Approximation formula for complex spacing ratios in the Ginibre ensemble.

Recently, Sá, Ribeiro, and Prosen [Phys. Rev. X 10, 021019 (2020)10.1103/PhysRevX.10.021019] introduced complex spacing ratios to analyze eigenvalue correlations in non-Hermitian systems. At present there are no analytical results for the probability distribution of these ratios in the limit of large system size. We derive an approximation formula for the Ginibre universality class of random matrix theory which converges exponentially fast to the limit of infinite matrix size. We also give results for moments of the distribution in this limit.

Investigation of the neural basis of expectation-based analgesia in the human brainstem and spinal cord by means of functional magnetic resonance imaging.

PURPOSE: The expected intensity of pain resulting from a noxious stimulus has been observed to have a strong influence on the pain that is perceived. The neural basis of pain reduction, as a result of expecting lower pain, was investigated using functional magnetic resonance imaging (fMRI) in the brainstem and spinal cord. METHODS: Functional MRI studies were carried out in a region spanning the brainstem and cervical spinal cord in healthy participants. Participants were familiarized with a noxious heat stimulus and study procedures in advance, and were informed during each trial that either a heat calibrated to produce moderate pain (Base state), or a temperature 1 °C lower (Low state), would be applied to their hand. However, the Base temperature was applied in every trial. RESULTS: Pain ratings were significantly reduced as a result of expecting lower temperatures. FMRI results demonstrate blood oxygenation-level dependent (BOLD) signal variations in response to participants being informed of the stimulus to expect, in advance of stimulation, and in response to stimulation. Significant coordination of BOLD signals was also detected across specific brainstem and spinal cord regions, with connectivity strengths that varied significantly with the study condition, and with individual pain ratings. The results identify regions that are known to be involved with arousal and autonomic regulation. CONCLUSIONS: Expectation-based analgesia is mediated by descending regulation of spinal cord nociceptive responses. This regulation appears to be related to arousal and autonomic regulation, consistent with the cognitive/affective dimension of pain.