Simulating the Monty Hall problem in a DNA sequencing machine

The Monty Hall problem is a decision problem with an answer that is surprisingly counter-intuitive yet provably correct. Here we simulate and prove this decision in a high-throughput DNA sequencing machine, using a simple encoding. All possible scenarios are represented by DNA oligonucleotides, and gameplay decisions are implemented by sequencing these oligonucleotides from specific positions, with a single run simulating more than 12,000,000 independent games. This work highlights high-throughput DNA sequencing as a new tool that could extend existing capabilities and enable new encoding schemes for problems in DNA computing.     

Scattering of Tollmien-Schlichting waves by localized roughness in transonic boundary layers

The laminar-turbulent transition in boundary-layer flows is often affected by wall imperfections, because the latter may interact with either the freestream perturbations or the oncoming boundary-layer instability modes, leading to a modification of the accumulation of the normal modes. The present paper particularly focuses on the latter mechanism in a transonic boundary layer, namely, the effect of a two-dimensional(2 D) roughness element on the oncoming Tollmien-Schlichting(T-S) modes when they propagate through the region of the rapid mean-flow distortion induced by the roughness. The wave scattering is analyzed by adapting the local scattering theory developed for subsonic boundary layers(WU, X. S. and DONG, M. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794, 68–108(2006)) to the transonic regime, and a transmission coefficient is introduced to characterize the effect of the roughness. In the sub-transonic regime, in which the Mach number is close to, but less than, 1, the scattering system reduces to an eigenvalue problem with the transmission coefficient being the eigenvalue; while in the super-transonic regime, in which the Mach number is slightly greater than 1, the scattering system becomes a high-dimensional group of linear equations with the transmission coefficient being solved afterward. In the largeReynolds-number asymptotic theory, the K′arm′an-Guderley parameter is introduced to quantify the effect of the Mach number. A systematical parametric study is carried out,and the dependence of the transmission coefficient on the roughness shape, the frequency of the oncoming mode, and the K′arm′an-Guderley parameter is provided.     

Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics

The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions.     

Comparative analysis of nucleosides,nucleobases, and amino acids in different parts of Angelicae Sinensis Radix by ultra high performance liquid chromatography coupled to triple quadrupole tandem mass spectrometry

A rapid and sensitive ultra high performance liquid chromatography coupled to triple quadrupole tandem mass spectrometry method was established and employed to determine 21 nucleosides, nucleobases, and amino acids in 60 samples from different parts of Angelicae Sinensis Radix. The established methods were validated by good linearity (r² > 0.9937), limits of detection (0.12–77.75 ng/mL), limits of quantitation (0.31–272.13 ng/mL), intra‐ and interday precisions (RSD ≤ 4.84%, RSD ≤ 6.26%), stability (RSD ≤ 5.92%), repeatability (RSD ≤ 7.14%), recovery (91.4–103.4%), and matrix effects (0.92–1.03). Chemical comparative analysis revealed that the content of total analytes in four parts of Angelicae Sinensis Radix were different, and exhibited the order: Head (14.89 mg/g) > Body (10.15 mg/g) > All (8.22 mg/g) > Tail (6.23 mg/g). Principal component analysis showed that the samples could be classified into four groups in accord with four different parts of Angelicae Sinensis Radix. The results could provide a scientific basis and reference for the quality control of Angelicae Sinensis Radix, and may be conducive to further research on the pharmacological activities of Angelicae Sinensis Radix.     

The observation of inherent spin Seebeck effect in Rh/YIG hybrid structure

Rhodium (Rh) is a 4d metal possessing a large spin orbit coupling strength and spin-Hall conductivity with a very small magnetic susceptibility, implying an insignificant magnetic proximity effect (MPE). We report here the observation of longitudinal spin Seebeck effect (LSSE) using Rh as a normal metal. A Rh film was sputtered on nanometer thick YIG films of highly crystalline nature and extremely low magnetic damping to obtain Rh/YIG hybrid structure. A clear thermal voltage V_th (SSE voltage) was obtained when a temperature gradient was applied on the Rh/YIG hybrid. The Rh film showed a very weak anomalous Hall resistance and the magneto-resistive testing clearly ruled out the magnetization of the Rh films via MPE. The anisotropic magnetoresistance (AMR) revealed a clear spin hall magnetoresistance (SMR) signal in Rh film implying a purely intrinsic spin current generation, free from any parasitic magnetic effects. The work can open a new window in the study of pure and uncontaminated spin current, generated in ferromagnetic insulators, using Rh as spin current detector.     

Experimental study of the effect of propellant asymmetrical distribution on anode current in a Hall effect thruster

This paper experimentally evaluated the effect of the disruption of the symmetrical distribution of the propellant on the characteristics of the anode current. The change in the asymmetry degree of the propellant distribution is achieved by supplying gas with a dual-cavity gas distributor. The results show that as the asymmetry degree increases, the magnitude of the anode current changes monotonically from a slow growth to a rapid growth, while the peak-to-peak value of the anode current exhibits a non-monotonic behavior. A preliminary analysis shows that the asymmetrical distribution of the propellant causes a nonuniform plasma generation along the azimuthal direction and consequently the appearance of an azimuthal electric field. The effect of the azimuthal electric field on the electron azimuthal drift as well as the induction of the electron axial drift are key factors that account for the change of the anode current and its oscillation.     

How do we understand mathematical practices in non-mathematical fields? Reflections inspired by cases from 12th and 13th century China

Recent studies of the history of mathematics have shed light on the diversity of mathematical practices in the ancient world. In this article, I address this issue from two perspectives. First, I analyze different mathematical instruments used in different domains in 12^th and 13^th century China. Second, by analyzing how the text is related to the problems written down in the same period, I argue that there existed two categories of mathematical problems. As a result, I suggest that problems, textual procedures, and material operations should be considered together when regarding various mathematical practices in mathematical and non-mathematical fields.     

卷积神经网络用于近红外光谱古筝面板木材分级

目前,我国乐器制作行业在古筝面板用木材等级的筛选上主要依赖于技师主观评判,但此法缺少科学理论的依据,效率低,客观性及出材率的提高等方面受到限制,无法满足乐器市场的大量需求。实现古筝面板用木材快速、智能化的分级工作是一个急需解决的课题。近红外光谱非常适用于测量含氢的有机物质。古筝面板木材主要化学成分的化学键均由含氢基团组成,不同等级板材的化学成分存在差异,这些差异反映在近红外光谱中,为判断木材等级提供了可能。同时卷积神经网络对非线性数据具有较强的特征提取能力,所以提出一种应用卷积神经网络模型对光谱数据进行分析的方法,进而判别木材的等级。应用了Savitzky Golay一阶、二阶微分两种预处理方法和核主成分分析、连续投影算法两种数据压缩方法,通过所设计的卷积神经网络模型以样本识别准确率和模型构建过程中的损失值作为判定指标选出最佳预处理和数据压缩方法。为了提高模型提取分析光谱数据的能力和避免过拟合现象,应用了多通道卷积核、批量归一化和early stopping策略,将通过两层卷积层提取的特征信息送入全连接层,从而充分提取剩余信息,通过Softmax函数获得板材的最终预测等级,从而确定了最终模型。最终Savitzky Golay一阶微分和核主成分分析为最佳数据处理方法,同时得出用于区分不同等级的古筝面板用木材的主要关键谱带,分别为1 163~1 243, 1 346~1 375和1 525~1 584 nm。将该模型应用于测试集样本,古筝面板用木材的等级识别准确率为95.5%。实验结果表明所提出的方法可以高效地处理光谱数据,有效识别区分不同等级的古筝面板用木材的关键特征,从而为广阔的乐器市场提供一定的技术支持。