Search

In this paper, we focus on some aspects of the relation of spacetime and quantum mechanics and the study counterparts (in Set) of the categorical local symmetries of smooth 4-manifolds. In the set-theoretic limit, there emerge some exotic smoothness structures on R 4 (hence the Riemannian nonvanishing curvature), which fit well with the quantum mechanical lattice of projections on infinite-dimensional Hilbert spaces. The method we follow is formalization localized on the open covers of the spacetime manifold. We discuss our findings in the context of the information paradox assigned to evaporating black holes. A black hole can evaporate entirely, but the smoothness structure of spacetime will be altered and, in this way, the missing information about the initial states of matter forming the black hole will be encoded. Thus, the possible global geometric remnant of black holes in spacetime is recognized as exotic 4-smoothness. The full-fledged verification of this proposal will presumably be possible within the scope of future quantum gravity theory research. [ABSTRACT FROM AUTHOR]

Logistic regression is the industry standard in credit risk modeling. Regulatory requirements for model explainability have halted the implementation of more advanced, non-linear machine learning algorithms, even though more accurate predictions would benefit consumers and banks alike. Deep neural networks are certainly some of the most prominent non-linear algorithms. In this paper, we propose a deep neural network model for behavioral credit rating. Behavioral models are used to assess the future performance of a bank's existing portfolio in order to meet the capital requirements introduced by the Basel regulatory framework, which are designed to increase the banks' ability to absorb large financial shocks. The proposed deep neural network was trained on two different datasets: the first one contains information on loans between 2009 and 2013 (during the financial crisis) and the second one from 2014 to 2018 (after the financial crisis); combined, they include more than 1.5 million examples. The proposed network outperformed multiple benchmarks and was evenly matched with the XGBoost model. Long-term credit rating performance is also presented, as well as a detailed analysis of the reprogrammed facilities' impact on model performance. [ABSTRACT FROM AUTHOR]