Rieke, Warland, de Ruyter van Steveninck and Bialek.

**Spikes: Exploring the Neural Code.**

Link to the publishers' page.

Summary: Neural computation in terms of information theory and statistical decision theory.

Our perception of the world is driven by input from the sensory nerves. This input arrives encoded as sequences of identical spikes. Much of neural computation involves processing these spike trains. What does it mean to say that a certain set of spikes is the right answer to a computational problem? In what sense does a spike train convey information about the sensory world? Spikes begins by providing precise formulations of these and related questions about the representation of sensory signals in neural spike trains. The answers to these questions are then pursued in experiments on sensory neurons.The authors invite the reader to play the role of a hypothetical observer inside the brain who makes decisions based on the incoming spike trains. Rather than asking how a neuron responds to a given stimulus, the authors ask how the brain could make inferences about an unknown stimulus from a given neural response. The flavor of some problems faced by the organism is captured by analyzing the way in which the observer can make a running reconstruction of the sensory stimulus as it evolves in time. These ideas are illustrated by examples from experiments on several biological systems.

Intended for neurobiologists with an interest in mathematical analysis of neural data as well as the growing number of physicists and mathematicians interested in information processing by "real" nervous systems, Spikes provides a self-contained review of relevant concepts in information theory and statistical decision theory. A quantitative framework is used to pose precise questions about the structure of the neural code. These questions in turn influence both the design and analysis of experiments on sensory neurons.

Here's another one:

Chris Eliasmith and Charles H. Anderson

**Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems**

Link to publishers' page.

For years, researchers have used the theoretical tools of engineering to understand neural systems, but much of this work has been conducted in relative isolation. In Neural Engineering, Chris Eliasmith and Charles Anderson provide a synthesis of the disparate approaches current in computational neuroscience, incorporating ideas from neural coding, neural computation, physiology, communications theory, control theory, dynamics, and probability theory. This synthesis, they argue, enables novel theoretical and practical insights into the functioning of neural systems. Such insights are pertinent to experimental and computational neuroscientists and to engineers, physicists, and computer scientists interested in how their quantitative tools relate to the brain.The authors present three principles of neural engineering based on the representation of signals by neural ensembles, transformations of these representations through neuronal coupling weights, and the integration of control theory and neural dynamics. Through detailed examples and in-depth discussion, they make the case that these guiding principles constitute a useful theory for generating large-scale models of neurobiological function. A software package written in MatLab for use with their methodology, as well as examples, course notes, exercises, documentation, and other material, are available on the Web.

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