# iaf_psc_exp_ps_lossless – Current-based leaky integrate-and-fire neuron with exponential-shaped postsynaptic currents predicting the exact number of spikes using a state space analysis¶

## Description¶

iaf_psc_exp_ps_lossless is the precise state space implementation of the leaky integrate-and-fire model neuron with exponential postsynaptic currents that uses time reversal to detect spikes 1. This is the most exact implementation available.

Time-reversed state space analysis provides a general method to solve the threshold-detection problem for an integrable, affine or linear time evolution. This method is based on the idea of propagating the threshold backwards in time, and see whether it meets the initial state, rather than propagating the initial state forward in time and see whether it meets the threshold.

Note

If tau_m is very close to tau_syn_ex or tau_syn_in, the model will numerically behave as if tau_m is equal to tau_syn_ex or tau_syn_in, respectively, to avoid numerical instabilities.

For implementation details see the IAF_neurons_singularity notebook.

## Parameters¶

The following parameters can be set in the status dictionary.

E_L |
mV |
Resting membrane potential |

C_m |
pF/mum^2 |
Specific capacitance of the membrane |

tau_m |
ms |
Membrane time constant |

tau_syn_ex |
ms |
Excitatory synaptic time constant |

tau_syn_in |
ms |
Inhibitory synaptic time constant |

t_ref |
ms |
Duration of refractory period |

V_th |
mV |
Spike threshold |

I_e |
pA |
Constant input current |

V_min |
mV |
Absolute lower value for the membrane potential. |

V_reset |
mV |
Reset value for the membrane potential. |

## Remarks¶

This model transmits precise spike times to target nodes (on-grid spike time and offset). If this node is connected to a spike_recorder, the property “precise_times” of the spike_recorder has to be set to true in order to record the offsets in addition to the on-grid spike times.

The iaf_psc_delta_ps neuron accepts connections transmitting CurrentEvents. These events transmit stepwise-constant currents which can only change at on-grid times.

In the current implementation, tau_syn_ex and tau_syn_in must be equal. This is because the state space would be 3-dimensional otherwise, which makes the detection of threshold crossing more difficult [1]. Support for different time constants may be added in the future, see issue #921.

For details about exact subthreshold integration, please see Integrating neural models using exact integration.

## References¶

- 1
Krishnan J, Porta Mana P, Helias M, Diesmann M and Di Napoli E (2018) Perfect Detection of Spikes in the Linear Sub-threshold Dynamics of Point Neurons. Front. Neuroinform. 11:75. doi: 10.3389/fninf.2017.00075

## Sends¶

SpikeEvent

## Receives¶

SpikeEvent, CurrentEvent, DataLoggingRequest