In this work we study, by simulation in a two dimensional lattice, the influence of diverse param... more In this work we study, by simulation in a two dimensional lattice, the influence of diverse parameters of the interaction potential on the geometry of a system of particles. The geometry of the system is described by means of the scaling behaviour of concentration, quantified by the fractal box-counting dimension, and the configurations are sampled by means of the Metropolis
The molecular reorientation model of Fainerman et al. is conceptually adapted to explain the dyna... more The molecular reorientation model of Fainerman et al. is conceptually adapted to explain the dynamic surface tension behavior in polyelectrolyte/surfactant systems with opposite charges. The equilibrium surface tension curves and the adsorption dynamics may be explained by assuming that there are two different states for surfactant molecules at the interface. One of these states corresponds to the adsorption of the surfactant as monomers, and the other to the formation of a mixed complex at the surface. The model also explains the plateaus that appear in the dynamic surface tension curves and gives a picture of the adsorption process.
The study of community structure has been a hot topic of research over the last years. But, while... more The study of community structure has been a hot topic of research over the last years. But, while successfully applied in several areas, the concept lacks of a general and precise notion. Facts like the hierarchical structure and heterogeneity of complex networks make it difficult to unify the idea of community and its evaluation. The global functional known as modularity is probably the most used technique in this area. Nevertheless, its limits have been deeply studied. Local techniques as the ones by Lancichinetti et al. and Palla et al. arose as an answer to the resolution limit and degeneracies that modularity has. Here we start from the algorithm by Lancichinetti et al. and propose a unique growth process for a fitness function that, while being local, finds a community partition that covers the whole network, updating the scale parameter dynamically. We test the quality of our results by using a set of benchmarks of heterogeneous graphs. We discuss alternative measures for eva...
Running Title: Testing on random trees To distinguish between populations of trees, we consider t... more Running Title: Testing on random trees To distinguish between populations of trees, we consider the hypothesis test proposed recently by Balding, Ferrari, Fraiman and Sued (BFFS–test). A direct approach to calculate effectively the test statistic is quite difficult, since it is based on a supremum defined over the space of all trees, which grows exponentially fast. We show how to transform this problem into a max-flow over a network which can be solved using a Ford Fulkerson algorithm in polynomial time on the maximal number of vertices of the random tree. We also describe conditions that imply the characterization of the measure by the marginal distributions of each node of the random tree, which validate the use of the BFFS–test for measure discrimination. The performance of the test is studied via simulations on Galton-Watson processes.
En este trabajo analizamos algunas tecnicas recientemente introducidas para el analisis de escala... more En este trabajo analizamos algunas tecnicas recientemente introducidas para el analisis de escala de datos experimentales o simulados. El estudio del comportamiento de escala de los coeficientes ondita ha sido propuesto como una extension del analisis multifractal. En el caso de las onditas de Haar se ha comprobado ademas que esta alternativa permite detectar regularidades geometricas que indican una desviacion respecto al comportamiento multifractal; la relacion entre los coeficientes ondita y los contenidos de cajas de los metodos usuales del calculo multifractal es en este caso inmediata. En este trabajo estudiamos estos dos aspectos del comportamiento de escala de los coeficientes ondita usando la base de Daubechies (D4), aplicando el analisis con fines comparativos a algunos casos unidimensionales previamente estudiados, y en dos dimensiones a configuraciones obtenidas por simulacion de Monte Carlo.
In this paper we address the problem of identifying differences between populations of trees. Bes... more In this paper we address the problem of identifying differences between populations of trees. Besides the theoretical relevance of this problem, we are interested in testing if trees characterizing protein sequences from different families constitute samples of significantly different distributions. In this context, trees are obtained by modelling protein sequences as Variable Length Markov Chains (VLMC), estimating the relevant motifs that are sufficient to predict the next amino acid in the sequence. We assign to each protein family an underlying VLMC model, which induces a distribution on the space of all trees. Our goal is to test if two (or more) populations of trees comes from different distributions. Our approach is based on a hypothesis test proposed recently by Balding et al (2004) (BFFS–test), which involves a Kolmogorov type statistics that roughly speaking, maximizes the difference between the expected distance structure that characterize the samples of the populations. ...
Community structure is relevant to understand the properties of social networks and predict their... more Community structure is relevant to understand the properties of social networks and predict their behavior. But when this study includes the dynamic evolution, finding these communities and following them through time can be even more useful: it may help us to understand how social networks grow and to develop constructive models. In this article we analyze a dynamic blog dataset with a static community detection algorithm based on modularity, and then we use a similarity measure in order to follow the communities through time. Finally we develop a tool to visualize the dynamics of the network. This tool provides a fast intuition about the evolution of the community structure.
In this paper we address the problem of identifying differences between populations of trees. An ... more In this paper we address the problem of identifying differences between populations of trees. An example of such populations are estimations of the context tree of a Variable Length Markov Chain, an important modeling tool that have been used recently for protein classification without sequence alignment. Our approach is based on a hypothesis test proposed recently by Balding et al (2004) (BFFS–test), which involves a Kolmogorov type statistics that roughly speaking, maximizes the difference between the expected distance structure that characterize the samples of the populations. This characteristic make it suitable even for applications where the populations have the same expected mean tree, but a different occupancy node probability (marginal expected value) at some node. A naive approach to calculate effectively the test statistic is quite difficult, since it is based on a supremo defined over the space of all trees, which grows exponentially fast. We show how to transform this p...
Modularity was introduced as a measure of goodness for the community structure induced by a parti... more Modularity was introduced as a measure of goodness for the community structure induced by a partition of the set of vertices in a graph. Then, it also became an objective function used to find good partitions, with high success. Nevertheless, some works have shown a scaling limit and certain instabilities when finding communities with this criterion. Modularity has been studied proposing several formalisms, as hamiltonians in a Potts model or laplacians in spectral partitioning. In this paper we present a new probabilistic formalism to analyze modularity, and from it we derive an algorithm based on weakly optimal partitions. This algorithm obtains good quality partitions and also scales to large graphs.
We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "... more We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "contracted diameter less or equal to 2" condition, with minimal degree greater or equal to k, and some natural hypothesis on the edges connecting one graph to the other, the resulting graph is also k-edge-connected.
In this work we study, by simulation in a two dimensional lattice, the influence of diverse param... more In this work we study, by simulation in a two dimensional lattice, the influence of diverse parameters of the interaction potential on the geometry of a system of particles. The geometry of the system is described by means of the scaling behaviour of concentration, quantified by the fractal box-counting dimension, and the configurations are sampled by means of the Metropolis
Resumen Discutimos la autoría del soneto con primer verso «Si las penas que dais son verdaderas»,... more Resumen Discutimos la autoría del soneto con primer verso «Si las penas que dais son verdaderas», por siglos atribuido sin dudas a Cristóbal de Castillejo pero publicado recientemente por varios autores como escrito por Juan Boscán. Pensamos que esta última atribución es errónea, quizás motivada por el título «Soneto de Boscán» que Velasco, editor en 1573 de la obra de Castillejo, le puso a este soneto. La comparación de dos versiones de la obra de Castillejo que incluyen este soneto nos permite apreciar cuán fino poeta era el autor, y cuán escrupuloso en sus revisiones. Abstract We discuss the authorship of the sonnet whose first line is «Si las penas que dais son verdaderas». For centuries it was undoubtedly attributed to Cristóbal de Castillejo but recently it has been published by several authors as written by Juan Boscán. We think that this final allocation is erroneous and it was perhaps motivated by the title "Soneto de Boscán" that Velasco, editor of the work of Castillejo, put to this sonnet in 1573. The comparison of two versions of the work of Castillejo, both including this sonnet, allows us to appreciate what a fine poet the author was, and how careful he was with his revisions.
We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "cont... more We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "contracted diameter less or equal to 2" condition, with minimal degree greater or equal to k, and some natural hypothesis on the edges connecting one graph to the other, the resulting graph is also k-edge-connected.
In this work we study, by simulation in a two dimensional lattice, the influence of diverse param... more In this work we study, by simulation in a two dimensional lattice, the influence of diverse parameters of the interaction potential on the geometry of a system of particles. The geometry of the system is described by means of the scaling behaviour of concentration, quantified by the fractal box-counting dimension, and the configurations are sampled by means of the Metropolis
The molecular reorientation model of Fainerman et al. is conceptually adapted to explain the dyna... more The molecular reorientation model of Fainerman et al. is conceptually adapted to explain the dynamic surface tension behavior in polyelectrolyte/surfactant systems with opposite charges. The equilibrium surface tension curves and the adsorption dynamics may be explained by assuming that there are two different states for surfactant molecules at the interface. One of these states corresponds to the adsorption of the surfactant as monomers, and the other to the formation of a mixed complex at the surface. The model also explains the plateaus that appear in the dynamic surface tension curves and gives a picture of the adsorption process.
The study of community structure has been a hot topic of research over the last years. But, while... more The study of community structure has been a hot topic of research over the last years. But, while successfully applied in several areas, the concept lacks of a general and precise notion. Facts like the hierarchical structure and heterogeneity of complex networks make it difficult to unify the idea of community and its evaluation. The global functional known as modularity is probably the most used technique in this area. Nevertheless, its limits have been deeply studied. Local techniques as the ones by Lancichinetti et al. and Palla et al. arose as an answer to the resolution limit and degeneracies that modularity has. Here we start from the algorithm by Lancichinetti et al. and propose a unique growth process for a fitness function that, while being local, finds a community partition that covers the whole network, updating the scale parameter dynamically. We test the quality of our results by using a set of benchmarks of heterogeneous graphs. We discuss alternative measures for eva...
Running Title: Testing on random trees To distinguish between populations of trees, we consider t... more Running Title: Testing on random trees To distinguish between populations of trees, we consider the hypothesis test proposed recently by Balding, Ferrari, Fraiman and Sued (BFFS–test). A direct approach to calculate effectively the test statistic is quite difficult, since it is based on a supremum defined over the space of all trees, which grows exponentially fast. We show how to transform this problem into a max-flow over a network which can be solved using a Ford Fulkerson algorithm in polynomial time on the maximal number of vertices of the random tree. We also describe conditions that imply the characterization of the measure by the marginal distributions of each node of the random tree, which validate the use of the BFFS–test for measure discrimination. The performance of the test is studied via simulations on Galton-Watson processes.
En este trabajo analizamos algunas tecnicas recientemente introducidas para el analisis de escala... more En este trabajo analizamos algunas tecnicas recientemente introducidas para el analisis de escala de datos experimentales o simulados. El estudio del comportamiento de escala de los coeficientes ondita ha sido propuesto como una extension del analisis multifractal. En el caso de las onditas de Haar se ha comprobado ademas que esta alternativa permite detectar regularidades geometricas que indican una desviacion respecto al comportamiento multifractal; la relacion entre los coeficientes ondita y los contenidos de cajas de los metodos usuales del calculo multifractal es en este caso inmediata. En este trabajo estudiamos estos dos aspectos del comportamiento de escala de los coeficientes ondita usando la base de Daubechies (D4), aplicando el analisis con fines comparativos a algunos casos unidimensionales previamente estudiados, y en dos dimensiones a configuraciones obtenidas por simulacion de Monte Carlo.
In this paper we address the problem of identifying differences between populations of trees. Bes... more In this paper we address the problem of identifying differences between populations of trees. Besides the theoretical relevance of this problem, we are interested in testing if trees characterizing protein sequences from different families constitute samples of significantly different distributions. In this context, trees are obtained by modelling protein sequences as Variable Length Markov Chains (VLMC), estimating the relevant motifs that are sufficient to predict the next amino acid in the sequence. We assign to each protein family an underlying VLMC model, which induces a distribution on the space of all trees. Our goal is to test if two (or more) populations of trees comes from different distributions. Our approach is based on a hypothesis test proposed recently by Balding et al (2004) (BFFS–test), which involves a Kolmogorov type statistics that roughly speaking, maximizes the difference between the expected distance structure that characterize the samples of the populations. ...
Community structure is relevant to understand the properties of social networks and predict their... more Community structure is relevant to understand the properties of social networks and predict their behavior. But when this study includes the dynamic evolution, finding these communities and following them through time can be even more useful: it may help us to understand how social networks grow and to develop constructive models. In this article we analyze a dynamic blog dataset with a static community detection algorithm based on modularity, and then we use a similarity measure in order to follow the communities through time. Finally we develop a tool to visualize the dynamics of the network. This tool provides a fast intuition about the evolution of the community structure.
In this paper we address the problem of identifying differences between populations of trees. An ... more In this paper we address the problem of identifying differences between populations of trees. An example of such populations are estimations of the context tree of a Variable Length Markov Chain, an important modeling tool that have been used recently for protein classification without sequence alignment. Our approach is based on a hypothesis test proposed recently by Balding et al (2004) (BFFS–test), which involves a Kolmogorov type statistics that roughly speaking, maximizes the difference between the expected distance structure that characterize the samples of the populations. This characteristic make it suitable even for applications where the populations have the same expected mean tree, but a different occupancy node probability (marginal expected value) at some node. A naive approach to calculate effectively the test statistic is quite difficult, since it is based on a supremo defined over the space of all trees, which grows exponentially fast. We show how to transform this p...
Modularity was introduced as a measure of goodness for the community structure induced by a parti... more Modularity was introduced as a measure of goodness for the community structure induced by a partition of the set of vertices in a graph. Then, it also became an objective function used to find good partitions, with high success. Nevertheless, some works have shown a scaling limit and certain instabilities when finding communities with this criterion. Modularity has been studied proposing several formalisms, as hamiltonians in a Potts model or laplacians in spectral partitioning. In this paper we present a new probabilistic formalism to analyze modularity, and from it we derive an algorithm based on weakly optimal partitions. This algorithm obtains good quality partitions and also scales to large graphs.
We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "... more We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "contracted diameter less or equal to 2" condition, with minimal degree greater or equal to k, and some natural hypothesis on the edges connecting one graph to the other, the resulting graph is also k-edge-connected.
In this work we study, by simulation in a two dimensional lattice, the influence of diverse param... more In this work we study, by simulation in a two dimensional lattice, the influence of diverse parameters of the interaction potential on the geometry of a system of particles. The geometry of the system is described by means of the scaling behaviour of concentration, quantified by the fractal box-counting dimension, and the configurations are sampled by means of the Metropolis
Resumen Discutimos la autoría del soneto con primer verso «Si las penas que dais son verdaderas»,... more Resumen Discutimos la autoría del soneto con primer verso «Si las penas que dais son verdaderas», por siglos atribuido sin dudas a Cristóbal de Castillejo pero publicado recientemente por varios autores como escrito por Juan Boscán. Pensamos que esta última atribución es errónea, quizás motivada por el título «Soneto de Boscán» que Velasco, editor en 1573 de la obra de Castillejo, le puso a este soneto. La comparación de dos versiones de la obra de Castillejo que incluyen este soneto nos permite apreciar cuán fino poeta era el autor, y cuán escrupuloso en sus revisiones. Abstract We discuss the authorship of the sonnet whose first line is «Si las penas que dais son verdaderas». For centuries it was undoubtedly attributed to Cristóbal de Castillejo but recently it has been published by several authors as written by Juan Boscán. We think that this final allocation is erroneous and it was perhaps motivated by the title "Soneto de Boscán" that Velasco, editor of the work of Castillejo, put to this sonnet in 1573. The comparison of two versions of the work of Castillejo, both including this sonnet, allows us to appreciate what a fine poet the author was, and how careful he was with his revisions.
We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "cont... more We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "contracted diameter less or equal to 2" condition, with minimal degree greater or equal to k, and some natural hypothesis on the edges connecting one graph to the other, the resulting graph is also k-edge-connected.
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Papers by Jorge Busch