We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables’ trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system’s mean CFL number agrees with the full model’s.

Reticulate evolution through the interchanging of genetic components across organisms can impact significantly on the fitness and adaptation of species. Bread wheat (Triticum aestivum subsp. aestivum) is one of the most important crops in the world. Allopolyploid speciation, frequent hybridization, extensive introgression, and occasional horizontal gene transfer (HGT) have been shaping a typical paradigm of reticulate evolution in bread wheat and its wild relatives, which is likely to have a substantial influence on phenotypic traits and environmental adaptability of bread wheat. In this review, we outlined the evolutionary history of bread wheat and its wild relatives with a highlight on the interspecific hybridization events, demonstrating the reticulate relationship between species/subspecies in the genera Triticum and Aegilops. Furthermore, we discussed the genetic mechanisms and evolutionary significance underlying the introgression of bread wheat and its wild relatives. An in-depth understanding of the evolutionary process of Triticum species should be beneficial to future genetic study and breeding of bread wheat.

Background: Pittosporum tobira (Thunb.) Aiton is an aromatic medicinal plant widely cultivated in the world. However, the essential oils (EOs) from P. tobira flowers for anti-cancer potential is still not systematically studied. The present aim to elucidate the phytochemical composition of the EOs and to explore mechanism of anticancer action. Methods: The EOs were extracted and analyzed by headspace solid-phase microextraction (HS-SPME) with gas chromatography-mass spectrometry (GC-MS). Volatile components were identified according to Kovats retention index (KI) and NIST database. The anti-neoplasm mechanisms of the EOs was comprehensively investigated in lung carcinoma A549 and H460 cells. Results: A total of 47 secondary metabolites representing 94.18% of the EOs were successfully identified: monoterpenes and sesquiterpenes were the dominant terpenoids. The EOs exhibited antiproliferative activity on A549 and H460 lung carcinoma cells. Hoechst 33324 fluorescent staining indicated the typical characteristics of apoptosis and induced cycle phase arrest. AnnexinV/PI staining revealed that the number of apoptotic cells was increased. Furthermore, the EOs also induced the caspase-mediated mitochondrial apoptosis pathway. Conclusions: Findings suggest that the full-scale chemical composition and first characterization of anticancer activities of the EOs, it could be used for integrative natural anti-cancer agents in health care should be pay more attention.