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We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare–bath time correlation function (TCF) given by the bosonic fluctuation–dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density. 

Abstract Objective: This study investigates speech decoding from neural signals captured by intracranial electrodes. Most prior works can only work with electrodes on a 2D grid (i.e., Electrocorticographic or ECoG array) and data from a single patient. We aim to design a deep-learning model architecture that can accommodate both surface (ECoG) and depth (stereotactic EEG or sEEG) electrodes. The architecture should allow training on data from multiple participants with large variability in electrode placements. The model should not have subject-specific layers, and the trained model should perform well on participants unseen during training. Approach: We propose a novel transformer-based model architecture named SwinTW that can work with arbitrarily positioned electrodes by leveraging their 3D locations on the cortex rather than their positions on a 2D grid. We train subject-specific models using data from a single participant and multi-subject models exploiting data from multiple participants. Main Results: The subject-specific models using only low-density 8x8 ECoG data achieved high decoding Pearson Correlation Coefficient with ground truth spectrogram (PCC=0.817), over N=43 participants, significantly outperforming our prior convolutional ResNet model and the 3D Swin transformer model. Incorporating additional strip, depth, and grid electrodes available in each participant (N=39) led to further improvement (PCC=0.838). For participants with only sEEG electrodes (N=9), subject-specific models still enjoy comparable performance with an average PCC=0.798. A single multi-subject model trained on ECoG data from 15 participants yielded comparable results (PCC=0.837) as 15 models trained individually for these participants (PCC=0.831). Furthermore, the multi-subject models achieved high performance on unseen participants, with an average PCC=0.765 in leave-one-out cross-validation. Significance: The proposed SwinTW decoder enables future speech decoding approaches to utilize any electrode placement that is clinically optimal or feasible for a particular participant, including using only depth electrodes, which are more routinely implanted in chronic neurosurgical procedures. The success of the single multi-subject model when tested on participants within the training cohort demonstrates that the model architecture is capable of exploiting data from multiple participants with diverse electrode placements. The architecture’s flexibility in training with both single-subject and multi-subject data, as well as grid and non-grid electrodes, ensures its broad applicability. Importantly, the generalizability of the multi-subject models in our study population suggests that a model trained using paired acoustic and neural data from multiple patients can potentially be applied to new patients with speech disability where acoustic-neural training data is not feasible. 

When we vocalize, our brain distinguishes self-generated sounds from external ones. A corollary discharge signal supports this function in animals; however, in humans, its exact origin and temporal dynamics remain unknown. We report electrocorticographic recordings in neurosurgical patients and a connectivity analysis framework based on Granger causality that reveals major neural communications. We find a reproducible source for corollary discharge across multiple speech production paradigms localized to the ventral speech motor cortex before speech articulation. The uncovered discharge predicts the degree of auditory cortex suppression during speech, its well-documented consequence. These results reveal the human corollary discharge source and timing with far-reaching implication for speech motor-control as well as auditory hallucinations in human psychosis.