Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals

We present criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen-Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen-Macaulayness of the second symbolic power or of all symbolic powers of a Stanley-Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen-Macaulay. In particular, all symbolic powers are Cohen-Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen-Macaulayness can pass from a symbolic power to another symbolic powers in different ways.Comment: The published version of this paper contains a gap in the proofs of Theorem 2.5 and Theorem 3.5. This version corrects the proofs with almost the same arguments. Moreover, we have to modify the definition of tight complexes in Theorem 2.5. These changes don't affect other things in the published version. A corrigendum has been sent to the journa

Three-Way Tensor Decompositions: A Generalized Minimum Noise Subspace Based Approach

Tensor decomposition has recently become a popular method of multi-dimensional data analysis in various applications. The main interest in tensor decomposition is for dimensionality reduction, approximation or subspace purposes. However, the emergence of “big data” now gives rise to increased computational complexity for performing tensor decomposition. In this paper, motivated by the advantages of the generalized minimum noise subspace (GMNS) method, recently proposed for array processing, we proposed two algorithms for principal subspace analysis (PSA) and two algorithms for tensor decomposition using parallel factor analysis (PARAFAC) and higher-order singular value decomposition (HOSVD). The proposed decomposition algorithms can preserve several desired properties of PARAFAC and HOSVD while substantially reducing the computational complexity. Performance comparisons of PSA and tensor decomposition of our proposed algorithms against the state-of-the-art ones were studied via numerical experiments. Experimental results indicated that the proposed algorithms are of practical values

Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey

Principal component analysis (PCA) and subspace estimation (SE) are popular data analysis tools and used in a wide range of applications. The main interest in PCA/SE is for dimensionality reduction and low-rank approximation purposes. The emergence of big data streams have led to several essential issues for performing PCA/SE. Among them are (i) the size of such data streams increases over time, (ii) the underlying models may be time-dependent, and (iii) problem of dealing with the uncertainty and incompleteness in data. A robust variant of PCA/SE for such data streams, namely robust online PCA or robust subspace tracking (RST), has been introduced as a good alternative. The main goal of this paper is to provide a brief survey on recent RST algorithms in signal processing. Particularly, we begin this survey by introducing the basic ideas of the RST problem. Then, different aspects of RST are reviewed with respect to different kinds of non-Gaussian noises and sparse constraints. Our own contributions on this topic are also highlighted

DICHLODIPHENYLTRICHLOETHANES (DDTS) RESIDUES IN TAM GIANG-CAU HAI AND LANG CO LAGOONS, VIETNAM

Joint Research on Environmental Science and Technology for the Eart

The impact of oil prices, real effective exchange rate and inflation on economic activity: Novel evidence for Vietnam

The goal of this paper is to examine the impact of oil prices on Vietnam's economic activity using vector autoregressive (VAR) modeling and cointegration techniques. We use monthly data for the period 1995-2009 and include inflation and the real effective exchange rate as additional determinants of economic activity. We find evidence of a long-run relationship between oil prices, inflation, exchange rate, and economic activity. The results suggest that both oil prices and the real effective exchange rates have strongly significant impact on economic activity. An increase in oil price or depreciation may enhance economic activity. Vietnamese economic activity is influenced more by changes of value of Vietnamese currency than the fluctuations of oil prices. Inflation has a positive impact on economic activity however its impact is not highly significant. This suggests that moderate inflation is helpful rather than harmful to economic activity.Oil price, Economic activity, Vietnam