Logistic growth on networks: Exact solutions for the susceptible-infected model.

The susceptible-infected (SI) model is the most basic of all compartmental models used to describe the spreading of information through a population. Despite its apparent simplicity, the analytic solution of this model on networks is still lacking. We address this problem here using a novel formulation inspired by the mathematical treatment of many-body quantum systems. This allows us to organize the time-dependent expectation values for the state of individual nodes in terms of contributions from subgraphs of the network. We compute these contributions systematically and find a set of symmetry relations among subgraphs of differing topologies. We use our novel approach to compute the spreading of information on three different sample networks. The exact solution, which matches with Monte Carlo simulations, visibly departs from the mean-field results.

Prognostic Model of COVID-19 Severity and Survival among Hospitalized Patients Using Machine Learning Techniques.

We conducted a statistical study and developed a machine learning model to triage COVID-19 patients affected during the height of the COVID-19 pandemic in Hong Kong based on their medical records and test results (features) collected during their hospitalization. The correlation between the values of these features is studied against discharge status and disease severity as a preliminary step to identify those features with a more pronounced effect on the patient outcome. Once identified, they constitute the inputs of four machine learning models, Decision Tree, Random Forest, Gradient and RUSBoosting, which predict both the Mortality and Severity associated with the disease. We test the accuracy of the models when the number of input features is varied, demonstrating their stability; i.e., the models are already highly predictive when run over a core set of (6) features. We show that Random Forest and Gradient Boosting classifiers are highly accurate in predicting patients' Mortality (average accuracy ∼99%) as well as categorize patients (average accuracy ∼91%) into four distinct risk classes (Severity of COVID-19 infection). Our methodical and broad approach combines statistical insights with various machine learning models, which paves the way forward in the AI-assisted triage and prognosis of COVID-19 cases, which is potentially generalizable to other seasonal flus.

Mapping fermion and boson systems onto the Fock space of harmonic oscillators.

The fluctuation-dissipation theorem (FDT) is very general and applies to a broad variety of different physical phenomena in condensed matter physics. With the help of the FDT and following the famous work of Caldeira and Leggett, we show that, whenever linear response theory applies, any generic bosonic or fermionic system at finite temperature T can be mapped onto a fictitious system of free-harmonic oscillators. To the best of our knowledge, this is the first time that such a mapping is explicitly worked out. This finding provides further theoretical support to the phenomenological harmonic oscillator models commonly used in condensed matter. Moreover, our result helps in clarifying an interpretation issue related to the presence and physical origin of the Bose-Einstein factor in the FDT.