PDE-guided reservoir computing for image denoising with small data.

While network-based techniques have shown outstanding performance in image denoising in the big data regime requiring massive datasets and expensive computation, mathematical understanding of their working principles is very limited. Not to mention, their relevance to traditional mathematical approaches has not attracted much attention. Therefore, we suggest how reservoir computing networks can be strengthened in combination with conventional partial differential equation (PDE) methods for image denoising, especially in the small data regime. Given image data, PDEs generate sequential datasets enhancing desired image features, which provide the network with a better guideline for training in reservoir computing. The proposed procedure, reservoir computing in collaboration with PDEs (RCPDE), offers a synergetic combination of data-driven network-based methods and mathematically well-established PDE methods. It turns out that RCPDE outperforms both the usual reservoir computing and existing PDE approaches in image denoising. Furthermore, RCPDE also excels deep neural networks such as a convolutional neural network both in quality and in time in the small data regime. We believe that RCPDE reveals the great potential of reservoir computing in collaboration with various mathematically justifiable dynamics for better performance as well as for better mathematical understanding.

Association between Working Hours and Self-Rated Health.

This study compared the association between working hours and self-rated health (SRH) according to sex, socioeconomic status, and working conditions. In all, 25,144 participants were selected from the Korea National Health and Nutrition Examination Survey (KNHANES), conducted from 2010 to 2018. The risks of poor SRH, according to working hours, were investigated using multiple logistic regression. Both short and long working hours were associated with poor SRH. Men working short hours and women working long hours were at risk of poor SRH. Workers with fewer than nine years of education were at risk of poor SRH when working short hours, whereas workers with more than nine years of education were at risk when working long hours. Similarly, simple laborers were at risk of poor SRH when working short hours, while managers and professional workers were at risk when working long hours. When working for short hours, paid employees were at risk of poor SRH. Workers with a non-fixed work schedule showed no risk of poor SRH when working long or short hours. In conclusion, workers working short hours with low education and workers working long hours with high education were at risk of poor SRH. Working conditions were significantly related to the association between SRH and working hours.

Recurrent synchronization of coupled oscillators with spontaneous phase reformation.

Self-organizing and spontaneous breaking are seemingly opposite phenomena and hardly captured in a single model. We develop a second order Kuramoto model with phase-induced damping which shows phase locking together with spontaneous synchrony breaking and reformation. In a relatively large regime where the interacting force and the damping ratio are of the same order, the dynamics of the oscillators alternates in an irregular cycle of synchronization, formation-breaking, and reorganization. While the oscillators keep coming back to phase-locked states, their phase distribution repeatedly reforms. Also, the interevent time between bursty deviation from the synchronization states follows a power-law distribution, which implies that the synchronized states are maintained near a tipping point.