A hybrid coupled cluster-machine learning algorithm: Development of various regression models and benchmark applications.

The iterative solution of the coupled cluster equations exhibits a synergistic relationship among the various cluster amplitudes. The iteration scheme is analyzed as a multivariate discrete time propagation of nonlinearly coupled equations, which is dictated by only a few principal cluster amplitudes. These principal amplitudes usually correspond to only a few valence excitations, whereas all other cluster amplitudes are enslaved and behave as auxiliary variables [Agarawal et al., J. Chem. Phys. 154, 044110 (2021)]. We develop a coupled cluster-machine learning hybrid scheme where various supervised machine learning strategies are introduced to establish the interdependence between the principal and auxiliary amplitudes on-the-fly. While the coupled cluster equations are solved only to determine the principal amplitudes, the auxiliary amplitudes, on the other hand, are determined via regression as unique functionals of the principal amplitudes. This leads to significant reduction in the number of independent degrees of freedom during the iterative optimization, which saves significant computation time. A few different regression techniques have been developed, which have their own advantages and disadvantages. The scheme has been applied to several molecules in their equilibrium and stretched geometries, and our scheme, with all the regression models, shows a significant reduction in computation time over the canonical coupled cluster calculations without unduly sacrificing the accuracy.

EEG-based source localization with enhanced virtual aperture using second order statistics.

For the past few decades source localization, based on EEG modality, has been a very active area of research. EEG signal provides temporal resolution in millisecond range that can capture rapidly changing patterns of brain activity but it has a low spatial resolution as compared to techniques like fMRI, PET, CT scan, etc. So, one of the motives of this research is to improve the spatial resolution of the EEG signal. Many successful attempts have been made to localise the active neural sources using EEG signals with the introduction of techniques like MNE, LORETA, sLORETA, FOCUSS, etc. But these techniques require a large number of electrodes for correct localization of a few sources. This paper aims at providing a new method for the localization of EEG sources with a fewer electrode. This is achieved by exploiting the second-order statistics to enhance the aperture and solve the EEG localization problem. The comparison of the proposed method with the state-of-the-art methods is done by observing the localization error with variation in SNR, number of snapshots (time samples), number of active sources, and number of electrodes. The results show that the proposed method can detect a greater number of sources with fewer electrodes and with higher accuracy as compared to methods available in the literature. Real -time EEG signal during an arithmetic task is considered and the proposed algorithm clearly shows a sparse activity in the frontal region.

Tuning the Photoluminescence Anisotropy of Semiconductor Nanocrystals.

Semiconductor nanocrystals are promising optoelectronic materials. Understanding their anisotropic photoluminescence is fundamental for developing quantum-dot-based devices such as light-emitting diodes, solar cells, and polarized single-photon sources. In this study, we experimentally and theoretically investigate the photoluminescence anisotropy of CdSe semiconductor nanocrystals with various shapes, including plates, rods, and spheres, with either wurtzite or zincblende structures. We use defocused wide-field microscopy to visualize the emission dipole orientation and find that spheres, rods, and plates exhibit the optical properties of 2D, 1D, and 2D emission dipoles, respectively. We rationalize the seemingly counterintuitive observation that despite having similar aspect ratios (width/length), rods and long nanoplatelets exhibit different defocused emission patterns by considering valence band structures calculated using multiband effective mass theory and the dielectric effect. The principles are extended to provide general relationships that can be used to tune the emission dipole orientation for different materials, crystalline structures, and shapes.