Constructing polynomial libraries for reservoir computing in nonlinear dynamical system forecasting.

Reservoir computing is an effective model for learning and predicting nonlinear and chaotic dynamical systems; however, there remains a challenge in achieving a more dependable evolution for such systems. Based on the foundation of Koopman operator theory, considering the effectiveness of the sparse identification of nonlinear dynamics algorithm to construct candidate nonlinear libraries in the application of nonlinear data, an alternative reservoir computing method is proposed, which creates the linear Hilbert space of the nonlinear system by including nonlinear terms in the optimization process of reservoir computing, allowing for the application of linear optimization. We introduce an implementation that incorporates a polynomial transformation of arbitrary order when fitting the readout matrix. Constructing polynomial libraries with reservoir-state vectors as elements enhances the nonlinear representation of reservoir states and more easily captures the complexity of nonlinear systems. The Lorenz-63 system, the Lorenz-96 system, and the Kuramoto-Sivashinsky equation are used to validate the effectiveness of constructing polynomial libraries for reservoir states in the field of state-evolution prediction of nonlinear and chaotic dynamical systems. This study not only promotes the theoretical study of reservoir computing, but also provides a theoretical and practical method for the prediction of nonlinear and chaotic dynamical system evolution.

New features of edge-selectively hydroxylated graphene nanosheets as NIR-II photothermal agent and sonothermal agent for tumor therapy.

Second near-infrared (NIR-II) laser-mediated photothermal therapy and sonothermal therapy using low-intensity focused ultrasound exposure for tumors have attracted increasing attention owing to their ability to penetrate deep tissues and provide noninvasive ablation with high therapeutic efficacy. However, their applications were limited by the shortness of optimal NIR-II photothermal agents and sonothermal agents. In this study, we discovered that the edge-selectively hydroxylated graphene nanosheets (EHG NSs) with excellent water dispersibility and an "intact conjugated plane" were not only an outstanding NIR-II photothermal agent but also an effective sonothermal agent for tumor therapy. EHG NSs were incorporated into an injectable adhesive thermosensitive hydrogel with a characteristic sol-gel phase transition behavior. EHG NSs endowed the injectable hydrogel with an exceptional photothermal effect under the laser irradiation (1064 nm, 1.0 W cm-2) as well as an effective sonothermal effect under ultrasonic exposure (3.0 MHz, 2.1 W cm-2), effectively killing tumor cells in vitro and inhibiting tumor growth after intratumoral injection. Especially, the NIR-II photothermal therapy based on the hybrid hydrogel completely ablated the primary tumors and effectively activated systemic anti-tumor immune responses benefiting from the protein adsorption capacity of the injectable hydrogel, significantly inhibiting the growth of the distal tumors. Collectively, EHG nanosheets loaded in the injectable hydrogel will be a promising "all-rounder" for noninvasive deep penetrating thermotherapy and a potent platform that integrates various therapies.