An Orthogonal Least Squares Based Approach to FIR Designs

This paper is concerned with the application of forward Orthogonal Least Squares (OLS) algorithm to the design of Finite Impulse Response (FIR) filters. The focus of this study is a new FIR filter design procedure and to compare this with traditional methods known as the fir2() routine provided by MATLAB.

A NEW SUFFICIENT CONDITION FOR SPARSE RECOVERY WITH MULTIPLE ORTHOGONAL LEAST SQUARES

A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤0.094.Compared with the existing results,our sufficient condition is not related to the sparsity level K.

REQUIRED NUMBER OF ITERATIONS FOR SPARSE SIGNAL RECOVERY VIA ORTHOGONAL LEAST SQUARES

In countless applications,we need to reconstruct a K-sparse signal x∈R n from noisy measurements y=Φx+v,whereΦ∈R^(m×n)is a sensing matrix and v∈R m is a noise vector.Orthogonal least squares(OLS),which selects at each step the column that results in the most significant decrease in the residual power,is one of the most popular sparse recovery algorithms.In this paper,we investigate the number of iterations required for recovering x with the OLS algorithm.We show that OLS provides a stable reconstruction of all K-sparse signals x in[2.8K]iterations provided thatΦsatisfies the restricted isometry property(RIP).Our result provides a better recovery bound and fewer number of required iterations than those proposed by Foucart in 2013.

Microbiomics and metabolomics insights into the microbial regulation on the formation of flavor components in the traditional fermentation process of Chinese Hongqu aged vinegar

This study aimed to investigate microbial succession and metabolic dynamics during the traditional fermentation of Hongqu aged vinegar,and explore the core functional microbes closely related to the formation of flavor components.Microbiome analysis demonstrated that Lactobacillus,Acetobacter,Bacillus,Enterobacter,Lactococcus,Leuconostoc and Weissella were the predominant bacterial genera,while Aspergillus piperis,Aspergillus oryzae,Monascus purpureus,Candida athensensis,C.xylopsoci,Penicillium ochrosalmoneum and Simplicillium aogashimaense were the predominant fungal species.Correlation analysis revealed that Acetobacter was positively correlated with the production of tetramethylpyrazine,acetoin and acetic acid,Lactococcus showed positive correlation with the production of 2-nonanone,2-heptanone,ethyl caprylate,ethyl caprate,1-hexanol,1-octanol and 1-octen-3-ol,C.xylopsoci and C.rugosa were positively associated with the production of diethyl malonate,2,3-butanediyl diacetate,acetoin,benzaldehyde and tetramethylpyrazine.Correspondingly,non-volatile metabolites were also detected through ultra-performance liquid chromatography-quadrupole time-of-flight mass spectrometry.A variety of amino acids and functional dipeptides were identified during the traditional brewing of Hongqu aged vinegar.Correlation analysis revealed that Lactobacillus was significantly associated with DL-lactate,indolelactic acid,D-(+)-3-phenyllactic acid,pimelic acid,pregabalin and 3-aminobutanoic acid.This study is useful for understanding flavor formation mechanism and developing effective strategies for the suitable strains selection to improve the flavor quality of Hongqu aged vinegar.

A nonlinear PCA algorithm based on RBF neural networks

Traditional PCA is a linear method, but most engineering problems are nonlinear. Using the linear PCA in nonlinear problems may bring distorted and misleading results. Therefore, an approach of nonlinear principal component analysis (NLPCA) using radial basis function (RBF) neural network is developed in this paper. The orthogonal least squares (OLS) algorithm is used to train the RBF neural network. This method improves the training speed and prevents it from being trapped in local optimization. Results of two experiments show that this NLPCA method can effectively capture nonlinear correlation of nonlinear complex data, and improve the precision of the classification and the prediction.

A novel NIRS modelling method with OPLS-SPA and MIX-PLS for timber evaluation

The identification of timber properties is important for safe application.Near Infrared Spectroscopy(NIRS)technology is widely-used because of its simplicity,efficiency,and positive environmental attributes.However,in its application,weak signals are extracted from complex,overlapping and changing information.This study focused on the stability of NIR modeling.The Orthogonal Partial Least Squares(OPLS)and Successive Projections Algorithm(SPA)eliminates noise and extracts effective spectra,and an ensemble learning method MIX-PLS,is applied to establish the model.The elastic modulus of timber is taken as an example,and 201 wood samples of three species,Xylosmacongesta(Lour.)Merr.,Acer pictum subsp.mono,and Betula pendula,samples were divided into three groups to investigate modelling performance.The results show that OPLS can preprocess the near-infrared spectroscopy information according to the target object in the face of the system error and reduce errors to minimum.SPA finally selects 13 spectral bands,simplifies the NIR spectral data and improves model accuracy.The Pearson's correlation coefficient of Calibration(Rc)and the Pearson's correlation coefficient of Prediction(Rp)of Mix Partial Least Squares(MIX-PLS)were 0.95 and 0.90,and Root Mean Square Error of Calibration(RMSEC)and Root Mean Square Error of Prediction(RMSEP)are 2.075 and 6.001,respectively,which shows the model has good generalization abilities.

The improved element-free Galerkin method forthree-dimensional wave equation

The paper presents the improved element-free Galerkin （IEFG） method for three-dimensional wave propa- gation. The improved moving least-squares （IMLS） approx- imation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares （MLS） approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a dis- cretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scal- ing parameter, number of nodes and the time step length are considered for the convergence study.