Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed. Views interconnect these developments and establish that the axiomatizations are equivalent in the sense of being mutually interpretable. A realm also contains an external interface that is convenient for users of the library who want to apply the concepts and facts of the theory without delving into the details of how the concepts and facts were developed. We illustrate the utility of realms through a series of examples. We also give an outline of the mechanisms that are needed to create and maintain realms.Comment: As accepted for CICM 201

A Universal Machine for Biform Theory Graphs

Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages and emphasize computation. Combining the complementary strengths of both approaches while mending their complementary weaknesses has been an important goal of the mechanized mathematics community for some time. We pick up on the idea of biform theories and interpret it in the MMTt/OMDoc framework which introduced the foundations-as-theories approach, and can thus represent both logics and programming languages as theories. This yields a formal, modular framework of biform theory graphs which mixes specifications and implementations sharing the module system and typing information. We present automated knowledge management work flows that interface to existing specification/programming tools and enable an OpenMath Machine, that operationalizes biform theories, evaluating expressions by exhaustively applying the implementations of the respective operators. We evaluate the new biform framework by adding implementations to the OpenMath standard content dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final publication is available at http://link.springer.com

The energy spectrum of cosmic rays beyond the turn-down around 10^17 eV as measured with the surface detector of the Pierre Auger Observatory

We present a measurement of the cosmic-ray spectrum above 100 PeV using the part of the surface detector of the Pierre Auger Observatory that has a spacing of 750 m. An inflection of the spectrum is observed, confirming the presence of the so-called second-knee feature. The spectrum is then combined with that of the 1500 m array to produce a single measurement of the flux, linking this spectral feature with the three additional breaks at the highest energies. The combined spectrum, with an energy scale set calorimetrically via fluorescence telescopes and using a single detector type, results in the most statistically and systematically precise measurement of spectral breaks yet obtained. These measurements are critical for furthering our understanding of the highest energy cosmic rays

Reconstruction of events recorded with the surface detector of the Pierre Auger Observatory

Cosmic rays arriving at Earth collide with the upper parts of the atmosphere, thereby inducing extensive air showers. When secondary particles from the cascade arrive at the ground, they are measured by surface detector arrays. We describe the methods applied to the measurements of the surface detector of the Pierre Auger Observatory to reconstruct events with zenith angles less than 60o using the timing and signal information recorded using the water-Cherenkov detector stations. In addition, we assess the accuracy of these methods in reconstructing the arrival directions of the primary cosmic ray particles and the sizes of the induced showers

Predicting attitudinal and behavioral responses to COVID-19 pandemic using machine learning

At the beginning of 2020, COVID-19 became a global problem. Despite all the efforts to emphasize the relevance of preventive measures, not everyone adhered to them. Thus, learning more about the characteristics determining attitudinal and behavioral responses to the pandemic is crucial to improving future interventions. In this study, we applied machine learning on the multinational data collected by the International Collaboration on the Social and Moral Psychology of COVID-19 (N = 51,404) to test the predictive efficacy of constructs from social, moral, cognitive, and personality psychology, as well as socio-demographic factors, in the attitudinal and behavioral responses to the pandemic. The results point to several valuable insights. Internalized moral identity provided the most consistent predictive contribution-individuals perceiving moral traits as central to their self-concept reported higher adherence to preventive measures. Similar results were found for morality as cooperation, symbolized moral identity, self-control, open-mindedness, and collective narcissism, while the inverse relationship was evident for the endorsement of conspiracy theories. However, we also found a non-neglible variability in the explained variance and predictive contributions with respect to macro-level factors such as the pandemic stage or cultural region. Overall, the results underscore the importance of morality-related and contextual factors in understanding adherence to public health recommendations during the pandemic.Published versio