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Biology is witnessing a transformation towards a more quantitative science, based on the major technological breakthroughs of the past decade. In this transformation, biology is incorporating mathematical modeling techniques and computational approaches towards numerical simulations, model analysis, and quantitativepredictions.An importantgoalis to formalizeandanalyzethe ev- changing inter-connections between components (often on di?erent time and space scales), their in?uence on one another, regulatory patterns, alternative pathways, etc. Formal reasoning rather than empirical observations...

Much current research in computer science is concerned with two questions: is a program correct? And how can we improve a correct program preserving correctness? This latter question is known as the refinement of programs and the purpose of this book is to consider these questions in a formal setting. In fact, correctness turns out to be a special case of refinement and so the focus is on refinement. Although a reasonable background knowledge is assumed from mathematics and CS, the book is a self-contained introduction suitable for graduate students and researchers coming to this subject for...

Mathematics is based on proofs. The proof shows the logical reasoning behind a theorem, allows us to understand the meaning of it, its limitations and its consequences. Without a proof, a theorem is like magic; with a proof it is (sometimes more, sometimes less) self evident. But proofs are considered difficult in mathematics education of today, in particular at secondary level, and are therefore often avoided in teaching. When proofs are given, they are often informal and the underlying logic is not explicated. The purpose of this book is to put forward an alternative method for teaching...

The LNCS journal Transactions on Computational Systems Biology is devoted to inter- and multidisciplinary research in the fields of computer science and life sciences and supports a paradigmatic shift in the techniques from computer and information science to cope with the new challenges arising from the systems oriented point of view of biological phenomena. This, the 13th Transactions on Computational Systems Biology volume, guest edited by Ralph-Johan Back, Ion Petre, and Erik de Vink, focuses on Computational Models for Cell Processes and features a number of carefully selected and...