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Waveform-relaxation methods for ordinary and stochastic differential equations with applications in distributed neural network simulations / eingereicht von Jan Hahne, M. Sc. Wuppertal, 29.05.2018
Content
Acknowledgments
Foreword
Contents
Introduction
Review of basic material
Ordinary differential equations
Runge-Kutta methods
Stochastic differential equations
Selected numerical methods
Stochastic delay differential equations
Spiking neural network simulators
NEST - NEural Simulation Tool
Waveform-relaxation methods for ODEs
Literature review
An ODE-waveform-relaxation method suitable for spiking neural network simulators
Restrictions and requirements
The method
Convergence analysis
Waveform-relaxation methods for SDEs
Literature review
A SDE-waveform-relaxation method suitable for spiking neural network simulators
Restrictions and requirements
The method
Convergence analysis
Application in computational neuroscience I: Including gap junctions in a spiking neural network simulator
Framework
Algorithmic and numerical implementation
Connection infrastructure
Communication infrastructure
Iterative neuronal updates
Neuron model
User interface
Numerical results
Setup
Pair of gap-junction coupled neurons
Network with combined dynamics of chemical synapses and gap junctions
Performance of the gap-junction framework in NEST
Discussion
Application in computational neuroscience II: Including rate models in a spiking neural network simulator
Rate models
Framework
Restrictions
Implementation
Reduction of communication using waveform-relaxation techniques
User interface
Numerical results
Stability and accuracy of integration methods
Performance of the NEST implementation
Applications
Discussion
Conclusions & Outlook
List of Figures
List of Tables
List of Algorithms & Scripts
List of Notations
Bibliography