1,619 research outputs found
On Multifractal Structure in Non-Representational Art
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
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
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
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
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
Scale-dependent heterogeneity in fracture data sets and grayscale images
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
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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