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Internet users are very familiar with the results of a search query displayed as a ranked list of snippets. Each textual snippet shows a content summary of the referred document (or webpage) and a link to it. This display has many advantages, for example, it affords easy navigation and is straightforward to interpret. Nonetheless, any user of search engines could possibly report some experience of disappointment with this metaphor. Indeed, it has limitations in particular situations, as it fails to provide an overview of the document collection retrieved. Moreover, depending on the nature of the query--for example, it may be too general, or ambiguous, or ill expressed--the desired information may be poorly ranked, or results may contemplate varied topics. Several search tasks would be easier if users were shown an overview of the returned documents, organized so as to reflect how related they are, content wise. We propose a visualization technique to display the results of web queries aimed at overcoming such limitations. It combines the neighborhood preservation capability of multidimensional projections with the familiar snippet-based representation by employing a multidimensional projection to derive two-dimensional layouts of the query search results that preserve text similarity relations, or neighborhoods. Similarity is computed by applying the cosine similarity over a "bag-of-words" vector representation of collection built from the snippets. If the snippets are displayed directly according to the derived layout, they will overlap considerably, producing a poor visualization. We overcome this problem by defining an energy functional that considers both the overlapping among snippets and the preservation of the neighborhood structure as given in the projected layout. Minimizing this energy functional provides a neighborhood preserving two-dimensional arrangement of the textual snippets with minimum overlap. The resulting visualization conveys both a global view of the query results and visual groupings that reflect related results, as illustrated in several examples shown.

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São Paulo is the most populous state in Brazil, home to around 22% of the country’s population. The total number of Covid-19-infected people in São Paulo has reached more than 1 million, while its total death toll stands at 25% of all the country’s fatalities. Joining the Brazilian academia efforts in the fight against Covid-19, in this paper we describe a unified framework for monitoring and forecasting the Covid-19 progress in the state of São Paulo. More specifically, a freely available, online platform to collect and exploit Covid-19 time-series data is presented, supporting decision-makers while still allowing the general public to interact with data from different regions of the state. Moreover, a novel forecasting data-driven method has also been proposed, by combining the so-called Susceptible-Infectious-Recovered-Deceased model with machine learning strategies to better fit the mathematical model’s coefficients for predicting Infections, Recoveries, Deaths, and Viral Reproduction Numbers. We show that the obtained predictor is capable of dealing with badly conditioned data samples while still delivering accurate 10-day predictions. Our integrated computational system can be used for guiding government actions mainly in two basic aspects: real-time data assessment and dynamic predictions of Covid-19 curves for different regions of the state. We extend our analysis and investigation to inspect the virus spreading in Brazil in its regions. Finally, experiments involving the Covid-19 advance in other countries are also given.

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Existing algorithms for building layouts from geometric primitives are typically designed to cope with requirements such as orthogonal alignment, overlap removal, optimal area usage, hierarchical organization, among others. However, most techniques are able to tackle just a few of those requirements simultaneously, impairing their use and flexibility. In this work we propose a novel methodology for building layouts from geometric primitives that concurrently addresses a wider range of requirements. Relying on multidimensional projection and mixed integer optimization, our approach arranges geometric objects in the visual space so as to generate well structured layouts that preserve the semantic relation among objects while still making an efficient use of display area. Moreover, scalability is handled through a hierarchical representation scheme combined with navigation tools. A comprehensive set of quantitative comparisons against existing geometry-based layouts and applications on text, image, and video data set visualization prove the effectiveness of our approach.

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