ZONAL SPHERICAL POLYNOMIALS WITH MINIMAL L_1-NORM

Radial functions have become a useful tool in numerical mathematics. On the sphere they have to be identified with the zonal functions. We investigate zonal polynomials with mass concentration at the pole, in the sense of their L1-norm is attaining the minimum value. Such polynomials satisfy a complicated system of nonlinear e-quations (algebraic if the space dimension is odd, only) and also a singular differential equation of third order. The exact order of decay of the minimum value with respect to the polynomial degree is determined. By our results we can prove that some nodal systems on the sphere, which are defined by a minimum-property, are providing fundamental matrices which are diagonal-dominant or bounded with respect to the ∞-norm, at least, as the polynomial degree tends to infinity.

Design of Polynomial Fuzzy Neural Network Classifiers Based on Density Fuzzy C-Means and L2-Norm Regularization

In this paper, polynomial fuzzy neural network classifiers (PFNNCs) is proposed by means of density fuzzy c-means and L2-norm regularization. The overall design of PFNNCs was realized by means of fuzzy rules that come in form of three parts, namely premise part, consequence part and aggregation part. The premise part was developed by density fuzzy c-means that helps determine the apex parameters of membership functions, while the consequence part was realized by means of two types of polynomials including linear and quadratic. L2-norm regularization that can alleviate the overfitting problem was exploited to estimate the parameters of polynomials, which constructed the aggregation part. Experimental results of several data sets demonstrate that the proposed classifiers show higher classification accuracy in comparison with some other classifiers reported in the literature.

平均曲率L^2范数有界的双极小子流形

证明了满足一定曲率条件的黎曼流形中平均曲率L2范数有界的双极小子流形必是极小子流形,并讨论了一个更一般的结果和几个推论.

Joint 2D DOA and Doppler frequency estimation for L-shaped array using compressive sensing

A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.

Robust Latent Factor Analysis for Precise Representation of High-Dimensional and Sparse Data

High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.

Block Sparse Recovery via Mixed l_2/l_1 Minimization

We consider efficient methods for the recovery of block sparse signals from underdetermined system of linear equations. We show that if the measurement matrix satisfies the block RIP with δ2s 〈 0.4931, then every block s-sparse signal can be recovered through the proposed mixed l2/ll-minimization approach in the noiseless case and is stably recovered in the presence of noise and mismodeling error. This improves the result of Eldar and Mishali （in IEEE Trans. Inform. Theory 55： 5302-5316, 2009）. We also give another sufficient condition on block RIP for such recovery method： 58 〈 0.307.

具有抽象约束的l-稳定函数的多目标优化问题的二阶充分条件

对于多目标优化问题而言,二阶最优性条件在优化理论中占有非常重要的地位,尤其是多目标问题的二阶充分条件,因为它能保证求得的解确实是原问题的有效解。在已有的无约束l-稳定函数多目标优化问题的二阶充分条件的基础上,借助定向距离函数和l-稳定函数的性质及引入的广义二阶Peano(Dini)方向导数,进一步刻画了具有抽象约束的l-稳定函数的多目标优化问题的二阶孤立极小点的二阶充分条件。

ENHANCED BLOCK-SPARSE SIGNAL RECOVERY PERFORMANCE VIA TRUNCATED l2\l1-2 MINIMIZATION

In this paper,we investigate truncated l2\l1-2 minimization and its associated alternating direction method of multipliers(ADMM)algorithm for recovering the block sparse signals.Based on the block restricted isometry property(Block-RIP),a theoretical analysis is presen ted to guarantee the validity of proposed method.Our theore tical resul ts not only show a less error upper bound,but also promote the former recovery condition of truncated l1-2 method for sparse signal recovery.Besides,the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.

LMI Approach to Observer-based FD Systems Designing

Increasing the robustness to the unknown uncertainty and simultaneously enhancing the sensibility to the faults is one of the important issues considered in the fault detection development. Considering the L2-gain of residual system, this paper deals the observer-based fault detection problem. By using of H∞ control theory,an LMI approach to design fault detection observer is given. A numerical example is used to illustrate the effectiveness of the proposed approach.

EQUIVALENCE BETWEEN NONNEGATIVE SOLUTIONS TO PARTIAL SPARSE AND WEIGHTED l_1-NORM MINIMIZATIONS

Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different from other conditions based on the spark property, the mutual coherence, the null space property （NSP） and the restricted isometry property （RIP）, the RSP- based conditions are easier to be verified. Moreover, the proposed conditions guarantee not only the strong equivalence, but also the equivalence between the two problems. First, according to the foundation of the strict complemenrarity theorem of linear programming, a sufficient and necessary condition, satisfying the RSP of the sensing matrix and the full column rank property of the corresponding sub-matrix, is presented for the unique nonnegative solution to the weighted l1-norm minimization problem. Then, based on this condition, the equivalence conditions between the two problems are proposed. Finally, this paper shows that the matrix with the RSP of order k can guarantee the strong equivalence of the two problems.

CONVERGENCE ANALYSIS OF MIXED VOLUME ELEMENT-CHARACTERISTIC MIXED VOLUME ELEMENT FOR THREE-DIMENSIONAL CHEMICAL OIL-RECOVERY SEEPAGE COUPLED PROBLEM

The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.

Sum of squares methods for minimizing polynomial forms over spheres and hypersurfaces

Abstract This paper studies the problem of minimizing a homogeneous polynomial （form） f（x） over the unit sphere Sn-1 = {x ∈ R^n： ｜｜X｜｜2 = 1}. The problem is NP-hard when f（x） has degree 3 or higher. Denote by fmin （resp. fmax） the minimum （resp. maximum） value of f（x） on S^n-1. First, when f（x） is an even form of degree 2d, we study the standard sum of squares （SOS） relaxation for finding a lower bound of the minimum .fmin ：max γ s.t.f（x）-γ.｜｜x｜｜2^2d is SOS.Let fos be be the above optimal value. Then we show that for all n ≥ 2d,Here, the constant C（d） is independent of n. Second, when f（x） is a multi-form and ^-1 becomes a muilti-unit sphere, we generalize the above SOS relaxation and prove a similar bound. Third, when f（x） is sparse, we prove an improved bound depending on its sparsity pattern; when f（x） is odd, we formulate the problem equivalently as minimizing a certain even form, and prove a similar bound. Last, for minimizing f（x） over a hypersurface H（g） = {x E lRn： g（x） = 1} defined by a positive definite form g（x）, we generalize the above SOS relaxation and prove a similar bound.

THE HIGH ORDER BLOCK RIP CONDITION FOR SIGNAL RECOVERY

In this paper,we consider the recovery of block sparse signals,whose nonzero entries appear in blocks (or clusters)rather than spread arbitrarily throughout the signal,from incomplete linear measurements.A high order sufficient condition based on block RIP is obtained to guarantee the stable recovery of all block sparse signals in the presence of noise,and robust recovery when signals are not exactly block sparse via mixed l2/l1 minimization.Moreover,a concrete example is established to ensure the condition is sharp.The significance of the results presented in this paper lies in the fact that recovery may be possible under more general conditions by exploiting the block structure of the sparsity pattern instead of the conventional sparsity pattern.

Angel estimation via frequency diversity of the SIAR radar based on Bayesian theory

The orthogonal signals of multi-carrier-frequency emission and multiple antennas receipt module are used in SIAR radar.The corresponding received echo is equivalent to non-uniform spatial sampling after the frequency diversity process.As using the traditional Fourier transform will result in the target spectral with large sidelobe,the method presented in this paper firstly makes the preordering treatment for the position of the received antenna.Then,the Bayesian maximum posteriori estimation with l2-norm weighted constraint is utilized to achieve the equivalent uniform array echo.The simulations present the spectrum estimation in angle precision estimation of multiple targets under different SNRs,different virtual antenna numbers and different elevations.The estimation results confirm the advantage of SIAR radar both in array expansion and angle estimation.

On the k-sample Behrens-Fisher problem for high-dimensional data

For several decades, much attention has been paid to the two-sample Behrens-Fisher (BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures. Little work, however, has been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal populations with unequal covariance structures. In this paper we study this challenging problem via extending the famous Scheffe’s transformation method, which reduces the k-sample BF problem to a one-sample problem. The induced one-sample problem can be easily tested by the classical Hotelling’s T 2 test when the size of the resulting sample is very large relative to its dimensionality. For high dimensional data, however, the dimensionality of the resulting sample is often very large, and even much larger than its sample size, which makes the classical Hotelling’s T 2 test not powerful or not even well defined. To overcome this difficulty, we propose and study an L 2-norm based test. The asymptotic powers of the proposed L 2-norm based test and Hotelling’s T 2 test are derived and theoretically compared. Methods for implementing the L 2-norm based test are described. Simulation studies are conducted to compare the L 2-norm based test and Hotelling’s T 2 test when the latter can be well defined, and to compare the proposed implementation methods for the L 2-norm based test otherwise. The methodologies are motivated and illustrated by a real data example.

链霉菌M-Z18膜蛋白ε-聚赖氨酸降解酶的分离纯化、酶学性质及应用

【目的】研究链霉菌Streptomyces sp.M-Z18ε-聚赖氨酸降解酶(Pld)的分离纯化及其生理生化特性,并利用该酶制备低聚合度ε-聚赖氨酸(ε-PL)。【方法】菌体细胞经超声破碎、NaSCN溶解和HiTrapTMButyl HP疏水层析制备到Pld,随后研究了其酶学性质、动力学和降解ε-PL过程,最后利用常量稀释法比较了不同聚合度范围ε-PL的最小抑菌浓度。【结果】从Streptomyces sp.M-Z18细胞膜上分离纯化到Pld,纯化倍数为80.4倍,回收率达到59.3%。以L-赖氨酰对硝基苯胺为底物,酶促反应的最适温度为37℃,最适pH为7.0,动力学常数Km为0.621 mmol/L,Vmax为701.16 nmol/min·mg;酶活在pH 7.0-10.0和50℃以下稳定。降解ε-PL实验发现,纯化到的Pld以内切方式降解ε-PL。抑菌实验表明,高聚合度ε-PL(30-35)对细菌的抑制效果较好,而低聚合度ε-PL(8-20)更有利于抑制酵母菌的生长,各种聚合度ε-PL对霉菌的生长抑制均较差。【结论】从ε-PL产生菌中分离纯化到内切型ε-PL降解酶,发现不同聚合度范围ε-PL对微生物的抑制能力存在显著差异。