This paper presents an analytical investigation into the dynamics of Weyl pairs within magnetized helicoidal graphene nanoribbons (GNRs). By embedding a curved surface into flat Minkowski space–time, we derive a fully covariant two-body Dirac equation specific to this system. We begin by formulating a non-perturbative wave equation that governs the relative motion of the Weyl pairs and obtains exact solutions. Our results demonstrate the influence of the uniform magnetic field and the number of twists on the dynamics of Weyl pairs in GNRs, providing precise energy values that lay a robust foundation for future research. Furthermore, we examine the material’s response to perturbation fields by calculating the polarization function and investigating how twisting and magnetic fields affect this response. Our findings indicate that, in principle, the material’s properties, which are crucial for practical applications, can be effectively controlled by precisely tuning the magnetic field and the number of twists in GNRs.

Inferring the state and unknown parameters of a network of coupled oscillators is of utmost importance. This task is made harder when only partial and noisy observations are available, which is a typical scenario in realistic high-dimensional systems. The general task of inference falls under data assimilation (DA), and a commonly used assimilation method is the ensemble Kalman filter. Employing network-specific localization of the forecast covariance, an ensemble Kalman filter with state space augmentation is shown to yield highly accurate estimates of both the oscillator phases and unknown model parameters in the case where only a subset of oscillator phases are observed. By contrast, standard DA methods yield poor results. We demonstrate the effectiveness of our approach for Kuramoto oscillators and for networks of theta neurons, using a variety of network topologies.