Neural Fields: Theory And Applications
by James Wright /
2014 / English / PDF
11.3 MB Download
Neural field theory has a long-standing tradition in the
mathematical and computational neurosciences. Beginning almost 50
years ago with seminal work by Griffiths and culminating in the
1970ties with the models of Wilson and Cowan, Nunez and Amari, this
important research area experienced a renaissance during the
1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright
and Haken. Since then, much progress has been made in both, the
development of mathematical and numerical techniques and in
physiological refinement und understanding. In contrast to
large-scale neural network models described by huge connectivity
matrices that are computationally expensive in numerical
simulations, neural field models described by connectivity kernels
allow for analytical treatment by means of methods from functional
analysis. Thus, a number of rigorous results on the existence of
bump and wave solutions or on inverse kernel construction problems
are nowadays available. Moreover, neural fields provide an
important interface for the coupling of neural activity to
experimentally observable data, such as the electroencephalogram
(EEG) or functional magnetic resonance imaging (fMRI). And finally,
neural fields over rather abstract feature spaces, also called
dynamic fields, found successful applications in the cognitive
sciences and in robotics. Up to now, research results in neural
field theory have been disseminated across a number of distinct
journals from mathematics, computational neuroscience, biophysics,
cognitive science and others. There is no comprehensive collection
of results or reviews available yet. With our proposed book Neural
Field Theory, we aim at filling this gap in the market. We received
consent from some of the leading scientists in the field, who are
willing to write contributions for the book, among them are two of
the founding-fathers of neural field theory: Shun-ichi Amari and
Jack Cowan.
Neural field theory has a long-standing tradition in the
mathematical and computational neurosciences. Beginning almost 50
years ago with seminal work by Griffiths and culminating in the
1970ties with the models of Wilson and Cowan, Nunez and Amari, this
important research area experienced a renaissance during the
1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright
and Haken. Since then, much progress has been made in both, the
development of mathematical and numerical techniques and in
physiological refinement und understanding. In contrast to
large-scale neural network models described by huge connectivity
matrices that are computationally expensive in numerical
simulations, neural field models described by connectivity kernels
allow for analytical treatment by means of methods from functional
analysis. Thus, a number of rigorous results on the existence of
bump and wave solutions or on inverse kernel construction problems
are nowadays available. Moreover, neural fields provide an
important interface for the coupling of neural activity to
experimentally observable data, such as the electroencephalogram
(EEG) or functional magnetic resonance imaging (fMRI). And finally,
neural fields over rather abstract feature spaces, also called
dynamic fields, found successful applications in the cognitive
sciences and in robotics. Up to now, research results in neural
field theory have been disseminated across a number of distinct
journals from mathematics, computational neuroscience, biophysics,
cognitive science and others. There is no comprehensive collection
of results or reviews available yet. With our proposed book Neural
Field Theory, we aim at filling this gap in the market. We received
consent from some of the leading scientists in the field, who are
willing to write contributions for the book, among them are two of
the founding-fathers of neural field theory: Shun-ichi Amari and
Jack Cowan.
