1,619 research outputs found

    On Multifractal Structure in Non-Representational Art

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    Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific color (``blobs''), as well as patterns formed by the luminance gradient between adjacent colors (``edges''). It is found that the analysis method applied to ``blobs'' cannot distinguish between artists of the same movement, yielding a multifractal spectrum of dimensions between about 1.5-1.8. The method can distinguish between different types of images, however, as demonstrated by studying a radically different type of art. The data suggests that the ``edge'' method can distinguish between artists in the same movement, and is proposed to represent a toy model of visual discrimination. A ``fractal reconstruction'' analysis technique is also applied to the images, in order to determine whether or not a specific signature can be extracted which might serve as a type of fingerprint for the movement. However, these results are vague and no direct conclusions may be drawn.Comment: 53 pp LaTeX, 10 figures (ps/eps

    Micro-Macro Analysis of Complex Networks

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    Complex systems have attracted considerable interest because of their wide range of applications, and are often studied via a \u201cclassic\u201d approach: study a specific system, find a complex network behind it, and analyze the corresponding properties. This simple methodology has produced a great deal of interesting results, but relies on an often implicit underlying assumption: the level of detail on which the system is observed. However, in many situations, physical or abstract, the level of detail can be one out of many, and might also depend on intrinsic limitations in viewing the data with a different level of abstraction or precision. So, a fundamental question arises: do properties of a network depend on its level of observability, or are they invariant? If there is a dependence, then an apparently correct network modeling could in fact just be a bad approximation of the true behavior of a complex system. In order to answer this question, we propose a novel micro-macro analysis of complex systems that quantitatively describes how the structure of complex networks varies as a function of the detail level. To this extent, we have developed a new telescopic algorithm that abstracts from the local properties of a system and reconstructs the original structure according to a fuzziness level. This way we can study what happens when passing from a fine level of detail (\u201cmicro\u201d) to a different scale level (\u201cmacro\u201d), and analyze the corresponding behavior in this transition, obtaining a deeper spectrum analysis. The obtained results show that many important properties are not universally invariant with respect to the level of detail, but instead strongly depend on the specific level on which a network is observed. Therefore, caution should be taken in every situation where a complex network is considered, if its context allows for different levels of observability

    A robust adaptive wavelet-based method for classification of meningioma histology images

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    Intra-class variability in the texture of samples is an important problem in the domain of histological image classification. This issue is inherent to the field due to the high complexity of histology image data. A technique that provides good results in one trial may fail in another when the test and training data are changed and therefore, the technique needs to be adapted for intra-class texture variation. In this paper, we present a novel wavelet based multiresolution analysis approach to meningioma subtype classification in response to the challenge of data variation.We analyze the stability of Adaptive Discriminant Wavelet Packet Transform (ADWPT) and present a solution to the issue of variation in the ADWPT decomposition when texture in data changes. A feature selection approach is proposed that provides high classification accuracy

    History of art paintings through the lens of entropy and complexity

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    Art is the ultimate expression of human creativity that is deeply influenced by the philosophy and culture of the corresponding historical epoch. The quantitative analysis of art is therefore essential for better understanding human cultural evolution. Here we present a large-scale quantitative analysis of almost 140 thousand paintings, spanning nearly a millennium of art history. Based on the local spatial patterns in the images of these paintings, we estimate the permutation entropy and the statistical complexity of each painting. These measures map the degree of visual order of artworks into a scale of order-disorder and simplicity-complexity that locally reflects qualitative categories proposed by art historians. The dynamical behavior of these measures reveals a clear temporal evolution of art, marked by transitions that agree with the main historical periods of art. Our research shows that different artistic styles have a distinct average degree of entropy and complexity, thus allowing a hierarchical organization and clustering of styles according to these metrics. We have further verified that the identified groups correspond well with the textual content used to qualitatively describe the styles, and that the employed complexity-entropy measures can be used for an effective classification of artworks.Comment: 10 two-column pages, 5 figures; accepted for publication in PNAS [supplementary information available at http://www.pnas.org/highwire/filestream/824089/field_highwire_adjunct_files/0/pnas.1800083115.sapp.pdf

    Resolving structural variability in network models and the brain

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    Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar diagnostics presented in statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling---in addition to several summary statistics, including the mean clustering coefficient, shortest path length, and network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be embedded in anatomical brain regions tend to produce distributions that are similar to those extracted from the brain. We also find that network models hardcoded to display one network property do not in general also display a second, suggesting that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.Comment: 24 pages, 11 figures, 1 table, supplementary material

    Texture Analysis Methods for Medical Image Characterisation

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    Scale-dependent heterogeneity in fracture data sets and grayscale images

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    Lacunarity is a technique developed for multiscale analysis of spatial data and can quantify scale-dependent heterogeneity in a dataset. The present research is based on characterizing fracture data of various types by invoking lacunarity as a concept that can not only be applied to both fractal and non-fractal binary data but can also be extended to analyzing non-binary data sets comprising a spectrum of values between 0 and 1. Lacunarity has been variously modified in characterizing fracture data from maps and scanlines in tackling five different problems. In Chapter 2, it is shown that normalized lacunarity curves can differentiate between maps (2-dimensional binary data) belonging to the same fractal-fracture system and that clustering increases with decreasing spatial scale. Chapter 4 analyzes spacing data from scanlines (1-dimensional binary data) and employs log-transformed lacunarity curves along with their 1st derivatives in identifying the presence of fracture clusters and their spatial organization. This technique is extended to 1-dimensional non-binary data in chapter 5 where spacing is integrated with aperture values and a lacunarity ratio is invoked in addressing the question of whether large fractures occur within clusters. Finally, it is investigated in chapter 6 if lacunarity can find differences in clustering along various directions of a fracture netowork thus identifying differentially-clustered fracture sets. In addition to fracture data, chapter 3 employs lacunarity in identifying clustering and multifractal behavior in synthetic and natural 2-dimensional non-binary patterns in the form of soil thin sections. Future avenues for research include estimation of 2-dimensional clustering from 1-dimensional samples (e.g., scanlines and well-data), forward modeling of fracture networks using lacunarity, and the possible application of lacunarity in delineating shapes of other geologic patterns such as channel beds

    Hyperbolic Geometry of Complex Networks

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    We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as non-interacting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure
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