Path integral approach to universal dynamics of reservoir computers.

In this work, we give a characterization of the reservoir computer (RC) by the network structure, especially the probability distribution of random coupling constants. First, based on the path integral method, we clarify the universal behavior of the random network dynamics in the thermodynamic limit, which depends only on the asymptotic behavior of the second cumulant generating functions of the network coupling constants. This result enables us to classify the random networks into several universality classes, according to the distribution function of coupling constants chosen for the networks. Interestingly, it is revealed that such a classification has a close relationship with the distribution of eigenvalues of the random coupling matrix. We also comment on the relation between our theory and some practical choices of random connectivity in the RC. Subsequently, we investigate the relationship between the RC's computational power and the network parameters for several universality classes. We perform several numerical simulations to evaluate the phase diagrams of the steady reservoir states, common-signal-induced synchronization, and the computational power in the chaotic time series inference tasks. As a result, we clarify the close relationship between these quantities, especially a remarkable computational performance near the phase transitions, which is realized even near a nonchaotic transition boundary. These results may provide us with a new perspective on the designing principle for the RC.

[A case of splenic injury after colonoscopy].

An 81-year-old woman lost consciousness and was taken to our hospital 3 days after colonoscopy was performed as a follow-up of endoscopic mucosal resection done 1 year ago for early sigmoid colon cancer detection. She had left hypochondrial pain. Based on abdominal contrast-enhanced computed tomography (CT) findings, she was diagnosed with abdominal bleeding due to injury to the lower splenic pole, and an urgent splenectomy was performed. In this case, there was no abdominal trauma to cause splenic injury. Injury to the lower splenic pole during colonoscopy was considered due to the adhesion found in the abdominal cavity. It is possible that the hemorrhage did not stop because she was taking antiplatelet drugs.