Human cancer cell lines are used in research to study the biology of cancer and to test cancer treatments. Recently there are already some large panels of several hundred human cancer cell lines which are characterized with genomic and pharmacological data. The ability to predict drug responses using these pharmacogenomics data can facilitate the development of precision cancer medicines. Although several methods have been developed to address the drug response prediction, there are many challenges in obtaining accurate prediction. Based on the fact that similar cell lines and similar drugs exhibit similar drug responses, we adopted a similarity-regularized matrix factorization (SRMF) method to predict anticancer drug responses of cell lines using chemical structures of drugs and baseline gene expression levels in cell lines. Specifically, chemical structural similarity of drugs and gene expression profile similarity of cell lines were considered as regularization terms, which were incorporated to the drug response matrix factorization model. We first demonstrated the effectiveness of SRMF using a set of simulation data and compared it with two typical similarity-based methods. Furthermore, we applied it to the Genomics of Drug Sensitivity in Cancer (GDSC) and Cancer Cell Line Encyclopedia (CCLE) datasets, and performance of SRMF exceeds three state-of-the-art methods. We also applied SRMF to estimate the missing drug response values in the GDSC dataset. Even though SRMF does not specifically model mutation information, it could correctly predict drug-cancer gene associations that are consistent with existing data, and identify novel drug-cancer gene associations that are not found in existing data as well. SRMF can also aid in drug repositioning. The newly predicted drug responses of GDSC dataset suggest that mTOR inhibitor rapamycin was sensitive to non-small cell lung cancer (NSCLC), and expression of AK1RC3 and HINT1 may be adjunct markers of cell line sensitivity to rapamycin. Our analysis showed that the proposed data integration method is able to improve the accuracy of prediction of anticancer drug responses in cell lines, and can identify consistent and novel drug-cancer gene associations compared to existing data as well as aid in drug repositioning.

The repairable parallel system is an essential part of the maintenance support for high technology systems. The uncertain lifetimes and repair times of repairable parallel systems are usually treated as the stochastic variables, which have crisp para

Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Different from randomness and fuzziness, uncertainty theory provides a new mathematical model for uncertain phenomena. Distance and similarity measure have played an important role in uncertainty theory as well as many other disciplines. This paper first proposes some new distances between uncertain variables. Then the definition of the degree of similarity between uncertain variables is introduced and several similarity measures between uncertain variables are generated from distance measures. Finally, the distance and similarity measures proposed are applied to pattern recognition.

Various approaches of Petri nets can be achieved as system security and information flow in the healthcare recording system inside any medical or health-related business. Petri net system formal modeling is essential as well as important to track down the records and secure information inside a preformed health organization. In this paper, we mainly focused on the formal model Petri net which security mechanism is controlled by public key encryption where PN based modeling is preferred. This Petri net is a mathematical modeling to solve graphical notation for step by step processes that include choice, repetition, and circumstantial execution. Petri nets offer widely mathematical applications of discrete and continuous event execution semiotics, with an efficient mathematical analysis processing theory. We sure that our formal model will lay a solid foundation to minimize the risks and overcome the security risks in the healthcare industry.

A hybrid variable is a new tool to describe the quantities with fuzziness and randomness. Chance theory is a hybrid of probability theory and credibility theory. The definition of the degree of similarity between hybrid variables is introduced based on chance theory. Several similarity measures between hybrid variables are proposed and corresponding proofs are given. Finally, the similarity measure between actual hybrid variables are computed as examples.