“The first man on the street” - tracing a famous Hilbert quote (1900) back to Gergonne (1825)

A short, catchy, and in its content somewhat exaggerated, quote allows us to draw a connection through three-quarters of a century between two leaders of mathematics who apparently held somewhat similar philosophical, pedagogical, and political views. In addition to providing some new facets to the biographies of Gergonne and Hilbert, our article relates to increasing demands for the dissemination of mathematical knowledge and to corresponding structural changes within mathematics during the 19th century

Investigating diagrammatic reasoning with deep neural networks

Diagrams in mechanised reasoning systems are typically en- coded into symbolic representations that can be easily processed with rule-based expert systems. This relies on human experts to define the framework of diagram-to-symbol mapping and the set of rules to reason with the symbols. We present a new method of using Deep artificial Neu- ral Networks (DNN) to learn continuous, vector-form representations of diagrams without any human input, and entirely from datasets of dia- grammatic reasoning problems. Based on this DNN, we developed a novel reasoning system, Euler-Net, to solve syllogisms with Euler diagrams. Euler-Net takes two Euler diagrams representing the premises in a syl- logism as input, and outputs either a categorical (subset, intersection or disjoint) or diagrammatic conclusion (generating an Euler diagram rep- resenting the conclusion) to the syllogism. Euler-Net can achieve 99.5% accuracy for generating syllogism conclusion. We analyse the learned representations of the diagrams, and show that meaningful information can be extracted from such neural representations. We propose that our framework can be applied to other types of diagrams, especially the ones we don’t know how to formalise symbolically. Furthermore, we propose to investigate the relation between our artificial DNN and human neural circuitry when performing diagrammatic reasoning

Excess mortality among the elderly in 12 European countries, February and March 2012

In February and March 2012, excess deaths among the elderly have been observed in 12 European countries that carry out weekly monitoring of all-cause mortality. These preliminary data indicate that the impact of influenza in Europe differs from the recent pandemic and post-pandemic seasons. The current excess mortality among the elderly may be related to the return of influenza A(H3N2) virus, potentially with added effects of a cold snap

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Pooling European all-cause mortality: methodology and findings for the seasons 2008/2009 to 2010/2011

Several European countries have timely all-cause mortality monitoring. However, small changes in mortality may not give rise to signals at the national level. Pooling data across countries may overcome this, particularly if changes in mortality occur simultaneously. Additionally, pooling may increase the power of monitoring populations with small numbers of expected deaths, e.g. younger age groups or fertile women. Finally, pooled analyses may reveal patterns of diseases across Europe. We describe a pooled analysis of all-cause mortality across 16 European countries. Two approaches were explored. In the ‘summarized' approach, data across countries were summarized and analysed as one overall country. In the ‘stratified' approach, heterogeneities between countries were taken into account. Pooling using the ‘stratified' approach was the most appropriate as it reflects variations in mortality. Excess mortality was observed in all winter seasons albeit slightly higher in 2008/09 than 2009/10 and 2010/11. In the 2008/09 season, excess mortality was mainly in elderly adults. In 2009/10, when pandemic influenza A(H1N1) dominated, excess mortality was mainly in children. The 2010/11 season reflected a similar pattern, although increased mortality in children came later. These patterns were less clear in analyses based on data from individual countries. We have demonstrated that with stratified pooling we can combine local mortality monitoring systems and enhance monitoring of mortality across Europ

A Recommendation System for Meta-modeling: A Meta-learning Based Approach

Various meta-modeling techniques have been developed to replace computationally expensive simulation models. The performance of these meta-modeling techniques on different models is varied which makes existing model selection/recommendation approaches (e.g., trial-and-error, ensemble) problematic. To address these research gaps, we propose a general meta-modeling recommendation system using meta-learning which can automate the meta-modeling recommendation process by intelligently adapting the learning bias to problem characterizations. The proposed intelligent recommendation system includes four modules: (1) problem module, (2) meta-feature module which includes a comprehensive set of meta-features to characterize the geometrical properties of problems, (3) meta-learner module which compares the performance of instance-based and model-based learning approaches for optimal framework design, and (4) performance evaluation module which introduces two criteria, Spearman\u27s ranking correlation coefficient and hit ratio, to evaluate the system on the accuracy of model ranking prediction and the precision of the best model recommendation, respectively. To further improve the performance of meta-learning for meta-modeling recommendation, different types of feature reduction techniques, including singular value decomposition, stepwise regression and ReliefF, are studied. Experiments show that our proposed framework is able to achieve 94% correlation on model rankings, and a 91% hit ratio on best model recommendation. Moreover, the computational cost of meta-modeling recommendation is significantly reduced from an order of minutes to seconds compared to traditional trial-and-error and ensemble process. The proposed framework can significantly advance the research in meta-modeling recommendation, and can be applied for data-driven system modeling