The Pontryagin duality of sequential limits of topological Abelian groups

We prove that direct and inverse limits of sequences of reflexive Abelian groups that are metrizable or k -spaces, but not necessarily locally compact, are reflexive and dual of each other provided some extra conditions are satisfied by the sequences

Topological analysis of tapped granular media using persistent homology

We use the first Betti number of a complex to analyze the morphological structure of granular samples in mechanical equilibrium. We investigate two-dimensional granular packings after a tapping process by means of both simulations and experiments. States with equal packing fraction obtained with different tapping intensities are distinguished after the introduction of a filtration parameter which determines the particles (nodes in the network) that are joined by an edge. This is accomplished by just using the position of the particles obtained experimentally and no other information about the possible contacts, or magnitude of force

Precompact noncompact reflexive abelian groups

We present a series of examples of precompact, noncompact, reflexive topological Abelian groups. Some of them are pseudocompact or even countably compact, but we show that there exist precompact non-pseudocompact reflexive groups as well. It is also proved that every pseudocompact Abelian group is a quotient of a reflexive pseudocompact group with respect to a closed reflexive pseudocompact subgroup

Quantifying disorder in colloidal films spin-coated onto patterned substrates

Polycrystals of thin colloidal deposits, with thickness controlled by spin-coating speed, exhibit axial symmetry with local 4-fold and 6-fold symmetric structures, termed orientationally correlated polycrystals (OCPs). While spin-coating is a very facile technique for producing large-area colloidal deposits, the axial symmetry prevents us from achieving true long-range order. To obtain true long-range order, we break this axial symmetry by introducing a patterned surface topography and thus eliminate the OCP character. We then examine symmetry- independent methods to quantify order in these disordered colloidal deposits. We find that all the information in the bond-orientational order parameters is well captured by persistent homology analysis methods that only use the centers of the particles as input data. It is expected that these methods will prove useful in characterizing other disordered structures

Conceptual organization and retrieval in semantic memory: the differential role of switching and clustering, acquisition and impairment in neurodegenerative conditions

Semantic memory organization and retrieval is a cutting edge topic that is being studied from different fields such as Linguistics, Psychology, Computer Science and Neuroscience. The aim of this thesis is to improve the understanding of conceptual organization and retrieval by means of network theory and the use of semantic verbal fluency tests (animals) in an unsupervised fashion. Conceptual organization will be studied here as a complex network attached to a dual-mechanism of information retrieval, i.e. switching and clustering. The chapters are organized as follows: 1. An introduction to the concepts of human brain, memory and network theory. 2. A study of the frequency patterns obtained from the verbal fluency tests. 3. Development of a statistical method for the unsupervised generation of a conceptual network and the insilico evaluation of switching and clustering. Such evaluation together with the definition of accessibility and diffusivity measurements allowed the decoupling of switching and clustering functioning. 4. Study of switcher random walks (by means of finite Markov chains) as an exploration-propagation paradigm in a number of insilico network models. 5. Modelization of the switching-clustering retrieval on the conceptual network obtained in chapter 3. 6. Amodel of concept acquisition and semantic growth based on frequency of concepts. 7. Study of the lexical access impairment in three different neurodegenerative conditions: Multiple Sclerosis, Mild Cognitive Impairment and Alzheimer’s disease. 8. General conclusions and outlook of this work

The Pontryagin duality of sequential limits of topological Abelian groups

We prove that direct and inverse limits of sequences of reflexive Abelian groups that are metrizable or k -spaces, but not necessarily locally compact, are reflexive and dual of each other provided some extra conditions are satisfied by the sequences

Apuntes del curso "Introducción a la estadística con R"

Estadística descriptiva, lectura / escritura, manipulación de bases de datos, Markdown, gráficos, inferencia, regresión lineal, anov

Apuntes del curso "Introducción a la estadística con R"

Estadística descriptiva, lectura / escritura, manipulación de bases de datos, Markdown, gráficos, inferencia, regresión lineal, anov

Conceptual organization and retrieval in semantic memory: the differential role of switching and clustering, acquisition and impairment in neurodegenerative conditions

Semantic memory organization and retrieval is a cutting edge topic that is being studied from different fields such as Linguistics, Psychology, Computer Science and Neuroscience. The aim of this thesis is to improve the understanding of conceptual organization and retrieval by means of network theory and the use of semantic verbal fluency tests (animals) in an unsupervised fashion. Conceptual organization will be studied here as a complex network attached to a dual-mechanism of information retrieval, i.e. switching and clustering. The chapters are organized as follows: 1. An introduction to the concepts of human brain, memory and network theory. 2. A study of the frequency patterns obtained from the verbal fluency tests. 3. Development of a statistical method for the unsupervised generation of a conceptual network and the insilico evaluation of switching and clustering. Such evaluation together with the definition of accessibility and diffusivity measurements allowed the decoupling of switching and clustering functioning. 4. Study of switcher random walks (by means of finite Markov chains) as an exploration-propagation paradigm in a number of insilico network models. 5. Modelization of the switching-clustering retrieval on the conceptual network obtained in chapter 3. 6. Amodel of concept acquisition and semantic growth based on frequency of concepts. 7. Study of the lexical access impairment in three different neurodegenerative conditions: Multiple Sclerosis, Mild Cognitive Impairment and Alzheimer’s disease. 8. General conclusions and outlook of this work

On self-aggregations of min-subgroups

Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions. However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets