Bayesian Linear Regression for estimation of the Fractal Dimension of the Cerebral Cortex

The cerebral cortex presents self-similarity in a proper interval of spatial scales, a property typical of natural objects exhibiting fractal geometry. Its complexity therefore can be characterized by the value of its fractal dimension (FD). In the computation of this metric, it has usually been employed a frequentist approach to probability, with point estimator methods yielding only the optimal values of the FD. In our study, we aimed at retrieving a more complete evaluation of the FD by utilizing a Bayesian model for the linear regression analysis of the box-counting algorithm. We used T1-weighted MRI data of 86 healthy subjects (age 44.2 ± 17.1 years, mean ± standard deviation, 48% males) in order to gain insights into the confidence of our measure and investigate the relationship between mean Bayesian FD and age. Our approach yielded a stronger and significant (P < .001) correlation between mean Bayesian FD and age as compared to the previous implementation. Thus, our results make us suppose that the Bayesian FD is a more truthful estimation for the fractal dimension of the cerebral cortex compared to the frequentist FD.

Analysis of COVID-related symptoms from a database of Italian tweets

Twitter is a highly popular social media which on one hand allows information transmission in real time and on the other hand represents a source of open access homogeneous text data. We propose an analysis of the most common self-reported COVID symptoms from a dataset of Italian tweets to investigate the evolution of the pandemic in Italy from the end of September 2020 to the end of January 2021. After manually filtering tweets actually describing COVID symptoms from the database - which contains words related to fever, cough and sore throat - we discuss usefulness of such filtering. We then compare our time series with the daily data of new hospitalisations in Italy, with the aim of building a simple linear regression model that accounts for the delay which is observed from the tweets mentioning individual symptoms to new hospitalisations. We discuss both the results and limitations of linear regression given that our data suggests that the relationship between time series of symptoms tweets and of new hospitalisations changes towards the end of the acquisition.