Nicolò Cangiotti

Alessia andò, Nicolò Cangiotti, Mattia Sensi

In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more than a century ago, and exponential integrators, which date back to the 1960s. This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience.

Michele Loi, Marcello Di Bello, Nicolò Cangiotti

The growing philosophical literature on algorithmic fairness has examined statistical criteria such as equalized odds and calibration, causal and counterfactual approaches, and the role of structural and compounding injustices. Yet an important dimension has been overlooked: whether the evidential value of an algorithmic output itself depends on structural injustice. We contrast a predictive policing algorithm, which relies on historical crime data, with a camera-based system that records ongoing offenses, where both are designed to guide police deployment. In evaluating the moral acceptability of acting on a piece of evidence, we must ask not only whether the evidence is probative in the actual world, but also whether it would remain probative in nearby worlds without the relevant injustices. The predictive policing algorithm fails this test, but the camera-based system passes it. When evidence fails the test, it is morally problematic to use it punitively, more so than evidence that passes the test.

Marcello Di Bello, Nicolò Cangiotti, Michele Loi

By combining the philosophical literature on statistical evidence and the interdisciplinary literature on algorithmic fairness, we revisit recent objections against classification parity in light of causal analyses of algorithmic fairness and the distinction between predictive and diagnostic evidence. We focus on trial proceedings as a black-box classification algorithm in which defendants are sorted into two groups by convicting or acquitting them. We defend a novel principle, causal equal protection, that combines classification parity with the causal approach. In the do-calculus, causal equal protection requires that individuals should not be subject to uneven risks of classification error because of their protected or socially salient characteristics. The explicit use of protected characteristics, however, may be required if it equalizes these risks.