Deep Learning for Stable Monotone Dynamical Systems

Monotone systems, originating from real-world (e.g., biological or chemical) applications, are a class of dynamical systems that preserves a partial order of system states over time. In this work, we introduce a feedforward neural networks (FNNs)-based method to learn the dynamics of unknown stable nonlinear monotone systems. We propose the use of nonnegative neural networks and batch normalization, which in general enables the FNNs to capture the monotonicity conditions without reducing the expressiveness. To concurrently ensure stability during training, we adopt an alternating learning method to simultaneously learn the system dynamics and corresponding Lyapunov function, while exploiting monotonicity of the system.~The combination of the monotonicity and stability constraints ensures that the learned dynamics preserves both properties, while significantly reducing learning errors. Finally, our techniques are evaluated on two complex biological and chemical systems

Excitation and propagation of surface plasmon polaritons on a non-structured surface with a permittivity gradient.

Accompanied by the rise of plasmonic materials beyond those based on noble metals and the development of advanced materials processing techniques, it is important to understand the plasmonic behavior of materials with large-scale inhomogeneity (such as gradient permittivity materials) because they cannot be modeled simply as scatterers. In this paper, we theoretically analyze the excitation and propagation of surface plasmon polaritons (SPPs) on a planar interface between a homogeneous dielectric and a material with a gradient of negative permittivity. We demonstrate the following: (i) free-space propagating waves and surface waves can be coupled by a gradient negative-permittivity material and (ii) the coupling can be enhanced if the material permittivity variation is suitably designed. This theory is then verified by numerical simulations. A direct application of this theory, rainbow trapping, is also proposed, considering a realistic design based on doped indium antimonide. This theory may lead to various applications, such as ultracompact spectroscopy and dynamically controllable generation of SPPs

Co-extraction of high-quality RNA and DNA from rubber tree (Hevea brasiliensis)

High-quality nucleic acids are the basic requirement for performing genomic research. A reliable and efficient method was developed for co-extracting high-quality DNA and RNA from rubber tree (Hevea brasiliensis) in this study. Polyethylene glycol (PEG) and cetyltrimethylammonium bromide (CTAB) extraction buffer with high concentrations of polyvinylpyrrolidone (PVP) and β-mercaptoethanol was used in this study. The results show that 3.2% polyethylene glycol 8000 is the optimal concentration for successful separation of DNA and RNA. Spectrophotometric determination (A260/A280 and A260/A230 ratios), agarose electrophoresis analysis and reverse transcription (RT-PCR) of isolated nucleic acids indicate that high-quality DNA and RNA were extracted by this method. The general applicability of this method was also evaluated, and the results show that it was suitable for a variety of plants.Key words: Hevea brasiliensis, polyethylene glycol (PEG), nucleic acid, co-extraction, higher plants

data and code

This dataset is derived from rhizosphere and bulk soils of coniferous forests in the eastern Tibetan Plateau. Including soil organic carbon, nitrogen and phosphorus nutrients, microbial physiological properties, enzyme activity, soil PH, climate factors, amino sugars and other indicators. It is mainly used to analyze the cumulative efficiency of rhizosphere amino sugars, its driving factors and microbial regulation mechanism.In data processing, R software was used to analyze the relationship between microbial physiological properties and soil nutrient availability, and the codes used were submitted to this dataset simultaneously.</p