Abstract: Palliative care is referred to a set of programs for patients that suffer life-limiting illnesses. These programs aim to maximize the quality of life (QoL) for the last stage of life. They are currently based on clinical evaluation of the risk of 1-year mortality. The main aim of this work is to develop and validate machine-learning-based models to predict the exitus of a patient within the next year using data gathered at hospital admission. Five machine-learning techniques were applied using a retrospective dataset. The evaluation was performed with five metrics computed by a resampling strategy: Accuracy, the area under the ROC curve, Specificity, Sensitivity, and the Balanced Error Rate. All models reported an AUC ROC from 0.857 to 0.91. Specifically, Gradient Boosting Classifier was the best model, producing an AUC ROC of 0.91, a sensitivity of 0.858, a specificity of 0.808, and a BER of 0.1687. Information from standard procedures at hospital admission combined with machine learning techniques produced models with competitive discriminative power. Our models reach the best results reported in the state of the art. These results demonstrate that they can be used as an accurate data-driven palliative care criteria inclusion.

Abstract: We reconstruct the extra-galactic gamma-ray source-count distribution, or dN/dS, of resolved and unresolved sources by adopting machine learning techniques. Specifically, we train a convolutional neural network on synthetic 2-dimensional sky-maps, which are built by varying parameters of underlying source-counts models and incorporate the FermiLAT instrumental response functions. The trained neural network is then applied to the Fermi-LAT data, from which we estimate the source count distribution down to flux levels a factor of 50 below the Fermi-LAT threshold. We perform our analysis using 14 years of data collected in the (1, 10) GeV energy range. The results we obtain show a source count distribution which, in the resolved regime, is in excellent agreement with the one derived from cataloged sources, and then extends as dN/dS " S-2 in the unresolved regime, down to fluxes of 5 center dot 10-12 cm-2 s-1. The neural network architecture and the devised methodology have the flexibility to enable future analyses to study the energy dependence of the source-count distribution.

Abstract: We present a novel methodology based on Physics-Informed Neural Networks (PINNs) for solving systems of partial differential equations admitting discontinuous solutions. Our method, called Gradient-Annihilated PINNs (GA-PINNs), introduces a modified loss function that forces the model to partially ignore high-gradients in the physical variables, achieved by introducing a suitable weighting function. The method relies on a set of hyperparameters that control how gradients are treated in the physical loss. The performance of our methodology is demonstrated by solving Riemann problems in special relativistic hydrodynamics, extending earlier studies with PINNs in the context of the classical Euler equations. The solutions obtained with the GA-PINN model correctly describe the propagation speeds of discontinuities and sharply capture the associated jumps. We use the relative l(2) error to compare our results with the exact solution of special relativistic Riemann problems, used as the reference ''ground truth'', and with the corresponding error obtained with a second-order, central, shock-capturing scheme. In all problems investigated, the accuracy reached by the GA-PINN model is comparable to that obtained with a shock-capturing scheme, achieving a performance superior to that of the baseline PINN algorithm in general. An additional benefit worth stressing is that our PINN-based approach sidesteps the costly recovery of the primitive variables from the state vector of conserved variables, a well-known drawback of grid-based solutions of the relativistic hydrodynamics equations. Due to its inherent generality and its ability to handle steep gradients, the GA-PINN methodology discussed in this paper could be a valuable tool to model relativistic flows in astrophysics and particle physics, characterized by the prevalence of discontinuous solutions.