S-rough sets and the discovery of F-hiding knowledge

Singular rough sets （S-rough sets） have three classes of forms： one-directional S-rough sets, dual of onedirectional S-rough sets, and two-directional S-rough sets. Dynamic, hereditary, mnemonic, and hiding properties are the basic characteristics of S-rough sets. By using the S-rough sets, the concepts of f-hiding knowledge, F-hiding knowledge, hiding degree, and hiding dependence degree are given. Then, both the hiding theorem and the hiding dependence theorem of hiding knowledge are proposed. Finally, an application of hiding knowledge is discussed.

Re-estimation of China's Degree of Trade Dependence and External Imbalance: Value-added Statistics in the Global Production Chain

The distortion of GDP and foreign trade data has exaggerated China＇s foreign trade dependence degree and external imbalance degree. The distortion of GDP is mainly caused by the difference between the exchange rate method and purchasing power parity （PPP） estimation. The distortion of trade data includes double counting of customs statistics as well as the discrepancy between the international trade flows of goods and of capital caused by the ownership issue. The re-estimation of China＇s trade dependence degree and external imbalance degree reveals that according to official statistics, in 2007 the dependence degree of China＇s foreign trade decreased to 31.59 percent from 68.02 percent and its imbalance degree decreased to 2.11 percent from 10.13 percent. Therefore, it is utterly groundless to accuse China of ＂manipulating the exchange rate.＂

Degree dependence entropy descriptor for complex networks

In order to supply better accordance for mod eling and simulation of complex networks, a new degree dependence entropy （DDE） descriptor is proposed to describe the degree dependence relationship and corre sponding characteristic in this paper. First of all, degrees of vertices and the shortest path lengths between all pairs of ,ertices are computed. Then the degree dependence matrices under different shortest path lengths are con structed. At last the DDEs are extracted from the degree dependence matrices. Simulation results show that the DDE descriptor can reflect the complexity of degree dependence relationship in complex networks; high DDE indicates complex degree dependence relationship; low DDE indicates the opposite one. The DDE can be seen as a quantitative statistical characteristic, which is meaningful for networked modeling and simulation.

Linear dependence of the degree of aggregation on the solvent aggregating power (SAgP)

With k_8/k_(16), the ratio of the hydrolytic rate-constants of p-nitrophenyl octanoate (C8) to hexadecanoate (C16), as the indicator of the degree of aggregation, the linear dependence of the deg- ree of aggregation on solvent aggregating power (SAgP) has been established in five aquiorgano sol- vents, each within a certain range of volume fraction ( values) of the organic cosolvent. The mea- ning of this linearity has been discussed.