Siu-Pang Yung

Wavelet based methods on patterned fabric defect detection

The wavelet transform (WT) has been developed over 20 years and successfully applied in defect detection on plain (unpatterned) fabric. This paper is on the use of the wavelet transform to develop an automated visual inspection method for defect detection on patterned fabric. A method called direct thresholding (DT) based on WT detailed subimages has been developed. The golden image subtraction method (GIS) is also introduced. GIS is an efficient and fast method, which can segment out the defective regions on patterned fabric effectively. In this paper, the method of wavelet preprocessed golden image subtraction (WGIS) has been developed for defect detection on patterned fabric or repetitive patterned texture. This paper also presents a comparison of the three methods. It can be concluded that the WGIS method provides the best detection result. The overall detection success rate is 96.7% with 30 defect-free images and 30 defective patterned images for one common kind of patterned Jacquard fabric.

Linear-Quadratic Mean Field Games

We provide a comprehensive study of a general class of linear-quadratic mean field games. We adopt the adjoint equation approach to investigate the unique existence of their equilibrium strategies. Due to the linearity of the adjoint equations, the optimal mean field term satisfies a forward–backward ordinary differential equation. For the one-dimensional case, we establish the unique existence of the equilibrium strategy. For a dimension greater than one, by applying the Banach fixed point theorem under a suitable norm, a sufficient condition for the unique existence of the equilibrium strategy is provided, which is independent of the coefficients of controls in the underlying dynamics and is always satisfied whenever the coefficients of the mean field term are vanished, and hence, our theories include the classical linear-quadratic stochastic control problems as special cases. As a by-product, we also establish a neat and instructive sufficient condition, which is apparently absent in the literature and only depends on coefficients, for the unique existence of the solution for a class of nonsymmetric Riccati equations. Numerical examples of nonexistence of the equilibrium strategy will also be illustrated. Finally, a similar approach has been adopted to study the linear-quadratic mean field type stochastic control problems and their comparisons with mean field games.

Riesz basis property of serially connected Timoshenko beams

In this paper we study the Riesz basis property of serially connected Timoshenko beams with joint and boundary feedback controls. Suppose that the left end of the whole beam is clamped and the right end is free. At intermediate nodes, the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous. The collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system. We prove that the operator determined by the closed loop system has compact resolvent and generates a C 0 semigroup in an appropriate Hilbert space. We also show that there is a sequence of the generalized eigenvectors of the operator that forms a Riesz basis with parentheses. Hence the spectrum determined growth condition holds. Therefore if the imaginary axis is not an asymptote of the spectrum, then the closed loop system is exponentially stable. Finally, we give a conclusion remark to explain that our result can be applied not only on the serially connected Timoshenko beams.

Repulsive force based snake model to segment and track neuronal axons in 3D microscopy image stacks

The branching patterns of axons and dendrites are fundamental structural properties that affect the synaptic connectivity of axons. Although today three-dimensional images of fluorescently labeled processes can be obtained to study axonal branching, there are no robust methods of tracing individual axons. This paper describes a repulsive force based snake model to segment and track axonal profiles in 3D images. This new method segments all the axonal profiles in a 2D image and then uses the results obtained from that image as prior information to help segment the adjacent 2D image. In this way, the segmentation successfully connects axonal profiles over hundreds of images in a 3D image stack. Individual axons can then be extracted based on the segmentation results. The utility and performance of the method are demonstrated using 3D axonal images obtained from transgenic mice that express fluorescent protein.

On the C0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam

In this paper, we show that a linear unbounded operator associated with an Euler–Bernoulli beam equation under shear boundary feedback generates a C0-semig roup in the underlyingstate Hilbert space. This provides an answer to a longtime unsolved problem due to the lack of dissipativity for the operator. The main steps are a careful estimation of the Green’s function and the verification of the Riesz basis property for the generalized eigenfunctions. As a consequence, we show that this semigroup is differentiable and exponentially stable, which is in sharp contrast to the properties possessed by most feedback controlled beams based on a passive design principle.

Optimal reinsurance under general law-invariant risk measures

In recent years, general risk measures play an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance decision problems using risk measures beyond the classical expected utility framework. In this paper, we first show that the stop-loss reinsurance is an optimal contract under law-invariant convex risk measures via a new simple geometric argument. A similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stop-loss reinsurances, insurance layers serve as the optimal solution. These two results highlight that law-invariant convex risk measure is better and more robust, in the sense that the corresponding optimal reinsurance still provides the protection coverage against extreme loss irrespective to the potential increment of its probability of occurrence, to expected larger claim than Value at Risk and Conditional Tail Expectation which are more commonly used. Several illustrative examples will be provided.

Exponential Stabilization of Laminated Beams with Structural Damping and Boundary Feedback Controls

We study the boundary stabilization of laminated beams with structural damping which describes the slip occurring at the interface of two-layered objects. By using an invertible matrix function with an eigenvalue parameter and an asymptotic technique for the first order matrix differential equation, we find out an explicit asymptotic formula for the matrix fundamental solutions and then carry out the asymptotic analyses for the eigenpairs. Furthermore, we prove that there is a sequence of generalized eigenfunctions that forms a Riesz basis in the state Hilbert space, and hence the spectrum determined growth condition holds. Furthermore, exponential stability of the closed-loop system can be deduced from the eigenvalue expressions. In particular, the semigroup generated by the system operator is a

Spectral analysis and system of fundamental solutions for Timoshenko beams

C_0

Riesz basis property of the generalized eigenvector system of a Timoshenko beam

-group due to the fact that the three asymptotes of the spectrum are parallel to the imaginary axis.

Using nonlinear diffusion and mean shift to detect and connect cross-sections of axons in 3D optical microscopy images.

We have found a unified method to analyse Timoshenko beams under various boundary conditions that occurred in practice. Explicit asymptotic expressions for the spectrum are obtained. Our method is very simple but effective because explicit formulas are obtained for the system of fundamental solutions, which are very useful for other purposes such as stability analysis. The eigenfunctions are also shown to form an orthogonal basis.