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.

Netherton syndrome in one Chinese adult with a novel mutation in the SPINK5 gene and immunohistochemical studies of LEKTI.

BACKGROUND: Netherton syndrome (NS) is a severe autosomal recessive ichthyosis. It is characterized by congenital ichthyosiform erythroderma, trichorrhexis invaginata, ichthyosis linearis circumflexa, atopic diathesis, and frequent bacterial infections. The disease is caused by mutations in the SPINK5 (serine protease inhibitor Kazal-type 5) gene, a new type of serine protease inhibitor involved in the regulation of skin barrier formation and immunity. We report one Chinese adult with NS. The patient had typical manifestation of NS except for trichorrhexis invaginata with an atopic diathesis and recurrent staphylococcal infections since birth. AIMS: To evaluate the gene mutation and of its product activity of SPINK5 gene in confirmation of the diagnosis of one Chinese adult with NS. MATERIALS AND METHODS: To screen mutations in the SPINK5 gene, 33 exons and flanking intron boundaries of SPINK5 were amplified with polymerase chain reaction (PCR) and used for direct sequencing. In addition, immunohistochemical staining of LEKTI (lymphoepithelial Kazal-type-related inhibitor) with specific antibody was used to confirm the diagnosis of NS. The results were compared with that of healthy individuals (twenty-five blood samples). RESULTS: A G318A mutation was found at exon 5 of patient's SPINK5 gene which is a novel missense mutation. The PCR amplification products with mutation-specific primer were obtained only from the DNA of the patients and their mother, but not from their father and 25 healthy individuals. Immunohistochemical studies indicated there was no LEKTI expression in NS patient's skin and there was a strong LEKTI expression in the normal human skin. CONCLUSION: In this report, we describe heterozygous mutation in the SPINK5 gene and expression of LEKTI in one Chinese with NS. The results indicate that defective expression of LEKTI in the epidermis and mutations of SPINK5 gene are reliable for diagnostic feature of NS with atypical clinical symptoms.