On the Addition and Comparison of Graphs Labeled with Stochastic Variables: Learnable Anatomical Catalogs

We provide an operator for the addition of a pair of graphs, labeled with continuous variables which are subject to stochastic variation. We also provide an operator for measuring dissimilarity between a pair of such graphs. We use such a representation and operators to model a collection of vascular anatomy which accounts for inter-individual variations in both branching structure and in vessel shape. The model may be incrementally acquired, and is thus a catalog of anatomy whose content may be learned. The model may be used in applications such as the reconstruction of vasculature in three-dimensions from x-ray images, which we briefly outline.     

Squeezed算符和Schwinger算符的几种显示表达式

通过角动量算符的拆解定理 ,把 Squeezed算符和 Schwinger算符的普通指数形式转换成正规排列和反正规排列的形式     

《王梵志诗校注》商补(续)

项楚《王梵志诗校注》为王梵志诗研究中最重要的文献 ,然其中亦不无可商兑补正之处     

关于Post-Gamma算子的点态近估计

综合利用概率论中的中心极限定理的一种渐近展开形式和Bojanic-Cheng方法,研究了Post-Gamma算子 对局部有界函数的点态逼近估计,得到精确的逼近阶,并进一步证明了此估计在连续点处是渐进最优的.     

Source Data Perturbation and consistent sets of safe tables

When tables are generated from a data file, the release of those tables should not reveal too detailed information concerning individual respondents. The disclosure of individual respondents in the microdata file can be prevented by applying disclosure control methods at the table level (by cell suppression or cell perturbation), but this may create inconsistencies among other tables based on the same data file. Alternatively, disclosure control methods can be applied at the microdata level, but these methods may change the data permanently and do not account for specific table properties. These problems can be circumvented by assigning a (single and fixed) weight factor to each respondent/record in the microdata file. Normally this weight factor is equal to 1 for each record, and is not explicitly incorporated in the microdata file. Upon tabulation, each contribution of a respondent is weighted multiplicatively by the respondent's weight factor. This approach is called Source Data Perturbation (SDP) because the data is perturbed at the microdata level, not at the table level. It should be noted, however, that the data in the original microdata is not changed; only a weight variable is added. The weight factors can be chosen in accordance with the SDC paradigm, i.e. such that the tables generated from the microdata are safe, and the information loss is minimized. The paper indicates how this can be done. Moreover it is shown that the SDP approach is very suitable for use in data warehouses, as the weights can be conveniently put in the fact tables. The data can then still be accessed and sliced and diced up to a certain level of detail, and tables generated from the data warehouse are mutually consistent and safe.     

关于Beta算子的渐近表示

本文主要给出了当f∈B（0‘ ∞）时Beta算子的一些渐近表示。     

1,2,3-三氰基-1,2,3-三对氯苯基环丙烷的合成

本文报告了对氯苯乙腈在DMSO存在下与四氯化碳的相转移催化反应,得到一个新化合物1,2,3—三氰基—1,2,3—三对氯苯基环丙烷,其结构通过元素分析、红外、核磁共振和质谱得到证实。初步探讨形成三元环化合物的反应机理。     

一类Bernstein-Durrmeyer算子线性组合的局部逼近阶

给出了一类Bernstein－Durrneyer算子的线性组合在一致逼近意义下的局部逼近阶．     

多元Gauss-Weierstrass算子的加权逼近

主要讨论多元Gauss－Weierstrass算子加Jacobi权逼近时的收敛阶,得出了在一致逼近意义下的正,逆定理及特征性     

Water Quality Failures in Distribution Networks—Risk Analysis Using Fuzzy Logic and Evidential Reasoning

The evaluation of the risk of water quality failures in a distribution network is a challenging task given that much of the available data are highly uncertain and vague, and many of the mechanisms are not fully understood. Consequently, a systematic approach is required to handle quantitative-qualitative data as well as a means to update existing information when new knowledge and data become available. Five general pathways (mechanisms) through which a water quality failure can occur in the distribution network are identified in this article. These include contaminant intrusion, leaching and corrosion, biofilm formation and microbial regrowth, permeation, and water treatment breakthrough (including disinfection byproducts formation). The proposed methodology is demonstrated using a simplified example for water quality failures in a distribution network. This article builds upon the previous developments of aggregative risk analysis approach. Each basic risk item in a hierarchical framework is expressed by a triangular fuzzy number, which is derived from the composition of the likelihood of a failure event and the associated failure consequence . An analytic hierarchy process is used to estimate weights required for grouping noncommensurate risk sources. The evidential reasoning is proposed to incorporate newly arrived data for the updating of existing risk estimates. The exponential ordered weighted averaging operators are used for defuzzification to incorporate attitudinal dimension for risk management. It is envisaged that the proposed approach could serve as a basis to benchmark acceptable risks in water distribution networks.