Emerging Issues Questioning the Current Treatment Strategies for Lumbar Disc Herniation.

Lumbar disc herniation is among the common phenotypes of degenerative lumbar spine diseases, significantly affecting patients' quality of life. The practice pattern is diverse. Choosing conservative measures or surgical treatments is still controversial in some areas.

Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks.

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model.

Data-assisted reduced-order modeling of extreme events in complex dynamical systems.

The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics, depends on the formulation and analysis of relevant, complex dynamical systems. Such dynamical systems are characterized by high intrinsic dimensionality with extreme events having the form of rare transitions that are several standard deviations away from the mean. Such systems are not amenable to classical order-reduction methods through projection of the governing equations due to the large intrinsic dimensionality of the underlying attractor as well as the complexity of the transient events.