Haruhiko Nishimura

Abstract The echo state network (ESN) is an excellent machine learning model for processing time-series data. This model, utilising the response of a recurrent neural network, called a reservoir, to input signals, achieves high training efficiency. Introducing time-history terms into the neuron model of the reservoir is known to improve the time-series prediction performance of ESN, yet the reasons for this improvement have not been quantitatively explained in terms of reservoir dynamics characteristics. Therefore, we hypothesised that the performance enhancement brought about by time-history terms could be explained by delay capacity, a recently proposed metric for assessing the memory performance of reservoirs. To test this hypothesis, we conducted comparative experiments using ESN models with time-history terms, namely leaky integrator ESNs (LI-ESN) and chaotic echo state networks (ChESN). The results suggest that compared with ESNs without time-history terms, the reservoir dynamics of LI-ESN and ChESN can maintain diversity and stability while possessing higher delay capacity, leading to their superior performance. Explaining ESN performance through dynamical metrics are crucial for evaluating the numerous ESN architectures recently proposed from a general perspective and for the development of more sophisticated architectures, and this study contributes to such efforts.

INTRODUCTION: Continuous monitoring of relative blood volume (percentage BV) in hemodialysis (HD) is critical for determining dry weight and preventing intradialytic hypotension. However, the cause of the blood volume variation remains unknown. This research aims to examine factors that influence the percentage BV. METHODS: We devised a formula based on coefficients ("a," "τ" and "b") to predict changes in percentage BV. "a" denotes a significant decrease in percentage BV in the early stages of HD. "τ" represents the transition from early to late phase of HD. "b" denotes the slope of the decrease in percentage BV in the late phase of HD. We measured the percentage BV in 18 patients with end-stage renal disease. The coefficients were estimated by fitting experimental data from patients using a least squares optimization algorithm. A correlation analysis of these parameters and patient predialysis data was performed. RESULTS: Ultrafiltration rate (UFR) was found to be negatively correlated with "b" (r = -0.851, p < 0.01). However, UFR was not significantly related to "a." Predialysis serum total protein level was negatively correlated with "a" (r = -0.531, p = 0.042). Predialysis serum albumin and predialysis sodium were not significantly correlated with "a" and "τ". Plasma osmolarity did not have a significant relationship with "a" and "τ". DISCUSSION/CONCLUSION: UFR influenced the decrease in percentage BV in the late phase but did not influence the decrease of percentage BV in the early phase. "a" was associated with predialysis serum total protein level level but not with plasma osmolality or predialysis sodium. This implies that colloid oncotic pressure is important for plasma refilling immediately after dialysis begins.During the change of percentage BV, the decrease in the early phase of dialysis was not related to UFR, but related to other parameters, especially predialysis total protein level. A decrease in the late phase of dialysis is related to UFR.