Nonlinear systems (vol. 2): applications to bilinear control
Nonlinear systems (vol. 2): applications to bilinear control
Projection frameworks for model reduction of weakly nonlinear systems
Proceedings of the 37th Annual Design Automation Conference
Krylov-subspace methods for reduced-order modeling in circuit simulation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Biophysics of Computation: Information Processing in Single Neurons (Computational Neuroscience Series)
$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
SIAM Journal on Matrix Analysis and Applications
Order reduction of bilinear MIMO dynamical systems using new block Krylov subspaces
Computers & Mathematics with Applications
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Projection-based approaches for model reduction of weakly nonlinear, time-varying systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Compact reduced-order modeling of weakly nonlinear analog and RF circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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The spatial component of input signals often carries information crucial to a neuron's function, but models mapping synaptic inputs to the transmembrane potential can be computationally expensive. Existing reduced models of the neuron either merge compartments, thereby sacrificing the spatial specificity of inputs, or apply model reduction techniques that sacrifice the underlying electrophysiology of the model. We use Krylov subspace projection methods to construct reduced models of passive and quasi-active neurons that preserve both the spatial specificity of inputs and the electrophysiological interpretation as an RC and RLC circuit, respectively. Each reduced model accurately computes the potential at the spike initiation zone (SIZ) given a much smaller dimension and simulation time, as we show numerically and theoretically. The structure is preserved through the similarity in the circuit representations, for which we provide circuit diagrams and mathematical expressions for the circuit elements. Furthermore, the transformation from the full to the reduced system is straightforward and depends on intrinsic properties of the dendrite. As each reduced model is accurate and has a clear electrophysiological interpretation, the reduced models can be used not only to simulate morphologically accurate neurons but also to examine computations performed in dendrites.