Estimating High Dimensional Covariance Matrices and its Applications

Estimating covariance matrices is an important part of portfolio selection, risk management, and asset pricing. This paper reviews the recent development in estimating high dimensional covariance matrices, where the number of variables can be greater than the number of observations. The limitations of the sample covariance matrix are discussed. Several new approaches are presented, including the shrinkage method, the observable and latent factor method, the Bayesian approach, and the random matrix theory approach. For each method, the construction of covariance matrices is given. The relationships among these methods are discussed.Factor analysis, Principal components, Singular value decomposition, Random matrix theory, Empirical Bayes, Shrinkage method, Optimal portfolios, CAPM, APT, GMM

Direct measurement of giant electrocaloric effect in BaTiO3 multilayer thick film structure beyond theoretical prediction

The electrocaloric effect of BaTiO3 multilayer thick film structure was investigated by direct measurement and theoretical calculation. The samples were prepared by the tape-casting method, which had 180 dielectric layers with an average thickness of 1.4\mu m. The thermodynamic calculation based on the polarization- temperature curves predicted a peak heat adsorption of 0.32J/g at 80^\circC under 176kV/cm electric field. The direct measurement via differential scanning calorimeter showed a much higher electrocaloric effect of 0.91J/g at 80^\circC under same electric field. The difference could result from the different trends of changes of electric polarization and lattice elastic energy under ultrahigh electric field.Comment: 11 pages, 4 figure

Detecting Oriented Text in Natural Images by Linking Segments

Most state-of-the-art text detection methods are specific to horizontal Latin text and are not fast enough for real-time applications. We introduce Segment Linking (SegLink), an oriented text detection method. The main idea is to decompose text into two locally detectable elements, namely segments and links. A segment is an oriented box covering a part of a word or text line; A link connects two adjacent segments, indicating that they belong to the same word or text line. Both elements are detected densely at multiple scales by an end-to-end trained, fully-convolutional neural network. Final detections are produced by combining segments connected by links. Compared with previous methods, SegLink improves along the dimensions of accuracy, speed, and ease of training. It achieves an f-measure of 75.0% on the standard ICDAR 2015 Incidental (Challenge 4) benchmark, outperforming the previous best by a large margin. It runs at over 20 FPS on 512x512 images. Moreover, without modification, SegLink is able to detect long lines of non-Latin text, such as Chinese.Comment: To Appear in CVPR 201

Root optimization of polynomials in the number field sieve

The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.Comment: 16 pages, 18 reference

Sharpening and generalizations of Shafer's inequality for the arc tangent function

In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined