Evolutionary Invasion Analysis of Modern Epidemics Highlights the Context-Dependence of Virulence Evolution.

Models are often employed to integrate knowledge about epidemics across scales and simulate disease dynamics. While these approaches have played a central role in studying the mechanics underlying epidemics, we lack ways to reliably predict how the relationship between virulence (the harm to hosts caused by an infection) and transmission will evolve in certain virus-host contexts. In this study, we invoke evolutionary invasion analysis-a method used to identify the evolution of uninvadable strategies in dynamical systems-to examine how the virulence-transmission dichotomy can evolve in models of virus infections defined by different natural histories. We reveal peculiar patterns of virulence evolution between epidemics with different disease natural histories (SARS-CoV-2 and hepatitis C virus). We discuss the findings with regards to the public health implications of predicting virus evolution, and in broader theoretical canon involving virulence evolution in host-parasite systems.

Learning transfer operators by kernel density estimation.

Inference of transfer operators from data is often formulated as a classical problem that hinges on the Ulam method. The conventional description, known as the Ulam-Galerkin method, involves projecting onto basis functions represented as characteristic functions supported over a fine grid of rectangles. From this perspective, the Ulam-Galerkin approach can be interpreted as density estimation using the histogram method. In this study, we recast the problem within the framework of statistical density estimation. This alternative perspective allows for an explicit and rigorous analysis of bias and variance, thereby facilitating a discussion on the mean square error. Through comprehensive examples utilizing the logistic map and a Markov map, we demonstrate the validity and effectiveness of this approach in estimating the eigenvectors of the Frobenius-Perron operator. We compare the performance of histogram density estimation (HDE) and kernel density estimation (KDE) methods and find that KDE generally outperforms HDE in terms of accuracy. However, it is important to note that KDE exhibits limitations around boundary points and jumps. Based on our research findings, we suggest the possibility of incorporating other density estimation methods into this field and propose future investigations into the application of KDE-based estimation for high-dimensional maps. These findings provide valuable insights for researchers and practitioners working on estimating the Frobenius-Perron operator and highlight the potential of density estimation techniques in this area of study.

On Geometry of Information Flow for Causal Inference.

Causal inference is perhaps one of the most fundamental concepts in science, beginning originally from the works of some of the ancient philosophers, through today, but also weaved strongly in current work from statisticians, machine learning experts, and scientists from many other fields. This paper takes the perspective of information flow, which includes the Nobel prize winning work on Granger-causality, and the recently highly popular transfer entropy, these being probabilistic in nature. Our main contribution will be to develop analysis tools that will allow a geometric interpretation of information flow as a causal inference indicated by positive transfer entropy. We will describe the effective dimensionality of an underlying manifold as projected into the outcome space that summarizes information flow. Therefore, contrasting the probabilistic and geometric perspectives, we will introduce a new measure of causal inference based on the fractal correlation dimension conditionally applied to competing explanations of future forecasts, which we will write G e o C y → x . This avoids some of the boundedness issues that we show exist for the transfer entropy, T y → x . We will highlight our discussions with data developed from synthetic models of successively more complex nature: these include the Hénon map example, and finally a real physiological example relating breathing and heart rate function.