Neural Fields

Dynamic Neural Field Theory for Motion Perception provides a new theoretical framework that permits a systematic analysis of the dynamic properties of motion perception. This framework uses dynamic neural fields as a key mathematical concept. The author demonstrates how neural fields can be applied for the analysis of perceptual phenomena and its underlying neural processes. Also, similar principles form a basis for the design of computer vision systems as well as the design of artificially behaving systems. The book discusses in detail the application of this theoretical approach to motion perception and will be of great interest to researchers in vision science, psychophysics, and biological visual systems.

Biophysical modelling of brain activity has a long and illustrious history and has recently profited from technological advances that furnish neuroimaging data at an unprecedented spatiotemporal resolution. Neuronal modelling is a very active area of research, with applications ranging from the characterization of neurobiological and cognitive processes, to constructing artificial brains in silico and building brain-machine interface and neuroprosthetic devices. Biophysical modelling has always benefited from interdisciplinary interactions between different and seemingly distant fields; ranging from mathematics and engineering to linguistics and psychology. This Research Topic aims to promote such interactions by promoting papers that contribute to a deeper understanding of neural activity as measured by fMRI or electrophysiology. In general, mean field models of neural activity can be divided into two classes: neural mass and neural field models. The main difference between these classes is that field models prescribe how a quantity characterizing neural activity (such as average depolarization of a neural population) evolves over both space and time as opposed to mass models, which characterize activity over time only; by assuming that all neurons in a population are located at (approximately) the same point. This Research Topic focuses on both classes of models and considers several aspects and their relative merits that: span from synapses to the whole brain; comparisons of their predictions with EEG and MEG spectra of spontaneous brain activity; evoked responses, seizures, and fitting data - to infer brain states and map physiological parameters.

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.

The 10-volume set LNCS 14254-14263 constitutes the proceedings of the 32nd International Conference on Artificial Neural Networks and Machine Learning, ICANN 2023, which took place in Heraklion, Crete, Greece, during September 26–29, 2023. The 426 full papers, 9 short papers and 9 abstract papers included in these proceedings were carefully reviewed and selected from 947 submissions. ICANN is a dual-track conference, featuring tracks in brain inspired computing on the one hand, and machine learning on the other, with strong cross-disciplinary interactions and applications.

This two volume set LNCS 5163 and LNCS 5164 constitutes the refereed proceedings of the 18th International Conference on Artificial Neural Networks, ICANN 2008, held in Prague Czech Republic, in September 2008. The 200 revised full papers presented were carefully reviewed and selected from more than 300 submissions. The second volume is devoted to pattern recognition and data analysis, hardware and embedded systems, computational neuroscience, connectionistic cognitive science, neuroinformatics and neural dynamics. it also contains papers from two special sessions coupling, synchronies, and firing patterns: from cognition to disease, and constructive neural networks and two workshops new trends in self-organization and optimization of artificial neural networks, and adaptive mechanisms of the perception-action cycle.

The two volume set, LNCS 10613 and 10614, constitutes the proceedings of then 26th International Conference on Artificial Neural Networks, ICANN 2017, held in Alghero, Italy, in September 2017. The 128 full papers included in this volume were carefully reviewed and selected from 270 submissions. They were organized in topical sections named: From Perception to Action; From Neurons to Networks; Brain Imaging; Recurrent Neural Networks; Neuromorphic Hardware; Brain Topology and Dynamics; Neural Networks Meet Natural and Environmental Sciences; Convolutional Neural Networks; Games and Strategy; Representation and Classification; Clustering; Learning from Data Streams and Time Series; Image Processing and Medical Applications; Advances in Machine Learning. There are 63 short paper abstracts that are included in the back matter of the volume.

This two volume set (LNCS 6791 and LNCS 6792) constitutes the refereed proceedings of the 21th International Conference on Artificial Neural Networks, ICANN 2011, held in Espoo, Finland, in June 2011. The 106 revised full or poster papers presented were carefully reviewed and selected from numerous submissions. ICANN 2011 had two basic tracks: brain-inspired computing and machine learning research, with strong cross-disciplinary interactions and applications.

​Waves in Neural Media: From Single Neurons to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The work provides a pedagogical account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. These include regular and singular perturbation methods, weakly nonlinear analysis, Evans functions and wave stability, homogenization theory and averaging, and stochastic processes. Also covered in the text are exact methods of solution where applicable. Historically speaking, the propagation of action potentials has inspired new mathematics, particularly with regard to the PDE theory of waves in excitable media. More recently, continuum neural field models of large-scale brain networks have generated a new set of interesting mathematical questions with regard to the solution of nonlocal integro-differential equations. Advanced graduates, postdoctoral researchers and faculty working in mathematical biology, theoretical neuroscience, or applied nonlinear dynamics will find this book to be a valuable resource. The main prerequisites are an introductory graduate course on ordinary differential equations or partial differential equations, making this an accessible and unique contribution to the field of mathematical biology.