紫色球杆菌视紫红质光谱特性的机器学习研究

近年来，机器学习等人工智能技术被应用于蛋白质工程，其在蛋白质结构、功能预测、催化活性等研究中具有独特优势。在未知蛋白质结构的情况下，将蛋白质序列和功能特性与机器学习相结合，基于序列-活性关系（innovative sequence-activity relationship，ISAR）算法，将蛋白质氨基酸序列数字化，用快速傅里叶变换（fast four transform，FFT）进行预处理，再进行偏最小二乘回归建模，可在数据集较少情况下拟合得到最佳模型。通过机器学习对紫色球杆菌视紫红质（gloeobacter violaceus rhodopsin，GR）的突变体蛋白质氨基酸序列与光谱最大吸收波长进行建模，获得了最佳模型。用最佳索引LEVM760106建模得到的确定系数R² 为0.944，均方误差E为11.64。用小波变换进行的预处理，其R² 虽也约为0.944，但E大于11.64，不及FFT进行的预处理。方法较好地解决了蛋白质序列与功能特性之间的数学建模问题，在蛋白质工程中可为预测更优的突变体提供支持。     

A molecular fluorophore in citric acid/ethylenediamine carbon dots identified and quantified by multinuclear solid-state nuclear magnetic resonance

The composition of fluorescent polymer nanoparticles, commonly referred to as carbon dots, synthesized by microwave-assisted reaction of citric acid and ethylenediamine was investigated by ¹³C, ¹³C{¹H}, ¹H─¹³C, ¹³C{¹⁴N}, and ¹⁵N solid-state nuclear magnetic resonance (NMR) experiments. ¹³C NMR with spectral editing provided no evidence for significant condensed aromatic or diamondoid carbon phases. ¹⁵N NMR showed that the nanoparticle matrix has been polymerized by amide and some imide formation. Five small, resolved ¹³C NMR peaks, including an unusual ═CH signal at 84 ppm (¹H chemical shift of 5.8 ppm) and ═CN₂ at 155 ppm, and two distinctive ¹⁵N NMR resonances near 80 and 160 ppm proved the presence of 5-oxo-1,2,3,5-tetrahydroimidazo[1,2-a]pyridine-7-carboxylic acid (IPCA) or its derivatives. This molecular fluorophore with conjugated double bonds, formed by a double cyclization reaction of citric acid and ethylenediamine as first shown by Y. Song, B. Yang, and coworkers in 2015, accounts for the fluorescence of the carbon dots. Cross-peaks in a ¹H─¹³C HETCOR spectrum with brief ¹H spin diffusion proved that IPCA is finely dispersed in the polyamide matrix. From quantitative ¹³C and ¹⁵N NMR spectra, a high concentration (18 ± 2 wt%) of IPCA in the carbon dots was determined. A pronounced gradient in ¹³C chemical-shift perturbations and peak widths, with the broadest lines near the COO group of IPCA, indicated at least partial transformation of the carboxylic acid of IPCA by amide or ester formation.     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Yb3+掺杂KY(WO4)2激光晶体生长、结构与光谱分析

采用顶部籽晶提拉法(TSSG)生长出Yb:KY(WO₄)₂(Yb:KYW)激光晶体.对预烧后的原料及晶体进行了XRD分析，结果表明，分别在920℃和600℃预烧8h后的熔质和助熔剂基本上形成一相，抑止了实验中的挥发问题；所生长的晶体为β-Yb:KYW，计算其晶格常数为a=1.063nm，b=1.034nm，c=0.755nm，β=130.75°.测得不同厚度样品的吸收光谱，结果表明样品在933nm和981nm有较强的吸收峰，计算出主峰981nm的吸收截面σ关键词： Yb:KYW TSSG法 晶体结构 光谱参数     

氪灯和氙灯光谱强度分布和光谱效率测量

氪灯、氙灯光谱强度分布和光谱效率测量是反映氪灯、氙灯性能的关键指标。介绍了一套新型的氪灯、氙灯光谱强度分布和光谱效率检测系统。该系统是一套测量连续发光灯和脉冲闪光灯发光性能及效果的综合检测设备。该检测单元采用计算机进行操控,人机界面良好,便于检验人员进行氪灯和氙灯光谱强度分布和光谱效率的批量检测。检验人员利用该系统可进行装机模拟试验和可靠性试验,可对氪灯和氙灯的性能进行必要的分析研究,不断地积累了氪灯和氙灯的检验数据和经验。     

Finite-Band Potentials with Trigonal Curves

We construct Dubrovin equations and trace formulas for finite-band operators with trigonal curves and present some examples.     

关于矩阵方程X+A*X-nA＝I的正定解

本文对任意正整数n界定了矩阵方程X A*X-nA=I的正定解的特征值的范围,给出了它的极大正定解一个充分条件.     

8 mm回旋行波管和返波管的三折螺旋波纹波导色散分析

 三折螺旋波纹波导使TE11模和TE21模相互耦合，其色散曲线能够在宽频带内与电子回旋共振，因此需要对色散方程进行研究。提出了适合工程实用的行波模式和返波模式的色散方程，并对方程中的耦合系数进行了简化，误差在1%左右。利用CST软件的VBA语言对螺旋波纹波导进行建模和计算，根据模拟得到的传输特性曲线的特点，提出一种模拟方法，将模拟与理论计算得到的色散曲线作对比，误差在5%左右。