
The vast majority of random processes in the real world have no memory — the next step in their development depends purely on their current state. Stochastic realizations are therefore defined purely in terms of successive eventtime pairs, and such systems are easy to simulate irrespective of their degree of complexity. However, whilst the associated probability equations are straightforward to write down, their solution usually requires the use of approximation and perturbation procedures. Traditional books, heavy in mathematical theory, often ignore such methods and attempt to force problems into a rigid framework of closedform solutions.

How could we use living cells to perform computation? Would our definition of computation change as a consequence of this? Could such a cellcomputer outperform digital computers? These are some of the questions that the study of Membrane Computing tries to answer and are at the base of what is treated by this monograph. Descriptional and computational complexity of models in Membrane Computing are the two lines of research on which is the focus here. In this context this book reports the results of only some of the models present in this framework. The models considered here represent a very relevant part of all the models introduced so far in the study of Membrane Computing. They are in between the most studied models in the field and they cover a broad range of features (using symbol objects or string objects, based only on communications, inspired by intra and intercellular processes, having or not having a tree as underlying structure, etc.) that gives a grasp of the enormous flexibility of this framework. Links with biology and Petri nets are constant through this book. This book aims also to inspire research. This book gives suggestions for research of various levels of difficulty and this book clearly indicates their importance and the relevance of the possible outcomes. Readers new to this field of research will find the provided examples particularly useful in the understanding of the treated topics.

From one cell to another, from one individual to another, and from one species to another, the content of DNA molecules is often similar. The organization of these molecules, however, differs dramatically, and the mutations that affect this organization are known as genome rearrangements. Combinatorial methods are used to reconstruct putative rearrangement scenarios in order to explain the evolutionary history of a set of species, often formalizing the evolutionary events that can explain the multiple combinations of observed genomes as combinatorial optimization problems. This book offers a comprehensive survey of this rapidly expanding application of combinatorial optimization. It can be used as a reference for experienced researchers or as an introductory text for a broader audience. Genome rearrangement problems have proved so interesting from a combinatorial point of view that the field now belongs as much to mathematics as to biology. The book takes a mathematically oriented approach, but provides biological background when necessary. It presents a series of models, beginning with the simplest (which is progressively extended by dropping restrictions), each constructing a genome rearrangement problem. The book also discusses an important generalization of the basic problem known as the median problem, surveys attempts to reconstruct the relationships between genomes with phylogenetic trees, and offers a collection of summaries and appendixes with additional information.

Research in systems biology requires the collaboration of researchers from diverse backgrounds, including biology, computer science, mathematics, statistics, physics, and biochemistry. These collaborations, necessary because of the enormous breadth of background needed for research in this field, can be hindered by differing understandings of the limitations and applicability of techniques and concerns from different disciplines. The emerging area of systems level modeling in cellular biology has lacked a critical and thorough overview. The book provides the necessary critical comparison of concepts and approaches, with an emphasis on their possible applications. It presents key concepts and their theoretical background, including the concepts of robustness and modularity and their exploitation to study biological systems; the bestknown modeling approaches, and their advantages and disadvantages; lessons from the application of mathematical models to the study of cellular biology; and available modeling tools and datasets, along with their computational limitations.

A universal goal of technological development is the enrichment of human life. The fast developments of nano/micro technologies enable us to directly handle a single cell or a single molecule. This capability propels the molecular based diagnostic and therapeutic technologies to a new horizon. In this book, we not only examine thestate ofart biotechnologies, but also present many cuttingedge research topics which will lead toward the next generation technologies for improving human health. With the capabilities of moving, stopping, mixing and concentrating minute amount of fluid and/or particles, microfluidic circuitry provides unprecedented functions for advancing sample preparation and cell culture processes. Integrated biomarker sensors with microfluidics, it becomes possible to detect diseases in extremely sensitive and specific manner. With the cutting edge optical techniques and proper surface molecular modification, we can study and manipulate biological processes in live cell. While we have made significant progresses in studying and controlling the phenomena in the nano/micro scale, human health is a system issue with a length in the order of a meter. A disparity of several orders of magnitude in the length scales presents significant challenges. Our current and future tasks are to develop the seamless integration processes from materials through devices and eventually into engineering systems. Our ultimate goal is that these nano/micro technology based systems can effectively interface and direct the biological complex system toward desired fate.