High Dimensionality Effects on the Efficient Frontier: A Tri-Nation Study

Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.

Research Progress of Two-d imensional Matrix Detectors in IMRT Dose Verification

With the continuous development of science and technolog ies in China,radiotherapy technology in medical field has been very significant ly developing,and intensity modulated radiation therapy(IMRT)technology has been the most widely used.This paper first introduces the components and types of two-dimensional matrix detector,two-dimensional ionization chamber matrix detector and two-dimensional semiconductor matrix detector,then analyzes the dosimetric characteristics of the two-dimensional matrix detector.In the end,the various applications of the two-dimensional matrix detector are analyzed and discussed in detail.The paper aims to promote the two-dimensional matrix detector’s development in the field of radiotherapy in China.

Model-free Adaptive Control for Spacecraft Attitude

A model-free adaptive control method is proposed for the spacecrafts whose dynamical parameters change over time and cannot be acquired accurately. The algorithm is based on full form dynamic linearization.A dimension reduction matrix is introduced to construct an augmented system with the same dimension input and output. The design of the controller depends on the system input and output data rather than the knowledge of the controlled plant. The numerical simulation results show that the improved controller can deal with different models with the same set of controller parameters,and the controller performance is better than that of PD controller for the time-varying system with disturbance.

Automatic Calculation of Dimension Chains in AutoCAD

In the course of mechanical part designing, process p lanning and assembling designing, we often have to calculate and analyse a dimen sion chain. Traditionally, a dimension chain is established and calculated m anually. With wide computer application in the field of mechanical design and ma nufacture, people began to use a computer to acquire and calculate a dimension c hain automatically. In reported work, a dimension chain can be established and c alculated automatically. However, dimension text values of dimensions composing a dimension chain and these dimensions’ tolerance’s upper values and lower valu es are put into a computer manually, which is inefficient and easy to make mis takes. In order to overcome above difficulties. it is very important to acquir e noted dimensions automatically, furthermore analyse and calculate a dimens ion chain, then show results. At present AutoCAD softwares of Autodesk company h ave been used popularly in mechanical designing. For automatically acquiring noted dimensions, analyzing and calculating a dimension chain in a design draw in AutoCAD, this paper introduces the solvable scheme of automatic dimension acq uisition and dimension chain calculation in AutoCAD by ObjectARX. ObjectARX is a developing tool for AutoCAD. In this paper a dimension chain is expressed b y three matrixes, which respectively stand for dimension text value matrix, tole rance’s upper value matrix and tolerance’s lower value matrix. The developed p rogram can be used to both calculate a assembling dimension chain, and a process dimension chain. When the program running in AutoCAD, noted dimensions comp osing a dimension chain in AutoCAD are selected in turn with a mouse, then the c omputer begin to calculate the dimension chain and results are shown in a dialog box. A running example is given in this paper.

Degradation algorithm of compressive sensing

The compressive sensing （CS） theory allows people to obtain signal in the frequency much lower than the requested one of sampling theorem. Because the theory is based on the assumption of that the location of sparse values is unknown, it has many constraints in practical applications. In fact, in many cases such as image processing, the location of sparse values is knowable, and CS can degrade to a linear process. In order to take full advantage of the visual information of images, this paper proposes the concept of dimensionality reduction transform matrix and then se- lects sparse values by constructing an accuracy control matrix, so on this basis, a degradation algorithm is designed that the signal can be obtained by the measurements as many as sparse values and reconstructed through a linear process. In comparison with similar methods, the degradation algorithm is effective in reducing the number of sensors and improving operational efficiency. The algorithm is also used to achieve the CS process with the same amount of data as joint photographic exports group （JPEG） compression and acquires the same display effect.