New results on multi-dimensional linear discriminant analysis

Fisher linear discriminant analysis is a well-known technique for dimensionality reduction and classification. The method was first formulated in 1936 by Fisher. In this paper we concentrate on three different formulations of the multi-dimensional problem. We provide a mathematical explanation why two of the formulations are equivalent and prove that this equivalency can be extended to a broader class of objective functions. The second contribution is a rate of convergence of a fixed point method for solving the third model.     

Some problems of linear differential equations on abstract spaces and unbounded perturbations of linear operator semigroup

This paper is a survey for development of linear distributed parameter system. At first we point out some questions existing in current study of control theory for the L^p linear system with an unbounded control operator and an unbounded observation operator, such as stabilization problem and observer theory that are closely relevant to state feedback operator. After then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup perturbations. As a principle, we propose a concept of admissible state feedback operator for system (A, B). Finally we give an existence result of admissible state feedback operators, including semigroup generation and the equivalent conditions of admissibility of state feedback operators, for an L^p well-posed system.     

A linear algorithm of the reference region model for DCE-MRI is robust and relaxes requirements for temporal resolution

Dynamic contrast enhanced MRI (DCE-MRI) has utility for improving clinical diagnoses of solid tumors, and for evaluating the early responses of anti-angiogenic chemotherapies. The Reference Region Model (RRM) can improve the clinical implementation of DCE-MRI by substituting the contrast enhancement of muscle for the Arterial Input Function that is used in traditional DCE-MRI methodologies. The RRM is typically fitted to experimental results with a non-linear least squares algorithm. This report demonstrates that this algorithm produces inaccurate and imprecise results when DCE-MRI results have low SNR or slow temporal resolution. To overcome this limitation, a linear least-squares algorithm has been derived for the Reference Region Model. This new algorithm improves accuracy and precision of fitting the Reference Region Model to DCE-MRI results, especially for voxel-wise analyses. This linear algorithm is insensitive to injection speeds, and has 300- to 8000-fold faster calculation speed relative to the non-linear algorithm. The linear algorithm produces more accurate results for over a wider range of permeabilities and blood volumes of tumor vasculature. This new algorithm, termed the Linear Reference Region Model, has strong potential to improve clinical DCE-MRI evaluations.     

CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).     

A new chaotic system without linear term and its impulsive synchronization

In this paper, a new chaotic system without linear term is presented by ordinary differential equations, and some basic dynamical properties are studied. Moreover, the impulsive synchronization problem of the new chaotic systems is investigated by using uncertain impulsive control matrix. Using the impulsive theory, sufficient conditions are derived for the synchronization of new chaotic systems. Numerical simulation example is provided to verify the effectiveness of the proposed approach.     

A new algorithm for minimizing convex functions over convex sets

Let be a convex set for which there is an oracle with the following property. Given any pointz∈ℝ ⁿ the oracle returns a “Yes” ifz∈S; whereas ifz∉S then the oracle returns a “No” together with a hyperplane that separatesz fromS. The feasibility problem is the problem of finding a point inS; the convex optimization problem is the problem of minimizing a convex function overS. We present a new algorithm for the feasibility problem. The notion of a volumetric center of a polytope and a related ellipsoid of maximum volume inscribable in the polytope are central to the algorithm. Our algorithm has a significantly better global convergence rate and time complexity than the ellipsoid algorithm. The algorithm for the feasibility problem easily adapts to the convex optimization problem.     

Discrete linear bilevel programming problem

In this paper, we analyze some properties of the discrete linear bilevel program for different discretizations of the set of variables. We study the geometry of the feasible set and discuss the existence of an optimal solution. We also establish equivalences between different classes of discrete linear bilevel programs and particular linear multilevel programming problems. These equivalences are based on concave penalty functions and can be used to design penalty function methods for the solution of discrete linear bilevel programs.Support of this work has been provided by the INIC (Portugal) under Contract 89/EXA/5, by INVOTAN, FLAD, and CCLA (Portugal), and by FCAR (Québec), NSERC, and DND-ARP (Canada).     

Elastic friction drive of surface acoustic wave motor

Importance of elastic deformation control to obtain large output force with a surface acoustic wave (SAW) motor is discussed in this paper. By adding pre-load to slider, stator and slider surfaces are deformed in a few tens nanometer. Appropriate deformation in normal direction against normal vibration displacement amplitude of SAW existed. By moderate deformation, the output force of the SAW motor was enlarged up to about 10 N and no-load speed was 0.7 m/s. To produce this performance, the transducer weight and slider size were only 4.2 g and 4 x 4 mm(2).By traveling wave propagation, surface particles of the SAW device move in elliptical motion. Due to the amplitude of the elliptical motion is 10 or 20 nm order, the contact condition of the slider is very critical. To control the contact condition, namely, the elastic deformation of the slider and stator surface in nanometer order, a lot of projections were fabricated on the slider surface. The projection diameter was 20 micro m. In static condition, the elastic deformation and stress were evaluated with the FEM analysis. From this calculation and the simulation result, it is consider that the wave crest is distorted, hence the elasticity has influence on the friction drive condition.Elastic deformation of the stator surface beneath the projection from the initial position were evaluated. In 4 x 4 mm(2) square area, the sliders had from 1089 to 23,409 projections. Depression was independent to the contact pressure. However, the output force depended on the depression although the projection density were different. From the view point of the output power of the motor, the proper depression was independent to the projection density. Around 25 nm depression, the output force and output power were maximized. This depression value was almost same as the vibration displacement amplitude of the stator transducer.     

神龙一号电子束质心运动测量研究

 在强流直线感应加速器中,电子束质心位置的控制是一项重要技术,要达到较好的控制效果,前提是对电子束质心位置进行准确的测量和定位。针对具有时间分辨的电子束质心位置的测量和确定,介绍了测量实验系统的建立和数据处理两个方面的研究工作。该处理方法在实际应用时能够将电子束质心位置的误差控制在1～2个像素内。用高速分幅相机以10 ns的时间间隔、3 ns的曝光时间获得了神龙一号加速器在漂移段出口处的电子束质心运动情况。结果表明：束的质心主要在半径为0.5 mm的区域内运动,束斑直径dFWHM值分别为8.4,8.8,8.5,9.3和7.6 mm,测量结果可以为束的调控提供准确参数。