This research presents a machine learning modeling process for detecting mental fatigue using three physiological signals: electrodermal activity, electrocardiogram, and respiration. It follows the conventional machine learning modeling pipeline, while emphasizing the significant contribution of the feature selection process, resulting in, not only a high-performance model, but also a relevant one. The employed feature selection process considers both statistical and contextual aspects of feature relevance. Statistical relevance was assessed through variance and correlation analyses between independent features and the dependent variable (fatigue state). A contextual analysis was based on insights derived from the experimental design and feature characteristics. Additionally, feature sequencing and set conversion techniques were employed to incorporate the temporal aspects of physiological signals into the training of machine learning models based on random forest, decision tree, support vector machine, k-nearest neighbors, and gradient boosting. An evaluation was conducted using a dataset acquired from a wearable electronic system (in third-party research) with physiological data from three subjects undergoing a series of tests and fatigue stages. A total of 18 tests were performed by the 3 subjects in 3 mental fatigue states. Fatigue assessment was based on subjective measures and reaction time tests, and fatigue induction was performed through mental arithmetic operations. The results showed the highest performance when using random forest, achieving an average accuracy and F1-score of 96% in classifying three levels of mental fatigue.

In non-perturbative non-Markovian open quantum systems, reaching either low temperatures with the hierarchical equations of motion (HEOM) or high temperatures with the Thermalized Time Evolving Density Operator with Orthogonal Polynomials Algorithm (T-TEDOPA) formalism in Hilbert space remains challenging. We compare different ways of modeling the environment. Sampling the Fourier transform of the bath correlation function, also called temperature dependent spectral density, proves to be very effective. T-TEDOPA [Tamascelli et al., Phys. Rev. Lett. 123, 090402 (2019)] uses a linear chain of oscillators with positive and negative frequencies, while HEOM is based on the complex poles of an optimized rational decomposition of the temperature dependent spectral density [Xu et al., Phys. Rev. Lett. 129, 230601 (2022)]. Resorting to the poles of the temperature independent spectral density and of the Bose function separately is an alternative when the problem due to the huge number of Bose poles at low temperatures is circumvented. Two examples illustrate the effectiveness of the HEOM and T-TEDOPA approaches: a benchmark pure dephasing case and a two-bath model simulating the dynamics of excited electronic states coupled through a conical intersection. We show the efficiency of T-TEDOPA to simulate dynamics at a finite temperature by using either continuous spectral densities or only all the intramolecular oscillators of a linear vibronic model calibrated from ab initio data of a phenylene ethynylene dimer.

The ability to prepare a specific superposition of electronic excited states leading to a transitory symmetry breaking of the electronic density in complex systems remains a challenging concern. We investigate how an initial coherence can be controlled by laser fields. The selected molecular system is a symmetric dimer of phenylene ethynylene presenting different interesting properties: Two bright nearly degenerate excited states coupled through a conical intersection are addressable by orthogonal transition dipole moments and are well separated from neighboring states. Creating a superposed state with equal weights corresponds to a right or left electronic localization as in the double-well system followed by a transitory oscillation between the two wells. To ensure a spectral bandwidth typically smaller than 0.25 eV, the pulse duration is in the tens of femtoseconds range, so nuclear motion cannot be neglected. Optimal control theory (OCT) is applied with guess fields that effectively create the target coherence in the absence of dephasing due to the vibrational baths. We analyze the field reshaping proposed by the control and we further fit a sequence of pulses on the optimal field. The overall result is efficient and robust disymmetry control over reasonable timescales of few tens of femtoseconds, exceeding the pulse duration. The monotonically convergent algorithm is combined with the hierarchical equations of motion (HEOM) able to treat strongly coupled non-Markovian dynamics. We also check the implementation of the combined OCT-HEOM approach in the tensor-train representation with propagation using the time-dependent variational method.

In this study, we reexamine a recent optimal control simulation targeting the preparation of a superposition of two excited electronic states in the ultraviolet (UV) range in a complex molecular system. We revisit this control from the perspective of reinforcement learning, offering an efficient alternative to conventional quantum control methods. The two excited states are addressable by orthogonal polarizations and their superposition corresponds to a right or left localization of the electronic density. The pulse duration spans tens of femtoseconds to prevent excitation of higher excited bright states which leads to a strong perturbation by the nuclear motions. We modify an open source software by Giannelli et al. [L. Giannelli et al., Phys. Lett. A 434, 128054 (2022)] that implements reinforcement learning with Lindblad dynamics, to introduce non-Markovianity of the surrounding reservoir either by time-dependent rates, or more exactly, by using the hierarchical equations of motion with the QuTip-BoFiN package. This extension opens the way to wider applications for non-Markovian environments, in particular when the active system interacts with a highly structured noise.