The Peano curve and counting occurrences of some patterns

We introduce Peano words, which are words corresponding to finite approximations of the Peano space filling curve. We then find the number of occurrences of certain patterns in these words.Comment: 9 pages, 1 figur

The sigma-sequence and counting occurrences of some patterns, subsequences and subwords

We consider sigma-words, which are words used by Evdokimov in the construction of the sigma-sequence. We then find the number of occurrences of certain patterns and subwords in these words.Comment: 10 page

Tag-systems for the Hilbert curve

Hilbert words correspond to finite approximations of the Hilbert space filling curve. The Hilbert infinite word H is obtained as the limit of these words. It gives a description of the Hilbert (infinite) curve. We give a uniform tag-system to generate automatically H and, by showing that it is almost cube-free, we prove that it cannot be obtained by simply iterating a morphism

Mapping boundaries of generative systems for design synthesis

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2007.Page 123 blank.Includes bibliographical references (p. 121-122).Architects have been experimenting with generative systems for design without a clear reference or theory of what, why or how to deal with such systems. In this thesis I argue for three points. The first is that generative systems in architecture are implemented at a skin-deep level as they are only used to synthesize form within confined domains. The second is that such systems can be only implemented if a design formalism is defined. The third is that generative systems can be deeper integrated within a design process if they were coupled with performance-based evaluation methods. These arguments are discussed in four chapters: 1- Introduction: a panoramic view of generative systems in architecture and in. computing mapping their occurrences and implementations. 2- Generative Systems for Design: highlights on integrating generative systems in architecture design processes; and discussions on six generative systems including: Algorithmic, Parametrics, L-systems, Cellular Automata, Fractals and Shape Grammars. 3- Provisional taxonomy: A summery table of systems properties and a classification of generative systems properties as discussed in the previous chapter 4- Conclusion: comments and explanations on why such systems are simplicity implemented within design.by Maher El-Khaldi.S.M

Integrated analysis of gene expression by association rules discovery

BACKGROUND: Microarray technology is generating huge amounts of data about the expression level of thousands of genes, or even whole genomes, across different experimental conditions. To extract biological knowledge, and to fully understand such datasets, it is essential to include external biological information about genes and gene products to the analysis of expression data. However, most of the current approaches to analyze microarray datasets are mainly focused on the analysis of experimental data, and external biological information is incorporated as a posterior process. RESULTS: In this study we present a method for the integrative analysis of microarray data based on the Association Rules Discovery data mining technique. The approach integrates gene annotations and expression data to discover intrinsic associations among both data sources based on co-occurrence patterns. We applied the proposed methodology to the analysis of gene expression datasets in which genes were annotated with metabolic pathways, transcriptional regulators and Gene Ontology categories. Automatically extracted associations revealed significant relationships among these gene attributes and expression patterns, where many of them are clearly supported by recently reported work. CONCLUSION: The integration of external biological information and gene expression data can provide insights about the biological processes associated to gene expression programs. In this paper we show that the proposed methodology is able to integrate multiple gene annotations and expression data in the same analytic framework and extract meaningful associations among heterogeneous sources of data. An implementation of the method is included in the Engene software package

Fractals and implications for mineral favorability maps: the example of iron oxide-copper-gold deposits from Carajás (PA)

Orientadores: Carlos Roberto de Souza Filho, Emmanuel John Muico CarranzaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de GeociênciasResumo: Desde a definição do conceito da geometria fractal na segunda metade do século XX, a importância dos fractais para a descrição e entendimento de feições geológicas gradualmente ganhou importância. Mais recentemente, diversos trabalhos têm sugerido que a distribuição espacial de depósitos minerais apresenta geometria fractal, a qual representaria a complexa interação de processos geológicos necessários para a gênese de uma mineralização. A manifestação da geometria fractal se dá através da invariância escalar, ou seja, a propriedade de uma feição conservar suas características geométricas independente da escala espacial. Esta característica é promissora para o estudo de depósitos minerais, pois sugere a possibilidade de que informações sobre a geometria da mineralização em uma escala possa ser usada para inferir aspectos da geometria em outras escalas. Uma vez que a geometria das mineralizações é consequência dos controles que atuaram durante e após sua formação, a possibilidade de estudos com uma abordagem fractal tem aplicações teóricas e práticas. Considerando o exposto, a presente pesquisa dedicou-se a investigar se de fato a geometria de depósitos minerais apresenta invariância escalar, e em caso positivo, que informações ela permite inferir sobre os controles de mineralização. Para esta investigação foi escolhida como área de estudo a região do depósito Iron Oxide-Copper-Gold (IOCG) de Sossego, na Província Mineral de Carajás (PA). Depósitos IOCG apresentam forte controle estrutural, que somados a farta disponibilidade de dados nas escalas regional, local e microscópica tornam a área da mina de Sossego ideal para a pesquisa proposta. Assim, os dados já disponíveis na literatura foram integrados com novas medidas estruturais e novas lâminas orientadas de amostras coletadas nas cavas da mina. A geometria da mineralização foi avaliada em três diferentes escalas: na escala regional examinou-se a distribuição espacial dos depósitos IOCG conhecidos; na escala local examinou-se a geometria das estruturas e corpos mineralizados no depósito de Sossego; na escala microscópica foi avaliada a geometria da distribuição espacial e da forma dos grãos de minerais de minério. O conjunto de resultados indica que os depósitos IOCG da região de Carajás, e em particular o depósito de Sossego, apresentam geometria fractal, conservando a orientação e anisotropia nas diferentes escalas. A orientação e anisotropia das mineralizações são aspectos geométricos que resultam diretamente do controle exercido pela trama estrutural subjacente. Desta forma, os resultados indicam que o controle estrutural gera a invariância escalar devido à influência que exerce sobre a permeabilidade das rochas, um fator essencial para a geração de depósitos hidrotermais. A permeabilidade é definida em escala microscópica através de planos de foliação, microfraturas e vênulas, as quais se relacionam diretamente com estruturas de escalas maiores, tais como zonas de cisalhamento, falhas e veios, criando uma rede permeável consistente através das escalas. No caso de Carajás, a geometria destas áreas permeáveis reflete a interação entre uma trama dúctil anterior, de permeabilidade difusa, e uma trama rúptil posterior, com permeabilidade focada. Os resultados deste trabalho sugerem que a abordagem fractal para o estudo da gênese de depósitos minerais tem potencial concreto para gerar resultados relevantes, inclusive para a avaliação da favorabilidade mineral de áreas em exploraçãoAbstract: Since the concept of fractal geometry was defined in the second half of the twentieth century, the importance of fractals for the description and understanding of geological features has gradually gained importance. More recent work has suggested that the spatial distribution of mineral deposits presents fractal geometry, which represents the complex interaction of geological processes necessary for the genesis of a mineralization. The manifestation of fractal geometry occurs through scale invariance, i.e. the property of a feature that conserves its geometrical characteristics independent of the spatial scale. This property is promising for the study of mineral deposits because it suggests the possibility that information about the geometry of a mineralization at one scale can be used to infer aspects of its geometry at other scales. Since mineralization geometry is a consequence of controls that acted during and after its formation, studies with a fractal approach have theoretical and practical applications. Considering the above, the present research investigated if the geometry of mineral deposits presents scale invariance, and if so, what information it permits to infer about the mineralization controls. For this investigation the study area chosen was the iron oxide-copper-gold (IOCG) Sossego deposit, in the Carajás Mineral Province (PA). IOCG deposits present strong structural control, which taken in conjunction with data availability at the regional, local and microscopic scales make the Sossego deposit area ideal for the proposed research. Thus, data already available in the literature were integrated with new structural measurements and new oriented thin sections of samples collected in the mine pits. Mineralization geometry was evaluated at three different scales: in the regional scale the spatial distribution of the known IOCG deposits was examined; in the local scale the geometry of the mineralized structures and orebodies at the Sossego deposit was examined; in the microscale the geometry of the spatial distribution and the shape of ore mineral grains were evaluated. The bulk of results indicate that the IOCG deposits of Carajás province, and in particular the Sossego deposit, present fractal geometry, conserving the orientation and anisotropy at the different scales. The orientation and anisotropy of the mineralization are geometric aspects that result directly from the control exerted by the underlying structural framework. As a consequence, the results indicate that the structural control generates the scale invariance due to its influence on rock permeability, an essential factor for the genesis of hydrothermal deposits. Permeability is defined at the microscale through foliation planes, microfractures and veinlets, which are directly related to structures of larger scales, such as shear zones, faults and veins, creating a consistent permeable network throughout the scales. In the case of Carajás, the geometry of these permeable areas reflects the interaction between an older ductile framework with diffuse permeability, and a posterior brittle network with focused permeability. The results of this work suggest that the fractal approach to the study of the genesis of mineral deposits has concrete potential to generate relevant results, including for the evaluation of the mineral favorability on exploration areasMestradoGeologia e Recursos NaturaisMestre em Geociências2015/11186-3401316/2014-9CAPESFAPESPCNP

Modeling memory effects in activity-driven networks

Activity-driven networks (ADNs) have recently emerged as a powerful paradigm to study the temporal evolution of stochastic networked systems. All the information on the time-varying nature of the system is encapsulated into a constant activity parameter, which represents the propensity to generate connections. This formulation has enabled the scientific community to perform effective analytical studies on temporal networks. However, the hypothesis that the whole dynamics of the system is summarized by constant parameters might be excessively restrictive. Empirical studies suggest that activity evolves in time, intertwined with the system evolution, causing burstiness and clustering phenomena. In this paper, we propose a novel model for temporal networks, in which a self-excitement mechanism governs the temporal evolution of the activity, linking it to the evolution of the networked system. We investigate the effect of self-excitement on the epidemic inception by comparing the epidemic threshold of a Susceptible-Infected-Susceptible model in the presence and in the absence of the self-excitement mechanism. Our results suggest that the temporal nature of the activity favors the epidemic inception. Hence, neglecting self-excitement mechanisms might lead to harmful underestimation of the risk of an epidemic outbreak. Extensive numerical simulations are presented to support and extend our analysis, exploring parameter heterogeneities and noise, transient dynamics, and immunization processes. Our results constitute a first, necessary step toward a theory of ADNs that accounts for memory effects in the network evolution

Use of Colour in Machine Vision: Colour Representation, Edge Detection with Colour, Segmentation of Colour Space and Colour Constancy

This report is a study of the role of colour and its use in machine vision. Intuitively, for low level image processing, colour provides greater discrimination than grey level for separating different homogenous regions in an image. The first part describes the use of colour in edge detection. In current vision systems, extracting object features such as lines and arcs relies on edge detection. The use of colour images (RGB) can offer additional confidence in the existence of an edge element in one plane when it is corroborated by pixels at the location on one or more of the other planes. The second part investigates the problems and techniques associated with colour image segmentation. A spectral segmentation algorithm based on locating the boundaries of each colour cluster in the spectral space is proposed. The third part investigates the use of colour features for object recognition. Colour information also provides a useful cue for object localisation and identification. The major issues that have to be addressed are colour constancy and representation, and also, their connections to segmentation. Finally, a system for locating object surfaces based on a simplified colour constancy and its colour representation is proposed

Extreme rainfall, flood scaling and flood policy options in the United States

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering; and, (S.M.)--Massachusetts Institute of Technology, Engineering Systems Division, 2000.Includes bibliographical references (leaves 220-227).River flood and rainfall have been shown to exhibit scale invariance behavior over a range of space and time scales. Although various approaches have been taken to investigate and model the various scaling aspects of rainfall and floods, little theoretical work has been done on the relation between the scaling of rainfall and flood. If available, such a theory would provide frequency estimate for extreme rainfall and floods outside the range of observations and could also be used to estimate floods at ungaged basins. The relationship between rainfall and flood scaling is the main focus of this thesis. We use a two step approach to investigate the relationship between exponent of peak flows and the scaling of rain. First, we use data analysis to verify existing theories that relate the multi scaling behavior of rainfall to the simple scaling behavior of the IDFs. Second, we use a model to relate the scaling of the IDFs to the scaling of peak flows with basin area. We find that, although temporal rainfall shows multiscaling, the IDFs exhibit simple scaling and peak floods show simple or mild multiscaling. We validate our findings by using U.S. peak annual flow data and rainfall from a few New England stations. Extreme floods damage mitigation requires sound and integrated policy making. We review the flood disaster mitigation situation in the U.S., carry out policy analysis and recommend options for a successful and sustainable flood disaster policy in the U.S.by Babar Mahmood Bhatti.S.M

Optimisation of surface coverage paths used by a non-contact robot painting system

This thesis proposes an efficient path planning technique for a non-contact optical “painting” system that produces surface images by moving a robot mounted laser across objects covered in photographic emulsion. In comparison to traditional 3D planning approaches (e.g. laminar slicing) the proposed algorithm dramatically reduces the overall path length by optimizing (i.e. minimizing) the amounts of movement between robot configurations required to position and orientate the laser. To do this the pixels of the image (i.e. points on the surface of the object) are sequenced using configuration space rather than Cartesian space. This technique extracts data from a CAD model and then calculates the configuration that the five degrees of freedom system needs to assume to expose individual pixels on the surface. The system then uses a closest point analysis on all the major joints to sequence the points and create an efficient path plan for the component. The implementation and testing of the algorithm demonstrates that sequencing points using a configuration based method tends to produce significantly shorter paths than other approaches to the sequencing problem. The path planner was tested with components ranging from simple to complex and the paths generated demonstrated both the versatility and feasibility of the approach