The Proper Generalized Decomposition With Application In Problems Of Dynamics

In this paper we address the new reduction method called Proper Generalized Decomposition (PGD) which is a discretization technique based on the use of separated representation of the unknown fields, specially well suited for solving multidimensional parametric equations. In this case, it is applied to the solution of dynamics problems. We will focus on the dynamic analysis of an one-dimensional rod with a unit harmonic load of frequency (ω) applied at a point of interest. In what follows, we will present the application of the methodology PGD to the problem in order to approximate the displacement field as the sum of the separated functions. We will consider as new variables of the problem, parameters models associated with the characteristic of the materials, in addition to the frequency. Finally, the quality of the results will be assessed based on an example.

Fast modularisation and aomic decomposition of ontologies using axiom dependency hypergraphs

In this paper we define the notion of an axiom dependency hypergraph, which explicitly represents how axioms are included into a module by the algorithm for computing locality-based modules. A locality-based module of an ontology corresponds to a set of connected nodes in the hypergraph, and atoms of an ontology to strongly connected components. Collapsing the strongly connected components into single nodes yields a condensed hypergraph that comprises a representation of the atomic decomposition of the ontology. To speed up the condensation of the hypergraph, we first reduce its size by collapsing the strongly connected components of its graph fragment employing a linear time graph algorithm. This approach helps to significantly reduce the time needed for computing the atomic decomposition of an ontology. We provide an experimental evaluation for computing the atomic decomposition of large biomedical ontologies. We also demonstrate a significant improvement in the time needed to extract locality-based modules from an axiom dependency hypergraph and its condensed version.

Strong Connectivity in Directed Hypergraphs and its Application to the Atomic Decomposition of Ontologies

Los hipergrafos dirigidos se han empleado en problemas relacionados con lógica proposicional, bases de datos relacionales, linguística computacional y aprendizaje automático. Los hipergrafos dirigidos han sido también utilizados como alternativa a los grafos (bipartitos) dirigidos para facilitar el estudio de las interacciones entre componentes de sistemas complejos que no pueden ser fácilmente modelados usando exclusivamente relaciones binarias. En este contexto, este tipo de representación es conocida como hiper-redes. Un hipergrafo dirigido es una generalización de un grafo dirigido especialmente adecuado para la representación de relaciones de muchos a muchos. Mientras que una arista en un grafo dirigido define una relación entre dos de sus nodos, una hiperarista en un hipergrafo dirigido define una relación entre dos conjuntos de sus nodos. La conexión fuerte es una relación de equivalencia que divide el conjunto de nodos de un hipergrafo dirigido en particiones y cada partición define una clase de equivalencia conocida como componente fuertemente conexo. El estudio de los componentes fuertemente conexos de un hipergrafo dirigido puede ayudar a conseguir una mejor comprensión de la estructura de este tipo de hipergrafos cuando su tamaño es considerable. En el caso de grafo dirigidos, existen algoritmos muy eficientes para el cálculo de los componentes fuertemente conexos en grafos de gran tamaño. Gracias a estos algoritmos, se ha podido averiguar que la estructura de la WWW tiene forma de “pajarita”, donde más del 70% del los nodos están distribuidos en tres grandes conjuntos y uno de ellos es un componente fuertemente conexo. Este tipo de estructura ha sido también observada en redes complejas en otras áreas como la biología. Estudios de naturaleza similar no han podido ser realizados en hipergrafos dirigidos porque no existe algoritmos capaces de calcular los componentes fuertemente conexos de este tipo de hipergrafos. En esta tesis doctoral, hemos investigado como calcular los componentes fuertemente conexos de un hipergrafo dirigido. En concreto, hemos desarrollado dos algoritmos para este problema y hemos determinado que son correctos y cuál es su complejidad computacional. Ambos algoritmos han sido evaluados empíricamente para comparar sus tiempos de ejecución. Para la evaluación, hemos producido una selección de hipergrafos dirigidos generados de forma aleatoria inspirados en modelos muy conocidos de grafos aleatorios como Erdos-Renyi, Newman-Watts-Strogatz and Barabasi-Albert. Varias optimizaciones para ambos algoritmos han sido implementadas y analizadas en la tesis. En concreto, colapsar los componentes fuertemente conexos del grafo dirigido que se puede construir eliminando ciertas hiperaristas complejas del hipergrafo dirigido original, mejora notablemente los tiempos de ejecucion de los algoritmos para varios de los hipergrafos utilizados en la evaluación. Aparte de los ejemplos de aplicación mencionados anteriormente, los hipergrafos dirigidos han sido también empleados en el área de representación de conocimiento. En concreto, este tipo de hipergrafos se han usado para el cálculo de módulos de ontologías. Una ontología puede ser definida como un conjunto de axiomas que especifican formalmente un conjunto de símbolos y sus relaciones, mientras que un modulo puede ser entendido como un subconjunto de axiomas de la ontología que recoge todo el conocimiento que almacena la ontología sobre un conjunto especifico de símbolos y sus relaciones. En la tesis nos hemos centrado solamente en módulos que han sido calculados usando la técnica de localidad sintáctica. Debido a que las ontologías pueden ser muy grandes, el cálculo de módulos puede facilitar las tareas de re-utilización y mantenimiento de dichas ontologías. Sin embargo, analizar todos los posibles módulos de una ontología es, en general, muy costoso porque el numero de módulos crece de forma exponencial con respecto al número de símbolos y de axiomas de la ontología. Afortunadamente, los axiomas de una ontología pueden ser divididos en particiones conocidas como átomos. Cada átomo representa un conjunto máximo de axiomas que siempre aparecen juntos en un modulo. La decomposición atómica de una ontología es definida como un grafo dirigido de tal forma que cada nodo del grafo corresponde con un átomo y cada arista define una dependencia entre una pareja de átomos. En esta tesis introducimos el concepto de“axiom dependency hypergraph” que generaliza el concepto de descomposición atómica de una ontología. Un modulo en una ontología correspondería con un componente conexo en este tipo de hipergrafos y un átomo de una ontología con un componente fuertemente conexo. Hemos adaptado la implementación de nuestros algoritmos para que funcionen también con axiom dependency hypergraphs y poder de esa forma calcular los átomos de una ontología. Para demostrar la viabilidad de esta idea, hemos incorporado nuestros algoritmos en una aplicación que hemos desarrollado para la extracción de módulos y la descomposición atómica de ontologías. A la aplicación la hemos llamado HyS y hemos estudiado sus tiempos de ejecución usando una selección de ontologías muy conocidas del área biomédica, la mayoría disponibles en el portal de Internet NCBO. Los resultados de la evaluación muestran que los tiempos de ejecución de HyS son mucho mejores que las aplicaciones más rápidas conocidas. ABSTRACT Directed hypergraphs are an intuitive modelling formalism that have been used in problems related to propositional logic, relational databases, computational linguistic and machine learning. Directed hypergraphs are also presented as an alternative to directed (bipartite) graphs to facilitate the study of the interactions between components of complex systems that cannot naturally be modelled as binary relations. In this context, they are known as hyper-networks. A directed hypergraph is a generalization of a directed graph suitable for representing many-to-many relationships. While an edge in a directed graph defines a relation between two nodes of the graph, a hyperedge in a directed hypergraph defines a relation between two sets of nodes. Strong-connectivity is an equivalence relation that induces a partition of the set of nodes of a directed hypergraph into strongly-connected components. These components can be collapsed into single nodes. As result, the size of the original hypergraph can significantly be reduced if the strongly-connected components have many nodes. This approach might contribute to better understand how the nodes of a hypergraph are connected, in particular when the hypergraphs are large. In the case of directed graphs, there are efficient algorithms that can be used to compute the strongly-connected components of large graphs. For instance, it has been shown that the macroscopic structure of the World Wide Web can be represented as a “bow-tie” diagram where more than 70% of the nodes are distributed into three large sets and one of these sets is a large strongly-connected component. This particular structure has been also observed in complex networks in other fields such as, e.g., biology. Similar studies cannot be conducted in a directed hypergraph because there does not exist any algorithm for computing the strongly-connected components of the hypergraph. In this thesis, we investigate ways to compute the strongly-connected components of directed hypergraphs. We present two new algorithms and we show their correctness and computational complexity. One of these algorithms is inspired by Tarjan’s algorithm for directed graphs. The second algorithm follows a simple approach to compute the stronglyconnected components. This approach is based on the fact that two nodes of a graph that are strongly-connected can also reach the same nodes. In other words, the connected component of each node is the same. Both algorithms are empirically evaluated to compare their performances. To this end, we have produced a selection of random directed hypergraphs inspired by existent and well-known random graphs models like Erd˝os-Renyi and Newman-Watts-Strogatz. Besides the application examples that we mentioned earlier, directed hypergraphs have also been employed in the field of knowledge representation. In particular, they have been used to compute the modules of an ontology. An ontology is defined as a collection of axioms that provides a formal specification of a set of terms and their relationships; and a module is a subset of an ontology that completely captures the meaning of certain terms as defined in the ontology. In particular, we focus on the modules computed using the notion of syntactic locality. As ontologies can be very large, the computation of modules facilitates the reuse and maintenance of these ontologies. Analysing all modules of an ontology, however, is in general not feasible as the number of modules grows exponentially in the number of terms and axioms of the ontology. Nevertheless, the modules can succinctly be represented using the Atomic Decomposition of an ontology. Using this representation, an ontology can be partitioned into atoms, which are maximal sets of axioms that co-occur in every module. The Atomic Decomposition is then defined as a directed graph such that each node correspond to an atom and each edge represents a dependency relation between two atoms. In this thesis, we introduce the notion of an axiom dependency hypergraph which is a generalization of the atomic decomposition of an ontology. A module in the ontology corresponds to a connected component in the hypergraph, and the atoms of the ontology to the strongly-connected components. We apply our algorithms for directed hypergraphs to axiom dependency hypergraphs and in this manner, we compute the atoms of an ontology. To demonstrate the viability of this approach, we have implemented the algorithms in the application HyS which computes the modules of ontologies and calculate their atomic decomposition. In the thesis, we provide an experimental evaluation of HyS with a selection of large and prominent biomedical ontologies, most of which are available in the NCBO Bioportal. HyS outperforms state-of-the-art implementations in the tasks of extracting modules and computing the atomic decomposition of these ontologies.

Aerodynamic database reconstruction via gappy high order singular value decomposition

Esta Tesis se centra en el desarrollo de un método para la reconstrucción de bases de datos experimentales incompletas de más de dos dimensiones. Como idea general, consiste en la aplicación iterativa de la descomposición en valores singulares de alto orden sobre la base de datos incompleta. Este nuevo método se inspira en el que ha servido de base para la reconstrucción de huecos en bases de datos bidimensionales inventado por Everson y Sirovich (1995) que a su vez, ha sido mejorado por Beckers y Rixen (2003) y simultáneamente por Venturi y Karniadakis (2004). Además, se ha previsto la adaptación de este nuevo método para tratar el posible ruido característico de bases de datos experimentales y a su vez, bases de datos estructuradas cuya información no forma un hiperrectángulo perfecto. Se usará una base de datos tridimensional de muestra como modelo, obtenida a través de una función transcendental, para calibrar e ilustrar el método. A continuación se detalla un exhaustivo estudio del funcionamiento del método y sus variantes para distintas bases de datos aerodinámicas. En concreto, se usarán tres bases de datos tridimensionales que contienen la distribución de presiones sobre un ala. Una se ha generado a través de un método semi-analítico con la intención de estudiar distintos tipos de discretizaciones espaciales. El resto resultan de dos modelos numéricos calculados en C F D . Por último, el método se aplica a una base de datos experimental de más de tres dimensiones que contiene la medida de fuerzas de una configuración ala de Prandtl obtenida de una campaña de ensayos en túnel de viento, donde se estudiaba un amplio espacio de parámetros geométricos de la configuración que como resultado ha generado una base de datos donde la información está dispersa. ABSTRACT A method based on an iterative application of high order singular value decomposition is derived for the reconstruction of missing data in multidimensional databases. The method is inspired by a seminal gappy reconstruction method for two-dimensional databases invented by Everson and Sirovich (1995) and improved by Beckers and Rixen (2003) and Venturi and Karniadakis (2004). In addition, the method is adapted to treat both noisy and structured-but-nonrectangular databases. The method is calibrated and illustrated using a three-dimensional toy model database that is obtained by discretizing a transcendental function. The performance of the method is tested on three aerodynamic databases for the flow past a wing, one obtained by a semi-analytical method, and two resulting from computational fluid dynamics. The method is finally applied to an experimental database consisting in a non-exhaustive parameter space measurement of forces for a box-wing configuration.

Aerodynamic database error filtering via high order singular value decomposition

Esta Tesis presenta un nuevo método para filtrar errores en bases de datos multidimensionales. Este método no precisa ninguna información a priori sobre la naturaleza de los errores. En concreto, los errrores no deben ser necesariamente pequeños, ni de distribución aleatoria ni tener media cero. El único requerimiento es que no estén correlados con la información limpia propia de la base de datos. Este nuevo método se basa en una extensión mejorada del método básico de reconstrucción de huecos (capaz de reconstruir la información que falta de una base de datos multidimensional en posiciones conocidas) inventado por Everson y Sirovich (1995). El método de reconstrucción de huecos mejorado ha evolucionado como un método de filtrado de errores de dos pasos: en primer lugar, (a) identifica las posiciones en la base de datos afectadas por los errores y después, (b) reconstruye la información en dichas posiciones tratando la información de éstas como información desconocida. El método resultante filtra errores O(1) de forma eficiente, tanto si son errores aleatorios como sistemáticos e incluso si su distribución en la base de datos está concentrada o esparcida por ella. Primero, se ilustra el funcionamiento delmétodo con una base de datosmodelo bidimensional, que resulta de la dicretización de una función transcendental. Posteriormente, se presentan algunos casos prácticos de aplicación del método a dos bases de datos tridimensionales aerodinámicas que contienen la distribución de presiones sobre un ala a varios ángulos de ataque. Estas bases de datos resultan de modelos numéricos calculados en CFD. ABSTRACT A method is presented to filter errors out in multidimensional databases. The method does not require any a priori information about the nature the errors. In particular, the errors need not to be small, neither random, nor exhibit zero mean. Instead, they are only required to be relatively uncorrelated to the clean information contained in the database. The method is based on an improved extension of a seminal iterative gappy reconstruction method (able to reconstruct lost information at known positions in the database) due to Everson and Sirovich (1995). The improved gappy reconstruction method is evolved as an error filtering method in two steps, since it is adapted to first (a) identify the error locations in the database and then (b) reconstruct the information in these locations by treating the associated data as gappy data. The resultingmethod filters out O(1) errors in an efficient fashion, both when these are random and when they are systematic, and also both when they concentrated and when they are spread along the database. The performance of the method is first illustrated using a two-dimensional toymodel database resulting fromdiscretizing a transcendental function and then tested on two CFD-calculated, three-dimensional aerodynamic databases containing the pressure coefficient on the surface of a wing for varying values of the angle of attack. A more general performance analysis of the method is presented with the intention of quantifying the randomness factor the method admits maintaining a correct performance and secondly, quantifying the size of error the method can detect. Lastly, some improvements of the method are proposed with their respective verification.

The decomposition of peroxynitrite does not yield nitroxyl anion and singlet oxygen

In a recent article [Khan, A. U., Kovacic, D., Kolbanovsky, A., Desai, M., Frenkel, K. & Geacintov, N. E. (2000) Proc. Natl. Acad. Sci. USA 97, 2984–2989], the authors claimed that ONOO−, after protonation to ONOOH, decomposes into 1HNO and 1O2 according to a spin-conserved unimolecular mechanism. This claim was based partially on their observation that nitrosylhemoglobin is formed via the reaction of peroxynitrite with methemoglobin at neutral pH. However, thermochemical considerations show that the yields of 1O2 and 1HNO are about 23 orders of magnitude lower than those of ⋅NO2 and ⋅OH, which are formed via the homolysis of ONOOH. We also show that methemoglobin does not form with peroxynitrite any spectrally detectable product, but with contaminations of nitrite and H2O2 present in the peroxynitrite sample. Thus, there is no need to modify the present view of the mechanism of ONOOH decomposition, according to which initial homolysis into a radical pair, [ONO⋅ ⋅OH]cage, is followed by the diffusion of about 30% of the radicals out of the cage, while the rest recombines to nitric acid in the solvent cage.

Singular value decomposition for genome-wide expression data processing and modeling

We describe the use of singular value decomposition in transforming genome-wide expression data from genes × arrays space to reduced diagonalized “eigengenes” × “eigenarrays” space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Rates of decomposition of ribose and other sugars: implications for chemical evolution.

The existence of the RNA world, in which RNA acted as a catalyst as well as an informational macromolecule, assumes a large prebiotic source of ribose or the existence of pre-RNA molecules with backbones different from ribose-phosphate. The generally accepted prebiotic synthesis of ribose, the formose reaction, yields numerous sugars without any selectivity. Even if there were a selective synthesis of ribose, there is still the problem of stability. Sugars are known to be unstable in strong acid or base, but there are few data for neutral solutions. Therefore, we have measured the rate of decomposition of ribose between pH 4 and pH 8 from 40 degrees C to 120 degrees C. The ribose half-lives are very short (73 min at pH 7.0 and 100 degrees C and 44 years at pH 7.0 and 0 degrees C). The other aldopentoses and aldohexoses have half-lives within an order of magnitude of these values, as do 2-deoxyribose, ribose 5-phosphate, and ribose 2,4-bisphosphate. These results suggest that the backbone of the first genetic material could not have contained ribose or other sugars because of their instability.

Decomposition of human behavior using model of competencies: application to robotic control system

For many years, humans and machines have shared the same physical space. To facilitate their interaction with humans, their social integration and for more rational behavior has been sought that the robots demonstrate human-like behavior. For this it is necessary to understand how human behavior is generated, discuss what tasks are performed and how relate to themselves, for subsequent implementation in robots. In this paper, we propose a model of competencies based on human neuroregulator system for analysis and decomposition of behavior into functional modules. Using this model allow separate and locate the tasks to be implemented in a robot that displays human-like behavior. As an example, we show the application of model to the autonomous movement behavior on unfamiliar environments and its implementation in various simulated and real robots with different physical configurations and physical devices of different nature. The main result of this work has been to build a model of competencies that is being used to build robotic systems capable of displaying behaviors similar to humans and consider the specific characteristics of robots.

Effect of the metal in the production of pollutants during the decomposition of two types of electric wires

Support for this work was provided by the Generalitat Valenciana (Spain) with projects PROMETEO/2009/043/FEDER, and by the Spanish MCT CTQ2008-05520.

Corn stover thermal decomposition in pyrolytic and oxidant atmosphere

The pyrolysis and combustion of corn stover were studied by dynamic thermogravimetry and derivate thermogravimetry (TG-DTG) at heating rates of 5, 10, 20 and 50 K min−1 at atmospheric pressure. For the simulation of pyrolysis and combustion processes a kinetic model based on the distribution of activation energies was used, with three pools of reactants (three pseudocomponents) because of the complexity of the biomass samples of agricultural origin. The experimental thermogravimetric data of pyrolysis and combustion processes were simultaneously fitted to determine a single set of kinetic parameters able to describe both processes at the different heating rates. The model proposed achieves a good correlation between the experimental and calculated curves, with an error of less than 4% for fitting four heating rates simultaneously. The experimental results and kinetic parameters may provide useful data for the design of thermo decomposition processing system using corn stover as feedstock. On the other hand, analysis of the main compounds in the evolved gas is given by means of a microcromatograph.

Study of the thermal decomposition of petrochemical sludge in a pilot plant reactor

The pyrolysis of a sludge produced in the waste water treatment plant of an oil refinery was studied in a pilot plant reactor provided with a system for condensation of semivolatile matter. The study comprises experiments at 350, 400, 470 and 530 °C in nitrogen atmosphere. Analysis of all the products obtained (gases, liquids and chars) are presented, with a thermogravimetric study of the char produced and analysis of main components of the liquid. In the temperature range studied, the composition of the gas fraction does not appreciably vary. In the liquids, the light hidrocarbon yield increases with increasing temperature, whereas the aromatic compounds diminish. The decomposition of the solid fraction has been analysed, finding a material that reacts rapidly with oxygen regardless of the conditions it is formed.

Model of Competencies for Decomposition of Human Behavior: Application to Control System of Robots

Humans and machines have shared the same physical space for many years. To share the same space, we want the robots to behave like human beings. This will facilitate their social integration, their interaction with humans and create an intelligent behavior. To achieve this goal, we need to understand how human behavior is generated, analyze tasks running our nerves and how they relate to them. Then and only then can we implement these mechanisms in robotic beings. In this study, we propose a model of competencies based on human neuroregulator system for analysis and decomposition of behavior into functional modules. Using this model allow separate and locate the tasks to be implemented in a robot that displays human-like behavior. As an example, we show the application of model to the autonomous movement behavior on unfamiliar environments and its implementation in various simulated and real robots with different physical configurations and physical devices of different nature. The main result of this study has been to build a model of competencies that is being used to build robotic systems capable of displaying behaviors similar to humans and consider the specific characteristics of robots.

Decomposition of two types of electric wires considering the effect of the metal in the production of pollutants

Combustion runs at 700 °C in a horizontal laboratory furnace were carried out on two different electric wires (PVC and halogen-free wire). Tests were performed in the presence and in the absence of the metal conductor of the wires. The analyses of the polycyclic aromatic hydrocarbons (PAHs), chlorobenzenes (CBzs), chlorophenols (CPhs), mono- to octa-chlorodibenzo-p-dioxin and dibenzofurans (PCDD/Fs), and dioxin-like PCBs are shown. Regarding semivolatile compounds, PAHs production decreases in the presence of metal, while a higher amount of chlorinated compounds are emitted. Respect to the PCDD/Fs, the PVC wire in the presence of metal presents the highest emission, with a much more emission of furans than dioxins. The maximum emission is with 2 or 3 chlorine atom PCDD/Fs. PCBs emission correlates with PCDD/F production and represents 3–4% of total toxicity, determined by using WHO2005 factors.