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

A computational analysis of protein-protein interaction networks in neurodegenerative diseases

<p>Abstract</p> <p>Background</p> <p>Recent developments have meant that network theory is making an important contribution to the topological study of biological networks, such as protein-protein interaction (PPI) networks. The identification of differentially expressed genes in DNA array experiments is a source of information regarding the molecular pathways involved in disease. Thus, considering PPI analysis and gene expression studies together may provide a better understanding of multifactorial neurodegenerative diseases such as Multiple Sclerosis (MS) and Alzheimer disease (AD). The aim of this study was to assess whether the parameters of degree and betweenness, two fundamental measures in network theory, are properties that differentiate between implicated (seed-proteins) and non-implicated nodes (neighbors) in MS and AD. We used experimentally validated PPI information to obtain the neighbors for each seed group and we studied these parameters in four networks: MS-blood network; MS-brain network; AD-blood network; and AD-brain network.</p> <p>Results</p> <p>Specific features of seed-proteins were revealed, whereby they displayed a lower average degree in both diseases and tissues, and a higher betweenness in AD-brain and MS-blood networks. Additionally, the heterogeneity of the processes involved indicate that these findings are not pathway specific but rather that they are spread over different pathways.</p> <p>Conclusion</p> <p>Our findings show differential centrality properties of proteins whose gene expression is impaired in neurodegenerative diseases.</p

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

Switcher-random-walks: a cognitive-inspired mechanism for network exploration

Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life specific experiences. The organization of concepts within semantic memory can be understood as a semantic network, where the concepts (nodes) are associated (linked) to others depending on perceptions, similarities, etc. Lexical access is the complementary part of this system and allows the retrieval of such organized knowledge. While conceptual information is stored under certain underlying organization (and thus gives rise to a specific topology), it is crucial to have an accurate access to any of the information units, e.g. the concepts, for efficiently retrieving semantic information for real-time needings. An example of an information retrieval process occurs in verbal fluency tasks, and it is known to involve two different mechanisms: -clustering-, or generating words within a subcategory, and, when a subcategory is exhausted, -switching- to a new subcategory. We extended this approach to random-walking on a network (clustering) in combination to jumping (switching) to any node with certain probability and derived its analytical expression based on Markov chains. Results show that this dual mechanism contributes to optimize the exploration of different network models in terms of the mean first passage time. Additionally, this cognitive inspired dual mechanism opens a new framework to better understand and evaluate exploration, propagation and transport phenomena in other complex systems where switching-like phenomena are feasible.Comment: 9 pages, 3 figures. Accepted in "International Journal of Bifurcations and Chaos": Special issue on "Modelling and Computation on Complex Networks

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