Test for Infinite Variance in Stock Returns

The existence of second order moment or the finite variance is a commonly used assumption in financial time series analysis. We examine the validation of this condition for main stock index return series by applying the extreme value theory. We compare the performances of the adaptive Hill’s estimator and the Smith’s estimator for the tail index using Monte Carlo simulations for both i.i.d data and dependent data. The simulation results show that the Hill’s estimator with adaptive data-based truncation number performs better in both cases. It has not only smaller bias but also smaller MSE when the true tail index α is not more than 2. Moreover, the Hill’s estimator shows precise results for the hypothesis test of infinite variance. Applying the adaptive Hill’s estimator to main stock index returns over the world, we find that for most indices, the second moment does exist for daily, weekly and monthly returns. However, an additional test for the existence of the fourth moment shows that generally the fourth moment does not exist, especially for daily returns. And these results don’t change when a Gaussian-GARCH effect is removed from the original return series

Complexity Analysis of Reed-Solomon Decoding over GF(2^m) Without Using Syndromes

For the majority of the applications of Reed-Solomon (RS) codes, hard decision decoding is based on syndromes. Recently, there has been renewed interest in decoding RS codes without using syndromes. In this paper, we investigate the complexity of syndromeless decoding for RS codes, and compare it to that of syndrome-based decoding. Aiming to provide guidelines to practical applications, our complexity analysis differs in several aspects from existing asymptotic complexity analysis, which is typically based on multiplicative fast Fourier transform (FFT) techniques and is usually in big O notation. First, we focus on RS codes over characteristic-2 fields, over which some multiplicative FFT techniques are not applicable. Secondly, due to moderate block lengths of RS codes in practice, our analysis is complete since all terms in the complexities are accounted for. Finally, in addition to fast implementation using additive FFT techniques, we also consider direct implementation, which is still relevant for RS codes with moderate lengths. Comparing the complexities of both syndromeless and syndrome-based decoding algorithms based on direct and fast implementations, we show that syndromeless decoding algorithms have higher complexities than syndrome-based ones for high rate RS codes regardless of the implementation. Both errors-only and errors-and-erasures decoding are considered in this paper. We also derive tighter bounds on the complexities of fast polynomial multiplications based on Cantor's approach and the fast extended Euclidean algorithm.Comment: 11 pages, submitted to EURASIP Journal on Wireless Communications and Networkin

China's tackling of online pornography: Puzzles, issues and trends

--Online pornography,obscenity and indecency,People's Republic of China,protection of minors,Internet regulation

A nodule on the forearm

Glomus tumors are benign tumors of the skin. Clinically, these tumors can present as solid, painful subcutaneous nodules, frequently seen on the hand (particularly subungual region). Glomangiomyomas are the least common histological type of glomus tumor. In the literature, there are only a few glomangiomyoma cases of the forearm location. We report a patient with a painful nodule, diagnosed as glomangiomyoma. Surgical excision was performed and no recurrence was observed after 5 years' follow-up

The bicrossed products of H4H_4 and H8H_8

Let $H_4$ and $H_8$ be the Sweedler's and Kac-Paljutkin Hopf algebras, respectively. In this paper we prove that any Hopf algebra which factorizes through $H_8$ and $H_4$ (equivalently, any bicrossed product between the Hopf algebras $H_8$ and $H_4$) must be isomorphic to one of the following four Hopf algebras: $H_8 \otimes H_4, H_{32,1}, H_{32,2}, H_{32,3}$. The set of all matched pair $(H_8, H_4, \triangleright, \triangleleft)$ is explicitly described, and then the associated bicrossed products is given by generators and relations

Weakly Supervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning

Separating audio mixtures into individual instrument tracks has been a long standing challenging task. We introduce a novel weakly supervised audio source separation approach based on deep adversarial learning. Specifically, our loss function adopts the Wasserstein distance which directly measures the distribution distance between the separated sources and the real sources for each individual source. Moreover, a global regularization term is added to fulfill the spectrum energy preservation property regardless separation. Unlike state-of-the-art weakly supervised models which often involve deliberately devised constraints or careful model selection, our approach need little prior model specification on the data, and can be straightforwardly learned in an end-to-end fashion. We show that the proposed method performs competitively on public benchmark against state-of-the-art weakly supervised methods

Distance Preserving Graph Simplification

Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph. Specifically, we construct a gate graph from a large graph so that for any "non-local" vertex pair (distance higher than some threshold) in the original graph, their shortest-path distance can be recovered by consecutive "local" walks through the gate vertices in the gate graph. We perform a theoretical investigation on the gate-vertex set discovery problem. We characterize its computational complexity and reveal the upper bound of minimum gate-vertex set using VC-dimension theory. We propose an efficient mining algorithm to discover a gate-vertex set with guaranteed logarithmic bound. We further present a fast technique for pruning redundant edges in a gate graph. The detailed experimental results using both real and synthetic graphs demonstrate the effectiveness and efficiency of our approach.Comment: A short version of this paper will be published for ICDM'11, December 201