Application of regularized logistic regression for movement-related potentials-based EEG classification

In order to improve classification accuracy, the regularized logistic regression is used to classify single-trial electroencephalogram （EEG）. A novel approach, named local sparse logistic regression （LSLR）, is proposed. The LSLR integrates the locality preserving projection regularization term into the framework of sparse logistic regression. It tries to maintain the neighborhood information of original feature space, and, meanwhile, keeps sparsity. The bound optimization algorithm and component-wise update are used to compute the weight vector in the training data, thus overcoming the disadvantage of the Newton-Raphson method and iterative re-weighted least squares （IRLS）. The classification accuracy of 80% is achieved using ten-fold cross-validation in the self-paced finger tapping data set. The results of LSLR are compared with SLR, showing the effectiveness of the proposed method.

LOCAL REGULARITY RESULT FOR SOLUTIONS OF OBSTACLE PROBLEMS

This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.

THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS

We use Hopf-Lax formula to study local regularity of solution to Hamilton- Jacobi （HJ） equations of multi-dimensional space variables with convex Hamiltonian. Then we give the large time generic form of the solution to HJ equation, i.e. for most initial data there exists a constant T 〉 0, which depends only on the Hamiltonian and initial datum, for t 〉 T the solution of the IVP （1.1） is smooth except for ~ smooth n-dimensional hypersurface, across which Du（x, t） is discontinuous. And we show that the hypersurface 1 tends asymptotically to a given hypersurface with rate t-1/4.

LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS

We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some coercivity and growth conditions with the naturalexponent 1 〈 p 〈 n, the obstacle function φ≥ 0, and the boundary data θ ∈ W1mp（Ω）.

Exploring Local Regularities for 3D Object Recognition

In order to find better simplicity measurements for 3D object recognition, a new set of local regularities is developed and tested in a stepwise 3D reconstruction method, including localized minimizing standard deviation of angles（L-MSDA）, localized minimizing standard deviation of segment magnitudes（L-MSDSM）, localized minimum standard deviation of areas of child faces （L-MSDAF）, localized minimum sum of segment magnitudes of common edges （L-MSSM）, and localized minimum sum of areas of child face （L-MSAF）. Based on their effectiveness measurements in terms of form and size distortions, it is found that when two local regularities： L-MSDA and L-MSDSM are combined together, they can produce better performance. In addition, the best weightings for them to work together are identified as 10% for L-MSDSM and 90% for L-MSDA. The test results show that the combined usage of L-MSDA and L-MSDSM with identified weightings has a potential to be applied in other optimization based 3D recognition methods to improve their efficacy and robustness.

LOCAL REGULARITY CRITERIA OF A SUITABLE WEAK SOLUTION TO MHD EQUATIONS

We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are HSlder continuous near boundary provided that the scaled mixed Lx,t^p,q-norm of the velocity vector field with 3/p ＋ 2/q 〈 2, 2 〈 q 〈 ∞ is sufficiently small near the boundary. Also, we will investigate that for this 3 2〈3 solution U ∈ Lx,t^p,q with 1 〈 3＋p ＋2/q＋≤3/2, 3 〈 p 〈 ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}（3/q＋2/q- 1）.

Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients

In this paper, we prove that the weak solutions u∈Wloc^1, p （Ω） （1 〈p〈∞） of the following equation with vanishing mean oscillation coefficients A（x）： -div[（A（x）△↓u·△↓u）p-2/2 A（x）△↓u＋│F（x）│^p-2 F（x）]=B（x, u, △↓u）, belong to Wloc^1, q （Ω）（A↓q∈（p, ∞）, provided F ∈ Lloc^q（Ω） and B（x, u, h） satisfies proper growth conditions where Ω ∪→R^N（N≥2） is a bounded open set, A（x）=（A^ij（x）） N×N is a symmetric matrix function.

Regularity for solutions to anisotropic obstacle problems

For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.

A novel multimode process monitoring method integrating LDRSKM with Bayesian inference

A local discriminant regularized soft k-means （LDRSKM） method with Bayesian inference is proposed for multimode process monitoring. LDRSKM extends the regularized soft k-means algorithm by exploiting the local and non-local geometric information of the data and generalized linear discriminant analysis to provide a better and more meaningful data partition. LDRSKM can perform clustering and subspace selection simultaneously, enhancing the separability of data residing in different clusters. With the data partition obtained, kernel support vector data description （KSVDD） is used to establish the monitoring statistics and control limits. Two Bayesian inference based global fault detection indicators are then developed using the local monitoring results associated with principal and residual subspaces. Based on clustering analysis, Bayesian inference and manifold learning methods, the within and cross-mode correlations, and local geometric information can be exploited to enhance monitoring performances for nonlinear and non-Gaussian processes. The effectiveness and efficiency of the proposed method are evaluated using the Tennessee Eastman benchmark process.

A REMARK ON THE HENSELIZATION OF A REGULAR LOCAL RING

The author gives simple characterization of the Henselization of an excellent regular localring.