Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Computation at the edge of chaos: phase transitions and emergent computation
CNLS '89 Proceedings of the ninth annual international conference of the Center for Nonlinear Studies on Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks on Emergent computation
Intelligence without representation
Artificial Intelligence
Structure theorems for nonlinear systems
Multidimensional Systems and Signal Processing
The nature of statistical learning theory
The nature of statistical learning theory
Spikes: exploring the neural code
Spikes: exploring the neural code
Models of Computation: Exploring the Power of Computing
Models of Computation: Exploring the Power of Computing
Spiking neurons and the induction of finite state machines
Theoretical Computer Science - Natural computing
Reducing Communication for Distributed Learning in Neural Networks
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Real-time computation at the edge of chaos in recurrent neural networks
Neural Computation
A Model for Fast Analog Computation Based on Unreliable Synapses
Neural Computation
Neural Systems as Nonlinear Filters
Neural Computation
On the Computational Power of Winner-Take-All
Neural Computation
On the Computational Power of Neural Microcircuit Models: Pointers to the Literature
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Movement Generation with Circuits of Spiking Neurons
Neural Computation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Optimizing Generic Neural Microcircuits through Reward Modulated STDP
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
Memory in linear recurrent neural networks in continuous time
Neural Networks
Self-organized short-term memory mechanism in spiking neural network
ICANNGA'11 Proceedings of the 10th international conference on Adaptive and natural computing algorithms - Volume Part I
On the capacity of transient internal states in liquid-state machines
ICANN'11 Proceedings of the 21st international conference on Artificial neural networks - Volume Part II
Topological constraints and robustness in liquid state machines
Expert Systems with Applications: An International Journal
Liquid state machine by spatially coupled oscillators
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part I
A hierachical configuration system for a massively parallel neural hardware platform
Proceedings of the 9th conference on Computing Frontiers
The Explanatory Role of Computation in Cognitive Science
Minds and Machines
Temporal finite-state machines: a novel framework for the general class of dynamic networks
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part II
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Complex real-time computations on multi-modal time-varying input streams are carried out by generic cortical microcircuits. Obstacles for the development of adequate theoretical models that could explain the seemingly universal power of cortical microcircuits for real-time computing are the complexity and diversity of their computational units (neurons and synapses), as well as the traditional emphasis on offline computing in almost all theoretical approaches towards neural computation. In this article, we initiate a rigorous mathematical analysis of the real-time computing capabilities of a new generation of models for neural computation, liquid state machines, that can be implemented with--in fact benefit from--diverse computational units. Hence, realistic models for cortical microcircuits represent special instances of such liquid state machines, without any need to simplify or homogenize their diverse computational units. We present proofs of two theorems about the potential computational power of such models for real-time computing, both on analog input streams and for spike trains as inputs.