## Observed Brain DynamicsThe biomedical sciences have recently undergone revolutionary change, due to the ability to digitize and store large data sets. In neuroscience, the data sources include measurements of neural activity measured using electrode arrays, EEG and MEG, brain imaging data from PET, fMRI, and optical imaging methods. Analysis, visualization, and management of these time series data sets is a growing field of research that has become increasingly important both for experimentalists and theorists interested in brain function. Written by investigators who have played an important role in developing the subject and in its pedagogical exposition, the current volume addresses the need for a textbook in this interdisciplinary area. The book is written for a broad spectrum of readers ranging from physical scientists, mathematicians, and statisticians wishing to educate themselves about neuroscience, to biologists who would like to learn time series analysis methods in particular and refresh their mathematical and statistical knowledge in general, through self-pedagogy. It may also be used as a supplement for a quantitative course in neurobiology or as a textbook for instruction on neural signal processing. The first part of the book contains a set of essays meant to provide conceptual background which are not technical and shall be generally accessible. Salient features include the adoption of an active perspective of the nervous system, an emphasis on function, and a brief survey of different theoretical accounts in neuroscience. The second part is the longest in the book, and contains a refresher course in mathematics and statistics leading up to time series analysis techniques. The third part contains applications of data analysis techniques to the range of data sources indicated above (also available as part of the Chronux data analysis platform from http://chronux.org), and the fourth part contains special topics. |

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action potentials algorithm analysis applied approach average bandwidth behavior biological brain chapter cluster coherence computed consider convergence correlation corresponding covariance decomposition defined degrees of freedom density dependent dimensional Dirichlet kernel discrete discussion dynamics eigenvalues electrodes entropy equation error example experimental Figure finite firing rate fMRI formal Fourier transform frequency Gaussian distribution given grid imaging interval jackknife large number likelihood linear model local regression mathematical matrix measure methods microscopic multiple multitaper multivariate mutual information nervous system neurons neuroscience noise Note obtained parameters peaks physics point process Poisson process polynomial prediction probability distribution problem procedure random variables regression rescaled response sample space sequence shows signal singular value Slepian spatial spectral estimate spectrum spike sorting spike train statistical stimulus stochastic process taper temporal theoretical theory tion trials variance vector visual voltage voxel waveforms window zero