Prediction of human-Streptococcus pneumoniae protein-protein interactions using logistic regression

Streptococcus pneumoniae is a major cause of mortality in children under five years old. In recent years, the emergence of antibiotic-resistant strains of S. pneumoniae increases the threat level of this pathogen. For that reason, the exploration of S. pneumoniae protein virulence factors should be considered in developing new drugs or vaccines, for instance by the analysis of host-pathogen protein-protein interactions (HP-PPIs). In this research, prediction of protein-protein interactions was performed with a logistic regression model with the number of protein domain occurrences as features. By utilizing HP-PPIs of three different pathogens as training data, the model achieved 57–77 % precision, 64–75 % recall, and 96–98 % specificity. Prediction of human-S. pneumoniae protein-protein interactions using the model yielded 5823 interactions involving thirty S. pneumoniae proteins and 324 human proteins. Pathway enrichment analysis showed that most of the pathways involved in the predicted interactions are immune system pathways. Network topology analysis revealed β-galactosidase (BgaA) as the most central among the S. pneumoniae proteins in the predicted HP-PPI networks, with a degree centrality of 1.0 and a betweenness centrality of 0.451853. Further experimental studies are required to validate the predicted interactions and examine their roles in S. pneumoniae infection.     

A new operational vector approach for time-fractional subdiffusion equations of distributed order based on hybrid functions

This research study deals with the numerical solutions of linear and nonlinear time-fractional subdiffusion equations of distributed order. The main aim of our approach is based on the hybrid of block-pulse functions and shifted Legendre polynomials. We produce a novel and exact operational vector for the fractional Riemann–Liouville integral and use it via the Gauss–Legendre quadrature formula and collocation method. Consequently, we reduce the proposed equations to systems of equations. The convergence and error bounds for the new method are investigated. Six problems are tested to confirm the accuracy of the proposed approach. Comparisons between the obtained numerical results and other existing methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method.     

Two-Phase Image Segmentation by Nonconvex Nonsmooth Models with Convergent Alternating Minimization Algorithms

Two-phase image segmentation is a fundamental task to partition an image into foreground and background. In this paper, two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation. They extend the convex regularization on the characteristic function on the image domain to the nonconvex case, which are able to better obtain piecewise constant regions with neat boundaries. By analyzing the proposed non-Lipschitz model, we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm. This leads to two alternating strongly convex subproblems which can be easily solved. Similarly, we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case. Using the Kurdyka-Łojasiewicz property of the objective function, we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem. Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.     

A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related To Hörmander's Vector Fields

In this paper, we consider the divergence degenerate elliptic equation with bounded coefficients constructed by Hörmander's vector fields. We prove a De Giorgi type result, i.e., the local Hölder continuity for the weak solutions to the equation by providing a De Giorgi type lemma and extending the Moser iteration to the setting here. As a consequence, the Harnack inequality of weak solutions is also given.     

Quantum Bayesian computation

Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research.     

超声全矩阵数据联合稀疏重构的多测量向量模型应用

针对单测量向量模型(Single Measurement Vector,SMV)等传统压缩感知方法处理超声全矩阵数据时,存在重构精度低和重构耗时长等问题,本文研究了多测量向量模型(Multiple Measurement Vectors,MMV)应用的可行性。针对铝合金试块中不同深度的φ2 mm横通孔,分别使用MMV模型中的多测量稀疏贝叶斯(Multiple Sparse Bayesian Learning,MSBL)算法和SMV模型中的稀疏贝叶斯(Sparse Bayesian Learning,SBL)算法进行超声全矩阵数据重构,并实施全聚焦成像。随后,引入归一化均方误差和阵列性能因子评价图像和信号的重构效果。实验结果表明,SBL算法在25%采样率时的归一化均方误差为1.9%,而MSBL算法仅需15%采样率即可达到相似效果且耗时更少。     

多组件学习器实现有机分子沸点的精准预测

沸点(BP)是有机分子液体的基本物理化学量, 也是化学工业生产中的重要参数. 有机分子的沸点由分子结构决定, 呈现复杂的结构-沸点关系, 函数法(Function Method)、基团贡献法(Group Contribution Method)等传统方法无法应对复杂多样有机分子结构的预测, 应用范围狭窄, 预测精度低. 本研究中, 我们利用基于人工神经网络(ANN)和支持向量机(SVM)的多组件学习器实现有机分子沸点的精准预测. 我们构建了基于可解释性描述符的ANN、基于相关性描述符的ANN及基于复合分子指纹的SVM三个异质模型, 并通过包含4550个各种类别的有机分子沸点的数据集进行训练得到了三个异质性学习器, 最后集成三个学习器对有机分子沸点进行预测. 相比于传统方法和此前的定量结构性质关系(QSPR)模型, 多组件模型结合了三种模型的优点, 展现出很好的预测精度和泛化能力以及低的过拟合, 实现了对多种类型有机分子的沸点的有效预测.     

The least-squares meshfree method for rigid-plasticity with frictional contact

The least-squares meshfree method (LSMFM) for rigid-plasticity based on J₂-flow rule and infinitesimal theory is proposed. In the least-squares formulation the squared residuals of the constitutive and equilibrium equations are minimized. Those residuals are represented in a form of first-order differential system using the velocity and stress components as nodal unknowns and thus the proposed formulation is a mixed-type method. Also the penalty scheme for the enforcement of the boundary and frictional contact conditions is devised and the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near the contact interface. The proposed method does not require any structure of extrinsic cells for the construction of shape functions, the treatment of incompressibility, the integration of variational formulation and the reconstruction of approximation. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are discussed.     

Optimization of support positions to minimize the maximal deflection of structures

In this paper, the design sensitivity analysis for the deflection of a beam or plate structure is first investigated with respect to the position of a simple support using the discrete method. Both elastic and rigid supports are taken into account, and closed-form formulae for the deflection sensitivity are developed straightforwardly. Then, on the basis of the design sensitivity analysis, a heuristic optimization algorithm, called the evolutionary shift method, is presented for support position optimization to minimize the maximal deflection of a structure with a fixed grid mesh scheme. In each iterative loop, the support with the highest efficiency is shifted in priority. To facilitate the convergence of the process, a polynomial interpolation technique is employed to evaluate the solution more accurately. The optimal solution is achieved gradually with a minimum modification of the support layout design. Finally, three numerical examples are presented to demonstrate the validities of the sensitivity analysis and the optimization method. Results show that support optimization can improve the structural behavior significantly.     

基于Gibbs矢量估计卫星轨道姿态的滤波算法研究

针对“矢量观测 陀螺”这种典型的三轴稳定卫星姿态确定系统模式,引入具有四元数优越性的Gibbs矢量作为姿态参数,提出了一种新的具有良好实时性能的轨道姿态估计方案。在方案设计中,为描述卫星轨道姿态的Gibbs矢量,推导出了基于四元数的运动学方程,并将QUEST法作为处理多矢量观测信息的压缩技术引入估计器,使得滤波修正算法得以简化。另外,针对单矢量观测情况,给出了能够加快状态估值收敛速度的改进协方差修正算法。仿真结果验证,新方案的姿态估计精度与传统的欧拉角估计法相当,而运算效率却明显高于欧拉角估计法。