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We discuss how machine learning methods can support the search for optimally dense packing shapes in a high-dimensional shape space. Using dimensional reduction, regression, and numerical optimization we find novel shapes that pack with up to 0.733 volume fraction.

 

Reading is a complex cognitive process that involves primary oculomotor function and high-level activities like attention focus and language processing. When we read, our eyes move by primary physiological functions while responding to language-processing demands. In fact, the eyes perform discontinuous twofold movements, namely, successive long jumps (saccades) interposed by small steps (fixations) in which the gaze “scans” confined locations. It is only through the fixations that information is effectively captured for brain processing. Since individuals can express similar as well as entirely different opinions about a given text, it is therefore expected that the form, content and style of a text could induce different eye-movement patterns among people. A question that naturally arises is whether these individuals’ behaviours are correlated, so that eye-tracking while reading can be used as a proxy for text subjective properties. Here we perform a set of eye-tracking experiments with a group of individuals reading different types of texts, including children stories, random word generated texts and excerpts from literature work. In parallel, an extensive Internet survey was conducted for categorizing these texts in terms of their complexity and coherence, considering a large number of individuals selected according to different ages, gender and levels of education. The computational analysis of the fixation maps obtained from the gaze trajectories of the subjects for a given text reveals that the average “magnetization” of the fixation configurations correlates strongly with their complexity observed in the survey. Moreover, we perform a thermodynamic analysis using the Maximum-Entropy Model and find that coherent texts were closer to their corresponding “critical points” than non-coherent ones, as computed from the Pairwise Maximum-Entropy method, suggesting that different texts may induce distinct cohesive reading activities. 

Abstract In many real-world networks, the ability to withstand targeted or global attacks; extinctions; or shocks is vital to the survival of the network itself, and of dependent structures such as economies (for financial networks) or even the planet (for ecosystems). Previous attempts to characterise robustness include nestedness of mutualistic networks or exploration of degree distribution. In this work we present a new approach for characterising the stability and robustness of networks with all-positive interactions by studying the distribution of the k-shell of the underlying network. We find that high occupancy of nodes in the inner and outer k-shells and low occupancy in the middle shells of financial and ecological networks (yielding a “U-shape” in a histogram of k-shell occupancy) provide resilience against both local targeted and global attacks. Investigation of this highly-populated core gives insights into the nature of a network (such as sharp transitions in the core composition of the stock market from a mix of industries to domination by one or two in the mid-1990s) and allow predictions of future network stability, e.g., by monitoring populations of “core” species in an ecosystem or noting when stocks in the core-dominant sector begin to move in lock-step, presaging a dramatic move in the market. Moreover, this “U-shape” recalls core-periphery structure, seen in a wide range of networks including opinion and internet networks, suggesting that the “U-shaped” occupancy histogram and its implications for network health may indeed be universal.