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We could start writing this book by saying, with several other authors, that the brain is the most powerful and complex information processing device known, whether naturally developed or created artificially. Although we fully agree with this statement, in doing so we would be misleading the reader, in the sense that the present book basically aims to formalize the knowledge concerning brain physiology accumulated over the past few decades. Instead of merely describing the complexity of the cerebral str- ture or presenting a collection of commentaries and reviews of interesting experimental results, we take into account novel achievements in quantum information and quantum computation, and avail ourselves of recently - veloped mathematical tools. Neuroscience was bom in the 19'~ century with the works of Paul Brocca. However, this fledgling field experienced a boom only in recent times, following the development of powerful non-invasive techniques for probing the neural circuitry supporting the complex cognitive functions of the human brain. Although sophisticated mathematical models and phy- cal theories are the basic tools behind the conceptual foundations and a- lytical implementation of these modem techniques, to the best of our knowledge no effort was made to formalize the actual knowledge about brain function into a coherent theoretical framework incorporating the - cent developments in mathematical and physical science. Addressing this lack was our first motivation in writing this book.

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This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.

During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software.

This book describes the development and design of a unique combined data and power management infrastructure for small satellites. This new edition became necessary because in the frame of the system's impressive evolution from an academic prototype to one of today's most advanced core avionics, many elements were upgraded to their next technology generation and diverse new components complement the upgraded design. All elements are presented in updated respectively new chapters.

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