Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

An efficient approach of modelling the flexural cracking behaviour of un-notched plain concrete prisms subject to monotonic and cyclic loading

In the field of vibration-based damage detection of concrete structures efficient damage models are needed to better understand changes in the vibration properties of cracked structures. These models should quantitatively replicate the damage mechanisms in concrete and easily be used as damage detection tools. In this paper, the flexural cracking behaviour of plain concrete prisms subject to monotonic and cyclic loading regimes under displacement control is tested experimentally and modelled numerically. Four-point bending tests on simply supported un-notched prisms are conducted, where the cracking process is monitored using a digital image correlation system. A numerical model, with a single crack at midspan, is presented where the cracked zone is modelled using the fictitious crack approach and parts outside that zone are treated in a linear-elastic manner. The model considers crack initiation, growth and closure by adopting cyclic constitutive laws. A multi-variate Newton-Raphson iterative solver is used to solve the non-linear equations to ensure equilibrium and compatibility at the interface of the cracked zone. The numerical results agree well with the experiments for both loading scenarios. The model shows good predictions of the degradation of stiffness with increasing load. It also approximates the crack-mouth-opening-displacement when compared with the experimental data of the digital image correlation system. The model is found to be computationally efficient as it runs full analysis for cyclic loading in less than 2. min, and it can therefore be used within the damage detection process. © 2013 Elsevier Ltd.

Cubically convergent iterations for invariant subspace computation

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

A Grassman-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh Quotient Iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with recently proposed Newton algorithms on Riemannian manifolds.

Optimization on manifolds: Methods and applications

This paper provides an introduction to the topic of optimization on manifolds. The approach taken uses the language of differential geometry, however,we choose to emphasise the intuition of the concepts and the structures that are important in generating practical numerical algorithms rather than the technical details of the formulation. There are a number of algorithms that can be applied to solve such problems and we discuss the steepest descent and Newton's method in some detail as well as referencing the more important of the other approaches.There are a wide range of potential applications that we are aware of, and we briefly discuss these applications, as well as explaining one or two in more detail. © 2010 Springer -Verlag Berlin Heidelberg.

Fast and effective analysis methods for fiber Raman amplifiers

A series of new single-step methods and their corresponding algorithms with automatic step size adjustment for model equations of fiber Raman amplifiers are proposed and compared in this paper. On the basis of the Newton-Raphson method, multiple shooting algorithms for the two-point boundary value problems involved in solving Raman amplifier propagation equations are constructed. A verified example shows that, compared with the traditional Runge-Kutta methods, the proposed methods can increase the accuracy by more than two orders of magnitude under the same conditions. The simulations for Raman amplifier propagation equations demonstrate that our methods can increase the computing speed by more than 5 times, extend the step size significantly, and improve the stability in comparison with the Dormand-Prince method. The numerical results show that the combination of the multiple shooting algorithms and the proposed methods has the capacity to rapidly and effectively solve the model equations of multipump Raman amplifiers under various conditions such as co-, counter- and bi-directionally pumped schemes, as well as dual-order pumped schemes.

Density Gradient Ultracentrifugation of Nanotubes: Interplay of Bundling and Surfactants Encapsulation

Density gradient ultracentrifugation (DGU) has emerged as a promising tool to prepare chirality enriched nanotube samples. Here, we assess the performance of different surfactants for DGU. Bile salts (e.g., sodium cholate (SC), sodium deoxycholate (SDC), and sodium taurodeoxycholate (TDC)) are more effective in individualizing Single Wall Carbon Nanotubes (SWNTs) compared to linear chain surfactants (e.g., sodium dodecylbenzene sulfonate (SDBS) and sodium dodecylsulfate (SDS)) and better suited for DGU. Using SC, a narrower diameter distribution (0.69-0.81 nm) is achieved through a single DGU step on CoMoCAT tubes, when compared to SDC and TDC (0.69-0.89 nm). No selectivity is obtained using SDBS. due to its ineffectiveness in debundling. We assign the reduce selectivity of dihydroxy bile salts (S DC and TDC) in comparison with trihydroxy SC to the formation of secondary micelles. This is determined by the number and position of hydroxyl ( OH) groups on the a-side of the steroid backbone. We also enrich CoMoCAT SWNT in the 0.84-0.92 nm range using the Pluronic F98 triblock copolymer. Mixtures of bile salts (SC) and linear chain surfactants (SOS) are used to enrich metallic and semiconducting laser-ablation grown SWNTs. We demonstrate enrichment of a single chirality, (6,5), combining diameter and metallic versus semiconductillg separation on CoMoCAT samples.

Parallel Fully-Implicit Computation of Magnetohydrodynamics Acceleration Experiments

A three-dimensional MHD solver is described in the paper. The solver simulates reacting flows with nonequilibrium between translational-rotational, vibrational and electron translational modes. The conservation equations are discretized with implicit time marching and the second-order modified Steger-Warming scheme, and the resulted linear system is solved iteratively with Newton-Krylov-Schwarz method that is implemented by PETS,: package. The results of convergence tests arc plotted, which show good scalability and convergence around twice faster when compared with the DPLR method. Then five test runs are conducted simulating the experiments done at the NASA Ames MHD channel, and the calculated pressures, temperatures, electrical conductivity, back EMF, load factors and flow accelerations are shown to agree with the experimental data. Our computation shows that the electrical conductivity distribution is not uniform in the powered section of the MHD channel, and that it is important to include Joule heating in order to calculate the correct conductivity and the MHD acceleration.

超音速冷靶的性质与应用

对超音速冷靶的形成机理进行了系统介绍,并利用热力学、流体力学、Newton力学对超音速靶的形成过程和性质参数进行简要推导,并根据推导结果编写程序计算了气体靶的各种参数及其与冷靶喷嘴各种参数的关系,得到了不同实验条件下超音速靶的性质参数,与实验测得的数据吻合很好.最后,依据理论计算和实验结果的验证发现:降低靶气体的初始温度、初始气压及提高抽速,可以有效地减小气体靶的横向动量分散,有利于提高粒子与原子分子碰撞实验中反冲离子动量测量精度.实际中,在综合考虑实验中气体的初始气压的同时,还需要降低靶气体的初始温度,提高气体的抽速.

The generalized second law of thermodynamics in generalized gravity theories

We investigate the generalized second law of thermodynamics (GSL) in generalized theories of gravity. We examine the total entropy evolution with time including the horizon entropy, the non-equilibrium entropy production, and the entropy of all matter, field and energy components. We derive a universal condition to protect the generalized second law and study its validity in different gravity theories. In Einstein gravity (even in the phantom-dominated universe with a Schwarzschild black hole), Lovelock gravity and braneworld gravity, we show that the condition to keep the GSL can always be satisfied. In f ( R) gravity and scalar-tensor gravity, the condition to protect the GSL can also hold because the temperature should be positive, gravity is always attractive and the effective Newton constant should be an approximate constant satisfying the experimental bounds.

基于半监督学习的P2P协议识别

协议识别是进行有效的网络管理与控制的重要条件，由于新的P2P软件（以Skype,Emule，BitComet，迅雷为代表）开始使用加密协议和协议伪装等技术手段来防止被网管探测、识别、封堵，传统的根据协议特征码来识别的方式已经难以识别这些软件产生的流量。基于流量特征的P2P协议识别的方法是目前研究的主要方向，将机器学习的理论与模型运用到协议识别领域是发展的一个趋势。通过对传输层数据包(包括TCP和UDP数据包)进行分析，并结合P2P系统所表现出来的流量特征，来识别某个网络流是否属于P2P。这类方法包括：TCP/UDP端口识别技术、网络直径分析技术、节点角色分析技术、协议对分析技术和地址端口对分析技术等，但是其准确性和识别率不如特征码识别。本文就基于半监督聚类的模型运用到识别具体P2P应用的可能性进行了分析与实验，提出了一种基于Newton-Raphson方法学习特征权值矩阵的训练的办法，在依据P2P应用特征选取连接特征的基础上进一步提高系统识别准确率和召回率。在本文的实验环境下，针对具体的BitComet和Emule应用的识别器的识别率和召回率均达到了85%左右，在加密协议的识别上取得了不错的效果。如何优化系统的识别准确率和召回率，提高系统效率是本文重点研究并试图解决的问题，主要包括以下三个方面的成果：一、实验并分析了基于半监督学习的聚类模型在加密P2P应用识别上的效果，同时总结了一套分析P2P协议特征的办法。二、将Newton-Raphson方法引入到连接特征的选取上，将特征权值矩阵用于距离的计算，进一步提高了训练和识别的效果。三、基于KD-Tree的识别器的实现使得整个在线识别过程能在内核的协议层高效实现，有效的控制了系统的计算复杂度。

Correlation analysis of the structures and gas-liquid chromatographic retention indices of amines

Quantitative structure-retention relationship(QSRR) was studied for amines to gas-liquid chromatography on three stationary phases of different polarities with the topological indices A(m) (A(m1), A(m2), A(m3)) and gravitational index GI. The algorithm of "Leaps and Bounds" was performed for selection of the variables. And the multi-regression and the quasi-Newton neural networks were employed for the calculation with better results.

Structure-activity relationships for antiplasmodial activity among aminoquinolines

The extended gravitational index G(Q) and quantum-chemical descriptors were calculated for the relationship analysis of aminoquinolines. An evolutionary algorithm was described for variable selection and building QSAR models. And the quasi-newton neural networks were employed with better results.

海水和海泥中阴极保护系统的边界元计算

随着人们对能源需求的不断增加，深海海洋油气开发已引起了人们越来越大的兴趣，随之而来的是对海洋构筑物的设计和防护提出了更高的要求。由于在传统的阴极保护工程设计中，大多采用实际测量或经验估计的方法来掌握电位分布规律，很难真实的反映构筑物的实际状态，为了确保安全，往往采用较大的安全系数，不但会造成金属材料的浪费，而且还会在构筑物的局部造成保护不足或过保护。 本文研究了边界元方法（BEM）利用数值仿真技术对阴极保护状态下的海洋构筑物的保护状态进行模拟，从而获得阴极保护状态下的金属材料的电位分布。采用常数单元对于二维问题进行了研究，推导出了边界积分方程的离散化形式，并结合阴极保护环境下的阳极和阴极的极化曲线作为边界条件，建立了线性方程组。采用Newton-Raphson 迭代法和分段拟线性化的方法对边界条件做了线性化处理，应用FORTRAN语言开发出阴极保护的边界元仿真求解程序CPBEM，并利用该程序选择合适的算例进行了验证，结果表明该程序是有效和可行的。 通过管线钢在不同温度海泥埋片的腐蚀失重实验，证明了如果有充足的氧的供给的情况下，温度每增加10oC，腐蚀速度便增加一倍。阴极保护系统数值仿真的精确度最主要的影响因素就是阴极和阳极的极化曲线。而金属材料的极化曲线往往受到多种环境因素的影响，本文系统的讨论了在海泥介质中两种管线钢的腐蚀行为，对管线钢极化行为产生影响的各种环境因素，以及这些因素与金属的腐蚀速度之间的关系。首次将灰关联分析的手段运用到海泥介质的腐蚀，研究了环境因素对于ERW，SML两种管线钢在海泥中的腐蚀速率的影响。