of rewriting texts so they are easier to understand. Recent research has applied sequence-to-sequence (Seq2Seq) models to this task, focusing largely on training-time improvements via reinforcement…

Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…

Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…

Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…

Discrete Morse theory helps us compute the homology groups of simplicial complexes in an efficient manner. A "good" gradient vector field reduces the number of critical simplices, simplifying the homology calculations by reducing them to…

Text simplification aims at making a text easier to read and understand by simplifying grammar and structure while keeping the underlying information identical. It is often considered an all-purpose generic task where the same…