Geometric lattice structure of covering and its application to attribute reduction through matroids

The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice to study the attribute reduction issues of information systems

Geometric lattice structure of covering-based rough sets through matroids

Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Geometric lattice has widely used in diverse fields, especially search algorithm design which plays important role in covering reductions. In this paper, we construct four geometric lattice structures of covering-based rough sets through matroids, and compare their relationships. First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by the covering, and its characteristics including atoms, modular elements and modular pairs are studied. We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets. Second, sufficient and necessary conditions for three types of covering upper approximation operators to be closure operators of matroids are presented. We exhibit three types of matroids through closure axioms, and then obtain three geometric lattice structures of covering-based rough sets. Third, these four geometric lattice structures are compared. Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely geometric lattice, to study covering-based rough sets

Connectedness of graphs and its application to connected matroids through covering-based rough sets

Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and covering-based rough sets provide a systematic approach to this type of representation. In this paper, we study the connectedness of graphs through covering-based rough sets and apply it to connected matroids. First, we present an approach to inducing a covering by a graph, and then study the connectedness of the graph from the viewpoint of the covering approximation operators. Second, we construct a graph from a matroid, and find the matroid and the graph have the same connectedness, which makes us to use covering-based rough sets to study connected matroids. In summary, this paper provides a new approach to studying graph theory and matroid theory

Outage Probability of Dual-Hop Multiple Antenna AF Relaying Systems with Interference

This paper presents an analytical investigation on the outage performance of dual-hop multiple antenna amplify-and-forward relaying systems in the presence of interference. For both the fixed-gain and variable-gain relaying schemes, exact analytical expressions for the outage probability of the systems are derived. Moreover, simple outage probability approximations at the high signal to noise ratio regime are provided, and the diversity order achieved by the systems are characterized. Our results suggest that variable-gain relaying systems always outperform the corresponding fixed-gain relaying systems. In addition, the fixed-gain relaying schemes only achieve diversity order of one, while the achievable diversity order of the variable-gain relaying scheme depends on the location of the multiple antennas.Comment: Accepted to appear in IEEE Transactions on Communication

Floroindole confers protection against cecal ligation and puncture-induced sepsis via inhibition of NF-kB p65 phosphorylation

Purpose: To investigate the protective effect of floroindole against cecal ligation and puncture (CLP)- induced sepsis, as well as the underlying mechanism of action. Methods: Thirty-five 10–week-old male Wistar rats weighing 190 - 210 g (mean: 200.00 ± 10.10 g) were used for this study. The rats were randomly assigned to seven groups of five rats each, viz, normal control group, and six CLP groups. The CLP groups were those subjected to cecal ligation and puncture (CLP). The first 5 CLP groups received 2, 4, 6, 8 or 10 mg/kg floroindole, respectively, 1 h after CLP, via intraperitoneal route (i.p.) while the 6th CLP group served as untreated control. Western blotting, enzyme-linked immunosorbent assay (ELISA) and real-time quantitative polymerase chain reaction (qRT-PCR) were used for the assessment of the expression levels of tumor necrosis factor-α (TNF- α), interleukn-6 (IL-6), nucleotide-binding oligomerization domain 2 (NOD2) and p-NF-κB p65. Results: Cecal ligation and puncture (CLP) significantly and time-dependently upregulated the expressions of TNF-α, IL-6 and NOD2 in intestinal tissues of rats (p < 0.05). However, treatment with floroindole significantly, and dose-dependently down-regulated CLP-induced expressions of these proteins (p < 0.05). Treatment of rats with floroindole also significantly and dose-dependently inhibited CLP-induced phosphorylation of NF-κB p65 in rat ileum (p < 0.05). Conclusion: The results obtained in this study demonstrate that floroindole confers some degree of protection against CLP-induced sepsis via inhibition of NF-κB p65 phosphorylation

Deciphering and Targeting Epigenetics in Cancer Metastasis

Once cancer metastasizes to distant organs like the bone, liver, lung, and brain, it is in an advanced stage. Metastasis is a major contributor to cancer-associated deaths. Countless molecules and complex pathways are involved in the dissemination and colonization of cancer cells from a primary tumor at metastatic sites. Establishing the biological mechanisms of the metastatic process is crucial in finding open therapeutic windows for successful interventions. Emerging evidence suggested a variety of epigenetic regulations were identified to regulate cancer metastasis. Here we summarize the procedures and routes of cancer metastasis as well as the roles of epigenetics including ncRNA, DNA methylation, and histone modifications in common metastases. Then we further discuss the potentials and limitations of epigenetics-related target molecules in diagnosis, therapy, and prognosis