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Carcinogenesis is the multistep process by which normal cells undergo malignant transformation. The clinical expression of cancer may be prevented or delayed either by risk factor modification, such as quitting smoking, or by the administration of drugs to prevent or delay the clinical expression of the malignant phenotype. This chapter focuses on the latter approach, often referred to as ˵chemoprevention.″ Specifically, it addresses the two key issues distinguishing cancer prevention from cancer treatment agent development: selection of study endpoints and patient cohorts. In addition, a comprehensive update is provided of recently completed and ongoing phase 1, 2, and 3 prostate cancer prevention clinical trials conducted under the auspices of the Division of Cancer Prevention, NCI. [ABSTRACT FROM AUTHOR]

Convexity is an important property in nonlinear optimization since it allows to apply efficient local methods for finding global solutions. We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems. Our methods are implemented and publicly available in the open source computer algebra system Reduce. Our long term goal is to integrate Reduce as a ˵workhorse″ for symbolic computations into a numerical solver. [ABSTRACT FROM AUTHOR]