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

Prognostic value of routine laboratory variables in prediction of breast cancer recurrence.

The prognostic value of routine laboratory variables in breast cancer has been largely overlooked. Based on laboratory tests commonly performed in clinical practice, we aimed to develop a new model to predict disease free survival (DFS) after surgical removal of primary breast cancer. In a cohort of 1,596 breast cancer patients, we analyzed the associations of 33 laboratory variables with patient DFS. Based on 3 significant laboratory variables (hemoglobin, alkaline phosphatase, and international normalized ratio), together with important demographic and clinical variables, we developed a prognostic model, achieving the area under the curve of 0.79. We categorized patients into 3 risk groups according to the prognostic index developed from the final model. Compared with the patients in the low-risk group, those in the medium- and high-risk group had a significantly increased risk of recurrence with a hazard ratio (HR) of 1.75 (95% confidence interval [CI] 1.30-2.38) and 4.66 (95% CI 3.54-6.14), respectively. The results from the training set were validated in the testing set. Overall, our prognostic model incorporating readily available routine laboratory tests is powerful in identifying breast cancer patients who are at high risk of recurrence. Further study is warranted to validate its clinical application

Dielectric Response of Sr Doped CaCu₃Ti₄O₁₂ Ceramics

Ca1−xSrxCu3Ti4O12 (x=0, 0.1, and 0.2) ceramics were fabricated and their dielectric properties were investigated. It was found that the dielectric constant significantly decreased with the increase of Sr content at low temperature region (\u3c250 K) and remained almost unchanged at high temperature region (\u3e250 K). Three sets of relaxation peaks were observed in electric modulus plots, which were considered to be associated with grains, domain boundaries, and grain boundaries, respectively. Through the analysis of the heights and calculated activation energies of the relaxation peaks, it is strongly believed that the suppressed dielectric constant is related to the change of domain boundaries with Sr doping. ©2007 American Institute of Physic

Antiperovskite Li3OCl Superionic Conductor Films for Solid-State Li-Ion Batteries.

Antiperovskite Li3OCl superionic conductor films are prepared via pulsed laser deposition using a composite target. A significantly enhanced ionic conductivity of 2.0 × 10-4 S cm-1 at room temperature is achieved, and this value is more than two orders of magnitude higher than that of its bulk counterpart. The applicability of Li3OCl as a solid electrolyte for Li-ion batteries is demonstrated

Mapping of biophysical and biochemical properties of coastal tidal wetland habitats with Landsat 8

Coastal tidal wetlands are significant and vulnerable aquatic ecosystems. Quantitative remote sensing of biophysical and biochemical properties in coastal tidal wetland habitats through the inversion of physical models has vital practical significance for monitoring ecosystem function, environmental restoration, the global carbon, and nitrogen cycles. The objectives of this research were to map leaf area index (LAI), chlorophyll content, as well as the sensible heat flux, latent heat flux, and productivity in Chongming Dongtan coastal tidal wetland habitats of China and to provide a mapping protocol of biophysical and biochemical properties in Chongming Dongtan wetland for environmental protection and restoration as well as assessment and monitoring. In order to obtain significant information for biodiversity protection and management, a method based on the Soil Canopy Observation of Photosynthesis and Energy fluxes model and lookup table approach has been developed. The results derived from our study contain the reflectance values of Scirpus mariqueter and Phragmites australis spectra are lower than those commonly found for vegetated areas. This may be caused by the dark soil background and low LAI. Moreover, as for the values of latent heat flux (between 120 and 190 W m - 2) and productivity (between 3 and 14 μmol m - 2 s - 1), mudflats are lower than vegetation. However, the values of sensible heat flux (between 140 and 170 W m - 2) of mudflats are higher than that of vegetation. </p

Virtual screening of the inhibitors targeting at the viral protein 40 of Ebola virus

Multilingual abstracts in the six official working languages of the United Nations. (PDF 373 kb