Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal ...

Tras el nacimiento de Bitcoin, se ha producido una profunda transformación en los mercados digitales y la bolsa, dando ...

En este trabajo fin de grado se estudian tantos los métodos actuales como el contexto en el ámbito de empresas, investigaciones ...

Un río atmosférico (RA) es una banda alargada y estrecha de humedad muy concentrada en la parte inferior de la troposfera ...

En este trabajo, repasamos detalladamente el planteamiento de un problema de aprendizaje supervisado en general, sobre ...

One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such ...

In this paper, we prove that when a n-D cubical set is continuously well-composed (CWC), that is, when the boundary of its ...

Durante los últimos años, el mundo del Bitcoin y las criptomonedas ha revolucionado por completo el concepto de pago y ...

The automatic recognition of a person’s emotional state has become a very active research field that involves scientists ...

¿Cómo se infieren formas a partir de datos? Se pueden emplear técnicas del álgebra y la topología computacional para ...

Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data ...

Machine learning is drawn from a dataset that needs to be explained. Following this aim, a model is described to make ...

La homología persistente es una técnica que se usa para analizar la evolución de una cierta propiedad algebraica, la ...

Topology plays an important role in computer vision by capturing the structure of the objects. Nevertheless, its potential ...

In this note, we provide an algorithm that, starting with a Sullivan algebra gives us its minimal model. More concretely, ...

Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial ...

A continuación, se expone en este documento la memoria del trabajo de fin de grado basado en el análisis de datos de ...

In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting ...

The notion of persistence partial matching, as a generalization of partial matchings between persistence modules, is ...

This paper provides a theoretical characterization of monotonically connected image surface regions, called slope regions. ...

This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational ...

It is well-known that artificial neural networks are universal approximators. The classical existence result proves that, ...

Emotion recognition consists of a series of processes to detect human emotions from facial human expressions. Humans ...

In this paper, we de ne a new avour of well-composedness, called Euler well-composedness, in the general setting of regular ...

In this paper, we prove that the two avours of well-compo- sedness called Continuous Well-Composedness (shortly CWCness), ...

Filtration simplification consists of simplifying a given filtration while simultaneously controlling the perturbation in ...

In this paper, we study how basis-independent partial matchings induced by morphisms between persistence modules (also ...

One of the main drawbacks of the practical use of neural networks is the long time needed in the training process. Such ...

An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident ...

In this study, a new method based on topological entropy, the so‐called persistent entropy, is presented for addressing ...

In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such ...

In previous work we proposed a combinatorial algorithm to \locally repair" the cubical complex Q(I) that is canonically ...

Emotion recognition and classification is a very active area of research. In this paper, we present a first approach to ...

A digital image can be perceived as a 2.5D surface consisting of pixel coordinates and the intensity of pixel as height ...

The canon of the baroque Spanish literature has been thoroughly studied with philological techniques. The major representatives ...

The vertices of the neighborhood graph of a digital picture P can be interpolated to form a 2-manifold M with critical ...

It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a ...

We propose an algorithm for persistence homology computation of orientable 2-dimensional (2D) manifolds with or without ...

In this paper we provide a new characterization of cell de- composition (called slope complex) of a given 2-dimensional ...

In this note, we give an algorithm that starting with a Sullivan algebra gives us its minimal model. This algorithm is a ...

Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called ...

The discrete version of a continuous surface sampled at optimum sampling rate can be well expressed in form of a neighborhood ...

Topological data analysis (TDA) aims to obtain useful information from data sets using topological concepts. In particular, ...

Persistent entropy of persistence barcodes, which is based on the Shannon entropy, has been recently defined and successfully ...

Neural networks present big popularity and success in many fields. The large training time process problem is a very ...

Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. ...

A 3D binary image I can be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted ...

Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at ...

In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing ...

Topology is the branch of mathematics that studies shapes and maps among them. From the algebraic definition of topology ...

In this paper, we propose a method to compute, in parallel, the homology groups of closed meshes (i.e., orientable 2D ...

In this paper, we present a new image segmentation algorithmwhich is based on local binary patterns (LBPs) and the ...

We build upon the work developed in [4] in which we presented a method to “locally repair” the cubical complex Q(I) ...

Gait recognition is nowadays an important biometric technique for video surveillance tasks, due to the advantage of using ...

In persistent homology, the persistence barcode encodes pairs of simplices meaning birth and death of homology classes. ...

In this paper, a new codification of Local Binary Patterns (LBP) is given using graph pyramids. The LBP code characterizes ...

Taking as input a time-varying sequence of two-dimensional (2D) binary images, we develop an algorithm for computing a ...

A binary three-dimensional (3D) image II is well-composed if the boundary surface of its continuous analog is a 2D manifold. ...

In this abstract we extend ideas and results submitted to [3] in which a new codification of Local Binary Patterns (LBP) ...

Let \(I=(\mathbb {Z}^3,26,6,B)\) be a three-dimensional (3D) digital image, let \(Q(I)\) be an associated cubical complex, ...

In this paper, a topological approach for monitoring human activities is presented. This approach makes possible to protect ...

There are surveillance scenarios where it is important to emit an alarm when a person carrying an object is detected. In ...

In this paper, we show that contraction operations preserve the homology of nD generalized maps, under some conditions. ...

In this paper, a topological approach for gait-based gender recognition is presented. First, a stack of human silhouettes, ...

In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs ...

This Demo presents an application for gait recognition using persistent homology. Using a background subtraction approach, ...

Let I=(Z3,26,6,B) be a 3D digital image, let Q(I) be the associated cubical complex and let ∂Q(I) be the subcomplex of ...

Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology ...

In this paper, we present an efficient way for computing homology generators of nD generalized maps. The algorithm proceeds ...

This paper shows an image/video application using topological invariants for human gait recognition. Using a background ...

In this paper, we formalize the notion of lambda-AT-model (where λ is a non-null integer) for a given chain complex, which ...

In this paper, we establish a correspondence between the incremental algorithm for computing AT-models [8,9] and the one ...

This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable ...

Well-composed 3D digital images, which are 3D binary digital images whose boundary surface is made up by 2D manifolds, ...

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological ...

Let I be a 3D digital image, and let Q(I) be the associated cubical complex. In this paper we show how to simplify the ...

Cohomology groups and the cohomology ring of three-dimensional (3D) objects are topological invariants that characterize ...

It has been an honor and a pleasure to organize the 3rd International Workshop on Computational Topology in Image Context, ...

This paper shows an image/video application using topological invariants in human gait recognition. The 3D volume of a ...

An algorithm to compute a minimal length basis of representative cocycles of cohomology generators for 2D images is proposed. ...

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological ...

In this paper, we combine two complementary techniques for computing homol- ogy: Incremental Algorithm for computing ...

Starting from an nD geometrical object, a cellular subdivision of such an object provides an algebraic counterpart from ...

When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing ...

Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the ...

Para introducir este trabajo es necesario hablar de TOPOLOG´IA. La topología es la rama de las matemáticas que estudia las ...

We deal with the problem of obtaining explicit simplicial formu- lae defining the classical Adem cohomology operations at ...

In this paper, algorithms for computing integer (co)homology of a simplicial complex of any dimension are designed, extending ...

In this paper, we deal with the problem of the computation of the homology of a finite simplicial complex after an “elementary ...

This paper offers an algorithmic solution to the problem of obtaining “economical” formulae for some maps in Simplicial ...

This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary–valued images, ...

We propose a method for computing the cohomology ring of three-dimensional (3D) digital binary-valued pictures. We obtain ...

We reinterpret the classical theory of cocyclic operations in terms of permutations and homotopy equivalences of ...

Proponemos un método para visualizar conceptos altamente abstractos en objetos tridimensionales, representados éstos como ...

We propose a method for calculating cohomology operations on finite simplicial complexes. Of course, there exist well–known ...

We propose a method for computing the Z 2–cohomology ring of a simplicial complex uniquely associated with a three–dimensional ...

This review tackles the problem of the high computational complexity lying in most algorithms in algebraic topology and ...

Steenrod cohomology operations are algebraic tools for distinguishing non–homeomorphic topological spaces. In this paper, ...

En este art´ıculo, se pretende dar una visi´on general y lo m´as divulgativa posible sobre los prop´ositos y objetivos del ...

En esta memoria se establece un enfoque puramente combinatorio de las operaciones cohomológicas de Steenrod y Adem a nivel ...

We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the ...

In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing ...

We present here a combinatorial method for computing Steenrod squares of a simplicial set X. This method is essentially ...