Clustering basado en redes bayesianas con predictoras continuas: aplicaciones en neurociencia

Desentrañar el funcionamiento del cerebro es uno de los principales desafíos a los que se enfrenta la ciencia actual. Un área de estudio que ha despertado muchas expectativas e interés es el análisis de la estructura cortical desde el punto de vista morfológico, de manera que se cree una simulación del cerebro a nivel molecular. Con ello se espera poder profundizar en el estudio de numerosas enfermedades neurológicas y patológicas. Con el desarrollo de este proyecto se persigue el estudio del soma y de las espinas desde el punto de vista de la neuromorfología teórica. Es común en el estado del arte que en el análisis de las características morfológicas de una neurona en tres dimensiones el soma sea ignorado o, en el mejor de los casos, que sea sustituido por una simple esfera. De hecho, el concepto de soma resulta abstracto porque no se dispone de una dfinición estricta y robusta que especifique exactamente donde finaliza y comienzan las dendritas. En este proyecto se alcanza por primera vez una definición matemática de soma para determinar qué es el soma. Con el fin de simular somas se ahonda en los atributos utilizados en el estado del arte. Estas propiedades, de índole genérica, no especifican una morfología única. Es por ello que se propone un método que agrupe propiedades locales y globales de la morfología. En disposición de las características se procede con la categorización del cuerpo celular en distintas clases a partir de un nuevo subtipo de red bayesiana dinámica adaptada al espacio. Con ello se discute la existencia de distintas clases de somas y se descubren las diferencias entre los somas piramidales de distintas capas del cerebro. A partir del modelo matemático se simulan por primera vez somas virtuales. Algunas morfologías de espinas han sido atribuidas a ciertos comportamientos cognitivos. Por ello resulta de interés dictaminar las clases existentes y relacionarlas con funciones de la actividad cerebral. La clasificación más extendida (Peters y Kaiserman-Abramof, 1970) presenta una definición ambigua y subjetiva dependiente de la interpretación de cada individuo y por tanto discutible. Este estudio se sustenta en un conjunto de descriptores extraídos mediante una técnica de análisis topológico local para representaciones 3D. Sobre estos datos se trata de alcanzar el conjunto de clases más adecuado en el que agrupar las espinas así como de describir cada grupo mediante reglas unívocas. A partir de los resultados, se discute la existencia de un continuo de espinas y las propiedades que caracterizan a cada subtipo de espina. ---ABSTRACT---Unravel how the brain works is one of the main challenges faced by current science. A field of study which has aroused great expectations and interest is the analysis of the cortical structure from a morphological point of view, so that a molecular level simulation of the brain is achieved. This is expected to deepen the study of many neurological and pathological diseases. This project seeks the study of the soma and spines from the theoretical neuromorphology point of view. In the state of the art it is common that when it comes to analyze the morphological characteristics of a three dimension neuron the soma is ignored or, in the best case, it is replaced by a simple sphere. In fact, the concept of soma is abstract because there is not a robust and strict definition on exactly where it ends and dendrites begin. In this project a mathematical definition is reached for the first time to determine what a soma is. With the aim to simulate somas the atributes applied in the state of the art are studied. These properties, generic in nature, do not specify a unique morphology. It is why it was proposed a method to group local and global morphology properties. In arrangement of the characteristics it was proceed with the categorization of the celular body into diferent classes by using a new subtype of dynamic Bayesian network adapted to space. From the result the existance of different classes of somas and diferences among pyramidal somas from distinct brain layers are discovered. From the mathematical model virtual somas were simulated for the first time. Some morphologies of spines have been attributed to certain cognitive behaviours. For this reason it is interesting to rule the existent classes and to relate them with their functions in the brain activity. The most extended classification (Peters y Kaiserman-Abramof, 1970) presents an ambiguous and subjective definition that relies on the interpretation of each individual and consequently it is arguable. This study was based on the set of descriptors extracted from a local topological analysis technique for 3D representations. On these data it was tried to reach the most suitable set of classes to group the spines as well as to describe each cluster by unambiguous rules. From these results, the existance of a continuum of spines and the properties that characterize each spine subtype were discussed .

Multidrug resistance proteins QacA and QacB from Staphylococcus aureus: membrane topology and identification of residues involved in substrate specificity.

The closely related multidrug efflux pumps QacA and QacB, from the bacterial pathogen Staphylococcus aureus, both confer resistance to various toxic organic cations but differ in that QacB mediates lower levels of resistance to divalent cations. Cloning and nucleotide sequencing of the qacB gene revealed that qacB differs from qacA by only seven nucleotide substitutions. Random hydroxylamine mutagenesis of qacB was undertaken, selecting for variants that conferred increased resistance to divalent cations. Both QacA and the QacB mutants capable of conferring resistance to divalent cations contain an acidic residue at either amino acid 322 or 323, whereas QacB contains uncharged residues in these positions. Site-directed mutagenesis of qacA confirmed the importance of an acidic residue within this region of QacA in conferring resistance to divalent cations. Membrane topological analysis using alkaline phosphatase and beta-galactosidase fusions indicated that the QacA protein contains 14 transmembrane segments. Thus, QacA represents the first membrane transport protein shown to contain 14 transmembrane segments, and confirms that the major facilitator superfamily contains a family of proteins with 14 transmembrane segments.

Quantum similarity topological indices definition, analysis and comparison with classical molecular topological indices

Es mostra que, gracies a una extensió en la definició dels Índexs Moleculars Topològics, s'arriba a la formulació d'índexs relacionats amb la teoria de la Semblança Molecular Quàntica. Es posa de manifest la connexió entre les dues metodologies: es revela que un marc de treball teòric sòlidament fonamentat sobre la teoria de la Mecànica Quàntica es pot connectar amb una de les tècniques més antigues relacionades amb els estudis de QSPR. Es mostren els resultats per a dos casos d'exemple d'aplicació d'ambdues metodologies

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Quantum similarity topological indices definition, analysis and comparison with classical molecular topological indices

Es mostra que, gracies a una extensió en la definició dels Índexs Moleculars Topològics, s'arriba a la formulació d'índexs relacionats amb la teoria de la Semblança Molecular Quàntica. Es posa de manifest la connexió entre les dues metodologies: es revela que un marc de treball teòric sòlidament fonamentat sobre la teoria de la Mecànica Quàntica es pot connectar amb una de les tècniques més antigues relacionades amb els estudis de QSPR. Es mostren els resultats per a dos casos d'exemple d'aplicació d'ambdues metodologies

Topological multi-contour decomposition for image analysis and image retrieval

Successful classification, information retrieval and image analysis tools are intimately related with the quality of the features employed in the process. Pixel intensities, color, texture and shape are, generally, the basis from which most of the features are Computed and used in such fields. This papers presents a novel shape-based feature extraction approach where an image is decomposed into multiple contours, and further characterized by Fourier descriptors. Unlike traditional approaches we make use of topological knowledge to generate well-defined closed contours, which are efficient signatures for image retrieval. The method has been evaluated in the CBIR context and image analysis. The results have shown that the multi-contour decomposition, as opposed to a single shape information, introduced a significant improvement in the discrimination power. (c) 2008 Elsevier B.V. All rights reserved,

Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

Performance Analysis of Topological Quantum Error Correcting Codes

In the last few years there has been a great development of techniques like quantum computers and quantum communication systems, due to their huge potentialities and the growing number of applications. However, physical qubits experience a lot of nonidealities, like measurement errors and decoherence, that generate failures in the quantum computation. This work shows how it is possible to exploit concepts from classical information in order to realize quantum error-correcting codes, adding some redundancy qubits. In particular, the threshold theorem states that it is possible to lower the percentage of failures in the decoding at will, if the physical error rate is below a given accuracy threshold. The focus will be on codes belonging to the family of the topological codes, like toric, planar and XZZX surface codes. Firstly, they will be compared from a theoretical point of view, in order to show their advantages and disadvantages. The algorithms behind the minimum perfect matching decoder, the most popular for such codes, will be presented. The last section will be dedicated to the analysis of the performances of these topological codes with different error channel models, showing interesting results. In particular, while the error correction capability of surface codes decreases in presence of biased errors, XZZX codes own some intrinsic symmetries that allow them to improve their performances if one kind of error occurs more frequently than the others.

Iis--integrated Interactome System: A Web-based Platform For The Annotation, Analysis And Visualization Of Protein-metabolite-gene-drug Interactions By Integrating A Variety Of Data Sources And Tools.

High-throughput screening of physical, genetic and chemical-genetic interactions brings important perspectives in the Systems Biology field, as the analysis of these interactions provides new insights into protein/gene function, cellular metabolic variations and the validation of therapeutic targets and drug design. However, such analysis depends on a pipeline connecting different tools that can automatically integrate data from diverse sources and result in a more comprehensive dataset that can be properly interpreted. We describe here the Integrated Interactome System (IIS), an integrative platform with a web-based interface for the annotation, analysis and visualization of the interaction profiles of proteins/genes, metabolites and drugs of interest. IIS works in four connected modules: (i) Submission module, which receives raw data derived from Sanger sequencing (e.g. two-hybrid system); (ii) Search module, which enables the user to search for the processed reads to be assembled into contigs/singlets, or for lists of proteins/genes, metabolites and drugs of interest, and add them to the project; (iii) Annotation module, which assigns annotations from several databases for the contigs/singlets or lists of proteins/genes, generating tables with automatic annotation that can be manually curated; and (iv) Interactome module, which maps the contigs/singlets or the uploaded lists to entries in our integrated database, building networks that gather novel identified interactions, protein and metabolite expression/concentration levels, subcellular localization and computed topological metrics, GO biological processes and KEGG pathways enrichment. This module generates a XGMML file that can be imported into Cytoscape or be visualized directly on the web. We have developed IIS by the integration of diverse databases following the need of appropriate tools for a systematic analysis of physical, genetic and chemical-genetic interactions. IIS was validated with yeast two-hybrid, proteomics and metabolomics datasets, but it is also extendable to other datasets. IIS is freely available online at: http://www.lge.ibi.unicamp.br/lnbio/IIS/.

Topology Studies of Hydrodynamics Using Two-Particle Correlation Analysis

The effects of fluctuating initial conditions are studied in the context of relativistic heavy ion collisions where a rapidly evolving system is formed. Two-particle correlation analysis is applied to events generated with the NEXSPHERIO hydrodynamic code, starting with fluctuating nonsmooth initial conditions (IC). The results show that the nonsmoothness in the IC survives the hydroevolution and can be seen as topological features of the angular correlation function of the particles emerging from the evolving system. A long range correlation is observed in the longitudinal direction and in the azimuthal direction a double peak structure is observed in the opposite direction to the trigger particle. This analysis provides clear evidence that these are signatures of the combined effect of tubular structures present in the IC and the proceeding collective dynamics of the hot and dense medium.

The dimerization and topological specificity functions of MinE reside in a structurally autonomous C-terminal domain

Correct placement of the division septum in Escherichia coli requires the co-ordinated action of three proteins, MinC, MinD and MinE. MinC and MinD interact to form a non-specific division inhibitor that blocks septation at all potential division sites. MinE is able to antagonize MinCD in a topologically sensitive manner, as it restricts MinCD activity to the unwanted division sites at the cell poles, Here, we show that the topological specificity function of MinE residues in a structurally autonomous, trypsin-resistant domain comprising residues 31-88, Nuclear magnetic resonance (NMR) and circular dichroic spectroscopy indicate that this domain includes both alpha and beta secondary structure, while analytical ultracentrifugation reveals that it also contains a region responsible for MinE homodimerization. While trypsin digestion indicates that the anti-MinCD domain of MinE (residues 1-22) does not form a tightly folded structural domain, NMR analysis of a peptide corresponding to MinE(1-22) indicates that this region forms a nascent helix in which the peptide rapidly interconverts between disordered (random coil) and alpha-helical conformations, This suggests that the N-terminal region of MinE may be poised to adopt an alpha-helical conformation when it interacts with the target of its anti-MinCD activity, presumably MinD.

Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

Exploratory geospatial data analysis using self-organizing maps

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Ciência e Sistemas de Informação Geográfica

Brain network analysis of patients with Temporal Lobe Epilepsy

Patients with Temporal Lobe Epilepsy (TLE) suffer from widespread subtle white matter abnormalities and abnormal functional connectivity extending beyond the affected lobe, as revealed by Diffusion Tensor MR Imaging, volumetric and functional MRI studies. Diffusion Spectrum Imaging (DSI) is a diffusion imaging technique with high angular resolution for improving the mapping of white matter pathways. In this study, we used DSI, connectivity matrices and topological measures to investigate how the alteration in structural connectivity influences whole brain structural networks. Eleven patients with right-sided TLE and hippocampal sclerosis and 18 controls underwent our DSI protocol at 3T. The cortical and subcortical grey matters were parcellated into 86 regions of interest and the connectivity between every region pair was estimated using global tractography and a connectivity matrix (the adjacency matrix of the structural network). We then compared the networks of patients and controls using topological measures. In patients, we found a higher characteristic path length and a lower clustering coefficient compared to controls. Local measures at node level of the clustering and efficiency showed a significant difference after a multiple comparison correction (Bonferroni). These significant nodes were located within as well outside the temporal lobe, and the localisation of most of them was consistent with regions known to be part of epileptic networks in TLE. Our results show altered connectivity patterns that are concordant with the mapping of functional epileptic networks in patients with TLE. Further studies are needed to establish the relevance of these findings for the propagation of epileptic activity, cognitive deficits in medial TLE and outcome of epilepsy surgery in individual patients.