Local projection stabilized finite element method for Navier-Stokes equations

This paper extends the results of Matthies, Skrzypacz, and Tubiska for the Oseen problem to the Navier-Stokes problem. For the stationary incompressible Navier- Stokes equations, a local projection stabilized finite element scheme is proposed. The scheme overcomes convection domination and improves the restrictive inf-sup condition. It not only is a two-level approach but also is adaptive for pairs of spaces defined on the same mesh. Using the approximation and projection spaces defined on the same mesh, the scheme leads to much more compact stencils than other two-level approaches. On the same mesh, besides the class of local projection stabilization by enriching the approximation spaces, two new classes of local projection stabilization of the approximation spaces are derived, which do not need to be enriched by bubble functions. Based on a special interpolation, the stability and optimal prior error estimates are shown. Numerical results agree with some benchmark solutions and theoretical analysis very well.

Nonconforming local projection stabilization for generalized Oseen equations

A new method of nonconforming local projection stabilization for the gen- eralized Oseen equations is proposed by a nonconforming inf-sup stable element pair for approximating the velocity and the pressure. The method has several attractive features. It adds a local projection term only on the sub-scale （H ≥ h）. The stabilized term is simple compared with the residual-free bubble element method. The method can handle the influence of strong convection. The numerical results agree with the theoretical expectations very well.

Improved Local Projection for the Generalized Stokes Problem

We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties.An important feature of the methods is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations.Although the stability of the method has been established,for the homogeneous Stokes equations,the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space.This makes it much simpler and more attractive.The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations.

Fault Diagnosis Model Based on Feature Compression with Orthogonal Locality Preserving Projection

Based on feature compression with orthogonal locality preserving projection（OLPP）,a novel fault diagnosis model is proposed in this paper to achieve automation and high-precision of fault diagnosis of rotating machinery.With this model,the original vibration signals of training and test samples are first decomposed through the empirical mode decomposition（EMD）,and Shannon entropy is constructed to achieve high-dimensional eigenvectors.In order to replace the traditional feature extraction way which does the selection manually,OLPP is introduced to automatically compress the high-dimensional eigenvectors of training and test samples into the low-dimensional eigenvectors which have better discrimination.After that,the low-dimensional eigenvectors of training samples are input into Morlet wavelet support vector machine（MWSVM） and a trained MWSVM is obtained.Finally,the low-dimensional eigenvectors of test samples are input into the trained MWSVM to carry out fault diagnosis.To evaluate our proposed model,the experiment of fault diagnosis of deep groove ball bearings is made,and the experiment results indicate that the recognition accuracy rate of the proposed diagnosis model for outer race crack、inner race crack and ball crack is more than 90%.Compared to the existing approaches,the proposed diagnosis model combines the strengths of EMD in fault feature extraction,OLPP in feature compression and MWSVM in pattern recognition,and realizes the automation and high-precision of fault diagnosis.

Locality Preserving Discriminant Projection for Speaker Verification

In this paper, a manifold subspace learning algorithm based on locality preserving discriminant projection (LPDP) is used for speaker verification. LPDP can overcome the deficiency of the total variability factor analysis and locality preserving projection (LPP). LPDP can effectively use the speaker label information of speech data. Through optimization, LPDP can maintain the inherent manifold local structure of the speech data samples of the same speaker by reducing the distance between them. At the same time, LPDP can enhance the discriminability of the embedding space by expanding the distance between the speech data samples of different speakers. The proposed method is compared with LPP and total variability factor analysis on the NIST SRE 2010 telephone-telephone core condition. The experimental results indicate that the proposed LPDP can overcome the deficiency of LPP and total variability factor analysis and can further improve the system performance.

Face recognition using illuminant locality preserving projections

A novel supervised manifold learning method was proposed to realize high accuracy face recognition under varying illuminant conditions. The proposed method, named illuminant locality preserving projections （ILPP）, exploited illuminant directions to alleviate the effect of illumination variations on face recognition. The face images were first projected into low dimensional subspace, Then the ILPP translated the face images along specific direction to reduce lighting variations in the face. The ILPP reduced the distance between face images of the same class, while increase the dis tance between face images of different classes. This proposed method was derived from the locality preserving projections （LPP） methods, and was designed to handle face images with various illumi nations. It preserved the face image＇ s local structure in low dimensional subspace. The ILPP meth od was compared with LPP and discriminant locality preserving projections （DLPP）, based on the YaleB face database. Experimental results showed the effectiveness of the proposed algorithm on the face recognition with various illuminations.

A Comparative Study of Locality Preserving Projection and Principle Component Analysis on Classification Performance Using Logistic Regression

There are a variety of classification techniques such as neural network, decision tree, support vector machine and logistic regression. The problem of dimensionality is pertinent to many learning algorithms, and it denotes the drastic raise of computational complexity, however, we need to use dimensionality reduction methods. These methods include principal component analysis (PCA) and locality preserving projection (LPP). In many real-world classification problems, the local structure is more important than the global structure and dimensionality reduction techniques ignore the local structure and preserve the global structure. The objectives is to compare PCA and LPP in terms of accuracy, to develop appropriate representations of complex data by reducing the dimensions of the data and to explain the importance of using LPP with logistic regression. The results of this paper find that the proposed LPP approach provides a better representation and high accuracy than the PCA approach.

A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations

In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.

Which return regime induces overconfidence behavior?Artificial intelligence and a nonlinear approach

Overconfidence behavior,one form of positive illusion,has drawn considerable attention throughout history because it is viewed as the main reason for many crises.Investors’overconfidence,which can be observed as overtrading following positive returns,may lead to inefficiencies in stock markets.To the best of our knowledge,this is the first study to examine the presence of investor overconfidence by employing an artificial intelligence technique and a nonlinear approach to impulse responses to analyze the impact of different return regimes on the overconfidence attitude.We examine whether investors in an emerging stock market(Borsa Istanbul)exhibit overconfidence behavior using a feed-forward,neural network,nonlinear Granger causality test and nonlinear impulseresponse functions based on local projections.These are the first applications in the relevant literature due to the novelty of these models in forecasting high-dimensional,multivariate time series.The results obtained from distinguishing between the different market regimes to analyze the responses of trading volume to return shocks contradict those in the literature,which is the key contribution of the study.The empirical findings imply that overconfidence behavior exhibits asymmetries in different return regimes and is persistent during the 20-day forecasting horizon.Overconfidence is more persistent in the low-than in the high-return regime.In the negative interest-rate period,a high-return regime induces overconfidence behavior,whereas in the positive interest-rate period,a low-return regime induces overconfidence behavior.Based on the empirical findings,investors should be aware that portfolio gains may result in losses depending on aggressive and excessive trading strategies,particularly in low-return regimes.

3D Face Reconstruction from a Single Image Using a Combined PCA-LPP Method

In this paper, we proposed a combined PCA-LPP algorithm toimprove 3D face reconstruction performance. Principal component analysis(PCA) is commonly used to compress images and extract features. Onedisadvantage of PCA is local feature loss. To address this, various studies haveproposed combining a PCA-LPP-based algorithm with a locality preservingprojection (LPP). However, the existing PCA-LPP method is unsuitable for3D face reconstruction because it focuses on data classification and clustering.In the existing PCA-LPP, the adjacency graph, which primarily shows the connectionrelationships between data, is composed of the e-or k-nearest neighbortechniques. By contrast, in this study, complex and detailed parts, such aswrinkles around the eyes and mouth, can be reconstructed by composing thetopology of the 3D face model as an adjacency graph and extracting localfeatures from the connection relationship between the 3D model vertices.Experiments verified the effectiveness of the proposed method. When theproposed method was applied to the 3D face reconstruction evaluation set,a performance improvement of 10% to 20% was observed compared with theexisting PCA-based method.

Stabilization for Equal-Order Polygonal Finite Element Method for High Fluid Velocity and Pressure Gradient

This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that are governed by Stokes equations system.This technique is constructed by a local pressure projection which is extremely simple,yet effective,to eliminate the poor or even non-convergence as well as the instability of equal-order mixed polygonal technique.In this research,some numerical examples of incompressible Stokes fluid flow that is coded and programmed by MATLAB will be presented to examine the effectiveness of the proposed stabilised method.

Tracking market and non-traditional sources of risks in procyclical and countercyclical hedge fund strategies under extreme scenarios:a nonlinear VAR approach

The subprime crisis was quite damaging for hedge funds.Using the local projection method(Jordà2004,2005,2009),we forecast the dynamic responses of the betas of hedge fund strategies to macroeconomic and financial shocks—especially volatility and illiquidity shocks—over the subprime crisis in order to investigate their market timing activities.In a robustness check,using TVAR(Balke 2000),we simulate the reaction of hedge fund strategies’betas in extreme scenarios allowing moderate and strong adverse shocks.Our results show that the behavior of hedge fund strategies regarding the monitoring of systematic risk is highly nonlinear in extreme scenarios—especially during the subprime crisis.We find that countercyclical strategies have an investment technology which differs from procyclical ones.During crises,the former seek to capture non-traditional risk premia by deliberately increasing their systematic risk while the later focus more on minimizing risk.Our results suggest that the hedge fund strategies’betas respond more to illiquidity uncertainty than to illiquidity risk during crises.We find that illiquidity and VIX shocks are the major drivers of systemic risk in the hedge fund industry.

ON THE DISCRETE MAXIMUM PRINCIPLE FOR THE LOCAL PROJECTION SCHEME WITH SHOCK CAPTURING

It is a well known fact that finite element solutions of convection dominated problems can exhibit spurious oscillations in the vicinity of boundary layers. One way to overcome this numerical instability is to use schemes that satisfy the discrete maximum principle. There are monotone methods for piecewise linear elements on simplices based on the up- wind techniques or artificial diffusion. In order to satisfy the discrete maximum principle for the local projection scheme, we add an edge oriented shock capturing term to the bilinear form. The analysis of the proposed stabilisation method is complemented with numerical examples in 2D.

A global perspective on macroprudential policy interaction with systemic risk,real economic activity,and monetary intervention

The study empirically assesses how macroprudential policy interacts with systemic risk,industrial production,and monetary intervention on a global level from January 2006 to December 2018.We adopt the aggregate proxies of these variables,capturing their global effects,and use a novel econometric technique,namely,smooth local projections.The study finds that global macroprudential policy leads the monetary policy,exhibiting a countercyclical pattern concerning industrial production.The latter has an inverse bidirectional linkage with systemic risk.Thus,an ex-ante tight macroprudential policy can indirectly mitigate global systemic risk through its pro-growth effect on industrial production,although no convincing evidence exists for the direct impact of a macroprudential intervention on systemic risk.The study results endure several extensions and a robustness check,which builds on alternative measures of global systemic stress and real economic activity,thereby legitimizing the increased importance attached to the macroprudential policy since the 2007–2009 global financial crisis.

Surface Detection of Continuous Casting Slabs Based on Curvelet Transform and Kernel Locality Preserving Projections

Longitudinal cracks are common defects of continuous casting slabs and may lead to serious quality accidents. Image capturing and recognition of hot slabs is an effective way for on-line detection of cracks, and recognition of cracks is essential because the surface of hot slabs is very complicated. In order to detect the surface longitudinal cracks of the slabs, a new feature extraction method based on Curvelet transform and kernel locality preserving projections （KLPP） is proposed. First, sample images are decomposed into three levels by Curvelet transform. Second, Fourier transform is applied to all sub-band images and the Fourier amplitude spectrum of each sub-band is computed to get features with translational invariance. Third, five kinds of statistical features of the Fourier amplitude spectrum are computed and combined in different forms. Then, KLPP is employed for dimensionality reduction of the obtained 62 types of high-dimensional combined features. Finally, a support vector machine （SVM） is used for sample set classification. Experiments with samples from a real production line of continuous casting slabs show that the algorithm is effective to detect longitudinal cracks, and the classification rate is 91.89%.

Performance monitoring of non-gaussian chemical processes with modes-switching using globality-locality preserving projection

In this paper, we propose a novel performance monitoring and fault detection method, which is based on modified structure analysis and globality and locality preserving （MSAGL） projection, for non-Gaussian processes with multiple operation conditions. By using locality preserving projection to analyze the embedding geometrical manifold and extracting the non-Gaussian features by independent component analysis, MSAGL preserves both the global and local structures of the data simultaneously. Furthermore, the tradeoff parameter of MSAGL is tuned adaptively in order to find the projection direction optimal for revealing the hidden structural information. The validity and effectiveness of this approach are illustrated by applying the proposed technique to the Tennessee Eastman process simulation under multiple operation conditions. The results demonstrate the advantages of the proposed method over conventional eigendecomposition-based monitoring methotis.

Adaptive Locally Weighted Projection Regression Method for Uncertainty Quantification

We develop an efficient,adaptive locally weighted projection regression(ALWPR)framework for uncertainty quantification(UQ)of systems governed by ordinary and partial differential equations.The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new localmodels.It effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics.The developed methodology provides predictions and confidence intervals at any query input and can dealwithmulti-output cases.Numerical examples are presented to show the accuracy and efficiency of the ALWPR framework including problems with non-smooth local features such as discontinuities in the stochastic space.

Reliable iris localization using integral projection function and 2D-shape properties

Iris recognition technology recognizes a human based on his/her iris pattern. However, the accuracy of the iris recognition technology depends on accurate iris localization. Localizing a pupil region in the presence of other low-intensity regions, such as hairs, eyebrows, and eyelashes, is a challenging task. This study proposes an iris localization technique that includes a localizing pupillary boundary in a sub-image by using an integral projection function and two-dimensional shape properties （e.g., area, geometry, and circularity）. The limbic boundary is localized using gradients and an error distance transform, and the boundary is regularized with active contours. Experimental results obtained from public databases show the superiority of the Drooosed techniaue over contemporary methods.

Outboard abnormal noise source localization method with curved surface projection based on time delay matching and weighting criterion

An improved localization method consisting of ＂filtering-time delay estimationhyperbolic localization＂ is proposed. Combining the empirical mode decomposition（EMD）and time delay estimation method based on generalized average magnitude difference function,the original signals are decomposed into intrinsic mode function（IMF） components. The energy distribution criterion and spectrum consistency criterion are used to select the IMFs, which can represent the physical characteristics of the source signal. Several sets of signals are applied to estimate the time delay, and then a vector matching criterion is proposed to select the correct time delay estimation. Considering the hydrophones location, a shell model is established and projected to a plane according to the quadrant before the hyperbolic localization. Results of mooring and sailing tests show that the proposed method improves the localization accuracy,and reduces the error caused by time delay estimation.

Assessment of Central Asian heat extremes by statistical downscaling:Validation and future projection for 2015-2100

Increasing heatwaves and extreme temperatures have recently been observed across Central Asia(CA).Accurately assessing and projecting the changing climate extremes at the local(station)scale required for climate risk management are therefore highly important.However,global and regional climate models often fail to represent the statistical distributions of observed daily extreme variables and hence extremes in complex terrain.In this work,we developed a statistical downscaling(SD)model to project summer daily maximum temperature(Tmax)and heatwave indices for 65 meteorological stations in CA toward 2100.The SD model involves first-order autoregression and multiple linear regression using large-scale Tmax and circulation indices(Cis)as predictors,and the model is cross-validated against historical observations.The local Tmax and heatwave indices are then projected for 2015-2100 driven by the output of a global climate model(CNRM-CM6-1)under four Shared Socioeconomic Pathways(SSP126,SSP245,SSP370,and SSP585).The application of the SD model significantly improves forecasting of the probability distribution(10th/90th percentiles)of Tmax at stations,particularly across mountainous regions.The model also captures interannual variability and the long-term trend in Tmax,consistent with synoptic-scale inputs.SD projections demonstrate strong warming trends of summer Tmax in CA toward 2100 with rates between 0.35-0.64℃ per decade based on the SSP245 and SSP370 seenarios.Consequently,heatwave occurrence is projected to rise by 1.0-5.0 and 2.0-7.0 d per decade under the SSP245 and SSP370 scenarios,respectively,by 2100.Duration,intensity,and amplitude of heatwaves rise at greater rates under higher-emission scenarios,particularly in southeastern CA.The proposed SD model serves as a useful tool for assessing local climate extremes,which are needed for regional risk management and policymaking for adaption to climate change.