Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

A fuzzy probabilistic inference methodology for constrained 3D human motion classification

Enormous uncertainties in unconstrained human motions lead to a fundamental challenge that many recognising algorithms have to face in practice: efficient and correct motion recognition is a demanding task, especially when human kinematic motions are subject to variations of execution in the spatial and temporal domains, heavily overlap with each other,and are occluded. Due to the lack of a good solution to these problems, many existing methods tend to be either effective but computationally intensive or efficient but vulnerable to misclassification. This thesis presents a novel inference engine for recognising occluded 3D human motion assisted by the recognition context. First, uncertainties are wrapped into a fuzzy membership function via a novel method called Fuzzy Quantile Generation which employs metrics derived from the probabilistic quantile function. Then, time-dependent and context-aware rules are produced via a genetic programming to smooth the qualitative outputs represented by fuzzy membership functions. Finally, occlusion in motion recognition is taken care of by introducing new procedures for feature selection and feature reconstruction. Experimental results demonstrate the effectiveness of the proposed framework on motion capture data from real boxers in terms of fuzzy membership generation, context-aware rule generation, and motion occlusion. Future work might involve the extension of Fuzzy Quantile Generation in order to automate the choice of a probability distribution, the enhancement of temporal pattern recognition with probabilistic paradigms, the optimisation of the occlusion module, and the adaptation of the present framework to different application domains.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A methodology for landscape characterisation based on GIS and spatially constrained multivariate analysis

Landscape is about the relationship between people and place and in 2000 was defined by the European Landscape Commission (ELC) as "an area as perceived by people whose character is the result of natural and human actions and interactions”. In the 70s the reason for studying the landscape was because of the necessity of attributing a value to it. Nowadays the motivations behind managing, conserving and enhancing the landscape is because the landscape is the place where people belong to and, consciously or not, recognise themselves. In addition, people identify different landscapes on the basis of the particular combinations of the elements in the landscape. As a consequence a landscape can be distinguished from another on the basis of its character which, according to the Landscape Character Assessment (LCA) guidance for England and Scotland (C. Swanwick and Land Use Consultant, 2002), is defined as “a distinct, recognisable and consistent pattern of elements in the landscape that makes one landscape different from the other rather than better or worse”. This definition was the starting point of a PhD research project aimed at developing and implementing a methodology able to identify and quantify the character of the Scottish landscape through the application of GIS and statistics. The reason for doing this research was to provide the landscape architects and practitioners with a tool that could help them to define the landscape character types in a more consistent, objective, and scientifically robust way. One of the objectives of the research was to identify the spatial patterns formed by the landscape elements by taking into account the influence of the spatial location. The first law of geography, which states that "everything is related to everything else but near things are more related than distant ones" (W Tobler, 1970), was transposed in the assumption of the presence of spatial autocorrelation amongst the data which contributes to form spatial patterns within the data. Since landscape comprises of many elements, data were also multivariate, thus the analysis required a method of calculation able to deal simultaneously with multivariate and spatial autocorrelation issues. MULTISPATI-PCA, a spatially constrained Principal Component Analysis, was the statistical technique applied for the analysis of the data whose results showed that it was possible to detect the spatial structure of the data and that each spatial pattern corresponded to a distinct landscape. Despite their importance in forming the character of the landscape, aesthetic and perceptual aspects were not inlcuded in MULTISPATI-PCA analysis. It was preferred to test the technique only on data that were quantifiable in a more objective way. Perhaps taking into account the human perception of the landscape can be the starting point for future investigation

Investigating the Spatial and Statistical Dimensions of Mortuary Choice in the Historical-Period Old City Cemetery in Roslyn, Washington

The historical-period Old City Cemetery in Roslyn, Washington contains individuals from diverse social backgrounds and exhibits considerable variation in mortuary expression. As such, the Old City Cemetery offers a unique opportunity to explore potential differences in social group mortuary practices spatially and statistically. Using burials in Roslyn’s Old City Cemetery, this project developed a methods framework to assess mortuary practice through demographics, burial location, and monument/plot attributes. I tested correlations between demographics and mortuary expression using spatial-statistical cluster analysis (Ripley’s K-Function), spatial density analysis (Kernel Density Estimation), and non-spatial statistical significance assessments (Factor analysis and Pearson’s R), and identified several demographic-based mortuary trends. Similarities in some ages and nationalities were significantly associated with choice in burial location and monument/plot attributes in the Old City Cemetery, suggesting social dynamics in historical-period Roslyn valued these demographic designations. I did not identify any significant trends in choice between similar occupations or causes of death. Cemetery chronology and known decade-based norms appeared partially responsible for burial location siting and choice in monument or plot attributes. This project serves to recommend the viability and importance of incorporating both spatial and statistical dimensions into mortuary analysis of historical-period cemeteries, and I offer that this framework can be applied in such contexts to investigate mortuary expression and social dynamics

What's Love Got to Do With It? Diamonds and the Accumulation of De Beers, 1935-55

What is accumulation? Visibly, accumulation is a quantitative process, demarcated in financial quantities. However, what is the meaning of those quantities? This question has been the subject of great debate within political economic thought. A new theory of accumulation, capital as power (CasP), argues that the financial quantities of accumulation express the distribution of power among the owners of capital over the qualitatively diverse, complex and mutating social order. With this dissertation, I explore the relationship between the quantities and qualities of accumulation by examining the De Beers diamond cartel, focusing on the period 1935-55. What does it mean to say capital is power in the specific setting of the global diamond assemblage? Research and analysis led me to focus on four important relationships that De Beers had to establish, maintain and transform in its struggle for differential accumulation: with diamonds themselves; with potential and actual diamond buyers; with governments; and, with families, especially the Oppenheimer family that controlled De Beers for over 80 years