Compressão fractal de imagens

Neste trabalho será apresentado um método recente de compressão de imagens baseado na teoria dos Sistemas de Funções Iteradas (SFI), designado por Compressão Fractal. Descrever-se-á um modelo contínuo para a compressão fractal sobre o espaço métrico completo Lp, onde será definido um operador de transformação fractal contractivo associado a um SFI local com aplicações. Antes disso, será introduzida a teoria dos SFIs no espaço de Hausdorff ou espaço fractal, a teoria dos SFIs Locais - uma generalização dos SFIs - e dos SFIs no espaço Lp. Fornecida a fundamentação teórica para o método será apresentado detalhadamente o algoritmo de compressão fractal. Serão também descritas algumas estratégias de particionamento necessárias para encontrar o SFI com aplicações, assim como, algumas estratégias para tentar colmatar o maior entrave da compressão fractal: a complexidade de codificação. Esta dissertação assumirá essencialmente um carácter mais teórico e descritivo do método de compressão fractal, e de algumas técnicas, já implementadas, para melhorar a sua eficácia.

Porosity imaged by a vector projection algorithm correlates with fractal dimension measured on 3D models obtained by microCT

International audience

Propuesta metodológica para el estudio de las nociones fundamentales de sistemas dinámicos, geometría fractal y teoría del caos usando el software Mathematica

Las matemáticas, como muchas otras áreas del pensamiento, han sufrido en el tercio central del siglo XX el impacto de la corriente filosófica estructuralista. Esta tendía a desplazar el centro de atención hacia los problemas de fundamentación por una parte, y por otra subrayaba la importancia de las estructuras abstractas como la de conjunto, grupo u otras, que se presentan en diversas áreas de las matemáticas. En general la corriente estructuralista impregna a las matemáticas de los métodos del álgebra y es compañera inevitable de una tendencia hacia la abstracción. El estructuralismo ha estado lejos de ser un factor determinante en el desarrollo de la producción matemática en el último siglo, ya que el volumen ingente de investigación volcada hacia las aplicaciones ha pesado de forma decisiva en el resultado global. Sin embargo, es en el ámbito de la enseñanza de las matemáticas donde la influencia del estructuralismo ha sido más profunda, penetrando en los programas a todos los niveles educativos y provocando que al estudiar matemáticas, los estudiantes se queden con la impresión de que no hay nada nuevo en matemáticas desde Euclides o Pitágoras, es decir, desde hace más de 2000 años. Con un poco de suerte, algunos se cree que las matemáticas dejaron de desarrollarse después de la creación del cálculo diferencial e integral (hace unos 300 años), en cambio no tenemos la misma impresión sobre otras ciencias como física, química o biología. La geometría fractal, cuyos primeros desarrollos datan de finales del siglo XIX, ha recibido durante los últimos treinta años, desde la publicación de los trabajos de Mandelbrot, una atención y un auge crecientes. Lejos de ser simplemente una herramienta de generación de impresionantes paisajes virtuales, la geometría fractal viene avalada por la teoría geométrica de la medida y por innumerables aplicaciones en ciencias tan dispares como la Física, la Química, la Economía o, incluso, la Informática.

ENGINEERING HIERARCHICAL MESO-/MICROPOROUS LAMELLAR ZEOLITES WITH VARIABLE TEXTURAL AND CATALYTIC PROPERTIES

Meso-/microporous zeolites combine the charactersitics of well-defined micropores of zeolite with efficient mass transfer consequences of mesopores to increase the efficiency of the catalysts in reactions involving bulky molecules. Different methods such as demetallation and templating have been explored for the synthesis of meso-/microporous zeolites. However, they all have limitations in production of meso-/microporous zeolites with tunable textural and catalytic properties using few synthesis steps. To address this challenge, a simple one-step dual template synthesis approach has been developed in this work to engineer lamellar meso-/microporous zeolites structures with tunable textural and catalytic properties. First, one-step dual template synthesis of meso-/microporous mordenite framework inverted (MFI) zeolite structures was investigated. Tetrapropyl ammonium hydroxide (TPAOH) and diquaternary ammonium surfactant ([C22H45-N+(CH3)2-C6H12-N+(CH3)2-C6H13]Br2, C22-6-6) were used as templates to produce micropores and mesopores, respectively. The variation in concentration ratios of dual templates and hydrothermal synthesis conditions resulted in production of multi-lamellar MFI and the hybrid lamellar-bulk MFI (HLBM) zeolite structures. The relationship between the morphology, porosity, acidity, and catalytic properties of these catalysts was systematically studied. Then, the validity of the proposed synthesis approach for production of other types of zeolites composites was examined by creating a meso-/microporous bulk polymorph A (BEA)-lamellar MFI (BBLM) composite. The resulted composite samples showed higher catalytic stability compared to their single component zeolites. The studies demonstrated the high potential of the one-step dual template synthesis procedure for engineering the textural and catalytic properties of the synthesized zeolites.

Entropy production in the early-cosmology pionic phase

We point out that in the early universe, for temperatures in the approximate interval 150-80 MeV (after the quark-gluon plasma), pions carried a large share of the entropy and supported the largest inhomogeneities. Its thermal conductivity (previously calculated) allows the characterization of entropy production due to equilibration (damping) of thermal fluctuations. Simple model distributions of thermal fluctuations are considered and the associated entropy production evaluated.

Detecting Free Riders in Collective Brands through a Hierarchical Choice Process

Free-riding behaviors exist in tourism and they should be analyzed from a comprehensive perspective; while the literature has mainly focused on free riders operating in a destination, the destinations themselves might also free ride when they are under the umbrella of a collective brand. The objective of this article is to detect potential free-riding destinations by estimating the contribution of the different individual destinations to their collective brands, from the point of view of consumer perception. We argue that these individual contributions can be better understood by reflecting the various stages that tourists follow to reach their final decision. A hierarchical choice process is proposed in which the following choices are nested (not independent): “whether to buy,” “what collective brand to buy,” and “what individual brand to buy.” A Mixed Logit model confirms this sequence, which permits estimation of individual contributions and detection of free riders.

Local optimal scale in a hierarchical segmentation method for satellite image: an OBIA approach for the agricultural landscape

Overrecentdecades,remotesensinghasemergedasaneffectivetoolforimprov- ing agriculture productivity. In particular, many works have dealt with the problem of identifying characteristics or phenomena of crops and orchards on different scales using remote sensed images. Since the natural processes are scale dependent and most of them are hierarchically structured, the determination of optimal study scales is mandatory in understanding these processes and their interactions. The concept of multi-scale/multi- resolution inherent to OBIA methodologies allows the scale problem to be dealt with. But for that multi-scale and hierarchical segmentation algorithms are required. The question that remains unsolved is to determine the suitable scale segmentation that allows different objects and phenomena to be characterized in a single image. In this work, an adaptation of the Simple Linear Iterative Clustering (SLIC) algorithm to perform a multi-scale hierarchi- cal segmentation of satellite images is proposed. The selection of the optimal multi-scale segmentation for different regions of the image is carried out by evaluating the intra- variability and inter-heterogeneity of the regions obtained on each scale with respect to the parent-regions defined by the coarsest scale. To achieve this goal, an objective function, that combines weighted variance and the global Moran index, has been used. Two different kinds of experiment have been carried out, generating the number of regions on each scale through linear and dyadic approaches. This methodology has allowed, on the one hand, the detection of objects on different scales and, on the other hand, to represent them all in a sin- gle image. Altogether, the procedure provides the user with a better comprehension of the land cover, the objects on it and the phenomena occurring.

Zoroastrianism, Cosmology, and Chaos: A Detailed Analysis of the Musical Composition, Druj Aeterni

Druj Aeterni is a large chamber ensemble piece for flute, clarinet, French horn, two trumpets, piano, two percussionists, string quintet, and electric bass. My composition integrates three intellectual pursuits and interests, ancient mythology, cosmology, and mathematics. The title of the piece uses Latin and the language of the Avesta, the holy book of Zoroastrianism, and comments upon a philosophical perspective based in string theory. I abstract the cosmological implications of string theory, apply them to the terminology and theology of Zoroastrianism, and then structure the composition in consideration of a possible reconciliation. The analysis that follows incorporates analytical techniques similar to David Cope’s style of Vectoral Analysis.

A Convenient Verisimilitude or Oppressive Internalization? Characterizing the Ethical Arguments surrounding Hierarchical Structures in Knowledge Organization Systems

This paper considers the ethical concerns that surface around hierarchy as structure in knowledge organization systems. In order to do this, I consider the relationship between semantics and structure and argue for a separation of the two in design and critique of knowledge organization systems. The paper closes with an argument that agency and intention, as ethical concerns in knowledge organization, lead us to argue for a neutral stance on hierarchy.

Caveat Fractal: Dissecting the Body of Indexing Theory, Uncovering Complexity, and Moving Toward Performativity

Research poster about indexing theory

Sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution

Understanding how virus strains offer protection against closely related emerging strains is vital for creating effective vaccines. For many viruses, including Foot-and-Mouth Disease Virus (FMDV) and the Influenza virus where multiple serotypes often co-circulate, in vitro testing of large numbers of vaccines can be infeasible. Therefore the development of an in silico predictor of cross-protection between strains is important to help optimise vaccine choice. Vaccines will offer cross-protection against closely related strains, but not against those that are antigenically distinct. To be able to predict cross-protection we must understand the antigenic variability within a virus serotype, distinct lineages of a virus, and identify the antigenic residues and evolutionary changes that cause the variability. In this thesis we present a family of sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution (SABRE), as well as an extended version of the method, the extended SABRE (eSABRE) method, which better takes into account the data collection process. The SABRE methods are a family of sparse Bayesian hierarchical models that use spike and slab priors to identify sites in the viral protein which are important for the neutralisation of the virus. In this thesis we demonstrate how the SABRE methods can be used to identify antigenic residues within different serotypes and show how the SABRE method outperforms established methods, mixed-effects models based on forward variable selection or l1 regularisation, on both synthetic and viral datasets. In addition we also test a number of different versions of the SABRE method, compare conjugate and semi-conjugate prior specifications and an alternative to the spike and slab prior; the binary mask model. We also propose novel proposal mechanisms for the Markov chain Monte Carlo (MCMC) simulations, which improve mixing and convergence over that of the established component-wise Gibbs sampler. The SABRE method is then applied to datasets from FMDV and the Influenza virus in order to identify a number of known antigenic residue and to provide hypotheses of other potentially antigenic residues. We also demonstrate how the SABRE methods can be used to create accurate predictions of the important evolutionary changes of the FMDV serotypes. In this thesis we provide an extended version of the SABRE method, the eSABRE method, based on a latent variable model. The eSABRE method takes further into account the structure of the datasets for FMDV and the Influenza virus through the latent variable model and gives an improvement in the modelling of the error. We show how the eSABRE method outperforms the SABRE methods in simulation studies and propose a new information criterion for selecting the random effects factors that should be included in the eSABRE method; block integrated Widely Applicable Information Criterion (biWAIC). We demonstrate how biWAIC performs equally to two other methods for selecting the random effects factors and combine it with the eSABRE method to apply it to two large Influenza datasets. Inference in these large datasets is computationally infeasible with the SABRE methods, but as a result of the improved structure of the likelihood, we are able to show how the eSABRE method offers a computational improvement, leading it to be used on these datasets. The results of the eSABRE method show that we can use the method in a fully automatic manner to identify a large number of antigenic residues on a variety of the antigenic sites of two Influenza serotypes, as well as making predictions of a number of nearby sites that may also be antigenic and are worthy of further experiment investigation.

Hierarchical spatial segregation of two Mediterranean vole species: the role of patch‑network structure and matrix composition

According to ecological theory, the coexistence of competitors in patchy environments may be facilitated by hierarchical spatial segregation along axes of environmental variation, but empirical evidence is limited. Cabrera and water voles show a metapopulation-like structure in Mediterranean farmland, where they are known to segregate along space, habitat, and time axes within habitat patches. Here, we assess whether segregation also occurs among and within landscapes, and how this is influenced by patch-network and matrix composition. We surveyed 75 landscapes, each covering 78 ha, where we mapped all habitat patches potentially suitable for Cabrera and water voles, and the area effectively occupied by each species (extent of occupancy). The relatively large water vole tended to be the sole occupant of landscapes with high habitat amount but relatively low patch density (i.e., with a few large patches), and with a predominantly agricultural matrix, whereas landscapes with high patch density (i.e.,many small patches) and low agricultural cover, tended to be occupied exclusively by the small Cabrera vole. The two species tended to co-occur in landscapes with intermediate patch-network and matrix characteristics, though their extents of occurrence were negatively correlated after controlling for environmental effects. In combination with our previous studies on the Cabrera-water vole system, these findings illustrated empirically the occurrence of hierarchical spatial segregation, ranging from withinpatches to among-landscapes. Overall, our study suggests that recognizing the hierarchical nature of spatial segregation patterns and their major environmental drivers should enhance our understanding of species coexistence in patchy environments.

Análisis de la dimensión fractal del género Quercus en el sur de Italia

En estudios anteriores propusimos un nuevo método para el estudio del género Quercus (Musarella et al., 2013), baseado en la dimensión fractal (DF). En este trabajo analizamos la DF del género Quercus en el sur de Italia, para ello utilizamos hojas de árboles pertenecientes a Q. robur subsp. brutia, Q. cerris, Q. congesta, Q. crenata, Q. ilex, Q. suber, Q. virginiana. De cada árbol se toman hojas de cada uno de los puntos cardinales para complejiada de la estructura morfológica de las hojas. Este análisis extrae información sobre los caracteres fenotípicos de las hojas utilizadas, tales como el número y morfologia de los nervios, ángulos nervios secundarios con principal, contorno de hojas, aspecto reticulado de la hoja etc. En nuestro análisis, no se han detectado diferencias significativas entre la DF en cada una de la orientaciones y la DF global para cada una de las especies. En este trabajo corroboramos estudios anteriores realizados por los autores, en los que se proponía una DF < 1,6 para Quercus esclerófilos y DF entre dos especies sea cero o su cociente sea uno, el grado de parentesco entre las dos especies es del 100%; DFA - DFB = 0; DFA/DFB = 1, la especie Ay B son iguales; por ello cuanto menor es la diferencia o bien cuanto más se acerque el cociente a 1, mayor es la semejanza entre las especies. Si este cociente tiene un valor alejado de 1 como ocurre entre vfvi/vfsu>2, las especies Q. virginiana y Q. suber están muy distantes entre sí. Además, la realización del Test de Rango Múltiple, que es un procedimiento de comparación para determinar cuáles medias son significativamente diferentes unas de otras, confirma los resultados obtenidos de la forma anteriormente expuesta. Conto et al. (2007) ponen de manifiesto el origen hibridógeno de Q. crenata, y según el análisis molecular existe una mayor similitud genética entre Q. crenata y Q. cerris, que entre Q. crenata y Q. suber. Los DF de Q. crenata 1,868; Q. cerris 1,677 y Q. suber 0,932; siendo DFQsu 0,745 y DFQsu = 1,8, lo que significa que existe gran diferencia fenotípica (genética) entre los parentales, se presenta una mayor semejanza entre Q. crenata y Q. cerris que entre Q. crenata y Q. suber, ya que la diferencia DFQcr-DFQce = 0,191 y DFQcr/DFQce = 1,1, por lo que tienen un fuerte grado de semejanza, mientras que DFQcr-DFQsu = 0,936 y DFQcr/DFQsu > 2, lo que pone de manifiesto las fuertes diferencias fenotípicas entre el híbrido y el parental.

Non-hierarchical cluster analysis for body weight, age at first egg, egg production and egg weight in a laying hen strain.

2016