Mean Squared Residue Based Biclustering Algorithms for the Analysis of Gene Expression Data

Computational Biology is the research are that contributes to the analysis of biological data through the development of algorithms which will address significant research problems.The data from molecular biology includes DNA,RNA ,Protein and Gene expression data.Gene Expression Data provides the expression level of genes under different conditions.Gene expression is the process of transcribing the DNA sequence of a gene into mRNA sequences which in turn are later translated into proteins.The number of copies of mRNA produced is called the expression level of a gene.Gene expression data is organized in the form of a matrix. Rows in the matrix represent genes and columns in the matrix represent experimental conditions.Experimental conditions can be different tissue types or time points.Entries in the gene expression matrix are real values.Through the analysis of gene expression data it is possible to determine the behavioral patterns of genes such as similarity of their behavior,nature of their interaction,their respective contribution to the same pathways and so on. Similar expression patterns are exhibited by the genes participating in the same biological process.These patterns have immense relevance and application in bioinformatics and clinical research.Theses patterns are used in the medical domain for aid in more accurate diagnosis,prognosis,treatment planning.drug discovery and protein network analysis.To identify various patterns from gene expression data,data mining techniques are essential.Clustering is an important data mining technique for the analysis of gene expression data.To overcome the problems associated with clustering,biclustering is introduced.Biclustering refers to simultaneous clustering of both rows and columns of a data matrix. Clustering is a global whereas biclustering is a local model.Discovering local expression patterns is essential for identfying many genetic pathways that are not apparent otherwise.It is therefore necessary to move beyond the clustering paradigm towards developing approaches which are capable of discovering local patterns in gene expression data.A biclusters is a submatrix of the gene expression data matrix.The rows and columns in the submatrix need not be contiguous as in the gene expression data matrix.Biclusters are not disjoint.Computation of biclusters is costly because one will have to consider all the combinations of columans and rows in order to find out all the biclusters.The search space for the biclustering problem is 2 m+n where m and n are the number of genes and conditions respectively.Usually m+n is more than 3000.The biclustering problem is NP-hard.Biclustering is a powerful analytical tool for the biologist.The research reported in this thesis addresses the problem of biclustering.Ten algorithms are developed for the identification of coherent biclusters from gene expression data.All these algorithms are making use of a measure called mean squared residue to search for biclusters.The objective here is to identify the biclusters of maximum size with the mean squared residue lower than a given threshold. All these algorithms begin the search from tightly coregulated submatrices called the seeds.These seeds are generated by K-Means clustering algorithm.The algorithms developed can be classified as constraint based,greedy and metaheuristic.Constarint based algorithms uses one or more of the various constaints namely the MSR threshold and the MSR difference threshold.The greedy approach makes a locally optimal choice at each stage with the objective of finding the global optimum.In metaheuristic approaches particle Swarm Optimization(PSO) and variants of Greedy Randomized Adaptive Search Procedure(GRASP) are used for the identification of biclusters.These algorithms are implemented on the Yeast and Lymphoma datasets.Biologically relevant and statistically significant biclusters are identified by all these algorithms which are validated by Gene Ontology database.All these algorithms are compared with some other biclustering algorithms.Algorithms developed in this work overcome some of the problems associated with the already existing algorithms.With the help of some of the algorithms which are developed in this work biclusters with very high row variance,which is higher than the row variance of any other algorithm using mean squared residue, are identified from both Yeast and Lymphoma data sets.Such biclusters which make significant change in the expression level are highly relevant biologically.

Biclustering Gene Expression Data using MSR Difference Threshold

Biclustering is simultaneous clustering of both rows and columns of a data matrix. A measure called Mean Squared Residue (MSR) is used to simultaneously evaluate the coherence of rows and columns within a submatrix. In this paper a novel algorithm is developed for biclustering gene expression data using the newly introduced concept of MSR difference threshold. In the first step high quality bicluster seeds are generated using K-Means clustering algorithm. Then more genes and conditions (node) are added to the bicluster. Before adding a node the MSR X of the bicluster is calculated. After adding the node again the MSR Y is calculated. The added node is deleted if Y minus X is greater than MSR difference threshold or if Y is greater than MSR threshold which depends on the dataset. The MSR difference threshold is different for gene list and condition list and it depends on the dataset also. Proper values should be identified through experimentation in order to obtain biclusters of high quality. The results obtained on bench mark dataset clearly indicate that this algorithm is better than many of the existing biclustering algorithms

Untersuchungen zur Verbreitung von Klasse II-Transposons wie Tn21, Tn501 und Tn3 in terrestrischen Habitaten

Mobile genetische Elementen wie Transposons wurden in unbelasteten Böden nachgewiesen. Hierzu wurden unterschiedliche Ansätze gewählt: Verschiedene, unbelastete Böden wurden mittels PCR auf das Vorhandensein von Markergenen, in diesem Fall Transposasen vom Typ Tn3, Tn21 und Tn501, hin untersucht. Hierzu wurde ein System entwickelt, welches es ermöglichte die Gesamt-DNA aus verschiedensten Böden mit einem System einfach und reproduzierbar zu extrahieren und anschließend mittels PCR zu untersuchen. Die mittlere Nachweisgrenze dieses Systems lag bei 9 x 10 *3 Templates / g Boden. Ein paralleler Ansatz erfolgte, indem aus den gleichen, unbelasteten Böden Bakterien mittels Selektivmedien isoliert wurden. Diese Isolate wurden anschließend auf genetische Marker hin untersucht. Transposons, bzw. Transposasen konnten in den unbelasteten Böden in weitaus geringerer Zahl als aus belasteten Böden bekannt nachgewiesen werden. Jedoch verhielten sich die unterschiedlichen Elemente in der Verteilung wie aus belasteten Böden bekannt. Am häufigsten wurde Tn21 dann Tn501 nachgewiesen. Tn3, nach dem auch gescreent wurde, konnte nicht nachgewiesen werden. Anschließend wurden diese Böden mittels Bodensäulen unter Laborbedingungen auf die Übertragung von potentiell transponierbaren Elementen aus der autochthonen Flora hin untersucht. Mittels dieses Experimentes konnte kein transponierbares Element nachgewiesen werden. Weiterhin wurden vorhandene Boden-Bakterienkollektive auf das Vorhandensein von Transposons mittels Gensondentechnik und PCR auf Transposasen hin gescreent. Auch hier konnten wiederum Signale zu Tn21, Tn501 und in diesem Falle auch Tn3 erhalten werden. Einige dieser Isolate wurden mittels Southern-Blot und Sequenzierung näher charakterisiert. Bei den Sequenzvergleichen einer so erhaltenen 2257 bp langen Sequenz wurde diese als Transposase der Tn21-Familie mit großer Homologie zur Transposase von Tn5060 bestimmt.

Stimulus Simplification and Object Representation: A Modeling Study

Tsunoda et al. (2001) recently studied the nature of object representation in monkey inferotemporal cortex using a combination of optical imaging and extracellular recordings. In particular, they examined IT neuron responses to complex natural objects and "simplified" versions thereof. In that study, in 42% of the cases, optical imaging revealed a decrease in the number of activation patches in IT as stimuli were "simplified". However, in 58% of the cases, "simplification" of the stimuli actually led to the appearance of additional activation patches in IT. Based on these results, the authors propose a scheme in which an object is represented by combinations of active and inactive columns coding for individual features. We examine the patterns of activation caused by the same stimuli as used by Tsunoda et al. in our model of object recognition in cortex (Riesenhuber 99). We find that object-tuned units can show a pattern of appearance and disappearance of features identical to the experiment. Thus, the data of Tsunoda et al. appear to be in quantitative agreement with a simple object-based representation in which an object's identity is coded by its similarities to reference objects. Moreover, the agreement of simulations and experiment suggests that the simplification procedure used by Tsunoda (2001) is not necessarily an accurate method to determine neuronal tuning.

CODAPACK3D. A new version of Compositional Data Package

The statistical analysis of compositional data should be treated using logratios of parts, which are difficult to use correctly in standard statistical packages. For this reason a freeware package, named CoDaPack was created. This software implements most of the basic statistical methods suitable for compositional data. In this paper we describe the new version of the package that now is called CoDaPack3D. It is developed in Visual Basic for applications (associated with Excel©), Visual Basic and Open GL, and it is oriented towards users with a minimum knowledge of computers with the aim at being simple and easy to use. This new version includes new graphical output in 2D and 3D. These outputs could be zoomed and, in 3D, rotated. Also a customization menu is included and outputs could be saved in jpeg format. Also this new version includes an interactive help and all dialog windows have been improved in order to facilitate its use. To use CoDaPack one has to access Excel© and introduce the data in a standard spreadsheet. These should be organized as a matrix where Excel© rows correspond to the observations and columns to the parts. The user executes macros that return numerical or graphical results. There are two kinds of numerical results: new variables and descriptive statistics, and both appear on the same sheet. Graphical output appears in independent windows. In the present version there are 8 menus, with a total of 38 submenus which, after some dialogue, directly call the corresponding macro. The dialogues ask the user to input variables and further parameters needed, as well as where to put these results. The web site http://ima.udg.es/CoDaPack contains this freeware package and only Microsoft Excel© under Microsoft Windows© is required to run the software. Kew words: Compositional data Analysis, Software

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table has n rows and m columns and all probabilities are non-null. This kind of table can be seen as an element in the simplex of n · m parts. In this context, the marginals are identified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclidean elements of the Aitchison geometry of the simplex can also be translated into the table of probabilities: subspaces, orthogonal projections, distances. Two important questions are addressed: a) given a table of probabilities, which is the nearest independent table to the initial one? b) which is the largest orthogonal projection of a row onto a column? or, equivalently, which is the information in a row explained by a column, thus explaining the interaction? To answer these questions three orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independent two-way tables and fully dependent tables representing row-column interaction. An important result is that the nearest independent table is the product of the two (row and column)-wise geometric marginal tables. A corollary is that, in an independent table, the geometric marginals conform with the traditional (arithmetic) marginals. These decompositions can be compared with standard log-linear models. Key words: balance, compositional data, simplex, Aitchison geometry, composition, orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure, contingency table

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data

Modelització numèrica d’un sistema de descàrrega d’una columna de la catedral d Girona mitjançant el mètode dels elements finits (anàlisi no lineal)

Aquest projecte consisteix en aplicar el càlcul no lineal en la modelització volumètrica numèrica de l’estructura del sistema de descàrrega d’una columna del claustre de la catedral de Girona mitjançant el mètode dels elements finits. A la Universitat de Girona s’ha fet diferents estudis del claustre de la catedral de Girona però sempre simulant un comportament lineal de les característiques dels materials. El programa utilitzat és la versió docent del programa ANSYS disponible al Dept. d’EMCI i l’element emprat ha sigut el SOLID65. Aquest element permet introduir característiques de no linealitat en els models i és adequat per a anàlisi no lineal d’elements com la pedra de Girona

Entering Data into Excel

Video on how to enter data into Excel. This includes setting up column headings, changing sheet names, using lists for categorical items, using validation on columns of data, plus how to check validation is operating correctly.

La cocina de los venenos. Aspectos de la criminalidad en el Nuevo Reino de Granada, siglos XVII-XVIII

Durante los siglos XVII y XVIII se presentaron varias querellas ante el Tribunal de Justicia Criminal del Nuevo Reino de Granada, en las que se denunciaba que había personas que ejercían los oficios médicos sin tener títulos que los acreditaran como facultativos en las artes curativas. Por ese entonces, se creía que quienes utilizaban yerbas y conjuros como métodos terapéuticos, por lo general mujeres, debían ser juzgadas como yerbateras-envenenadoras, porque no pretendían curar sino matar a quien consumiera sus preparados. El texto establece que los procesos criminales por envenenamiento constituyen un prisma en el que convergen diferentes problemáticas del periodo colonial neogranadino, relacionadas con la salud, los oficios médicos, las enfermedades, las creencias mágico-religiosas, el ideal de mujer en la época, la delincuencia, y las dinámicas de las instituciones españolas, entre otras. De esta manera, se estudió cómo fue la relación entre los aspectos jurídicos, las leyes criminales (dictadas por la Corona) y las conductas “desviadas” (relacionadas con el crimen por envenenamiento) de los habitantes del Nuevo Reino de Granada, entre los siglos XVII y XVIII. Para ello se revistaron desde diferentes perspectivas, varios temas del mundo colonial neogranadino, relacionados con los rumores, la comidilla, los chismes y la importancia de la comunicación hablada en el virreinato; el problema de la honra, como una de las virtudes más sobresalientes de la época y las creencias de la cultura popular con relación al envenenamiento y los diferentes métodos curativos.

El debate sobre las leyes de medios en Ecuador y Argentina: un análisis a dos periódicos colombianos 2009-2013

Este trabajo de grado estudia el modo como dos diarios colombianos, El Tiempo y El Espectador, presentaron la información sobre el debate de “Leyes de medios” en Ecuador y Argentina, desarrollado en los años recientes. El estudio analizó las noticias, columnas, editoriales, reportajes y entrevistas publicados desde el año 2009 (cuando se generalizó el debate) hasta 2013. La metodología facilitó el análisis comparativo de los dos periódicos y de sus posturas frente al debate de las leyes de medios. Se argumenta que los medios, como actores principales del debate, han tomado partido, en sus páginas editoriales e informativas, en contra de las políticas que buscan regular su actividad. Así, existe una persistencia en la prensa para imponer discursos con una ideología específica a través de los actores que son presentados en la construcción de los relatos, en este caso, dispuestos a contrariar la aprobación de las leyes de medios propuestas por el gobierno argentino y ecuatoriano. Se evidencia en el marco interpretativo de los textos periodísticos analizados, la guerra de poderes en países de la región latinoamericana que persiste entre los medios y los gobiernos.

Debate sobre política de drogas a través de la opinión en cuatro medios colombianos (2009-2013)

Este trabajo de grado aborda la contribución del periodismo en la configuración del debate en Colombia sobre política de drogas, a través de un análisis de contenido a las columnas y editoriales publicadas entre 2009 y 2013 en cuatro medios de referencia del país. Se identificaron los perfiles de quienes participaron, los argumentos y las políticas defendidas que plantearon, y la manera como presentaron sus opiniones en El Espectador, El Tiempo, La Silla Vacía y Semana. El desarrollo de la discusión en los textos demuestra una evolución respecto al tema en la medida que hay una transformación del paradigma punitivo hacia un camino menos restrictivo frente a la producción, el tráfico y consumo de drogas ilícitas. Se sugiere que los hechos coyunturales motivaron en parte dicho cambio al ejercer influencia en los giros y la visibilidad que toma el debate dentro de la prensa.

Prevalencia de enfermedad de Fabry en pacientes en lista de trasplante y posttrasplante renal en fundación cardioinfantil Bogotá

Introducción: La Enfermedad de Fabry (EF), es una enfermedad multisistémica de almacenamiento lisosomal ligada al cromosoma X que afecta principalmente a hombres, pero también puede causar significativa morbilidad en las mujeres heterocigotas (1–5). La deficiencia de la enzyma α-galactosidaseA (α-Gal A,) provoca acumulación de glicosfingolipidos que afectan diferentes tipos celulares entre ellos el endotelio vascular en vasos de pequeño calibre, células epiteliales y Músculo liso en el sistema cardiovascular (cardiomiocitos), sistema nervioso y células epiteliales tubulares del riñón (6,7). Complicaciones como la falla renal es la causa de muerte más frecuente en la EF (7,8). La incidencia se ha calculado en 1 de cada 117.000 nacidos vivos. (9). Objetivos: Determinar la prevalencia de la Enfermedad de Fabry en pacientes con Insuficiencia renal terminal que se encuentren en lista de trasplante y Post-trasplante Renal en Fundación Cardioinfantil Bogotá. Materiales y Métodos: Se realizó un estudio observacional en donde se evaluó la prevalencia de la EF en todos los sujetos mayores de 18 años que se encuentren en lista de trasplante y post-trasplante renal. Resultados: La prevalencia de Enfermedad de Fabry en 98 pacientes con enfermedad renal crónica fue de 7.1% para la muestra general y 12.9% para la muestra con etiología idiopática Conclusiones: La Enfermedad de Fabry es una importante casusa de Enfermedad Renal Crónica Terminal principalmente en el grupo de etiología idiopática. Palabras Clave: Enfermedad de Fabry (FA)

Select-divide-and-conquer method for large-scale configuration interaction

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0={T0egy, T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates KS with attributes above T1≤T0. An eigenproblem of dimension d0+d1 for S0+S 1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j≥2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0, 1, 2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S 0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24 × 106, involving 1.2 × 1012 nonzero matrix elements, and 8.4×109 Slater determinants

Proves de càrrega al claustre de la catedral de Girona

El projecte tracta de la realització de proves de càrrega al Claustre de la Catedral de Girona per tal de conèixer la càrrega que suporten les columnes de pedra del claustre. Un cop coneguda aquesta càrrega, es podrà decidir si son aptes o no per al canvi d’ús previst a la planta superior i es podrà aportar una resposta definitiva a una de les dues hipòtesis plantejades: si es forma o no arc de descàrrega a les columnes del Claustre. D’altre banda, es realitzarà una proposta de tractament de les columnes del Claustre que consistirà a escollir les que hauran de ser reparades i les que hauran de ser substituïdes, en base a una sèrie de càlculs numèrics