Variational mode decomposition-based EEG analysis for the classification of disorders of consciousness.

Aberrant alterations in any of the two dimensions of consciousness, namely awareness and arousal, can lead to the emergence of disorders of consciousness (DOC). The development of DOC may arise from more severe or targeted lesions in the brain, resulting in widespread functional abnormalities. However, when it comes to classifying patients with disorders of consciousness, particularly utilizing resting-state electroencephalogram (EEG) signals through machine learning methods, several challenges surface. The non-stationarity and intricacy of EEG data present obstacles in understanding neuronal activities and achieving precise classification. To address these challenges, this study proposes variational mode decomposition (VMD) of EEG before feature extraction along with machine learning models. By decomposing preprocessed EEG signals into specified modes using VMD, features such as sample entropy, spectral entropy, kurtosis, and skewness are extracted across these modes. The study compares the performance of the features extracted from VMD-based approach with the frequency band-based approach and also the approach with features extracted from raw-EEG. The classification process involves binary classification between unresponsive wakefulness syndrome (UWS) and the minimally conscious state (MCS), as well as multi-class classification (coma vs. UWS vs. MCS). Kruskal-Wallis test was applied to determine the statistical significance of the features and features with a significance of p < 0.05 were chosen for a second round of classification experiments. Results indicate that the VMD-based features outperform the features of other two approaches, with the ensemble bagged tree (EBT) achieving the highest accuracy of 80.5% for multi-class classification (the best in the literature) and 86.7% for binary classification. This approach underscores the potential of integrating advanced signal processing techniques and machine learning in improving the classification of patients with disorders of consciousness, thereby enhancing patient care and facilitating informed treatment decision-making.

Combined Quantum Mechanical and Quasi-Classical State-to-State Dynamical Study on the Isotopic Effect in H/D + LiH+/LiD+ → H2/HD/D2 + Li+ Reactions.

Coriolis-coupled quantum mechanical (QM-CC) and quasi-classical trajectory (QCT) calculations are carried out to investigate the dynamics of the H(D) + LiH+(v = 0, j = 0) → H2(HD) (v', j') + Li+ reactions on the ground electronic state potential energy surface reported by Martinazzo et al. (Martinazzo et al., J. Chem. Phys. 2003, 119, 11241). The QM-CC and QCT results at the initial state-selected and state-to-state levels are used to investigate the validity and accuracy of the QCT method for these exoergic barrierless reactions. Furthermore, the QCT method is used to understand the isotopic effects on reaction observables like total and state-to-state integral cross section, differential cross section, product energy disposal, and rate constants of H(D) + LiH+(v = 0, j = 0) → H2(HD) (v', j') + Li+ and H(D) + LiD+(v = 0, j = 0) → HD(D2) (v', j') + Li+ reactions. Attempts are also made to understand the impact of the isotopic substitution on the reaction mechanism. It is observed that QM-CC and QCT results closely follow each other at the initial state-selected and state-to-state levels. Noticeable kinematic effects of reagents on the reactivity and mechanism of the reactions are also observed.

Electronic nonadiabatic effects in the state-to-state dynamics of the H + H2 → H2 + H exchange reaction with a vibrationally excited reagent.

Out of the many major breakthroughs that the hydrogen-exchange reaction has led to, electronic nonadiabatic effects that are mainly due to the geometric phase has intrigued many. In this work we investigate such effects in the state-to-state dynamics of the H + H2 (v = 3, 4, j = 0) → H2 (v', j') + H reaction with a vibrationally excited reagent at energies corresponding to thermal conditions. The dynamical calculations are performed by a time-dependent quantum mechanical method both on the lower adiabatic potential energy surface (PES) and also using a two-states coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 1E' ground electronic manifold of the H3 system. The nonadiabatic couplings are considered here up to the quadratic term; however, the effect of the latter on the reaction dynamics is found to be very small. Adiabatic population analysis showed a minimal participation of the upper adiabatic surface even for the vibrationally excited reagent. A strong nonadiabatic effect appears in the state-to-state reaction probabilities and differential cross sections (DCSs). This effect is manifested as "out-of-phase" oscillations in the DCSs between the results of the uncoupled and coupled surface situations. The oscillations persist as a function of both scattering angle and collision energy in both the backward and forward scattering regions. The origins of these oscillations are examined in detail. The oscillations that appear in the forward direction are found to be different from those due to glory scattering, where the latter showed a negligibly small nonadiabatic effect. The nonadiabatic effects are reduced to a large extent when summed over all product quantum states, in addition to the cancellation due to integration over the scattering angle and partial wave summation.

Quantum interference in the mechanism of H + LiH+ → H2 + Li+ reaction dynamics.

In this work, the detailed reaction mechanism of the astrochemically relevant exoergic and barrierless H + LiH+ → H2 + Li+ reaction is investigated by both time-dependent wave packet and quasi-classical trajectory (QCT) methods on the ab initio electronic ground state potential energy surface reported by Martinazzo et al. [Martinazzo et al., J. Chem. Phys., 2003, 119, 11241]. The interference terms due to the coherence between the partial waves are quantified. When plotted along the scattering angle they reveal interference of constructive or destructive nature. Significant interference was found in the differential cross-section (DCS) which is a symbolic of the non-statistical nature of the reaction. This is further complemented by calculating the lifetime of the collision complex by the QCT method. It is found that the reaction follows a direct stripping mechanism at higher collision energies and yields forward scattered products from collisions involving high total angular momentum. At low collision energies, the reaction follows a mixed direct/indirect mechanism but with a dominant indirect contribution. The product state-resolved DCSs reveal that two opposite mechanisms co-exist, both at low and high collision energies. The microscopic scattering mechanism of the reaction is found to be unaffected by the ro-vibrational excitation of the reagent diatom.

Theoretical Study of the Energy Disposal Mechanism and the State-Resolved Quantum Dynamics of the H + LiH+ → H2 + Li+ Reaction.

Despite several studies in the literature, the detailed quantum state-to-state level mechanism of the astrophysically important exoergic barrierless H + LiH+ → H2 + Li+ reaction is yet to be understood. In this work, we have investigated the energy disposal mechanism of the reaction in terms of integral reaction cross section, product internal state distributions, differential cross section, and rate constant. Fully converged and Coriolis coupled quantum mechanical calculations based on a time-dependent wave packet method have been performed at the state-to-state level on the ab initio electronic ground state potential energy surface (PES) constructed by Martinazzo et al. (J. Chem. Phys. 2003, 119, 11241-11248). The agreement between the present quantum mechanical and previous quasi-classical results is found even at very low relative translational energies of reagents. A non-statistical inverse Boltzmann vibrational distribution for the product is found. This is attributed to the "attractive" nature of the underlying PES, which facilitates the excess energy release mostly as product vibration (60-80%). The energy disposal in products is found to be unaffected by the rovibrational excitation of the reagent diatom due to the weak coupling between the vibrational modes of the reagent and the product. The mild effect of collision energy on the product energy disposal is ascribed to the effective coupling between the translational modes of the reagent and the product. It is found that the collisions lead to the formation of the product H2 in its rovibrationally excited levels.

Effect of Reagent Vibration and Rotation on the State-to-State Dynamics of the Hydrogen Exchange Reaction, H + H2 → H2 + H.

State-to-state dynamics of the benchmark hydrogen exchange reaction H + H2 (v = 0-4, j = 0-3) → H2 (v', j') + H is investigated with the aid of the real wave packet approach of Gray and Balint-Kurti (J. Chem. Phys. 1998, 108, 950-962) and electronic ground BKMP2 potential energy surface of Boothroyd et al. (J. Chem. Phys. 1996, 104, 7139-7152). Initial state-selected and product state-resolved reaction probabilities, integral cross section, and product diatom vibrational and rotational level populations at a few collision energies are reported to elucidate the energy disposal mechanism. State-specific thermal rate constants are also calculated and compared with the available literature results. Coriolis coupling terms of the nuclear Hamiltonian are included, and calculations are parallelized over the helicity quantum number, Ω'. Attempts are made, in particular, to study the effect of reagent vibrational and rotational excitations on the dynamical attributes. It is found that the calculations become computationally expensive with reagent vibrational and rotational excitation. Reagent vibrational excitation is found to enhance the reactivity and has significant impact on the energy disposal to the vibrational and rotational degrees of freedom of the product. The interplay of reagent translational and vibrational energy on the product vibrational distribution unfolds an important aspect of the energy disposal mechanism. The effect of reagent rotation on the state-to-state dynamics is found not to be very significant, and the weak effect turns out to be specific to v'.