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Environmental Factors, Genes, and the Development of Human Cancers
Cancer is a complex disease. Only 5-10% of human cancers are hereditary in nature. Many of us think of environmental agents when we think of carcinogens. The environment includes all that surrounds us, and environmental influences include not only chemical, physical and biological toxicants, but also diet and lifestyle. In this broadest sense, the environment contributes substantially in the development of human cancer. This book will describe how environment contributes to malignant transformation leading to profound changes in the genetic and signaling networks that control the functioning of the cell. It will critically discuss the understanding of the effects of environment on the develo...
Power Sums, Gorenstein Algebras, and Determinantal Loci
This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry.
