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

A convolutional autoencoder approach for mining features in cellular electron cryo-tomograms and weakly supervised coarse segmentation

Cellular electron cryo-tomography enables the 3D visualization of cellular organization in the near-native state and at submolecular resolution. However, the contents of cellular tomograms are often complex, making it difficult to automatically isolate different in situ cellular components. In this paper, we propose a convolutional autoencoder-based unsupervised approach to provide a coarse grouping of 3D small subvolumes extracted from tomograms. We demonstrate that the autoencoder can be used for efficient and coarse characterization of features of macromolecular complexes and surfaces, such as membranes. In addition, the autoencoder can be used to detect non-cellular features related to sample preparation and data collection, such as carbon edges from the grid and tomogram boundaries. The autoencoder is also able to detect patterns that may indicate spatial interactions between cellular components. Furthermore, we demonstrate that our autoencoder can be used for weakly supervised semantic segmentation of cellular components, requiring a very small amount of manual annotation.Comment: Accepted by Journal of Structural Biolog

Fast filtering and animation of large dynamic networks

Detecting and visualizing what are the most relevant changes in an evolving network is an open challenge in several domains. We present a fast algorithm that filters subsets of the strongest nodes and edges representing an evolving weighted graph and visualize it by either creating a movie, or by streaming it to an interactive network visualization tool. The algorithm is an approximation of exponential sliding time-window that scales linearly with the number of interactions. We compare the algorithm against rectangular and exponential sliding time-window methods. Our network filtering algorithm: i) captures persistent trends in the structure of dynamic weighted networks, ii) smoothens transitions between the snapshots of dynamic network, and iii) uses limited memory and processor time. The algorithm is publicly available as open-source software.Comment: 6 figures, 2 table

The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Recent and forthcoming advances in instrumentation, and giant new surveys, are creating astronomical data sets that are not amenable to the methods of analysis familiar to astronomers. Traditional methods are often inadequate not merely because of the size in bytes of the data sets, but also because of the complexity of modern data sets. Mathematical limitations of familiar algorithms and techniques in dealing with such data sets create a critical need for new paradigms for the representation, analysis and scientific visualization (as opposed to illustrative visualization) of heterogeneous, multiresolution data across application domains. Some of the problems presented by the new data sets have been addressed by other disciplines such as applied mathematics, statistics and machine learning and have been utilized by other sciences such as space-based geosciences. Unfortunately, valuable results pertaining to these problems are mostly to be found only in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments, some "old" and some new. These are generally unknown to most of the astronomical community, but are vital to the analysis and visualization of complex datasets and images. In order for astronomers to take advantage of the richness and complexity of the new era of data, and to be able to identify, adopt, and apply new solutions, the astronomical community needs a certain degree of awareness and understanding of the new concepts. One of the goals of this paper is to help bridge the gap between applied mathematics, artificial intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in Astronomy, special issue "Robotic Astronomy